measurements
Steve Whittet
>...absolutely no evidence that any of the Egyptian terms
>under discussion referred to an area of approx. 40,000 sq. ft. The
>only term that even comes close is the <setat> or <st3t>, and it - on
>your own evidence - is only about 2/3 of an acre.
The ordinary cubit is 17.6", 100 such cubits are 1760/12 feet, 146 2/3 feet
This is exactly 1/36 English mile. 36 khet (measure of 100) cubits,
is 1 English mile. The Egyptians had a name for this measure of one
plowed field which they called the arura,
(Greek "aroura" or area; Latin "are")
In support of this we should recap some of the discussion thus far
We are agreed only that the acre originated as a measure of the plowed field.
It was common in antiquity to plow one field and leave another fallow
Eventually the two fields were combined together as one area.
Thia area became the acre.
1296 square khet are 1 square mile of 640 acres
The khet is 40/81 English acres.
The length of its furrow was the furlong, 220 yards, or 450 cubits
The space between furrows was the yard, 3 feet, or 2 cubits
The width of a plot was the rod, 5 1/2 yards, or 11 1/4 cubits
The unplowed border of the plot was the quarter, 1/4 yard, or 1/2 cubit
These were established as units of measure by the Egyptians
in the middle kingdom and were still in use in medieval Europe
As the horse replaced the oxen and as farming methods improved
three fields were used, planted in rotation with one fallow.
Our mile is derived from the Roman milliare.
Depending on the length of the foot used and how it was
defined this mile was 4,800, 4,840, 5,000 and ultimately 5,280 feet long
There are 4840 yards in an English acre, The Roman acre was the jugerum.
The Romans defined their mile as 8 stadia,
the stadia was taken by the Greeks
from the Egyptians as 600 Greek feet
The Greeks divided the stadia so that 10 feet make an arcana
60 feet make a plethron, 60, arcana or 10 plethron make a stadium
there were 100 Greek feet in a second of the earths equatorial circumference
To be right on the money they needed a foot of 309.24 mm
The Greek feet varied between 308.4mm and 309 mm as different values
for the earths equatorial circumference, mile, acre, minute, second
and degree were adopted.
In addition to their short foot, the Greeks had a medium foot
of 316 mm, 1/127,000,000 of the earths equatorial circumference
and a long foot of 332 mm, 1/121,000,000 of that measure
The Romans divided the stadia into 125 paces
When the pace became 5 feet the milliare increased from
8 stadia of 600 feet to 8 stadia of 625 feet,
and the milliare increased from 4,800 feet to 5,000 feet.
Our mile only increased to 5280 feet in the time of Queen Elizabeth.
>=====
>
>>>>>>>> Jomard found that the stadium was a unit
>>>>>>>>of land measure used in Egypt,...
>=====
>
Speaking of the Great Pyramid
>>>>>>Herodotus says
>
>>>>>>"it is a square.
>>>>>>8 of 100 each way
>>>>>>and the height the same"
Brian and I read this differently
>
>>>The crux of the matter, however, is
>>>that the sides of the base and the height are clearly stated to be
>>>equal, whatever their actual measurement may be.
>
>>Do you see the word "base" in there anywhere?
>
>It [i.e., the pyramid] is a square [in cross section], 8 [units] of
>100 each way [i.e., along each side of the square], and the height
>[is] the same.
1.)The Great Pyramid is not 8 units of 100 along the side of its base
2.)The measure of 100 units each way used by the Egyptians was the khet
3.)A measure of 8 times 100 units each way, is an area not a length
4.)We are told "and the height the same"
5.)The height is not an area
6.)The square of the height is an area
7.)The square of the height is the same as the area of the face
8.)This area is 8 square khet,or setat
>
>>>>The "8 of 100 *each way*" refered to is setat, and the
>>>>unit of 100 Royal cubits is the khet.
>
>>>Your interpretation is most implausible. A height is not an area
>
>>The square of a height is an area...
>
>But no reference is made to the square of the height.
We are given a square which is an area
we are told the area is 8 measures of 100 units each way
and told the height is the same;
the square of the height is the same
it is a square
it is the same area
it is 8 times 100 units each way
the unit is the pace (58.8") of the Roman milliare
>
>>the square of the height is compared to 8 of 100 each way
>>8 setats of 100 royal cubits each way
>
>Bizarre. My reading is much more straightforward. I shouldn't even
>be surprised to find that the original Greek won't support your
>interpretation.
>
>>>You may not understand this, but I suspect that Herodotos did; he was
>>>a pretty sharp cookie.
>
>>I agree with your assessment of Herodotus, but I think its a shame that
>>you won't admit it when you are this clearly wrong about what he said.
>
>I'm not. You are. I won't waste any more time on it unless someone
>says something useful about the Greek original.
Obviously Brian and I don't agree...
>
>=====
>
>>>>>>>I've deleted the calculations based on precise sizes for a hide and a
>>>>>>>knight's fee; as anyone at all knowledgeable about medieval English
>>>>>>>history knows, neither was a well-defined area.
>
>>>[One definition mentioned, given by Klein.]
>
>>>>Cite another definition given by Klein for this value.
>
>>>Wrong demand.
>
>>Brian fails to produce another definition, but instead maintains
>>the idea that a standard of measure is undefined. Occams razor cuts deep
...I gave you specific evidence of the variability
>of the unit, complete with a bibliographic reference. ...
Brian, if the unit is a variable then it isn't a standard of measure.
Since at least one Bodelarian manuscript did define it, what you
need to do is show what caused the lack of uniformity with the
established standard.
>'Wrong demand. All I have to do is demonstrate that the knight's fee
>was variable, regardless of what Klein may say. Try T. K. Keefe,
>_Feudal Assessments and the Political Community under Henry II and His
>Sons_ (Berkeley: Univ. of Calif. Press, 1983), Ch. II. "Something
>akin to a standardized fee did prevail on a few English baronies, but
>on most, like Peterborough, there was no uniformity." He goes on to
>explain, with data, that in the Midlands and north, fees contained
>from 1/2 up to sixty carucates; in the south a fee could be
>2,
The knights fee was divided into 8 parts just like the mile
was divided into 8 stadia. The hyde is 1/8 the knights fee
2 hides is 140 acres, 280 khet, 1/4 knights fee
>4,
4 hides is 280 acres, 560 khet, 1/2 knights fee
>5,
5 hides is 350 acres, 700 khet, 5/8 knights fee
>6,
6 hides is 420 acres, 840 khet, 3/4 knights fee
>7,
7 hides is 490 acres, 980 khet, 7/8 knights fee
>10,
10 hides is 700 acres, 1400 khet, 1 1/4 knights fee
and even 27 hides.
27 hides is 1890 acres, 3780 khet, 3 3/8 knights fee,
>Neither the carucate nor the hide was
>standardized.
On the contrary, you have just proven it was, and based
on the same binary doubling used by the Egyptians.
If it wasn't standardized as a measure the divisions of it
wouldn't follow a regular pattern.
Brian, just because one scholar doesn't understand the system
that doesn't mean that there was no system present. The knights
fee, carucate and hyde were medieval amalgamations of pre existing
units of measure.
We know that an acre is a plowed field which was divided into plots.
The width of a plot was a rod and the length was a furlong
The square rod was a perche of 272.25 square feet, 1/79 sq khet
The acre was 43,560 square feet, 4840 square yards
The acre was defined as 66 feet by 660 feet
(12 plots 1 rod in width x 1 furlong long,)
based on 6 plots to a square khet and 6 khets to a mile
which was defined as 8 stadia of 600 feet.
10 acres was a square rode (square furlong), 1/64 square mile, 20 sq khet
14 acres was a yerde 609840 square feet, 28 sq khet
70 acres was a hide 3,049,200 square feet, 140 sq khet
560 acres was a knights fee 24,393,600 square feet
640 acres was a square mile 1 1/7 knights fee, 27,878,400 square feet
> On the estates of Ramsey abbey, hides consisted of 80,
8 rodes, or 1 3/5 hydes, or 160 khet
>90,
9 rodes, or 1 4/5 hydes, or 320 khet
>96,
The knights fee is 560 acres and 7/8 mile
8 acres are 1/80 square mile, the old acre was defined as
1/8 x 180 mile. They are also 1/70 knights fee or 96 plots
8 acres is 16 sq khets
This unit is 12/70 knights fee or 12/80 = 3/20 square mile ,
(1/20 square mile is 32 acres or 64 sq khet)
>100,
10 rode
>108,
7 yerde, 1 rode
>120,
12 rode
>144,
18/70 knights fee or 9/40 square mile
>160,
16 rodes, or 1/4 square mile
>176,
22/70 knights fee
>201,
This one I don't know
>and
>256 acres,
32/70 knights fee
>and in Shropshire they averaged over 600 acres.
Does this suprise you? 600 acres is just 60 square rodes
>Norman fees were just as irregular as the English ones.'
You probably consider feet and inches irregular too!
>
>(Are you stupid enough to think that no one would notice, or are you
>just a masochist?)
I had hoped it wasn't necessary to embarass you Brian,
if you want to be a flamer...maybe it is.
You should have observed the regularity of the system,
These are far from random units.
>
>=====
>
>
>Brian M. Scott
steve
Alan M. Dunsmuir
In article <5uruko$e...@fridge-nf0.shore.net>, Steve Whittet
<whi...@shore.net> writes
>I had hoped it wasn't necessary to embarass you Brian,
>if you want to be a flamer...maybe it is.
>You should have observed the regularity of the system,
>These are far from random units.
I really do not see what anybody expects will be served, entering into
dispute with Steve. He is impervious to reason, logic, common-sense and
evidence.
He is either one of the most sophisticated trolls on the 'Net, or an
extremely sick individual. Since he has been operating thus for at least
three years now, which is well beyond the normal attention-span of
trolls, I am inclined towards the latter option. Perhaps he could most
profitably be coaxed into dispute (preferably via e-mail) with Jiri.
I wonder - is he continuing to carry out his referee duties in
sci.archaeology.mod?
--
Alan M. Dunsmuir
Were diu werlt alle min von deme mere unze an den Rijn
des wolt ih mih darben,
daz diu chunigen von Engellant lege an minen armen!
Peter Szabo
Alan M. Dunsmuir wrote:
>I really do not see what anybody expects will be served, entering into
>dispute with Steve. He is impervious to reason, logic, common-sense and
>evidence.
>
>He is either one of the most sophisticated trolls on the 'Net, or an
>extremely sick individual. Since he has been operating thus for at least
>three years now, which is well beyond the normal attention-span of
>trolls, I am inclined towards the latter option. Perhaps he could most
>profitably be coaxed into dispute (preferably via e-mail) with Jiri.
>
>I wonder - is he continuing to carry out his referee duties in
>sci.archaeology.mod?
>--
>Alan M. Dunsmuir
Notice that Mr. Dunsmuir here has always been incapable of following
his empty accusations with any points of fact. What is the term.. ad
hominem (sp?)?
He obviously has some unfulfilled vendetta against Steve, who is
certainly underserving of these crass and brutally rude insults.
Here, let me play at this game, too.
Hey Alan, you are a grumpy old fart, without an ounce of heart, logic,
or feeling, at least as far as your participation on this ng. Is it
just a sick need for venting as a relief from your miserable and
oveworked life? Here's an idea, Frag off!
My apologies to the more cultured folk out there, my normal
non-profane postings shall hopefully regain full control henceforth.
And, Mr. Dunsmui, unless you make any decent factual points I shall
hold myself back from flaming furthur. And I can't see you
accomplishing that...
Peter Szabo.
Realms of Archaea--------> http://users.uniserve.com/~peters5/zoomquk4.html
zoomQuake!---------------> http://users.uniserve.com/~peters5/
"The fool doth think he is wise, but the wise man knows himself to be a fool."
Steve Whittet
...snip...
>
> When a measurement is based upon the human body one does not need
>diffusion or even idependent invention, just the use of the obvious.
>When there was a need for standardization such as the cubit, each
>country had their own and different standard.
>
> These are parts of the body, easily available, and using them a
>person's forearm can be calibrated to the standard forearm to within a
>finger.
The measures called finger, palm, hand, fist, foot, cubit, etc; are
standards of measure. The issue is that as civilization develops to
the point where commerce is on an international level, fixed standards
of reliable value are required to do business.
Dynastic Egypt, The IVC and Mesopotamia reached that level
in the 3rd millenium BC. As other cultures reached that level
They used the same measures, to have done otherwise would have
resulted in the sort of confusion which led scholars of the
Middle Ages to look back to antiquity to try and restablish
what the standards had been.
>Common measures are too easy to come by.
Are they? Suppose I agree to pay you a talent of gold
in return for some cedar to build some boats.
A talent was a measure of volume based on the cube of the foot.
You and I use different values for the foot. You have big feet
so I get nice long planks for my boats. I have little feet so
you get a talent of gold that is about half the volume you
expected to recieve. Do you see any problems with that?
If you look carefully you will see that the standards are
geocommensurate indicating people went to some trouble to
find a uniform standard.
>
>Now if you want to make a case for diffusion, it is very simple,
>demonstrate common weights and volumes. When you make that comparison
>you find standardization across countries was introduced by Rome to
>facilitate commerce.
The weights and volumes are also common, based on cubes and cylinders
of the unit lengths. They have already been discussed at some length
in the thread. Compare the cube of a foot to the gallon for example
You will find that the cube an ordinary cubit of 17.698 inches on a
side holds 24 gallons, a royal cubit of 20.628 inches on a side
holds 38 gallons.
You should find "a pint's a pound the world around"
>
> If the explanation is diffusion then we would expect length,
>weights and volumes all to be common. That is not what we find at all.
Then you need to look more carefully.
>We find only the body based measures, lengths, to be similar but not
>indentical.
All measures are subject to change over time. If you follow the
changes carefully you will find that the original system was
pretty comprehensive.
>
> Thus the diffusion hypothesis fails.
only if you blow it off and don't look carefully. If you maintain that
the Greeks didn't borrow from the Egyptians or the Romans from the Greeks
or the Europeans from the Romans,then you need to show how and why they
independently invented things like hours and minutes, the remen, pace,
mile, acre, stadium, and degree as even multiples of the finger, palm,
hand, fist, foot and cubit. Explain why English weights and measures
of volume follow the same binary, septenary, octonary, decimal, unidecimal
and sexigesimal proportional system as the Egyptians.
steve
Steve Whittet
In article <34119076....@news.mindspring.com>, WWal...@freedom.orgO
says...
>
>On 6 Sep 1997 02:28:14 GMT, whi...@shore.net (Steve Whittet) wrote:
>
>>In article <340f9740...@news.csuohio.edu>, sc...@math.csuohio.edu× says.
>..
>
>>>What has that to do with their beliefs concerning the shape of the
>>>earth? Division of the day and night into units of a convenient size
>>>does not imply any particular cosmography.
>
>>How about divison of the hour into minutes?
>
> A renaissance development if I remember correctly. It is a
>useless measure with time keeping instruments before that.
The division of time into hours and minutes dates to the Middle kingdom.
The Egyptians assigned names to the different hours of the day and night
and to their division into minutes.
Gardiners "Egyptian Grammar" discusses this if you want to look it up.
steve
Steve Whittet
In article <3411b3cf...@news.csuohio.edu>, sc...@math.csuohio.eduO says...
>
>[sci.math snipped]
>
>I hadn't intended to bother, but the mostly linguistic and logical
>issues are pretty easy to dispose of.>>>The finger, palm, foot, and cubit are of course based on the human body.
>
>>No , they are mneomically keyed to parts of the Human body but
>>they are much more systematic than that. If standards of measure were
>>really based on parts of the human body there would be no way to get
>>a large mason to cut his stones in advance so they fit the layout done
>>by a tiny scribe. The whole point of this discussion is that civilization
>>requires commerce and commerce requires a well balanced set of scales.
>
>You apparently don't understand the expression 'based on'. These
>measures obviously *are* based on the dimensions of the human body;
>their names and in many cases definitions in a variety of cultures
>demonstrate that.
If you have in mind some neolithic farmer measuring the length of the
furrows in his field or their spacing apart by steping them off, I have
to ask you, why would he bother to?
"Primitive measurements" is an oxymoron. Only after people are already
sophisticated enough to have some divison of labor and social
stratification do people begin to do the sort of repetitive tasks
which make comparison to a standard necessary. If you are just
going to make one of something, why would you measure it?
The concept of measurement implies the need to make things fit
in accordance with a sense of what is right and proper.
Vitruvious discusses this rather nicely. The association with the
parts of the body came from a proportional system of grids developed
by the Egyptians for their inscriptions and wall paintings.
The idea of systematic proportion is incorporated in architecture
as the modulor. It shows up in the Greek orders as the columns
base diameter. In the Japanese system of the ken it is based on
floor mats. In the Egyptian system the grid is divided into palms.
Once again you want to just blow off what you don't understand.
>In other words, that is where the measures originated.
The measures did not originate with the parts of the body. They
were mapped to the body as a grid with the body parts used
symbolically to represent the measures, not the measures used
symbolically to represent the body.
>(And definitions based directly on body parts occur
>remarkably late. In the 16th c. Master Koebel, a surveyor, wrote: 'On
>a certain Sunday as they happen to come out of church, bid sixteen men
>to stop, tall ones and short ones, .... 16 men shall stand in line
>with the left feet touching, one behind the other. This distance
>shall be the right and lawfull Rood and one-sixteenth of it shall be
>the foot.')
The Europeans of the Dark Ages and even some modern people tend not to
give much thought to what a standard of measure is and just how long
they have been around in essentially the same form.
In the above anecdote: Master Koebel is a surveyor. He seems to be aware
that there is a need to standardise units of measure and he wants to build
some consensus for whatever standard he chooses. Was this idea or was
he the representative of the towns leading citizens who were getting
concerned about deeds and titles to land and such....
He may have been delegated for this responsibility by some
local cleric because as a surveyor he was thought to be an
expert on measures. Whether or not Master Kobel has any
actual knowledge of Greek and Roman units of measure the
clerics or the town elders who were probably engaging in this
effort are likely to suppose that he did.
He seems to be aware that there is some importance to the number 16
He may or may not know the Romans considered it the perfect number
and that their measures were generally divided into multiples of 16.
The Roman foot was divided into sixteen parts and additionally
1/16 a rod of 16.5 English feet in the 16th century is the Greek
Geographic foot.
Your example points to much the same concerns as probably led the
Egyptians to work out standards of measure in the first place.
In addition to surveying their fields the Egyptians had other
more subtle concerns.
It was important to them that scribes being trained to carve
inscriptions did so according to what was right and proper.
Words and images were expected to align neatly, to be plumb
and sqaure and level, to be properly proportionate.
This does not mean that an Egyptian of 2500 years ago
>used his own finger as anything but a very rough approximation to the
>actual Egyptian unit, any more than I would use my foot as anything
>but a very rough approximation to the English foot. Such complex
>cultures as the ancient Egyptian clearly require a considerable degree
>of standardization, but that standardization hardly obscures the
>rough-and-ready origin of the units.
I disagree. There is nothing rough and ready about the
origin of these units. The Egyptians worked them out from a grid
first and then mapped them to the body.
=========================
>>>However, before you blow a gasket I will grant that it
>>>seems likely that even if the Greeks were already using, say, the
>>>finger, or the foot, they nonetheless took over from the Egyptians
>>>some of the details of the system.
>
>>You mean like the palm, hand, foot, cubit royal cubit and remen
>>being the same even multiples of the finger.
>
>I think it likely that any system invented by human beings that
>included units named for the palm and for the finger would make the
>former 4 of the latter; it's implicit in human anatomy. After that
>the agreements are more persuasive, though perhaps not so much as you
>suppose. Consider, for example, a system that includes units
>originally based on the sizes of the finger, palm, and foot. It's
>quite plausible that when these become formalized measures rather than
>rough descriptions of the sizes of things, they will be standardized
>in such a way that the foot is a whole number of palms. And given
>human anatomy, the likeliest number is 4.
I would expect, given human anatomy the likeliest numbers would be
one,two,five or ten. Where does a system based on the number seven
come from?
>Since, as we've seen, the hand is likely to contain 4 fingers,
My hand has five fingers, one of them is a thumb. It is the
palm of the hand which contains four fingers.
What four fits with is the system of doubling used by the Egyptians
2,4,8,16,32,64, etc; but here you rapidly run out of similar sized
body parts so you have to begin to analogize.
>a foot of 16 fingers should come as no great surprise.
Sure, I will even allow that both a cubit of twenty four fingers
and a royal cubit of twenty eight fingers could be mapped to
different parts of the same forearm
Now explain the remen.
>I point this out not to argue against the possibility of Egyptian
>influence on Greek linear measures but rather to show that the matter
>is far less straightforward than you seem to believe.
==========
I don't disagree that at first glance the system is simple and intuitive.
Since the people using it used unit fractions to calculate and multiplied
and divided by doubling, even binary multiples is a very natural solution.
If a head happened not to fit the model that was developing it could be
pared down to its components and measured as a face from eyebrow to chin
and as a forehead from eyebrow to hairline.
Its the transition from measures linked to the body to measures of
volume and weight, time and distance which begin to get subtle.
>
>=====
>
>>The Greeks
>>tell us there are 600 feet in a stadium and 600 stadia in a degree.
>>Why isn't that a geocommensurate standard of measure?
>
>'The Greeks' isn't very specific. Eratosthenes reckoned 700 stades to
>a degree, and he was certainly Greek. A figure mentioned by Strabo,
>apparently accepted by Ptolemy, and still known (and influential) in
>the 15th c. corresponds to a value of 500 stades to a degree.
As I mentioned before, they took 600 stadia to a degree of latitude
and 500 stadia to a degree of longitude. Eratosthenes was just trying
to get the numbers he had to come out to the result he wanted. The
reason they weren't was that Egypts conquest by the Assyrians had
resulted in the Egyptians measures being replaced with the Assyrians
measures shortly after the Greeks first arrived in Egypt as mercenaries
fighting for Psalmenticus.
By Ptolomaic times the The Ptolomaic Greeks had libraries full of
Egyptian data which no longer added up properly with experimental
results. It must have been very frustrating.
>For all I know some Hellenistic Greeks did reckon 600 stades to a degree.
Yes
>But it's obvious that 'the Greeks' had a number of different values.
There was a short, medium and long Greek foot. The Greek geographic
foot was the short Greek foot of Athens 308.4 mm. They also had a foot
of 316 mm and one of 332 mm; aproximately 1/3 meter.
>This is also obvious when we recall that they had a number of different
>values for the circumference of the earth.
They had a pretty good value to start with
360 x 600 x 600 x 308.4 mm gives the equatorial circumference of
the earth as 24835.36 miles. We measure it as 24902.72 miles.
>This clearly shows that *they* didn't define the unit in terms of
>the earth's circumference.
I don't follow your logic here. You agree that they reckoned 600
stadia to a degree. and you know that each stadia was considered
to be 600 feet because there were 8 stadia and 4800 feet in the
Romans milliare. That means that they reckoned 100 feet were
1 second of degree. Then you say they didn't define the unit
in terms of the earths circumference? How does that follow?
>And since the ancient Egyptians, even if they had a unit corresponding
>to the Greek <stadion>, weren't in any position to make such a
>definition,
Now I understand, you are using circular logic.
Since they "weren't in a position to make such a definition"
assumes they weren't, which remains to be proved.
>it follows that any geocommensurability here is accidental.
This is a blatant non sequitor. You assume they were
too stupid to figure out how to measure the earths circumference,
so they couldn't have, so they didn't.
The Egyptians were sun worshipers, their temples were
solar observatories laid out so that the suns rays at the moment
of solstice traveled through narrow passageways for hundreds of feet
to illuminate precisely the face of the god.
The Pavement of the Great Pyramid is laid out so as to measure
the length of the shadow it throws.
Actually, even the Babylonians measured the degree.
>This isn't really surprising: it's not hard to estimate a
>whole (or even round) number of small units in a very large one when
>the latter is as ill-defined as the earth's circumference. Very small
>percentage errors in estimating the circumference have a considerable
>effect on the calculated number of stades per degree.
The Greeks tell us the apothem or slant side of the Great Pyramid
was a stadium in length. If that length was 356 royal cubits of 20.6"
or 611 English feet, that gives the value of 25,000 Miles,
Please don't even try to claim this was another coincidence
>For instance, Snell's 1615 figure for the equatorial circumference,
>the best up to that time, was too small by about 3.4%. That's an
>error of about 20 stades per degree. In other words, even at that
^^^^^^^^^^^
>relatively late date it would have been impossible to define a length
^^^^^^^^^^^^^^^^^^^^^^
>*accurately* in terms of the earth's circumference.
Your thought appears to be that the closer we are in history
to our own time, (regardlless of anything else such as methodology)
the better the numbers are going to be. Briam that is just plain
old garden variety ethnocentrism.
The fact is that after the Battle of Kadesh the Egyptian civilization
went into something of a decline. What the Greeks learned from was
a culture better than anything they knew, but a long way from the
standards set when Egypt was at its prime. The Greeks went downhill
from the Egyptians, the Romans went downhill from the Greeks. By the
time Europe was through with the Dark Ages European science was so far
behind the curve it wasn't even able to appreciate let alone do what
the Egyptians could do in the middle bronze age.
>Indeed, it's impossible for a more fundamental reason: even ignoring terrain, the
>earth is a sphere only to a first approximation. By the late 17th c.
>it was recognized that the earth was closer to an ellipsoid of
>revolution, and using current values we can calculate that the
>difference between a degree of latitude and a degree of longitude (at
>the equator) is about 1 <stadion>.
You are assuming, I guess,that because Europeans didn't become aware
of this again until the late 17th century, the well documented
knowledge of this in antiquity can be dismissed.
>
>And while we're on the subject, let's dispose of your claim that the
>metre is based on Egyptian linear measure. In 1791 the French defined
>it as one 10-millionth the length of the quarter meridian running from
>the north pole to the equator and passing through Paris. The actual
>value was then determined on the basis of elaborate measurements done
>between 1792 and 1798. These measurements were fairly good and
>resulted in a value that was off by only about 0.02%. I suppose that
>it's conceivable that they got the *idea* from a mistaken belief that
>the Egyptians had done something vaguely similar,
They got more than the idea, the got the Egyptian measures
as a check set.
>but the actual value is clearly independent and the result of their
>own measurements, which were of a precision unattainable much earlier anyway.
Actually, the definition of the meter as commensurate with the Earths
longitudinal circumference is off by only.06% less than the
Egyptian value so I wouldn't get too excited about it.
Earths polar semi axis is 6,378,206.4 m so the longitudinal
circumference is 10,018,863 m, not 10,000,000
>
>=====
>
>>Regardless of what you call them the Romans, Greeks, Egyptians
>>and most of the ancient world used the same measures which they got
>>from Egypt.
>
>I don't doubt that to some (possibly considerable) extent this is
>true. But it does not follow that any given Greek or Roman measure is
>ultimately of Egyptian origin.
Of course, just the finger, palm, hand, foot, cubit, remen, pace,
stadium, arura, mile, degree, minute, second, link, chain, rod,
yard, quarter, pole, perche, furlong, fathom, nail, ell, etc;
ad infinitum and all the other measures of weight and volume
I didn't bother to list....)
>Nor does it follow that *every*
>Egyptian measure has a Greek or Roman descendant. If you want to
>claim that there is a Greek unit corresponding to the Roman <digitus>,
>you must produce it, and much the easiest way to do so convincingly is
>to give its name.
What have we been doing for the last month? There is a one to one
correspondence right down the list.
>The same goes for the Egyptian units. In short, if
>you wish to demonstrate such a matching set for some particular unit,
>you must at the very least demonstrate that each of the cultures in
>question did indeed have something close to that unit, and for that
>demonstration the names are important.
>
>=====
>
>>>...You've produced no Greek measure approx. equal to the English acre,
and <acre> itself is certainly not a Greek word.
The Egyptian word is arura
The Greek word is aroura
The Latin word is are or area
The Enlish word is acre
>Your entire comment on this matter is a farrago of absurdities ('The
>Greeks may have been trying to get a good geocommensurate foot'),
>implausible speculation
Their foot was as geocommensurate as the meter.
Its a fact. Deal with it.
>('Its likely that [the acre] began as 660 x 64 feet, was converted to
>640 feet x 66 feet and was taken as 42,240 sq ft of 31.4 mm.'),
The doubling system goes 2,4,8,16,32,64 remember our area of
64 setats? The land is measured in strips, plowed fields,
64 of them to an acre.
(Klein p 77) says: "The old acre, equal in length to that of today
was formed in the example of the Bodelian document by a length of
660 feet times a breadth of 66 feet.
The Greek divisions were decimal with the arkana 10 feet
and the plethron 100 feet 60 plethra = 1 minute of degree
>arrant nonsense ('Later the acre was further rounded
>off to the Greek acre of 40,000 Greek Feet of 332 mm' - yet again
>you've confused square and linear measure), and unsupported assertion
>('This [Greek acre] became the Belgic foot of 33.2 cm'). My previous
>comment stands.
40,000 square Greek feet of 332 mm is 43,569 1/2 Emglish feet.
>
>>>>The Greeks had an acre of 40,000 Greek feet
>
>>>You've made this unsupported assertion before. If they had such a
>>>measure, what did they call it?
>
>>What difference does it make?
>
>Finding a Greek name for it would prove that the Greeks were at least
>familiar with it. That would go a long way toward convincing me that
>they actually had such a measure. At present the only 'evidence' on
>offer is your unsupported assertion. (That's not strictly speaking
>true, actually: your repeated failure to produce real evidence despite
>multiple requests might be considered *negative* evidence.)
The Ptolomaic Greeks used a term "schoenia" and or "aroura"
for the Egyptian arura, an area with a side of 100 cubits.
>
>>The Egyptians had the measures before
>>the Greeks and Romans did
>
>If you want to convince me that the Egyptians had *this* measure
>before the Greeks, you'll have to prove first that they both *had*
>such a measure. You haven't even done *that* yet!
>
>>"se t a t" ( 1 square khet, 10,000 square cubits) 21511 1/9 sq ft
>>40/81 acres
>
>Of the many units that you mentioned, this is the only one that is at
>all relevant, and it shows once again that the basic Egyptian unit of
>land was not comparable to the English acre. (And your arithmetic is
>off: the <setat> is about 29470 sq. ft., or about 2/3 of an acre.)
The cubit is 17.6 inches; the royal cubit is 20.6 inches
10,000 square cubits is 21511 1/9 sq ft 40/81 acres
10,000 square royal cubits is 29,269 sq ft 2/3 acres
Gardiner gives the setat as the square of the khet and the khet
as 100 cubits
Stechinni gives it as 1 side of land unit of 100 cubits
Gillings gives it as both but says the arura became the Greek schoenia
>
>=====
>
>>>>>>With a period when most peoples livelyhood depended on their fields
>>>>>>why shouldn't the word "acre", (are, area) have been one which
>>>>>>everybody used?
>
>>>>>Because none of those words existed at the time of ancient Egypt. And
>>>>>the language of ancient Egypt was unrelated to the Indo-European
>>>>>family of languages in which those words are found.
>
>>>>Apparently not...
>
>>>If this is intended to mean that ancient Egyptian was an Indo-European
>>>language, you're simply and wildly wrong.
>
>>That isn't what was said Brian.
>
>Your comment wasn't clear, so I was identifying the possible meaning
>to which I was responding.
>
>>You claimed "none of those words existed at the time of ancient Egypt."
>> ^^^^
>>That is apparently not the case.
>
>By 'ancient Egypt' I mean the era of the Great Pyramid and the Rhind
>Papyrus. The words in question were English <acre>, which in this
>form is medieval; <are>, a late 18th c. French adaptation of Latin
><area>; and Latin <area>. The first two plainly don't go back nearly
>far enough. The English term derives from an Old English word for
>cultivated land.
The Egyptian term is for plowed field.
The reason the Egyptian measure is essentially 1/2 the English measure
is that parcels of land used to be associated in pairs with one field
left fallow while the other was planted. The English acre takes both
fields as one.
The Egyptian word is arura
The Greek word is aroura
The Latin word is are or area
The Enlish word is acre
>The word originally did not denote a unit of
>measure, but merely cultivated land.
Actually it was carefully measured. The length of the furrow was the
furlong. The width of the plot was the rod and the space between
furrows was the yard. There were 12 plots of 5 furrows or 60
furrows to an acre.
>By the most generous definition the Old English language did not
>exist before the 5th c., so even the immediate ancestor to <acre>
>did not exist at the time of ancient Egypt.
I keep wondering if you are just trolling me or what. Words
exist even when formative languages are still dialects. Old
English is heavily Germanic, with Latin strongly influencing
the Germanic, Greek influencing the Latin and Egyptian
influencing the Greek. Along the way there are many
intermediaries. It wouldn't be hard to list several
dozen Egyptian or for that matter Sumarian words
which have come into English virtually unchanged.
That doesn't mean that Egyptian was an Indo European language
or for that matter a PIE, but it would be silly to deny that
some words have continued in recognizable form from the dawn
of time into the present day.
This leaves only Latin <area>. It's older, but it's still not
>old enough. There are some inscriptions from c.500 BCE that are in a
>very early form of Latin, but the form is markedly different from the
>familiar Latin of the 3rd c. BCE; anything much earlier would have be
>in any practical sense a different language, just as Old English is a
>different language from (any) Present-Day English.
>
>In short, what I said is correct: none of these words existed in
>ancient Egypt.
The Egyptian word is arura
The Greek word is aroura
The Latin word is are or area
The Enlish word is acre
>>Then you said
>
>>"the language of ancient Egypt was unrelated to the Indo-European
>>family of languages in which those words are found."
>
>>The Egyptians had a word "a r u ra" which was cognate
>
>Possibly they had such a word, but it can't be cognate, since the
>languages involved aren't related.
!!!!!!!!!!!!
You mean if it were cognate that would make the languages related?
Don't be silly. Any word can be cognate "Bebsi" is cognate for "Pepsi"
>At best it could be a borrowing;
Yes, it was "borrowed", Whatever you want to call it. The word was
lifted from the Egyptians by the Greeks; taken, purloined, stolen,
appropriated, walked off with, trouvered; whatever.
>and given the dates involved, the Greek term would presumably have
>been borrowed from the Egyptian. This, however, appears to be
>impossible.
!!!
There is a term for this. Sociologists call it cognative dissonace.
>I haven't the resources handy that would let me make
>certain, but it appears from the congruence of form and meaning that
>Greek <aroura> and Latin <aruum> are related. This, if true, suggests
>that the Greek word is of Indo-European rather than Egyptian origin.
The word comes from Egypt. Deal with it.
>If the same word were found in Egyptian, it would then be a borrowing
>from Greek, which violates the temporal sequence.
!!! Wow!!!!!!!!!
>It's far more likely that this is a coincidental resemblance.
A word for a land measure taken by the Ptolomaic Greeks from the Egyptians
is coincidentally a reference to the same area of land, coincidentally
a reference to a plowed field, coincidentally spelled and pronounced
the same, and related to the Latin and English cognates in the same way.
Indeed, it's not hard
>to find further evidence for that view. The Greek word is clearly
>derived from the verb meaning 'to plow', whose root is <aro->. This
>means that the final <-ra> is some sort of derivational affix. On the
>other hand, you give the Egyptian term as follows:
>
>'"a r u ra" are Egyptian hieroglyphics meaning [a word breathed from
>the mouth of ra](100 cubits) called a "schoenia" [sic] in Ptolomaic
>times'
The Egyptian meaning is the legal division of plowed land
which every Egyptian was entitled to possess as his own
on the word of the god Ra so long as he paid his taxes
and was a good law abiding citizen doing what was right
and proper. It is a land measure of plowed land
and a carefully measured property.
>According to your derivation of the word, the final <-ra> is related
>to the name of the god; if that's the case, it must be completely
>unrelated to the Greek derivational affix.
Is that really what you think? The Egyptian government went out
among the farmers after the floods had passed and measured their
property in the name of the Pharoah, the living manifestation
of the sun god Ra.; ie; Ra mes ses [sun birth quard]
(observes[midwifes] the birth of Ra)[makes the sun to rise]
>
>Finally, you've added what appears to be your own gloss, '100 royal
>cubits', and said that the unit 'was called a "schoenia" [sic] in
>Ptolomaic times'. In fact the <skhoinos> was apparently 60 stades.
>You've distinguished a 'grand' and a 'short' <skhoinos>, giving the
>latter as 60 feet.
Read more carefully
Gillings says
Arura "A unit of area", "equal to the area of a square
whose side was 100 royal cubits" "from land measures"
The linear length of 100 royal cubits was called a schoenia
in the time of the Ptolomies."
"khet, setat", "The common unit for linear measures of land
at the time of the RMP was the khet of 100 cubits. A setat
was a square khet or
10,000 square cubits."
"hayt" "The chief multiple of the cubit was the hayt,
rod or cord of 100 cubits"
Gillings cites Gardiner "Egyptian Grammer"
Gardiner says the arura was a plowed field and a land measure.
Stecchini gives 10 cannes = 1 side of land unit of 100 cubits, aroura"
and equates 10 cannes to 600 palms or about 147.6 feet
the land unit with that side is 1/2 acre
I've no independent warrant for this, but it
>doesn't matter. Neither unit is 100 royal cubits, and, more
>important, both are units of *linear* measure, not *area*.
The arura is a unit of land measure 147.6 feet to a side.
>As such they are prima facie unlikely to correspond to a term originally
>referring to a cultivated field.
It is an area and a plowed field of 1/2 acre
>>>However, <acre> as a term for a unit of measure originated in England
>>>after the 5th century, so there's not much chance of the Egyptians
>>>having got it from the Anglo-Saxons or vice versa.
>>(English) acre comes from (Latin)are or area which comes from
>>(Greek)aroura which comes from (Egyptian) "a r u ra"
>You don't know what you're talking about. The word <acre> is from Old
>English <aecer>, which is cognate with (but NOT derived from) Latin
><ager> 'land, territory; a cultivated field' and Greek <agros> 'field;
>land'. Greek <aroura> is related to the Greek and Latin verbs meaning
>'to plow' and is therefore most unlikely to be a borrowing from
>outside the Indo-European family. Latin <area> appears to be
>unrelated to any of these.
>>A cognate is a word which has a coresponding meaning.
>No, it isn't. There's a great deal more to it than that. Cognates
>must share descent from a common ancestor.
Of course, but this one does.
>Brian M. Scott
steve
Chris Marriott
In article <5ut3ei$p...@fridge-nf0.shore.net>, Steve Whittet
<whi...@shore.net> writes
>You should find "a pint's a pound the world around"
Is this a troll, Steve, or do you really believe that to be true?
Chris
----------------------------------------------------------------
Chris Marriott, Microsoft Certified Solution Developer.
SkyMap Software, U.K. e-mail: ch...@skymap.com
Visit our web site at http://www.skymap.com
William Wallace
On 7 Sep 1997 02:27:30 GMT, whi...@shore.net (Steve Whittet) wrote:
>>Now if you want to make a case for diffusion, it is very simple,
>>demonstrate common weights and volumes. When you make that comparison
>>you find standardization across countries was introduced by Rome to
>>facilitate commerce.
>The weights and volumes are also common, based on cubes and cylinders
>of the unit lengths. They have already been discussed at some length
>in the thread. Compare the cube of a foot to the gallon for example
>You will find that the cube an ordinary cubit of 17.698 inches on a
>side holds 24 gallons, a royal cubit of 20.628 inches on a side
>holds 38 gallons.
You were talking a good talk until you got here. Those, 24 and 38
gallons, do not appear as standard volumes any place. Nice try though.
>You should find "a pint's a pound the world around"
Only in the British Empire, a touch late for this arguement.
>> If the explanation is diffusion then we would expect length,
>>weights and volumes all to be common. That is not what we find at all.
>Then you need to look more carefully.
So far, other than assertion, you have not directed me to what
you examined to convince you. You certainly know what they are.
>>We find only the body based measures, lengths, to be similar but not
>>indentical.
>All measures are subject to change over time. If you follow the
>changes carefully you will find that the original system was
>pretty comprehensive.
Yes, the human body changes quite slowly for lengths but the
point here is for weights and volumes. What is a Kor of wheat and
compare it to the volume of other measures of volume.
>> Thus the diffusion hypothesis fails.
>only if you blow it off and don't look carefully. If you maintain that
>the Greeks didn't borrow from the Egyptians or the Romans from the Greeks
>or the Europeans from the Romans,then you need to show how and why they
>independently invented things like hours and minutes, the remen, pace,
>mile, acre, stadium, and degree as even multiples of the finger, palm,
>hand, fist, foot and cubit. Explain why English weights and measures
>of volume follow the same binary, septenary, octonary, decimal, unidecimal
>and sexigesimal proportional system as the Egyptians.
You are back to lengths again. The subject is weights and
volumes. You do not appear to be able to substanstiate your diffusion
claim for other than body part related lengths.
=====
Any sufficiently convoluted argument can be made to appear to be science
as the layman equates incomprehensibility with science.
William Wallace
On 7 Sep 1997 02:32:45 GMT, whi...@shore.net (Steve Whittet) wrote:
>In article <34119076....@news.mindspring.com>, WWal...@freedom.orgO
>says...
>>On 6 Sep 1997 02:28:14 GMT, whi...@shore.net (Steve Whittet) wrote:
>>>In article <340f9740...@news.csuohio.edu>, sc...@math.csuohio.eduв says.
>>..
>>>>What has that to do with their beliefs concerning the shape of the
>>>>earth? Division of the day and night into units of a convenient size
>>>>does not imply any particular cosmography.
>>>How about divison of the hour into minutes?
>> A renaissance development if I remember correctly. It is a
>>useless measure with time keeping instruments before that.
>The division of time into hours and minutes dates to the Middle kingdom.
>The Egyptians assigned names to the different hours of the day and night
>and to their division into minutes.
>Gardiners "Egyptian Grammar" discusses this if you want to look it up.
Excuse me, I will look into that. And I will grant half and
quarter hours. But in absense of information to the contrary, which I
will look for, I hold that no time keeping method was accurate enough
to make use of minutes.
Now if you are talking about astronomical observations, meaning
at night, that were divided into minutes I will not argue. But that is
a measure of angular displacement, not a measure of time save for the
specialists who would have made the connection but not as timekeeping
but as a correction of position. The division of the circle by 360 and
so forth was for another Sumerian purpose.
I will agree that a sundial can not help but be accurate down to
microseconds. I will also point out that the size of the sundial
needed to make use of minutes is far from a pocket watch. And the
skill to lay out minute measures on a curve is not something taken on
by other than a major project prior to the Renaissance. 60 does not
divide by halves and trisected angles are still a touch difficult.
Milo Gardner
Steve:
Thank you for the date for the language syntax side of time and
land measurements. Again, I stronly suspect that accurate time
measurement did not occur until water clocks were introduced,
well after the Middle Kingdom.
Regards to all,
Milo Gardner
On 7 Sep 1997, Steve Whittet wrote:
>=20
> In article <34119076....@news.mindspring.com>, WWal...@freedom.org=
O=20
> says...
> >
> >On 6 Sep 1997 02:28:14 GMT, whi...@shore.net (Steve Whittet) wrote:
> >
> >>In article <340f9740...@news.csuohio.edu>, sc...@math.csuohio.edu=
=D7 says.
> >..
> >
> >>>What has that to do with their beliefs concerning the shape of the
> >>>earth? Division of the day and night into units of a convenient size
> >>>does not imply any particular cosmography.
> >
> >>How about divison of the hour into minutes?
> >
> > A renaissance development if I remember correctly. It is a
> >useless measure with time keeping instruments before that.=20
>=20
> The division of time into hours and minutes dates to the Middle kingdom.
> The Egyptians assigned names to the different hours of the day and night
> and to their division into minutes.
>=20
> Gardiners "Egyptian Grammar" discusses this if you want to look it up.
>=20
>=20
> steve
>=20
>=20
>=20
Steve Whittet
In article <34132c14....@news.mindspring.com>, WWal...@freedom.org÷ says...
>
>On 7 Sep 1997 02:27:30 GMT, whi...@shore.net (Steve Whittet) wrote:
>
>>>...demonstrate common weights and volumes.
>>>...standardization across countries was introduced by Rome
>>>...to facilitate commerce.
standardization across countries was introduced by Egypt, and Mesopotamia
>
>>The weights and volumes are also common, based on cubes and cylinders
>>of the unit lengths. They have already been discussed at some length
>>in the thread. Compare the cube of a foot to the gallon for example
>>You will find that the cube an ordinary cubit of 17.698 inches on a
>>side holds 24 gallons, a royal cubit of 20.628 inches on a side
>>holds 38 gallons.
>
> You were talking a good talk until you got here. Those, 24 and 38
>gallons, do not appear as standard volumes any place. Nice try though.
hmmm... their being even multiples of the gallon isn't good enough
you want similar containers?
Most liquid measures had dry equivalents in multiples of bushels
such as the bushel, strike, bag and coomb where the gallon is roughly
24 gallons was 2 baths or epaths the equivalent of 1 dry bag or 3 bushels
38 gallons was a barrel or chaldron, the equivalent of the coomb of 4 bushels
>>You should find "a pint's a pound the world around"
>
>Only in the British Empire, a touch late for this arguement.
We still use some English measures in the US. Whats interesting
is that they represent three millenia of reasonably stable standards
which are now being ignorrantly elbowed aside by the metric system.
>
>>> If the explanation is diffusion then we would expect length,
>>>weights and volumes all to be common. That is not what we find at all.
>
>>Then you need to look more carefully.
>
> So far, other than assertion, you have not directed me to what
>you examined to convince you. You certainly know what they are.
Generally I was first impressed by the correspondence between the Egyptians
linear measures and our own. later I became aware that most measures
of weight and volume are defined as the cube whose side is a unit of
length. Thus the correspondence between the linear measures led to
a correspondence between measures of volume and weight.
The talent for example was the cube of the foot. The foot was Egyptian
in origin.
>
>>>We find only the body based measures, lengths, to be similar but not
>>>indentical.
>
>>All measures are subject to change over time. If you follow the
>>changes carefully you will find that the original system was
>>pretty comprehensive.
>
> Yes, the human body changes quite slowly for lengths but the
>point here is for weights and volumes. What is a Kor of wheat and
>compare it to the volume of other measures of volume.
The Egyptians used a unit called a khar to measure wheat, it was
1 1/2 cubic cubits. It had a side of two Roman pes. It was 12 buckets
or 6 bushels.
>
>>> Thus the diffusion hypothesis fails.
>
>>only if you blow it off and don't look carefully. If you maintain that
>>the Greeks didn't borrow from the Egyptians or the Romans from the Greeks
>>or the Europeans from the Romans,then you need to show how and why they
>>independently invented things like hours and minutes, the remen, pace,
>>mile, acre, stadium, and degree as even multiples of the finger, palm,
>>hand, fist, foot and cubit. Explain why English weights and measures
>>of volume follow the same binary, septenary, octonary, decimal, unidecimal
>>and sexigesimal proportional system as the Egyptians.
>
> You are back to lengths again. The subject is weights and
>volumes. You do not appear to be able to substanstiate your diffusion
>claim for other than body part related lengths.
I find the easiest way to compare units of volume is in cubic inches.
a bushel is 2219.3 cubic inches and a gallon is 231 cubic inches.
To find an Egyptian measure of volume which contains an even number
of English gallons is not likely to be a coincidence. To find two
such measures reduces the possibility that much further
231 x 24 = 5544 cu" this is the side of the cube of the ordinary cubit, 17.69"
321 x 38 = 8778 cu" this is the side of the cube of royal cubit, 20.628"
>
steve
Brian M. Scott
On 7 Sep 1997 06:52:24 GMT, whi...@shore.net (Steve Whittet) wrote:
I wrote:
>>>>The finger, palm, foot, and cubit are of course based on the human body.
>"Primitive measurements" is an oxymoron.
Not entirely. 'A day's travel on foot' is a primitive but useful
rough unit of measurement. I have seen artisans work in anatomical
units, which are fine for getting proportions right, for example; an
independent standard is needed only if someone else has to replicate
the work.
>The measures did not originate with the parts of the body. They
>were mapped to the body as a grid with the body parts used
>symbolically to represent the measures, not the measures used
>symbolically to represent the body.
This is a thoroughly implausible notion. The use of true anatomical
units, which can still be seen today, is the obvious precursor to
their standardization. (And even if it were true, your view could not
be demonstrated, so it's improper to state it as fact.)
>>(And definitions based directly on body parts occur
>>remarkably late. In the 16th c. Master Koebel, a surveyor, wrote: 'On
>>a certain Sunday as they happen to come out of church, bid sixteen men
>>to stop, tall ones and short ones, .... 16 men shall stand in line
>>with the left feet touching, one behind the other. This distance
>>shall be the right and lawfull Rood and one-sixteenth of it shall be
>>the foot.')
>The Europeans of the Dark Ages and even some modern people tend not to
>give much thought to what a standard of measure is and just how long
>they have been around in essentially the same form.
What on earth do the so-called Dark Ages have to do with 16th c.
England?
>In the above anecdote: Master Koebel is a surveyor. He seems to be aware
>that there is a need to standardise units of measure and he wants to build
>some consensus for whatever standard he chooses.
What *are* you talking about? What kind of choosing do you imagine
him doing in the 16th c.?
>He seems to be aware that there is some importance to the number 16
The only importance that 16 has here is that he is defining a Rood
(i.e., rod) to be 16 ft. This is mildly interesting, since the more
usual value had been 16.5 ft. for several centuries.
=====
>>>>However, before you blow a gasket I will grant that it
>>>>seems likely that even if the Greeks were already using, say, the
>>>>finger, or the foot, they nonetheless took over from the Egyptians
>>>>some of the details of the system.
>>>You mean like the palm, hand, foot, cubit royal cubit and remen
>>>being the same even multiples of the finger.
>>I think it likely that any system invented by human beings that
>>included units named for the palm and for the finger would make the
>>former 4 of the latter; it's implicit in human anatomy. After that
>>the agreements are more persuasive, though perhaps not so much as you
>>suppose. Consider, for example, a system that includes units
>>originally based on the sizes of the finger, palm, and foot. It's
>>quite plausible that when these become formalized measures rather than
>>rough descriptions of the sizes of things, they will be standardized
>>in such a way that the foot is a whole number of palms. And given
>>human anatomy, the likeliest number is 4.
>I would expect, given human anatomy the likeliest numbers would be
>one,two,five or ten.
What *are* you talking about? Are your feet approx. 1, 2, 5, or 10 of
your palms in length? Unless your anatomy is quite unusual, I suspect
that you'll find that they're closest to 4 (or perhaps 3) palms in
length.
=====
>>>The Greeks
>>>tell us there are 600 feet in a stadium and 600 stadia in a degree.
>>>Why isn't that a geocommensurate standard of measure?
>>'The Greeks' isn't very specific. Eratosthenes reckoned 700 stades to
>>a degree, and he was certainly Greek. A figure mentioned by Strabo,
>>apparently accepted by Ptolemy, and still known (and influential) in
>>the 15th c. corresponds to a value of 500 stades to a degree.
>As I mentioned before, they took 600 stadia to a degree of latitude
>and 500 stadia to a degree of longitude.
So they thought that the earth was a prolate spheroid with its long
axis through the poles, like an upright American football? I doubt it
very much.
>Eratosthenes was just trying
>to get the numbers he had to come out to the result he wanted.
Rubbish.
>>This is also obvious when we recall that [the Greeks] had a number
>>of different values for the circumference of the earth.
>They had a pretty good value to start with
>360 x 600 x 600 x 308.4 mm gives the equatorial circumference of
>the earth as 24835.36 miles. We measure it as 24902.72 miles.
Sheer silliness. They hadn't the instrumentation to measure the
earth's circumference to the nearest 0.01 mile. Moreover, you're
inconsistent. The equatorial circumference is 360 degrees of
*longitude*, so each degree should - according to you - have 500
stades, not 600.
>>This clearly shows that *they* didn't define the unit in terms of
>>the earth's circumference.
>I don't follow your logic here. You agree that they reckoned 600
>stadia to a degree.
I do not. Greek estimates of the number of stades in a degree are
known to have ranged at least from 500 to 700.
> and you know that each stadia was considered
>to be 600 feet because there were 8 stadia and 4800 feet in the
>Romans milliare. That means that they reckoned 100 feet were
>1 second of degree.
Once someone was subdividing the circle into seconds, it would have
been possible to note that there were, say, 80 to 120 feet in a second
of the earth's circumference; but that came long after the sizes of
the units in question were established, especially if the units are in
fact based on Egyptian originals.
> Then you say they didn't define the unit
>in terms of the earths circumference? How does that follow?
Attested Greek estimates of the earth's circumference varied by more
than a factor of 2 after Periclean Athens was but a memory. The
Athenian foot clearly predates these estimates and therefore could not
have been defined from them. Even if one accepts the absurd
proposition that the Egyptians had a value for the circumference, the
Greeks obviously didn't know it and therefore could not have used it
to define a foot.
>You assume [the Egyptians of 4500 BP] were
>too stupid to figure out how to measure the earths circumference,
>so they couldn't have, so they didn't.
I assume no such thing. Your insistence (in the face of repeated
correction) that I think the Old Kingdom Egyptians stupid is insulting
and very tiresome. Are you one of those annoying people who confuse
lack of knowledge with lack of brainpower? I'm sure that Old Kingdom
Egyptians spanned the usual range of mental abilities. But I've seen
no credible evidence that the Egyptians saw the earth as something
that even *has* a circumference, let alone that they had the
technology to make a very accurate determination.
>The Greeks tell us the apothem or slant side of the Great Pyramid
>was a stadium in length. If that length was 356 royal cubits of 20.6"
>or 611 English feet, that gives the value of 25,000 Miles,
>Please don't even try to claim this was another coincidence
Of course I think it was. I see no reason to believe that there's the
slightest significance to the fact that the slant height of the GP is
approximately 1/216,000 the earth's circumference. The idea that the
dimensions of the GP are intentionally related to the dimensions of
the earth is preposterous; I quite frankly don't see how any sane
person of even modest intelligence can think otherwise. (You are
welcome to draw the obvious inference.)
Your constellation of claims about the GP is absurd. You insist that
all of the following are intentional: (A) the slope of 14/11, which is
approx. 4/pi; (B) the incorporation in its dimensions of the amicable
numbers 220 and 284; and (C) the fact that the slant height was
approx. 1 stadion. Suppose for a moment that you set out to build a
pyramid with these three properties. If it has a slope of 14/11, and
the base is chosen to be 2b in length, the height must be 14x/11, and
the slant height will then be b * sqrt(1 + 196/121). If you want this
to be 1 stadion, you must choose b to be 1/sqrt(1 + 196/121) stades,
or about 0.62 stades. In other words, the height and base are
completely determined by the slope and the slant height. Now in order
to get (B), you must first find a pair of amicable numbers whose ratio
is very close to 14/11; the fact that there is such a pair that's
small enough to find is sheer luck. Let n be the smaller of these
numbers (i.e., in fact 220); to complete your program, you now need to
find that b/n is an existing unit of measure! In short, while you
might set out to arrange for (A), (B), and (C), success would be a
matter of luck (unless you think that the stadion and royal cubit were
defined *after* the GP was constructed and that the Egyptians could
control the distribution of amicable numbers).
>>For instance, Snell's 1615 figure for the equatorial circumference,
>>the best up to that time, was too small by about 3.4%. That's an
>>error of about 20 stades per degree. In other words, even at that
>>relatively late date it would have been impossible to define a length
>>*accurately* in terms of the earth's circumference.
>Your thought appears to be that the closer we are in history
>to our own time, (regardlless of anything else such as methodology)
>the better the numbers are going to be. Briam that is just plain
>old garden variety ethnocentrism.
Where do you get the idea that I don't consider methodology?
Considerations of methodology and technology underlie my view of the
matter. I've seen no credible evidence that the Egyptian worldview
even made the question meaningful for them. I've seen no credible
evidence that they had the mathematical methodology that underlies the
determinations by Eratosthenes and Poseidonios (or any other
determinations). And I've certainly seen no evidence that they had
the technology to use *any* method to get a precise and accurate
value. You may be able to sustain the delusion that they had the
theory, but about the instrumentation there should be no question.
>The Greeks went downhill
>from the Egyptians
This bears no resemblance to history as far as mathematics and
astronomy are concerned.
Speaking of the fact that the earth is more nearly an ellipsoid than a
sphere, Steve said:
>You are assuming, I guess,that because Europeans didn't become aware
>of this again until the late 17th century, the well documented
>knowledge of this in antiquity can be dismissed.
Produce the documentation.
=====
>[The Greeks'] foot was as geocommensurate as the meter.
>Its a fact. Deal with it.
It's a lunatic delusion. Deal with it.
=====
>>>>>The Greeks had an acre of 40,000 Greek feet
>>>>You've made this unsupported assertion before. If they had such a
>>>>measure, what did they call it?
>The Ptolomaic Greeks used a term "schoenia" and or "aroura"
>for the Egyptian arura, an area with a side of 100 cubits.
Which isn't even close to the acre and does not measure 40,000 sq.
ft., Greek or otherwise. (And you're confusing lengths and areas
again. The 'schoenia' was a length, not an area, so it obviously was
NOT a Ptolemaic Greek term for the Egyptian <arura>. The last time I
pointed this out, you told me to '[r]ead more carefully' and then
proved that I was right by quoting Gillings as follows: 'The linear
length of 100 royal cubits was called a schoenia in the time of the
Ptolomies.')
=====
[Steve made the hilarious claim that '(English) acre comes from
(Latin)are or area which comes from (Greek)aroura which comes from
(Egyptian) "a r u ra"'. I pointed out that <are> is a modern French
neologism based on Latin <area> and that the other postulated
derivations are simply wrong. Most of Steve's response merely
confirms his ignorance of the subject (e.g., confusion of cognates
with borrowings) and isn't worth comment, but some bits caught my
attention.]
>>By the most generous definition the Old English language did not
>>exist before the 5th c., so even the immediate ancestor to <acre>
>>did not exist at the time of ancient Egypt.
>I keep wondering if you are just trolling me or what.
What part of 'immediate ancestor' do you not understand?
>Words
>exist even when formative languages are still dialects. Old
>English is heavily Germanic, with Latin strongly influencing
>the Germanic,
Known borrowings from Latin before the Anglo-Saxon tribes migrated to
England amount to only about 170 lexical items. But Latin influence
is irrelevant to the early history of the word <acre>. The Old
English <aecer> and the related forms in other Germanic languages
(Gothic <akrs>, Old Icelandic <akr>, Old Frisian <ekker>, German
<acker>, etc.) are regularly derived from a Proto-Germanic *akraz,
which in turn corresponds regularly to IE *agros, which is also
represented by Latin <ager>, Greek <agros>, and Sanskrit <ajras>.
(This is evidently a very old Indo-European word.) The <c> of <aecer>
where Latin <ager> and Greek <agros> have <g> shows that the word was
affected by the First Sound Shift (Grimm's Law) and is part of the
Proto-Germanic word stock, so it cannot be a borrowing from Latin.
Had Latin <ager> been borrowed in Old English times, it would not have
had <c>. Indeed, the only borrowing went the other way: there is a
medieval Latin <acra> that was borrowed from the English word! (And
the unrelated Latin <area> doesn't even enter into the matter.)
>It wouldn't be hard to list several
>dozen Egyptian or for that matter Sumarian words
>which have come into English virtually unchanged.
By all means do so, being sure to indicate when they entered English
and in precisely what form.
Brian M. Scott
Steve Whittet
In article <EFo4tvAz...@chrism.demon.co.uk>, ch...@chrism.demon.co.uk says...
>
Technically there is some variance, Pints measure both dry and
liquid measure so it depends on whether you use a dry pint of
33.6 cu" or a liquid pint of 28.875 cu" and it of course depends
on what you are measuring how much it weighs.
Assuming a liquid measure of beer (or water) 1 cubic foot of beer is
1728 cu" and weighs just under 60 lbs. There are 59.84 pints
to a cubic foot.
Assuming a dry measure of grain, 1 cubic foot of barley is
1728 cu" and weighs about 52 lbs. There are 51.43 pints
to a cubic foot.
>
>Chris
steve
Chris Marriott
In article <5uviue$q...@fridge-nf0.shore.net>, Steve Whittet
<whi...@shore.net> writes
>>Only in the British Empire, a touch late for this arguement.
>
>We still use some English measures in the US. Whats interesting
>is that they represent three millenia of reasonably stable standards
>which are now being ignorrantly elbowed aside by the metric system.
The US pint is **NOT** an "English" measure.
The US pint is 16 fluid ounces. A pint in England is 20 fluid ounces -
ie 25% larger (and heavier!).
Michael Parry
In article <7fRX7tAX...@chrism.demon.co.uk>, Chris Marriott
<ch...@chrism.demon.co.uk> writes
>In article <5uviue$q...@fridge-nf0.shore.net>, Steve Whittet
><whi...@shore.net> writes
>>>Only in the British Empire, a touch late for this arguement.
>>
>>We still use some English measures in the US. Whats interesting
>>is that they represent three millenia of reasonably stable standards
>>which are now being ignorrantly elbowed aside by the metric system.
>
>The US pint is **NOT** an "English" measure.
>
>The US pint is 16 fluid ounces. A pint in England is 20 fluid ounces -
>ie 25% larger (and heavier!).
>
fluid ounce. It is MUCH better to use SI units.
--
Michael Parry mic...@unicorn-connection.co.uk
Slovakia: Quality Goods from the Heart of Europe
http://www.unicorn-connection.co.uk/slovakia/
Steve Whittet
In article <3413b98e...@news.csuohio.edu>, sc...@math.csuohio.eduد says...
>
>On 7 Sep 1997 06:52:24 GMT, whi...@shore.net (Steve Whittet) wrote:
>
>I wrote:
>>>>>The finger, palm, foot, and cubit are of course based on the human body.
>
>>"Primitive measurements" is an oxymoron.
>
>Not entirely. 'A day's travel on foot' is a primitive but useful
>rough unit of measurement. I have seen artisans work in anatomical
>units, which are fine for getting proportions right, for example; an
>independent standard is needed only if someone else has to replicate
>the work.
>
>>The measures did not originate with the parts of the body. They
>>were mapped to the body as a grid with the body parts used
>>symbolically to represent the measures, not the measures used
>>symbolically to represent the body.
>
>This is a thoroughly implausible notion. The use of true anatomical
>units, which can still be seen today, is the obvious precursor to
>their standardization. (And even if it were true, your view could not
>be demonstrated, so it's improper to state it as fact.)
Actually its the subject of Vitruvious "Ten Books on Architecture".
As to the grids, several hundred have been discovered and they are
now used to date inscriptions by the cannons of proportions used.
The assumption that there was a precursor to their standardization
while it may be intuitive, is hard to support in practice. The use of
grids goes back to the predynastic Naquada II cultures.
Prior to that there wasn't much use for measures. Even hunters rarely
traveled a days walk away from home. Within the territory they hunted
they knew every tree and rock.
Rather than saying "I will meet you a day's journey from here" they said
I will meet you at the Big Pine tree at the end of the field by the river".
People who don't have a need to give detailed instructions don't have a
need for measurements. If they are making something just for themselves
they can be pretty random about the placement. Very few artists measure
the placement of the things in their drawings.
Artisans have a tendency to "eyeball" things. The sort of place where
you observe a lack of measures is in the freeform foundations of
houses, in furniture made of slabs of wood; with a lack of square
corners there really isn't anything to measure to.
A place where measurement plays a role is in weaving, counting the threads
in a pattern, or in dividing up land, building a wooden boat, ...
>>>(And definitions based directly on body parts occur
>>>remarkably late. In the 16th c. Master Koebel, a surveyor, wrote: 'On
>>>a certain Sunday as they happen to come out of church, bid sixteen men
>>>to stop, tall ones and short ones, .... 16 men shall stand in line
>>>with the left feet touching, one behind the other. This distance
>>>shall be the right and lawfull Rood and one-sixteenth of it shall be
>>>the foot.')
>
>>The Europeans of the Dark Ages and even some modern people tend not to
>>give much thought to what a standard of measure is and just how long
>>they have been around in essentially the same form.
>
>What on earth do the so-called Dark Ages have to do with 16th c.
>England?
By the 16th century much had been lost. People knew it and tried to
reconstruct things as best they could. "A Canticle for Leibowitz" comes to mind.
>
>>In the above anecdote: Master Koebel is a surveyor. He seems to be aware
>>that there is a need to standardise units of measure and he wants to build
>>some consensus for whatever standard he chooses.
>
>What *are* you talking about? What kind of choosing do you imagine
>him doing in the 16th c.?
He must realise that if he defines the standards of measure greatly
differently from what they have always been some people stand to profit
and some to loose. If he makes the wrong choice he could get
tarred and feathered, lynched, stoned, impaled on a stake,
boiled in oil, wracked on a wheel, burned alive, excomunicated,
or kicked out of his guild.
>
>>He seems to be aware that there is some importance to the number 16
>
>The only importance that 16 has here is that he is defining a Rood
>(i.e., rod) to be 16 ft. This is mildly interesting, since the more
>usual value had been 16.5 ft. for several centuries.
Yes, he is a surveyor and the rod is a common surveyors measure
does he realise he is redefining this or not?
Remember king Athelstane defining the kings girth as 3 miles,
3 furlongs, 9 acres, 9 feet, 9 palms and 9 barleycorns?
Thats a radius of 18,250 feet. The kings girth extends
60 stadia of 608 1/3 English feet (600 Greek feet)
360 seconds or 6 minutes of degree from North to South.
>
>=====
>
>>>>>However, before you blow a gasket I will grant that it
>>>>>seems likely that even if the Greeks were already using, say, the
>>>>>finger, or the foot, they nonetheless took over from the Egyptians
>>>>>some of the details of the system.
>
>>>>You mean like the palm, hand, foot, cubit royal cubit and remen
>>>>being the same even multiples of the finger.
>
>>>I think it likely that any system invented by human beings that
>>>included units named for the palm and for the finger would make the
>>>former 4 of the latter; it's implicit in human anatomy. After that
>>>the agreements are more persuasive, though perhaps not so much as you
>>>suppose. Consider, for example, a system that includes units
>>>originally based on the sizes of the finger, palm, and foot. It's
>>>quite plausible that when these become formalized measures rather than
>>>rough descriptions of the sizes of things, they will be standardized
>>>in such a way that the foot is a whole number of palms. And given
>>>human anatomy, the likeliest number is 4.
>
>>I would expect, given human anatomy the likeliest numbers would be
>>one,two,five or ten.
>
>What *are* you talking about? Are your feet approx. 1, 2, 5, or 10 of
>your palms in length?
Given human anatomy the palm is not an immediately obvious standard.
One of something is obvious, 1 hand, 1 foot; or two hands, held side
by side, or five fingers, or ten when two hands are held side by side,
Hold your hand up in front of you. how many units do you see?
>Unless your anatomy is quite unusual, I suspect
>that you'll find that they're closest to 4 (or perhaps 3) palms in
>length.
I admit to my anatomy being unusual, "some men are longer than others",
but why would you measure a foot in palms? Try holding your palm in
a convenient position to measure your foot, ...
>
>=====
>
>>>>The Greeks
>>>>tell us there are 600 feet in a stadium and 600 stadia in a degree.
>>>>Why isn't that a geocommensurate standard of measure?
>
>>>'The Greeks' isn't very specific. Eratosthenes reckoned 700 stades to
>>>a degree, and he was certainly Greek. A figure mentioned by Strabo,
>>>apparently accepted by Ptolemy, and still known (and influential) in
>>>the 15th c. corresponds to a value of 500 stades to a degree.
>
>>As I mentioned before, they took 600 stadia to a degree of latitude
>>and 500 stadia to a degree of longitude.
>
>So they thought that the earth was a prolate spheroid with its long
>axis through the poles, like an upright American football? I doubt it
>very much.
No, they used two different length feet !!!
With one measure of the Greek foot used by the Romans between milestones
600 Greek stadia = 75 Roman miles (5000 pes of 11.69")
= 69.18 English miles, which is about right for latitude
With another measure of the Greek foot used for miles
= 625 Roman feet; 500 Greek stadia of 600 Greek feet
=312500 Roman feet = 62.5 Roman miles
===========================
>
>>Eratosthenes was just trying
>>to get the numbers he had to come out to the result he wanted.
>
>Rubbish.
You would like to think so.
=====================
>
>>>This is also obvious when we recall that [the Greeks] had a number
>>>of different values for the circumference of the earth.
>
>>They had a pretty good value to start with
>
>>360 x 600 x 600 x 308.4 mm gives the equatorial circumference of
>>the earth as 24835.36 miles. We measure it as 24902.72 miles.
>
>Sheer silliness. They hadn't the instrumentation to measure the
>earth's circumference to the nearest 0.01 mile.
Once again you throw out the data in favor of a preconcieved idea.
Did king Athelstane have the instrumentation to make the measurement?
Suppose I stand on top of a pyramid and have two assistants stand
at the eastern and western horizon . I adjust their position with
signals until I can see one on the backsight of my observation of
the other.
Each uncovers a torch when he observes the sun rise and I call out
when I see the torches for another assistant to note the
difference in time with a water clock or sundial. My assistant
informs me it took 8 minutes
I then have the distance between the two observers measured.
it works out that they were about 138 miles apart.
It takes 24 hours for the earth to revolve around the sun so
each degree is about 4 minutes of sidereal time. (366/365 x 4)
It took eight minutes so they are 2 degrees apart. 138/2
gives me a value of 69 miles to the degree. I get a value
for the Earths circumference of 24,840 miles.
==================================
>Moreover, you're inconsistent. The equatorial circumference
>is 360 degrees of *longitude*, so each degree should - according
>to you - have 500 stades, not 600.
>>As I mentioned before, they took 600 stadia to a degree of latitude
>>and 500 stadia to a degree of longitude.
No Brian. Longitude is vertical, Latitude is horizontal, The Equator
is horizontal so we measure it as if it were a section through the Earth
using degrees of Latitude.
Moving north from the equator As we increase our Longitude
the value of a degree of Latitude decreases.
>
>>>This clearly shows that *they* didn't define the unit in terms of
>>>the earth's circumference.
>
>>I don't follow your logic here. You agree that they reckoned 600
>>stadia to a degree.
>
>I do not. Greek estimates of the number of stades in a degree are
>known to have ranged at least from 500 to 700.
I have explained to you why that was.
>
>> and you know that each stadia was considered
>>to be 600 feet because there were 8 stadia and 4800 feet in the
>>Romans milliare. That means that they reckoned 100 feet were
>>1 second of degree.
>
>Once someone was subdividing the circle into seconds, it would have
>been possible to note that there were, say, 80 to 120 feet in a second
>of the earth's circumference; but that came long after the sizes of
>the units in question were established, especially if the units are in
>fact based on Egyptian originals.
It would have been perfectly natural for an Egyptian with hours and minutes
and a sexigesimal year to divide minutes into base 60 fractions.
>
>> Then you say they didn't define the unit
>>in terms of the earths circumference? How does that follow?
Where did I say that?
>
>Attested Greek estimates of the earth's circumference varied by more
>than a factor of 2 after Periclean Athens was but a memory. The
>Athenian foot clearly predates these estimates and therefore could not
>have been defined from them.
What you don't seem to realise is that the original calculations were
better than anything else that came along for a long time. The Greeks
were still making their living as pirates and mercenaries when the
Egyptians first began observing the sun and measuring its shadow
on the earth.
>Even if one accepts the absurd
>proposition that the Egyptians had a value for the circumference, the
>Greeks obviously didn't know it and therefore could not have used it
>to define a foot.
The Egyptians welcomed the Greeks into their libraries as children
and attempted to teach them, as they would any young scribe, the
accumulated observations of several millenia. They taught the Greeks
medicine, law, philosophy, history, science, art, music and a respect
for the wisdom of the ages.
>
>>You assume [the Egyptians of 4500 BP] were
>>too stupid to figure out how to measure the earths circumference,
>>so they couldn't have, so they didn't.
>
>I assume no such thing. Your insistence (in the face of repeated
>correction) that I think the Old Kingdom Egyptians stupid is insulting
>and very tiresome. Are you one of those annoying people who confuse
>lack of knowledge with lack of brainpower? I'm sure that Old Kingdom
>Egyptians spanned the usual range of mental abilities.
Ok, lets take that as a given, over three millenia the Egyptians
produced a fair crop of Imhoteps and were thanjful for it.
>But I've seen no credible evidence that the Egyptians saw the
>earth as something that even *has* a circumference,
Come on Brian, go look at their illustrations of the heavens.
The God Ptah who made the heavens wears a blue hemispherical
skull cap. The armature he made to support the heavens is a circle.
If you stand on top of a pyramid and look out over a flat desert
you can see the curvature of the earth. We have established that
these were no dummies so lets have no more of that "they didn't
know the earth had a circumference stuff".
>let alone that they had the technology to make a very accurate
>determination.
It doesn't take much technology Brian.
>
>>The Greeks tell us the apothem or slant side of the Great Pyramid
>>was a stadium in length. If that length was 356 royal cubits of 20.6"
>>or 611 English feet, that gives the value of 25,000 Miles,
>>Please don't even try to claim this was another coincidence
>
>Of course I think it was.
Why would I expect any more of you...
>I see no reason to believe that there's the
>slightest significance to the fact that the slant height of the GP is
>approximately 1/216,000 the earth's circumference.
Explain to me how this one monument happens to incorporate such a
long list of coincidences.
1.) Pi; inside, outside and in her ladies chambers.
2.) Phi
3.) An apothem a geocommensurate stadium long
4.) A face whose area is the square of the pyramids height
and an area of exactly eight times their standard land measure
which it turns out is where we get our acre.
5.) A rise and run which are Amicable numbers
6.) A pyramidion whose base perimeter is Pi royal cubits
7.) An apothem to the top of the pyramidion equal to the number
of days in the egyptian year
>The idea that the dimensions of the GP are intentionally related
>to the dimensions of the earth is preposterous;
Once again your method is to reject the data, and go with the
preconcieved idea. You can't deny the data so you call it a
coincidence. Is that your idea of a scientific method?
You have to be aware your credibility is not enhanced by
such posturing.
>I quite frankly don't see how any sane
>person of even modest intelligence can think otherwise. (You are
>welcome to draw the obvious inference.)
You sound like a Creationist. There are people who say the
same thing about most articles of faith. A believer believes
feverently, therefore it must be true and anything which
contradicts the belief must be ludicrous and false.
>
>Your constellation of claims about the GP is absurd. You insist that
>all of the following are intentional:
>(A) the slope of 14/11, which is approx. 4/pi;
You can't build a pyramid without knowing its pitch, Maybe you are
one of those poor deluded souls who thinks it was laid out with a wheel?
>(B) the incorporation in its dimensions of the amicable
>numbers 220 and 284;
The rise and run in royal cubits to the top of the pyramidion.
>(C) the fact that the slant height was approx. 1 stadion.
As reported by Agatharchydes of Cygnus for the truncated pyramid.
> Suppose for a moment that you set out to build a
>pyramid with these three properties. If it has a slope of 14/11, and
>the base is chosen to be 2b in length, the height must be 14x/11, and
>the slant height will then be b * sqrt(1 + 196/121). If you want this
>to be 1 stadion, you must choose b to be 1/sqrt(1 + 196/121) stades,
>or about 0.62 stades. In other words, the height and base are
>completely determined by the slope and the slant height.
So far what the Egyptians have done here is about as complicated
as framing a roof.
>Now in order to get (B), you must first find a pair of amicable
>numbers whose ratio is very close to 14/11; the fact that there
>is such a pair that's small enough to find is sheer luck.
Whew!!!, two paragraphs into this and you are back to coincidence
as your explanation. There was only one pair of amicable numbers
known in antiquity. 284:220; if you don't happen to see it already,
the pyramidion is staring you in the face.
>Let n be the smaller of these numbers (i.e., in fact 220);
>to complete your program, you now need to find that b/n is an
>existing unit of measure!
Any multiple of any unit of measure would do so far.
>In short, while you might set out to arrange for (A), (B), and (C),
>success would be a matter of luck
Lets substitute perhaps a millenia of experience (c 3,000 BC) for luck
and see where we get. You have a septenary number system which works
by binary doubling, octally decimally, unidecimally, sexigesimally.
Your calculations are based on working with fractions, you are familiar
with arithmetic and geometric progressions, squares and square roots
geometry, equations of the first and second degree, think of a number
problems and have begun to note that certain series of numbers have
useful properties so you put them in tables.
(unless you think that the stadion and royal cubit were
>defined *after* the GP was constructed and that the Egyptians could
>control the distribution of amicable numbers).
If the stadion and royal cubit are existing measures, (lets not forget
the 8 khets on the pyramids face), what could be more natural than
to incorporate them in your system of proportions?
>
=====================
>>>For instance, Snell's 1615 figure for the equatorial circumference,
>>>the best up to that time, was too small by about 3.4%. That's an
>>>error of about 20 stades per degree. In other words, even at that
>>>relatively late date it would have been impossible to define a length
>>>*accurately* in terms of the earth's circumference.
>
>>Your thought appears to be that the closer we are in history
>>to our own time, (regardless of anything else such as methodology)
>>the better the numbers are going to be. Briam that is just plain
>>old garden variety ethnocentrism.
>
>Where do you get the idea that I don't consider methodology?
even at that relatively late date it would have been impossible
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Doyou see how you give away what you are really thinking...?
>Considerations of methodology and technology underlie my view of the
>matter. I've seen no credible evidence that the Egyptian worldview
>even made the question meaningful for them.
That's probably true, but then you haven't made much of an effort
to study the matter. You would probably see a lot more evidence
if you looked for it. A mathematician could walk through a desert
full of pottery shards with them crunching into dust beneath his
feet without a care that he is destroying 3000 years of history.
Why? Because he just has no idea what to look for let alone
where to look.
>I've seen no credible evidence that they had the mathematical
>methodology that underlies the determinations by Eratosthenes
>and Poseidonios (or any other determinations).
"No evidence", huh?
I show you where Pliny says the well used by Erathosthnes was
dug for the purpose of making the measurement. You say "How do
you know he didn't dig it?" I say "because archaeologists
have found artifacts dating the well to long before Eratosthenes
was born." You say "Well then, Pliny must have made that part up"
See what I mean Brian, you have blinders on.
>And I've certainly seen no evidence that they had the technology
>to use *any* method to get a precise and accurate value.
What makes you think it required any great deal of technology?
> You may be able to sustain the delusion that they had the
>theory, but about the instrumentation there should be no question.
What,torches, signal flags, a mekhert, some knotted cords and a sundial
seem like heavy duty technology to you?
>
>>The Greeks went downhill
>>from the Egyptians
>
>This bears no resemblance to history as far as mathematics and
>astronomy are concerned.
Of course it does Brian, It took the Greeks centuries to regain even
the tip of the iceburg when it came to Egypt. They started with Thales
and were still learning things from the Egyptians with the Prolomies.
>
>Speaking of the fact that the earth is more nearly an ellipsoid than a
>sphere, Steve said:
>>You are assuming, I guess,that because Europeans didn't become aware
>>of this again until the late 17th century, the well documented
>>knowledge of this in antiquity can be dismissed.
>
>Produce the documentation.
Pythias measured the degree of latitude all the way from Marseilles
up to Iceland and noted how it decreased as he went north. You can read
about his studies in the commentaries of Strabo and Pliny. In case you
are interested the estimates made in antiquity were found to be within
about the same range of error from the value measured to establish
the meter as we have found the meter to be from the actual value.
>
>=====
>
>>[The Greeks'] foot was as geocommensurate as the meter.
>>Its a fact. Deal with it.
>
>It's a lunatic delusion. Deal with it.
No Brian, its an established fact. You can look at the value
Klein gives for the Greek foot, and compare it to other studies if
you like. It works out to 100 Greek feet equal 1 second of the earths
equatorial circumference. You can call it coincidence again, but you
can't dispute the data.
You are seriously depreciating your credibility by denying any facts you
don't happen to like.
>
>=====
>
>>>>>>The Greeks had an acre of 40,000 Greek feet
>
>>>>>You've made this unsupported assertion before. If they had such a
>>>>>measure, what did they call it?
>
>>The Ptolomaic Greeks used a term "schoenia" and or "aroura"
>>for the Egyptian arura, an area with a side of 100 cubits.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>
>Which isn't even close to the acre and does not measure 40,000 sq.
>ft., Greek or otherwise.
It is 1/2 acre. In antiquity fields were associated in pairs
one of which was left fallow. The acre simply considers the
pair as one field and the measure remains the same.
>(And you're confusing lengths and areas again.
No, The areas are defined as squares with sides of 100 cubits
The 'schoenia' was a length, not an area, so it obviously was
>NOT a Ptolemaic Greek term for the Egyptian <arura>.
It is the length of the side of the arura...sheesh... Brian
>The last time I pointed this out, you told me to '[r]ead more carefully' and then
>proved that I was right by quoting Gillings as follows: 'The linear
>length of 100 royal cubits was called a schoenia in the time of the
>Ptolomies.')
Please at least try and pay attention. The same relationship as existed
between khet and setat existed between schoenia and arura. The length
of the side is the khet or schoenia; the area is the setat or arura.
Now do you get it? It's "an area with a side of 100 cubits."
>
>=====
>
>[Steve made the hilarious claim that '(English) acre comes from
>(Latin)are or area which comes from (Greek)aroura which comes from
>(Egyptian) "a r u ra"'. I pointed out that <are> is a modern French
>neologism based on Latin <area> and that the other postulated
>derivations are simply wrong. Most of Steve's response merely
>confirms his ignorance of the subject (e.g., confusion of cognates
>with borrowings) and isn't worth comment, but some bits caught my
>attention.]
Brian admits the acre was borrowed but wants to weasel away
with another quibble. He claims it can't be a cognate even though
the spelling, pronunciation and meaning are virtually identical because
Egyptian isn't an Indo European language. That is simply foolish.
He goes so far as to argue that if the Greeks had the same word
as the Egyptians the Egyptians must have got the word from the Greeks !!!!!
despite the existence of an Egyptian hieroglyphic for the measure
of a plowed field of land defined as having the side of 100 cubits
going back to the middle kingdom.
>
>>>By the most generous definition the Old English language did not
>>>exist before the 5th c., so even the immediate ancestor to <acre>
>>>did not exist at the time of ancient Egypt.
>
>>I keep wondering if you are just trolling me or what.
>
>What part of 'immediate ancestor' do you not understand?
I don't want to make any comments on your antecedents
even if I do find them questionable...
>
>>Words exist even when formative languages are still dialects. Old
>>English is heavily Germanic, with Latin strongly influencing
>>the Germanic,
>
>Known borrowings from Latin before the Anglo-Saxon tribes migrated to
>England amount to only about 170 lexical items. But Latin influence
>is irrelevant to the early history of the word <acre>. The Old
>English <aecer> and the related forms in other Germanic languages
>(Gothic <akrs>, Old Icelandic <akr>, Old Frisian <ekker>, German
><acker>, etc.) are regularly derived from a Proto-Germanic *akraz,
>which in turn corresponds regularly to IE *agros, which is also
>represented by Latin <ager>, Greek <agros>, and Sanskrit <ajras>.
>(This is evidently a very old Indo-European word.)
No kidding...:) It goes backto c 3,000 BC...and Egypt!
The <c> of <aecer>
>where Latin <ager> and Greek <agros> have <g> shows that the word was
>affected by the First Sound Shift (Grimm's Law) and is part of the
>Proto-Germanic word stock, so it cannot be a borrowing from Latin.
On the contrary Brian, Latin can have the same word,
from the same source and people might even have recognized they
were the same word from the same source, and presume that any
differences were due topronucnciation if they thought about it
at all; just as we recognize finger, palm, hand, cubit and
remen go back a ways too.
>Had Latin <ager> been borrowed in Old English times, it would not have
>had <c>. Indeed, the only borrowing went the other way: there is a
>medieval Latin <acra> that was borrowed from the English word! (And
>the unrelated Latin <area> doesn't even enter into the matter.)
You just don't get it do you? By c 450 AD people had been plowing fields
for millenia. Everybody had about the same word, it meant the same thing.
>
>>It wouldn't be hard to list several
>>dozen Egyptian or for that matter Sumarian words
>>which have come into English virtually unchanged.
>
>By all means do so, being sure to indicate when they entered English
>and in precisely what form.
Why not just go back and look at Saida list of tree words, there was
a whole thread on this some months ago Brian.
>
>Brian M. Scott
steve
Steve Whittet
In article <rq46UFAk...@unicorn-connection.co.uk>, mic...@unicorn-connection.co.uk says...
>
>In article <7fRX7tAX...@chrism.demon.co.uk>, Chris Marriott
><ch...@chrism.demon.co.uk> writes
>>In article <5uviue$q...@fridge-nf0.shore.net>, Steve Whittet
>><whi...@shore.net> writes
>>>>Only in the British Empire, a touch late for this arguement.
>>>
>>>We still use some English measures in the US. Whats interesting
>>>is that they represent three millenia of reasonably stable standards
>>
>>The US pint is **NOT** an "English" measure.
Correct. Its actually an Egyptian measure which was adopted by the
Greeks and Romans first, then the English and now Americans.
>>
>>The US pint is 16 fluid ounces. A pint in England is 20 fluid ounces -
>>ie 25% larger (and heavier!).
The size of the ounce depends upo n whether you use a troy ounce
or an ounce avoirdupis.
>Even that is not right because a US fluid ounce is not the same as a UK
>fluid ounce. It is MUCH better to use SI units.
When both the British and Americans used
an ounce avoirdupis The US fluid ounce was 29.537 cc and the
slightly smaller British fluid ounce was 28.413 cc
When discussing alcoholic beverages, the jug or pint is 20 oz.
1/2 pint is a gill, 1/4 pint a jack, 1/8 pint a jock, 1/16 pint a joey.
Despite the fact that the English prefer their pint to be full of Guiness
when it comes to measures of alcohol they should know they are getting gipped.
Consider that the British gill is only 8.669 cu in.
In the United States we use a 1 1/4 oz shot glass which dispenses
20 1/2 drinks of 36.93 cubic cm from a fifth which is 56% more liquor
than the British 1/6 gill standard.
>>
We should certainly not ignore the fact that a dry pint is not the same size
as a liquid pint. A US Dry Pint is 33.6 cu inches and a liquid pint
is 28.875 cu". We can avoid any confusion in the size of the units
by comparing their volume in cubic inches.
.
Can you surmise the reasons for the differences? Dry measure was often
stored in storage rooms of a capacity given in cubic feet or cubits.
Liquid measure was often stored in cylinders or hemisperes such as
barrels, kegs, casks or amphora. If you were a brewer and got an order
for 500 kegs of beer you might have to order some grain to fill the order.
How many bushels would you need to make 500 kegs?
In the SI system you first have to calculate the volume of the keg in
cubic meters. In the English system you can convert directly. The ratios
of dry measure to liquid measure make the conversions a little easier.
Are SI units easier to work with. I would have to say no, not at all.
Once you understand the system, English measures are much easier to use.
As were the Egyptian measures they are derived from.
>Michael Parry
steve
Chris Marriott
In article <5v430n$4...@fridge-nf0.shore.net>, Steve Whittet
<whi...@shore.net> writes
>Are SI units easier to work with. I would have to say no, not at all.
Yes - definitely. In any computations involving conversion between
units, SI units are hugely simpler to work with, since they are
consistent, and "conversion factors" are nearly always powers of ten.
Consider, for example, any equations involving energy or power. What you
call the "English" system uses completely different sets of units
according to the form that the energy is manifested in - heat,
mechanical work, etc, with horrible conversion factors between them. The
SI system has one unit of energy - the Joule - which is used in all
situations.
>Once you understand the system, English measures are much easier to use.
>As were the Egyptian measures they are derived from.
Since you obviously KNOW how "English" measures work, Steve, how could
you possible make a statement as ludicrous as:
"A pint's a pound the world around"
as you did a few days ago? You know as well as I do that a pint differs
between the USA and most of the rest of the English-speaking world,
which uses the British definition of the pint. Whatever made you come up
with a statement as patently untrue as that?
Brian M. Scott
On 9 Sep 1997 04:12:52 GMT, whi...@shore.net (Steve Whittet) wrote
the usual reams, most of which I've ignored. I've re-ordered the
topics to put the (semi-)serious stuff first and the snide remarks and
slanging matches at the end.
Referring to the notion that such ostensibly anatomical measures as
the palm and foot 'did not originate with the parts of the body' but
'were mapped to the body as a grid', Steve says:
>Actually its the subject of Vitruvious "Ten Books on Architecture".
Vitruvius is hardly an authority on the history of these units. You
mistake after-the-fact theorizing for history.
>>>>(And definitions based directly on body parts occur
>>>>remarkably late. In the 16th c. Master Koebel, a surveyor, wrote: 'On
>>>>a certain Sunday as they happen to come out of church, bid sixteen men
>>>>to stop, tall ones and short ones, .... 16 men shall stand in line
>>>>with the left feet touching, one behind the other. This distance
>>>>shall be the right and lawfull Rood and one-sixteenth of it shall be
>>>>the foot.')
>>>The Europeans of the Dark Ages and even some modern people tend not to
>>>give much thought to what a standard of measure is and just how long
>>>they have been around in essentially the same form.
>>What on earth do the so-called Dark Ages have to do with 16th c.
>>England?
>By the 16th century much had been lost. People knew it and tried to
>reconstruct things as best they could. "A Canticle for Leibowitz" comes to mind.
I burst out laughing when I read this. Please, Steve, take the time
to read a little about at least the last 1000 years or so of Western
European history. You seem to think that the 16th c. was part of what
you are pleased to miscall the Dark Ages. The term, which has for
some time been out of favour amongst historians, traditionally covers
no more than the period c.500 - c.1000. In fact, by the end of the
16th c. most of what we know of Greek mathematics had already been
recovered, and algebra had been taken further than ever before.
=====
>why would you measure a foot in palms?
For the reason already given: to make large units integral multiples
of smaller ones. (Don't try to tell me that you don't recognize the
usefulness of such an arrangement: you've appealed to it in the past.)
=====
[Steve claimed '24835.36 miles' as a Greek value for the equatorial
circumference of the earth.]
>>Sheer silliness. They hadn't the instrumentation to measure the
>>earth's circumference to the nearest 0.01 mile.
>Suppose I stand on top of a pyramid and have two assistants stand
>at the eastern and western horizon . I adjust their position with
>signals until I can see one on the backsight of my observation of
>the other.
>Each uncovers a torch when he observes the sun rise and I call out
>when I see the torches for another assistant to note the
>difference in time with a water clock or sundial. My assistant
>informs me it took 8 minutes
You haven't persuaded me that this was possible. Remember, your view
of history requires this determination at a very early date in order
to set the sizes of linear measures. At such dates the Egyptian hours
weren't constant, since they divided real day and night into 12 hours
each, so any assumption that they were using constant minutes need a
*lot* of justification.
>I then have the distance between the two observers measured.
>it works out that they were about 138 miles apart.
You're assuming that a tangent 1 degree around the earth from your
position passes through the top of your pyramid. The secant of 1
degree exceeds 1.00015, and the radius of the earth exceeds 20,000,000
ft., so your pyramid must exceed 3000 ft. in height. (This is over 6
times the height of the GP.) At the very early date that your theory
requires, where in Egypt are you going to find a tall enough tower?
From a 500 ft. tower - a little more than the height of the Great
Pyramid - the horizon should be about 27 mi. away. That makes them
about 0.8 degrees apart, and you'd actually have to be able to measure
an interval of 3.2 min.
=====
>>Moreover, you're inconsistent. The equatorial circumference
>>is 360 degrees of *longitude*, so each degree should - according
>>to you - have 500 stades, not 600.
>No Brian. Longitude is vertical, Latitude is horizontal, The Equator
>is horizontal so we measure it as if it were a section through the Earth
>using degrees of Latitude.
>Moving north from the equator As we increase our Longitude
>the value of a degree of Latitude decreases.
You have it exactly backwards. Moving north from the equator we
increase our latitude. Eventually we reach the horse latitudes
(between about 30 and 35 degrees N) and enjoy a horse laugh about the
whole business.
=====
>>Speaking of the fact that the earth is more nearly an ellipsoid than a
>>sphere, Steve said:
>>>You are assuming, I guess,that because Europeans didn't become aware
>>>of this again until the late 17th century, the well documented
>>>knowledge of this in antiquity can be dismissed.
>>Produce the documentation.
>Pythias measured the degree of latitude all the way from Marseilles
>up to Iceland and noted how it decreased as he went north. You can read
>about his studies in the commentaries of Strabo and Pliny.
Given your earlier confusion about latitude and longitude, I suspect
that what Pytheas measured - if anything - was the size of a degree of
*longitude*. Its shrinkage would merely tend to confirm a spherical
model. This has nothing to do with measuring the flattening at the
poles, which is far too small to be measured by any instrumentation
available to Pytheas.
=====
[Steve claims that all of these features were intentionally
incorporated in the dimensions of the GP:
(A) the slope of 14/11, which is approx. 4/pi; (B) the amicable
numbers 220 and 284; (C) the fact that the slant height was approx. 1
stadion.]
As I pointed out before, (A) and (C) together completely determine the
dimensions of the pyramid. Once you settle on them, you have no
choice about the size. At that point the height and half-side are
given: either they give you a pair of amicable numbers, or they don't.
The fact that they do (after you add an extra 4 cubits at the top) is
a slightly fudged mathematical coincidence. In other words, while you
might set out to accomplish all three goals, it's only an accidental
peculiarity of the integers, helped along by those extra 4 cubits and
the ratio of stadion to cubit, that allows you to do so. There's no
guarantee ahead of time that after you've accomplished (A) and (C),
(B) will even be possible. If you wanted a different slope, or if the
ratio of stadion to cubit were different, you couldn't achieve both
(B) and (C) (along with your desired slope).
It's clear from your response to my previous attempt that you didn't
understand the point at all; if you show as little comprehension after
this attempt, we might as well drop the matter, which I suspect falls
in your intellectual blind spot.
=====
>>>>>>>The Greeks had an acre of 40,000 Greek feet
>>>>>>You've made this unsupported assertion before. If they had such a
>>>>>>measure, what did they call it?
>>>The Ptolomaic Greeks used a term "schoenia" and or "aroura"
>>>for the Egyptian arura, an area with a side of 100 cubits.
>>Which isn't even close to the acre and does not measure 40,000 sq.
>>ft., Greek or otherwise.
>It is 1/2 acre. In antiquity fields were associated in pairs
>one of which was left fallow. The acre simply considers the
>pair as one field and the measure remains the same.
Even this contrived explanation fails. The Greek <aroura> was approx.
equal to the Roman <iugerum>, and both were about 2/3 of an acre.
This is well-known and easily substantiated from a variety of sources.
You still have not produced a Greek 'acre' of approx. 40,000 sq. ft.
>>(And you're confusing lengths and areas again.
>> The 'schoenia' was a length, not an area, so it obviously was
>>NOT a Ptolemaic Greek term for the Egyptian <arura>.
>It is the length of the side of the arura...sheesh... Brian
Then it isn't a term for the <arura>, which is what you originally
said: 'The Ptolomaic Greeks used a term "schoenia" ... for the
Egyptian arura'. Don't blame me for your verbal incompetence.
=====
>>[Steve made the hilarious claim that '(English) acre comes from
>>(Latin)are or area which comes from (Greek)aroura which comes from
>>(Egyptian) "a r u ra"'. I pointed out that <are> is a modern French
>>neologism based on Latin <area> and that the other postulated
>>derivations are simply wrong. Most of Steve's response merely
>>confirms his ignorance of the subject (e.g., confusion of cognates
>>with borrowings) and isn't worth comment, but some bits caught my
>>attention.]
>Brian admits the acre was borrowed
Liar.
>but wants to weasel away
>with another quibble. He claims it can't be a cognate even though
>the spelling, pronunciation and meaning are virtually identical because
>Egyptian isn't an Indo European language. That is simply foolish.
No, it's not foolish; it's a matter of the definitions. A native
Egyptian word and a native Greek word cannot have common ancestry,
simply because the languages aren't related. Therefore they cannot be
cognate. The only ways an Egyptian and a Greek word can be related
are for one of them to be a borrowing from the other or for both to be
borrowed from a third language. I take it that <arura> is native
Egyptian. I could be wrong, but it appears to me that <aroura> is
native Greek. (Liddell-Scott-Jones appears to agree.) If that's the
case, the words are unrelated, and their similarity is indeed
coincidence. The only other possibility is that <aroura> is a Greek
borrowing, but in that case its apparent kinship with the Greek verb
'to plow' is an equally surprising coincidence.
>He goes so far as to argue that if the Greeks had the same word
>as the Egyptians the Egyptians must have got the word from the Greeks !!!!!
No, Steve, that's not what I said. Only you could have so badly
misunderstood. Go back and try again; I'll wait.
I will not deal further with the word 'acre'. I've given you the
correct information, which you could verify if you'd bother to learn a
little historical linguistics. From this discussion and others in
sci.lang it's apparent that you choose to remain ignorant, in effect
denying that there is such a subject, so further discussion is a
complete waste of time.
=====
>>>It wouldn't be hard to list several
>>>dozen Egyptian or for that matter Sumarian words
>>>which have come into English virtually unchanged.
>>By all means do so, being sure to indicate when they entered English
>>and in precisely what form.
>Why not just go back and look at Saida list of tree words, there was
>a whole thread on this some months ago Brian.
It's your improbable claim, so the onus is on you to produce the
evidence. Don't bother with Saida's compost.
=====
>>>>>The Greeks
>>>>>tell us there are 600 feet in a stadium and 600 stadia in a degree.
>>>>>Why isn't that a geocommensurate standard of measure?
>>>>'The Greeks' isn't very specific. Eratosthenes reckoned 700 stades to
>>>>a degree, and he was certainly Greek. A figure mentioned by Strabo,
>>>>apparently accepted by Ptolemy, and still known (and influential) in
>>>>the 15th c. corresponds to a value of 500 stades to a degree.
>>>As I mentioned before, they took 600 stadia to a degree of latitude
>>>and 500 stadia to a degree of longitude.
>>So they thought that the earth was a prolate spheroid with its long
>>axis through the poles, like an upright American football? I doubt it
>>very much.
>No, they used two different length feet !!!
It must have been very awkward to have to use two sets of rulers, one
for north-south dimensions and the other for east-west dimensions.
=====
>The Egyptians welcomed the Greeks into their libraries as children
>and attempted to teach them, as they would any young scribe, the
>accumulated observations of several millenia. They taught the Greeks
>medicine, law, philosophy, history, science, art, music and a respect
>for the wisdom of the ages.
Aww, how sweet! The wisdom of the ages, no less. (But you're
supposed to capitalize that, you know!)
=====
>Once again your method is to reject the data, and go with the
>preconcieved idea. You can't deny the data so you call it a
>coincidence. Is that your idea of a scientific method?
>You have to be aware your credibility is not enhanced by
>such posturing.
I'm aware that your credibility in these matters is non-existent and
that my willingness to divert myself with these arguments is seen by
some as a selfish waste of bandwidth.
>You sound like a Creationist.
Really? I have no use for creationists: they're fundamentally
irrational. So are you, at least on this subject, but you do
occasionally manage to be a little clever about it, when you stick to
mathematics and avoid linguistics.
Brian M. Scott
William Wallace
On 8 Sep 1997 01:04:14 GMT, whi...@shore.net (Steve Whittet) wrote:
>In article <34132c14....@news.mindspring.com>, WWal...@freedom.org÷ says...
>>On 7 Sep 1997 02:27:30 GMT, whi...@shore.net (Steve Whittet) wrote:
>>>>...demonstrate common weights and volumes.
>>>>...standardization across countries was introduced by Rome
>>>>...to facilitate commerce.
>standardization across countries was introduced by Egypt, and Mesopotamia
>>>The weights and volumes are also common, based on cubes and cylinders
>>>of the unit lengths. They have already been discussed at some length
>>>in the thread. Compare the cube of a foot to the gallon for example
>>>You will find that the cube an ordinary cubit of 17.698 inches on a
>>>side holds 24 gallons, a royal cubit of 20.628 inches on a side
>>>holds 38 gallons.
>> You were talking a good talk until you got here. Those, 24 and 38
>>gallons, do not appear as standard volumes any place. Nice try though.
>hmmm... their being even multiples of the gallon isn't good enough
>you want similar containers?
First, if it were such exact multples of a gallon you have an
ever more difficult problem to addess, that is, where did the measure
for ONE gallon come from? Along with this problem we have to ask
whether the chicken or the egg came first.
First and a half, as both numbers even then there is no way to
tell what the smallest common volume measure might be save that it was
two gallons or smaller. Thus the "gallon" measure is not supported.
Second, without checking your calculations, a mark down to the
throusandths of an inch borders upon ridiculous. Over lengths that
great they would change more than a 1/1000th of an inch with only a
few degrees of temperature change.
Even if were the case, scribing to that accuracy would have to be
on metal with an extremely fine tool. Then of course we have an even
worse problem with temperature. As there were no thermometers until
around 1750 and no practical way to control temperature until nearly
two centuries later, it is unclear of what value such accuracy could
possibly be.
Thus the absolutely even "gallon" measures appear to be the
result of reverse estimating the length of the cubit.
Finally, it is unclear how, without great effort in those days
and to no apparent value, one would manufacture a cubic measuring
device for a standard. Does on hollow out a stone? Create a cubic clay
pot? And where to we find people able to pick it up and pour out the
contents? I mean, filled with water, that is going to be heavy and
clearly very inconvenient.
Water is what, seven pounds per gallon? That is 168 and 266
pounds respectively exclusive of container weight. Lifting is one
thing but twisting to pour leads to spinal injuries (ask me some
time.)
So we have several problems here, starting with we can't say the
basic unit is anything other than two gallons, going through the quite
questionable accuracy of the cubit and finally to an impractically
sized measurement.
>>>You should find "a pint's a pound the world around"
>>
>>Only in the British Empire, a touch late for this arguement.
>We still use some English measures in the US. Whats interesting
>is that they represent three millenia of reasonably stable standards
>which are now being ignorrantly elbowed aside by the metric system.
The metric system is approaching two hundred years old. There are
very few holdouts and then only in theory.
>>>> If the explanation is diffusion then we would expect length,
>>>>weights and volumes all to be common. That is not what we find at all.
>>>Then you need to look more carefully.
>> So far, other than assertion, you have not directed me to what
>>you examined to convince you. You certainly know what they are.
>Generally I was first impressed by the correspondence between the Egyptians
>linear measures and our own. later I became aware that most measures
>of weight and volume are defined as the cube whose side is a unit of
>length. Thus the correspondence between the linear measures led to
>a correspondence between measures of volume and weight.
>The talent for example was the cube of the foot. The foot was Egyptian
>in origin.
Excuse me but there are references to a "talent of gold." Without
it being poured in in liquid form it is not an accurate measure. It
would also be unliftable if the container weighed nothing. And no one
has ever measured gold save by weight. It appears here the talent is
in fact a measure of weight.
If a talent of gold is in fact a cubic foot of gold we have here
a proverbial king's ransom. Yet references to a talent of gold
indicate it was more on the order of an ounce of gold.
>>>>We find only the body based measures, lengths, to be similar but not
>>>>indentical.
>>>All measures are subject to change over time. If you follow the
>>>changes carefully you will find that the original system was
>>>pretty comprehensive.
>> Yes, the human body changes quite slowly for lengths but the
>>point here is for weights and volumes. What is a Kor of wheat and
>>compare it to the volume of other measures of volume.
>The Egyptians used a unit called a khar to measure wheat, it was
>1 1/2 cubic cubits. It had a side of two Roman pes. It was 12 buckets
>or 6 bushels.
And this of course brings up the next problem. Containers were
not cubic. Producing a curved container to have a specific volume
content was a matter of artistry and judgement prior to computers.
Producing jars with specific and accurate volume measures is no
mean feat. It is not clear why one would start with a cubic measure
just to make it hard to standardize containers.
>>>> Thus the diffusion hypothesis fails.
>>
>>>only if you blow it off and don't look carefully. If you maintain that
>>>the Greeks didn't borrow from the Egyptians or the Romans from the Greeks
>>>or the Europeans from the Romans,then you need to show how and why they
>>>independently invented things like hours and minutes, the remen, pace,
>>>mile, acre, stadium, and degree as even multiples of the finger, palm,
>>>hand, fist, foot and cubit. Explain why English weights and measures
>>>of volume follow the same binary, septenary, octonary, decimal, unidecimal
>>>and sexigesimal proportional system as the Egyptians.
>> You are back to lengths again. The subject is weights and
>>volumes. You do not appear to be able to substanstiate your diffusion
>>claim for other than body part related lengths.
>I find the easiest way to compare units of volume is in cubic inches.
>a bushel is 2219.3 cubic inches and a gallon is 231 cubic inches.
>To find an Egyptian measure of volume which contains an even number
>of English gallons is not likely to be a coincidence. To find two
>such measures reduces the possibility that much further
>231 x 24 = 5544 cu" this is the side of the cube of the ordinary cubit, 17.69"
>321 x 38 = 8778 cu" this is the side of the cube of royal cubit, 20.628"
The "even" number of gallons is quite what is against you as the
largest common divisor is two gallons. BTW: You are talking British
gallons or do you mean American gallons? It is the difference between
five and four quarts respectively. Not a trivial difference.
I further point out that between the Roman Empire and the metric
system, there was no standardization in weights and measures in
Europe. There were many systems even in the same country.
Your assertion depends upon a one to one correspondance between
Egyptian and British whereas there was no correspondance between
British and other European systems. Thus you are claiming not only a
unique but highly unlikely connection. You will have to explain this
also.
Dave Welsh
Steve Whittet <whi...@shore.net> wrote in article
<5v2ic4$r...@fridge-nf0.shore.net>...
> In article <3413b98e...@news.csuohio.edu>, sc...@math.csuohio.eduо
says...
> >
> >On 7 Sep 1997 06:52:24 GMT, whi...@shore.net (Steve Whittet) wrote:
> >
> >I wrote:
> >>>>>The finger, palm, foot, and cubit are of course based on the human
body.
> >
Steve: You have a broad knowledge of the subject which I recognize, but ...
Scott: II found your posting reasoned and sensible. Still ...
I hope that everyone involved in this discussion understands the meaning of
the term
"controversialist." Perhaps I have not given the arguments the weight they
deserve, nevertheless the impression remains that the goal is controversy
not illumination ....
heat rather than light.
Pax! Fratres ...
We are all gathered in this group for the purpose of learning. Let us put
aside questions of who is more knowledgeable on some arcane subject (I
guarantee that NO ONE in this group can keep up with me when I pick the
topics) and return to the proper and noble objective, of increasing the
breadth of everyone's knowledge.
As a concrete suggestion, I would advance the concept that future
discussion should be of significant value to the previously uninvolved
reader, not an exercise in one-upmanship.
As an ethical issue, let me point out that while some may have access to
free bandwidth, the rest of us don't, and resent postings that are not of
benefit to the group as a whole.
The InterNet is an intellectual creation whose raison d' etre is free
discussion that provides insights not obtainable elsewhere. Let us remember
that there is more than one kind of "Spam" and keep our combative instincts
subject to the concept that we have a responsibility to the whole
community.
David Welsh
dwe...@oxford.net
Steve Whittet
In article <3415f1af....@news.mindspring.com>, WWal...@freedom.orgO says...
>
>On 8 Sep 1997 01:04:14 GMT, whi...@shore.net (Steve Whittet) wrote:
>
>>In article <34132c14....@news.mindspring.com>, WWal...@freedom.org÷ sa
>ys...
>
>>>On 7 Sep 1997 02:27:30 GMT, whi...@shore.net (Steve Whittet) wrote:
>
>>>>>...demonstrate common weights and volumes.
>>>>>...standardization across countries was introduced by Rome
>>>>>...to facilitate commerce.
>
>>standardization across countries was introduced by Egypt, and Mesopotamia
>
>>>>The weights and volumes are also common, based on cubes and cylinders
>>>>of the unit lengths. They have already been discussed at some length
>>>>in the thread. Compare the cube of a foot to the gallon for example
>>>>You will find that the cube an ordinary cubit of 17.698 inches on a
>>>>side holds 24 gallons, a royal cubit of 20.628 inches on a side
>>>>holds 38 gallons.
>
>>> You were talking a good talk until you got here. Those, 24 and 38
>>>gallons, do not appear as standard volumes any place. Nice try though.
>
>>hmmm... their being even multiples of the gallon isn't good enough
>>you want similar containers?
>
> First, if it were such exact multples of a gallon you have an
>ever more difficult problem to addess, that is, where did the measure
>for ONE gallon come from? Along with this problem we have to ask
>whether the chicken or the egg came first.
Egyptian units of length came first. Measures of volume were cubes
on the sides of the units of length.
>
> First and a half, as both numbers even then there is no way to
>tell what the smallest common volume measure might be save that it was
>two gallons or smaller. Thus the "gallon" measure is not supported.
Sure there is, you may need to do some reading to check me out here,
but you should find that most units of volume for dry measure are
defined as cubes and liquid measures are cylinders, barrels, casks,
niperkins, etc. Our gallon of 231 cubic inches came to us as a wine
gallon, but the English did not invent wine, nor for that matter
beer. At the wedding at Cana a Hebrew rabi provides wine for the
guests in units of a mettrette.
Liquid measures generally run a little over the dry measures. You
might want to compare the Biblical bath and epath of 12 gallons.
The Hebrews got their liquid measures from the Egyptians who had
a fondness for beer. The most common small liguid measure used by
the Egyptians was the Hinu.
>
> Second, without checking your calculations, a mark down to the
>throusandths of an inch borders upon ridiculous. Over lengths that
>great they would change more than a 1/1000th of an inch with only a
>few degrees of temperature change.
You can round them off to the nearest 1/16" if you like, how many
decimals will you use use to express even 1/8" of an inch (.125")
let alone 1/16" (.0625")?
>
>Even if were the case, scribing to that accuracy would have to be
>on metal with an extremely fine tool. Then of course we have an even
>worse problem with temperature. As there were no thermometers until
>around 1750 and no practical way to control temperature until nearly
>two centuries later, it is unclear of what value such accuracy could
>possibly be.
As I said, would you decimally express fractions of an inch to a single
decimal point?
> Thus the absolutely even "gallon" measures appear to be the
>result of reverse estimating the length of the cubit.
There are a number of sources which give us a fair range for the royal cubit
20.62" is favored by some archaeologists, IES Edwards, among them
20.59" is given by Gillings favoring Gardiner
Klein gives a range of cubits from all over the ancient world
whose fingers average about.735", giving 20.58"
Petrie chose 524 mm which is 20.6299..."
Stechinni makes a case for 525 mm 20.669"
Coles survey gives an average of 523.55 mm for the length of the
royal cubits used to make the great Pyramid. 20.61"
I generally use 20.6" as a round number unless I'm trying to show
at which end of the range of values a correlation falls.
20.628" is well within the range
> Finally, it is unclear how, without great effort in those days
>and to no apparent value, one would manufacture a cubic measuring
>device for a standard. Does on hollow out a stone? Create a cubic clay
>pot?
The Egyptians made wooden boxes with great skill. Grain
was stored in rooms made of clay bricks. As it happens
they did hollow out stones, thousands of alabaster vases
have been found with walls so thin you can see through them.
As to making pots, amphora and clay vessels of a given capacity,
If you layout a sheet of clay to a length which is 22/7 the
unit length of a standard of measure and roll it into a cylinder
which you fashion into a jug or jar and it happens that your units
of measure are multiples of Pi, then conversions are a piece of cake.
> And where to we find people able to pick it up and pour out the
>contents? I mean, filled with water, that is going to be heavy and
>clearly very inconvenient.
^^^^^^^^^^^^^^^^^^^^^^^^^^
You are talking about a people who built pyramids, but aside from
that, if the standards of measure are defined as the cube of a length
you just measure your granary and determine what proportion of its
capacity has been used.
>
> Water is what, seven pounds per gallon?
sea water is 64 lb per cu'
ice water is 56 lb per cu'
alcohol is 49 lb cu'
olive oil is 58 lb cu'
there are about 7 1/2 gallons to an English cubic foot
>That is 168 and 266
>pounds respectively exclusive of container weight.
For what container? With what inside it?
>Lifting is one thing but twisting to pour leads to spinal injuries
>(ask me some time.)
What point are you trying to make?
If this has something to do with containers and units of measure,
Most people who move bulk goods prefer to do so in the largest
possible container and the fewest possible trips.
>
> So we have several problems here, starting with we can't say the
>basic unit is anything other than two gallons, going through the quite
>questionable accuracy of the cubit and finally to an impractically
>sized measurement.
The basic unit is a linear measure taken as the side of a cube to
calculate volumes. For a gallon we have a liquid measure so instead
of a cube its a cylinder. 1 Hekat was 8 English pints (dry measure)
take a cylinder of diameter 2 palms (5.8") and height 3 palms (8.8")
It has a volume of PI r^2 h = 232.5 cubic inches
our gallon is 231 cu inches; not a bad correlation for 5000 years.
>>>>You should find "a pint's a pound the world around"
>>>
>>>Only in the British Empire, a touch late for this arguement.
>
>>We still use some English measures in the US. Whats interesting
>>is that they represent three millenia of reasonably stable standards
>>which are now being ignorrantly elbowed aside by the metric system.
>
> The metric system is approaching two hundred years old. There are
>very few holdouts and then only in theory.
In the long run the present fad for the metric system will become
an historical curiosity, a great anachronism. It has about as much
chance of surviving the next millenium as organized religion.
>
>>>>> If the explanation is diffusion then we would expect length,
>>>>>weights and volumes all to be common. That is not what we find at all.
>
>>>>Then you need to look more carefully.
>
>>> So far, other than assertion, you have not directed me to what
>>>you examined to convince you. You certainly know what they are.
>
>>Generally I was first impressed by the correspondence between the Egyptians
>>linear measures and our own. later I became aware that most measures
>>of weight and volume are defined as the cube whose side is a unit of
>>length. Thus the correspondence between the linear measures led to
>>a correspondence between measures of volume and weight.
>
>>The talent for example was the cube of the foot. The foot was Egyptian
>>in origin.
>
> Excuse me but there are references to a "talent of gold."
Sure, there were also talents of silver. Essentially the talent was
one cubic foot; The hekat was 4 quarts, the khar was 2/3 of a cubic
cubit or about 20 hekats, the hinu was 1/10 hekat.
>Without it being poured in in liquid form it is not an accurate measure.
Where does that bit of wierdness come from? The talent was a dry measure.
>It would also be unliftable if the container weighed nothing. And no one
>has ever measured gold save by weight. It appears here the talent is
>in fact a measure of weight.
I don't know how you can on the one hand assert that gold was measured by
a measure of volume, the talent, and on the other hand assert it was
never measured other than by weight. Of course the amount of gold
which filled a cubic foot (1205 pounds) was also a known value
but gold was more commonly measured by the minah, sheckel, drachma,
bekah, rebah, gerah, quedat and grain which were weights defined
as volumes by being fractions of the talent..
>
> If a talent of gold is in fact a cubic foot of gold we have here
>a proverbial king's ransom. Yet references to a talent of gold
>indicate it was more on the order of an ounce of gold.
A Hebrew talent or kikkor was 60 minahs 29,900 grams.
The Greek talent was 25,900 grams
>
>>>>>We find only the body based measures, lengths, to be similar but not
>>>>>indentical.
>
>>>>All measures are subject to change over time. If you follow the
>>>>changes carefully you will find that the original system was
>>>>pretty comprehensive.
>
>>> Yes, the human body changes quite slowly for lengths but the
>>>point here is for weights and volumes. What is a Kor of wheat and
>>>compare it to the volume of other measures of volume.
>
>>The Egyptians used a unit called a khar to measure wheat, it was
>>1 1/2 cubic cubits. It had a side of two Roman pes. It was 12 buckets
>>or 6 bushels.
>
> And this of course brings up the next problem. Containers were
>not cubic.
Storage rooms usually were rectangular solids which could be
divided up into cubic feet. of course if a cylindrical or hemispherical
container was used the Egyptiians were quite capable of calculating its volume.
Producing a curved container to have a specific volume
>content was a matter of artistry and judgement prior to computers.
>
> Producing jars with specific and accurate volume measures is no
>mean feat. It is not clear why one would start with a cubic measure
>just to make it hard to standardize containers.
Actually its pretty easy to convert from cubic to cylindrical
measures.
>
>>>>> Thus the diffusion hypothesis fails.
>>>
>>>>only if you blow it off and don't look carefully. If you maintain that
>>>>the Greeks didn't borrow from the Egyptians or the Romans from the Greeks
>>>>or the Europeans from the Romans,then you need to show how and why they
>>>>independently invented things like hours and minutes, the remen, pace,
>>>>mile, acre, stadium, and degree as even multiples of the finger, palm,
>>>>hand, fist, foot and cubit. Explain why English weights and measures
>>>>of volume follow the same binary, septenary, octonary, decimal, unidecimal
>>>>and sexigesimal proportional system as the Egyptians.
>
>>> You are back to lengths again. The subject is weights and
>>>volumes.
No the subject is measurements. Weights were defined as volumes
and volumes were defined as cubes with sides of a given length.
You do not appear to be able to substanstiate your diffusion
>>>claim for other than body part related lengths.
>
>>I find the easiest way to compare units of volume is in cubic inches.
>>a bushel is 2219.3 cubic inches and a gallon is 231 cubic inches.
>
>>To find an Egyptian measure of volume which contains an even number
>>of English gallons is not likely to be a coincidence. To find two
>>such measures reduces the possibility that much further
>
>>231 x 24 = 5544 cu" this is the side of the cube of the ordinary cubit, 17.69
>"
>>321 x 38 = 8778 cu" this is the side of the cube of royal cubit, 20.628"
>
> The "even" number of gallons is quite what is against you as the
>largest common divisor is two gallons. BTW: You are talking British
>gallons or do you mean American gallons? It is the difference between
>five and four quarts respectively. Not a trivial difference.
I am talking wine gallons, we can take it down to quarts or pints, gills,
ounces, whatever you like.
>
> I further point out that between the Roman Empire and the metric
>system, there was no standardization in weights and measures in
>Europe. There were many systems even in the same country.
Just because you don't yet know the systems of conversion doesn't mean
there was no standardization. Actually all the measures Egyptian,
Hebrew, Greek, Roman, English and American are amazingly consistent
with one another. Where there are variations there is usually a
discernable reason. For example a cubic measure with a side 5/4
the side of another cubic measure was taken as its double.
>
> Your assertion depends upon a one to one correspondance between
>Egyptian and British whereas there was no correspondance between
>British and other European systems. Thus you are claiming not only a
>unique but highly unlikely connection. You will have to explain this
>also.
You can read all about it for yourself in the cited reference material.
There was excellent correspondence between the English and other European
systems. The russians for example used a measure called an arshin
egual in length to the English foot.
steve
Paul Murray
>In article <5v430n$4...@fridge-nf0.shore.net>, Steve Whittet
><whi...@shore.net> writes
>>Are SI units easier to work with. I would have to say no, not at all.
Speaking as a Brit, by the time I went to school we were not even
taught most of what you call the English system (we call it the Imperial
system), and having grown up using the metric system for calculations in
my maths, physics and chemistry courses the idea of wanting to switch to
using the Imperial one seems incomprehensible.
The pint tends to be used now only to refer beer, anything else is
in litres, and while I still think of weight in stones and pounds, apart
from that I, and most of my generation, are metric to the core. To say that
the metric system will pass and the Imperial make a comeback is ignoring the
fact that entire generations will have grown up with the metric system and
wouldn't even know how to use the Imperial one if they wanted to.
-Paul
Steve Whittet
In article <6uGHHcAO...@chrism.demon.co.uk>, ch...@chrism.demon.co.uk says...
>
>In article <5v430n$4...@fridge-nf0.shore.net>, Steve Whittet
><whi...@shore.net> writes
>>Are SI units easier to work with. I would have to say no, not at all.
>
>units, SI units are hugely simpler to work with, since they are
>consistent, and "conversion factors" are nearly always powers of ten.
Actually any system can be simple if you know the system. Do you
divide a circle into grades or do you use degrees? Some parts of the
metric system never have and never will catch on. Do you tell time
in hours, minutes and seconds? What about your position? Are your
maps still using meridians of longitude which pass through Greenwich?
Is there no longer an English Pound? Are Horses no longer measured in
hands? Do they no longer race on courses measured in furlongs? Have
you given up your pint of Guiness?
>Consider, for example, any equations involving energy or power. What you
>call the "English" system uses completely different sets of units
>according to the form that the energy is manifested in - heat,
>mechanical work, etc, with horrible conversion factors between them.
Some units of energy and power are outside the scope of the discussion
as they were defined relatively recently and like the Metric System
are not well linked to the sensible structure of the Egyptian measures.
I find the linkage between time and distance in the old system
compelling. There are twice as many seconds in a century as there
are inches in the equatorial circumference of the earth. That makes
the foot and the second more geocommensurable than the meter.
>The SI system has one unit of energy - the Joule - which is used in all
>situations.
Actually, If you use the value for the palm (3"= 75mm), foot (12"= 300 mm)
cubit (18" 450 mm) and royal cubit (21" = 525 mm) defined by the Egyptians
in their units of measure you will find both English and metric units
are commensurable with it.
>>Once you understand the system, English measures are much easier to use.
>>As were the Egyptian measures they are derived from.
>
>Since you obviously KNOW how "English" measures work, Steve, how could
>you possible make a statement as ludicrous as:
>
>"A pint's a pound the world around"
A pound of barley fills a dry pint and a pint of water a wet pint
The English attempted to spread the pint around their Empire only
to find the measure or a close equivalent already in use in many places
because it is a convenient conversion between weight, volume and length.
If a wet pint is a pound it should be about 1/60 the cubic foot or talent
The Greeks and Hebrews used the Minah as 1/60 talent.
>
>as you did a few days ago? You know as well as I do that a pint differs
>between the USA and most of the rest of the English-speaking world,
>which uses the British definition of the pint.
Sure, one version is dry measure, for grain and the other
is wet measure for beer.
>Whatever made you come up with a statement as patently untrue as that?
I think you should look at the values a little more carefully.
Your education has essentially lobotomised from the record the
heritage of five millenia of history and made it difficult to
understand things like a linear measure of 100 Greek feet being
equal to 1 second of the Earths circumference.
>
>Chris
steve
William Wallace
If you have some other basis for your claim, fine. But it can NOT
be derived from the two measures you give. Only something with a
volume the equivalent of two gallons can be supported.
>but you should find that most units of volume for dry measure are
>defined as cubes and liquid measures are cylinders, barrels, casks,
>niperkins, etc. Our gallon of 231 cubic inches came to us as a wine
>gallon, but the English did not invent wine, nor for that matter
>beer. At the wedding at Cana a Hebrew rabi provides wine for the
>guests in units of a mettrette.
231 per gallon is a US gallon, not a british gallon. It is
unclear why an Egyptian measure would skip England and come directly
to the US.
>Liquid measures generally run a little over the dry measures. You
>might want to compare the Biblical bath and epath of 12 gallons.
>The Hebrews got their liquid measures from the Egyptians who had
>a fondness for beer. The most common small liguid measure used by
>the Egyptians was the Hinu.
When did archaeologists uncover these measuring devices?
>> Second, without checking your calculations, a mark down to the
>>throusandths of an inch borders upon ridiculous. Over lengths that
>>great they would change more than a 1/1000th of an inch with only a
>>few degrees of temperature change.
>You can round them off to the nearest 1/16" if you like, how many
>decimals will you use use to express even 1/8" of an inch (.125")
>let alone 1/16" (.0625")?
Inless you are not claiming the "inch" existed, whose known
origin is three barleycorns, fractions of an inch are not admissable.
>> Thus the absolutely even "gallon" measures appear to be the
>>result of reverse estimating the length of the cubit.
>There are a number of sources which give us a fair range for the royal cubit
>20.62" is favored by some archaeologists, IES Edwards, among them
>20.59" is given by Gillings favoring Gardiner
>Klein gives a range of cubits from all over the ancient world
>whose fingers average about.735", giving 20.58"
>Petrie chose 524 mm which is 20.6299..."
>Stechinni makes a case for 525 mm 20.669"
>Coles survey gives an average of 523.55 mm for the length of the
>royal cubits used to make the great Pyramid. 20.61"
>I generally use 20.6" as a round number unless I'm trying to show
>at which end of the range of values a correlation falls.
>20.628" is well within the range
>> Finally, it is unclear how, without great effort in those days
>>and to no apparent value, one would manufacture a cubic measuring
>>device for a standard. Does on hollow out a stone? Create a cubic clay
>>pot?
>The Egyptians made wooden boxes with great skill. Grain
>was stored in rooms made of clay bricks. As it happens
>they did hollow out stones,
These would not hold liquid.
>thousands of alabaster vases
>have been found with walls so thin you can see through them.
Making them useless for commerce. Without commerce there is no
value in a standard measure.
>As to making pots, amphora and clay vessels of a given capacity,
>If you layout a sheet of clay to a length which is 22/7 the
>unit length of a standard of measure and roll it into a cylinder
>which you fashion into a jug or jar and it happens that your units
>of measure are multiples of Pi, then conversions are a piece of cake.
This is a method of pot making that is otherwise unsupported. Not
until physics got into angular velocity did pi have a value in
measure.
>> And where to we find people able to pick it up and pour out the
>>contents? I mean, filled with water, that is going to be heavy and
>>clearly very inconvenient.
>^^^^^^^^^^^^^^^^^^^^^^^^^^
>You are talking about a people who built pyramids,
I do not see the relevance.
>but aside from
>that, if the standards of measure are defined as the cube of a length
>you just measure your granary and determine what proportion of its
>capacity has been used.
There are clearly many ways to do that which are much simpler and
convenient than what you suggest.
>> Water is what, seven pounds per gallon?
>sea water is 64 lb per cu'
>ice water is 56 lb per cu'
>alcohol is 49 lb cu'
>olive oil is 58 lb cu'
>
>there are about 7 1/2 gallons to an English cubic foot
>
>>That is 168 and 266
>>pounds respectively exclusive of container weight.
>
>For what container? With what inside it?
As for a gallon we are talking a liquid measure, water will do.
>>Lifting is one thing but twisting to pour leads to spinal injuries
>>(ask me some time.)
>What point are you trying to make?
>If this has something to do with containers and units of measure,
>Most people who move bulk goods prefer to do so in the largest
>possible container and the fewest possible trips.
First off, you have a standard to calibrate the containers used
in commerce. Then they are checked regularly to see if they are being
produced in the same size. If talking moving bulk grain the moving
container is unimportant as it is measured when loading and unloading.
If this is the measure it is too big for convenience. It is almost too
big to handle.
Second if you are talking liquid shipping containers, fine. A lot
of them must have been found by know. What is their volume?
>> So we have several problems here, starting with we can't say the
>>basic unit is anything other than two gallons, going through the quite
>>questionable accuracy of the cubit and finally to an impractically
>>sized measurement.
>The basic unit is a linear measure taken as the side of a cube to
>calculate volumes. For a gallon we have a liquid measure so instead
>of a cube its a cylinder. 1 Hekat was 8 English pints (dry measure)
>take a cylinder of diameter 2 palms (5.8") and height 3 palms (8.8")
>It has a volume of PI r^2 h = 232.5 cubic inches
>our gallon is 231 cu inches; not a bad correlation for 5000 years.
You are back to force fitting a linear measure that you have not
supported. Your claim is the gallon. That is not supported. If
anything is supported, it is something two gallons in size.
>>>>>You should find "a pint's a pound the world around"
>>>>
>>>>Only in the British Empire, a touch late for this arguement.
>>
>>>We still use some English measures in the US. Whats interesting
>>>is that they represent three millenia of reasonably stable standards
>>>which are now being ignorrantly elbowed aside by the metric system.
>> The metric system is approaching two hundred years old. There are
>>very few holdouts and then only in theory.
>In the long run the present fad for the metric system will become
>an historical curiosity, a great anachronism. It has about as much
>chance of surviving the next millenium as organized religion.
Until such time as their is evidence of that trend, I will file
that prediction away along with things from the psychic hotline.
>>>>>> If the explanation is diffusion then we would expect length,
>>>>>>weights and volumes all to be common. That is not what we find at all.
>>
>>>>>Then you need to look more carefully.
>>
>>>> So far, other than assertion, you have not directed me to what
>>>>you examined to convince you. You certainly know what they are.
>>
>>>Generally I was first impressed by the correspondence between the Egyptians
>>>linear measures and our own. later I became aware that most measures
>>>of weight and volume are defined as the cube whose side is a unit of
>>>length. Thus the correspondence between the linear measures led to
>>>a correspondence between measures of volume and weight.
>>
>>>The talent for example was the cube of the foot. The foot was Egyptian
>>>in origin.
>> Excuse me but there are references to a "talent of gold."
>Sure, there were also talents of silver. Essentially the talent was
>one cubic foot; The hekat was 4 quarts, the khar was 2/3 of a cubic
>cubit or about 20 hekats, the hinu was 1/10 hekat.
>>Without it being poured in in liquid form it is not an accurate measure.
>Where does that bit of wierdness come from? The talent was a dry measure.
There are air spaces unless liquid. Thus it is not nearly
accurate enough.
>>It would also be unliftable if the container weighed nothing. And no one
>>has ever measured gold save by weight. It appears here the talent is
>>in fact a measure of weight.
>I don't know how you can on the one hand assert that gold was measured by
>a measure of volume,
It is your assertion that a talent is a volume measure based upon
a cubic foot.
>the talent, and on the other hand assert it was
>never measured other than by weight. Of course the amount of gold
>which filled a cubic foot (1205 pounds)
Which pound are you referring to?
>was also a known value
>but gold was more commonly measured by the minah, sheckel, drachma,
>bekah, rebah, gerah, quedat and grain which were weights defined
>as volumes by being fractions of the talent..
It is not clear how you are getting to weights being defined by
volumes? That is a very "metric" concept.
>> If a talent of gold is in fact a cubic foot of gold we have here
>>a proverbial king's ransom. Yet references to a talent of gold
>>indicate it was more on the order of an ounce of gold.
>A Hebrew talent or kikkor was 60 minahs 29,900 grams.
>The Greek talent was 25,900 grams
By those measures we are talking on the order of a talent being
worth $250,000 or so and roughly the size of today's 1000 ounce ingot
which is no where near a cubic foot.
Clearly there are different measures referred to as a talent
which complicates things once more.
>>>>>>We find only the body based measures, lengths, to be similar but not
>>>>>>indentical.
>>>>>All measures are subject to change over time. If you follow the
>>>>>changes carefully you will find that the original system was
>>>>>pretty comprehensive.
>>>> Yes, the human body changes quite slowly for lengths but the
>>>>point here is for weights and volumes. What is a Kor of wheat and
>>>>compare it to the volume of other measures of volume.
>>>The Egyptians used a unit called a khar to measure wheat, it was
>>>1 1/2 cubic cubits. It had a side of two Roman pes. It was 12 buckets
>>>or 6 bushels.
>> And this of course brings up the next problem. Containers were
>>not cubic.
>Storage rooms usually were rectangular solids which could be
>divided up into cubic feet. of course if a cylindrical or hemispherical
>container was used the Egyptiians were quite capable of calculating its volume.
Any volume can be. This does not give evidence that it was done
with that in mind.
> Producing a curved container to have a specific volume
>>content was a matter of artistry and judgement prior to computers.
>> Producing jars with specific and accurate volume measures is no
>>mean feat. It is not clear why one would start with a cubic measure
>>just to make it hard to standardize containers.
>Actually its pretty easy to convert from cubic to cylindrical
>measures.
As noted, you have proposed a method of manufacture that is not
evidenced in the literature.
>>>>>> Thus the diffusion hypothesis fails.
>>>>>only if you blow it off and don't look carefully. If you maintain that
>>>>>the Greeks didn't borrow from the Egyptians or the Romans from the Greeks
>>>>>or the Europeans from the Romans,then you need to show how and why they
>>>>>independently invented things like hours and minutes, the remen, pace,
>>>>>mile, acre, stadium, and degree as even multiples of the finger, palm,
>>>>>hand, fist, foot and cubit. Explain why English weights and measures
>>>>>of volume follow the same binary, septenary, octonary, decimal, unidecimal
>>>>>and sexigesimal proportional system as the Egyptians.
>>>> You are back to lengths again. The subject is weights and
>>>>volumes.
>No the subject is measurements. Weights were defined as volumes
>and volumes were defined as cubes with sides of a given length.
Again, something you have not established by other than
coincidence at best and then rather dubious.
>You do not appear to be able to substanstiate your diffusion
>>>>claim for other than body part related lengths.
>>>I find the easiest way to compare units of volume is in cubic inches.
>>>a bushel is 2219.3 cubic inches and a gallon is 231 cubic inches.
>>>To find an Egyptian measure of volume which contains an even number
>>>of English gallons is not likely to be a coincidence. To find two
>>>such measures reduces the possibility that much further
>>>231 x 24 = 5544 cu" this is the side of the cube of the ordinary cubit, 17.69
>>"
>>>321 x 38 = 8778 cu" this is the side of the cube of royal cubit, 20.628"
>>
>> The "even" number of gallons is quite what is against you as the
>>largest common divisor is two gallons. BTW: You are talking British
>>gallons or do you mean American gallons? It is the difference between
>>five and four quarts respectively. Not a trivial difference.
>I am talking wine gallons, we can take it down to quarts or pints, gills,
>ounces, whatever you like.
What is a wine gallon? It traditionally came in quite large
containers, later casks, bottling be a relatively recent development.
And even now wine by the gallon isn't that common. However it still
does not tell whether it is British or American gallon or if this
"wine" gallon is either of them.
>> I further point out that between the Roman Empire and the metric
>>system, there was no standardization in weights and measures in
>>Europe. There were many systems even in the same country.
>Just because you don't yet know the systems of conversion doesn't mean
>there was no standardization. Actually all the measures Egyptian,
>Hebrew, Greek, Roman, English and American are amazingly consistent
>with one another. Where there are variations there is usually a
>discernable reason. For example a cubic measure with a side 5/4
>the side of another cubic measure was taken as its double.
May I point out the driving factor of the metric system was
commerce which is what lead to its adoption in Europe? People in
Europe agreed standardization was needed. It was quite obviously their
opinion that "amazingly consistant" was not good enough.
>> Your assertion depends upon a one to one correspondance between
>>Egyptian and British whereas there was no correspondance between
>>British and other European systems. Thus you are claiming not only a
>>unique but highly unlikely connection. You will have to explain this
>>also.
>You can read all about it for yourself in the cited reference material.
>There was excellent correspondence between the English and other European
>systems. The russians for example used a measure called an arshin
>egual in length to the English foot.
=====
Chris Marriott
In article <5v66vh$8...@fridge-nf0.shore.net>, Steve Whittet
<whi...@shore.net> writes
>Actually any system can be simple if you know the system. Do you
>divide a circle into grades or do you use degrees?
As a scientist, I nearly always measure angles in radians. Most "common"
angles are simple factors of "pi" in that system. "Degrees" are a rather
awkward system to work with, since whenever you want to actually *use*
an angle for a practical purpose, the first thing you normally do is
convert to radians anyway!
> Some parts of the
>metric system never have and never will catch on. Do you tell time
>in hours, minutes and seconds? What about your position? Are your
>maps still using meridians of longitude which pass through Greenwich?
You are of course perfectly correct in what you say - such things are
such a fundamental part of our culture, that they probably never will be
made metric. For units of length, mass, energy, power, etc, though I
find the SI system *hugely* simpler to work with.
"Imperial" units of length - inches, feet, yards, chains, furlongs,
miles, etc are a nightmare; consider the simple problem of multiplying
lengths - 1.53 metres multiplied by 10 is a trivial calculation; 1 yd 2
ft 3.5" multiplied by 10 is not.
>
>Is there no longer an English Pound?
If you're talking about weights, then everyday life in the UK uses kg
virtually exclusively. *Everything* in shops in marked in, and sold by,
the kilogram, not by the pound. If you're talking about our currency,
then that's been "decimal" for some 25-odd years now.
> Are Horses no longer measured in
>hands?
Actually, they aren't, no. "Hands" officially went out of use about a
year ago.
> Do they no longer race on courses measured in furlongs?
Yes, they do, and a cricket pitch is 1 chain long. Traditions die hard.
With the noteable exception of road distances (which are still measured
in miles), again, the UK is almost totally metric. Lengths and distances
are measured in metres, not inches, feet, and yards.
> Have
>you given up your pint of Guiness?
Can't stand the stuff personally. Virtually all liquids are now measured
in and sold by the litre, eg garages sell petrol (gasoline) by the
litre, not by the gallon. The 3 exceptions to this I can think of are
milk, beer, and blood, which are still measured in pints!
Brian M. Scott
On 10 Sep 1997 13:22:57 GMT, whi...@shore.net (Steve Whittet) wrote:
>Is there no longer an English Pound?
Yes, but for many years it's been divided into 100 (new) pence, not
into 20 shillings of 12 pence each.
Brian M. Scott
Richard Carr
Paul Murray wrote:
>
> >In article <5v430n$4...@fridge-nf0.shore.net>, Steve Whittet
> ><whi...@shore.net> writes
> >>Are SI units easier to work with. I would have to say no, not at all.
>
> Speaking as a Brit, by the time I went to school we were not even
> taught most of what you call the English system (we call it the Imperial
> system), and having grown up using the metric system for calculations in
> my maths, physics and chemistry courses the idea of wanting to switch to
> using the Imperial one seems incomprehensible.
> The pint tends to be used now only to refer beer, anything else is
> in litres, and while I still think of weight in stones and pounds, apart
> from that I, and most of my generation, are metric to the core. To say that
> the metric system will pass and the Imperial make a comeback is ignoring the
> fact that entire generations will have grown up with the metric system and
> wouldn't even know how to use the Imperial one if they wanted to.
>
> -Paul
I think also that one still gets pints of milk (especially from the
milkman- as opposed to cartons). I wouldn't know 1st hand about beer,
but it's fairly likely you get 5 pounds of potatoes rather than 2
kilograms. I'd also be inclined to think that you know your height in
feet and inches as well as in metres.
Incomprehensible seems a bit odd too, after all, many of the
transformations from Imperial to metric are affine.
Peter Szabo
Brian M. Scott wrote:
>On 9 Sep 1997 04:12:52 GMT, whi...@shore.net (Steve Whittet) wrote
>>
>>He claims it can't be a cognate even though
>>the spelling, pronunciation and meaning are virtually identical because
>>Egyptian isn't an Indo European language. That is simply foolish.
>
>No, it's not foolish; it's a matter of the definitions. A native
>Egyptian word and a native Greek word cannot have common ancestry,
>simply because the languages aren't related. Therefore they cannot be
>cognate. The only ways an Egyptian and a Greek word can be related
>are for one of them to be a borrowing from the other or for both to be
>borrowed from a third language. I take it that <arura> is native
>Egyptian. I could be wrong, but it appears to me that <aroura> is
>native Greek. (Liddell-Scott-Jones appears to agree.) If that's the
>case, the words are unrelated, and their similarity is indeed
>coincidence. The only other possibility is that <aroura> is a Greek
>borrowing, but in that case its apparent kinship with the Greek verb
>'to plow' is an equally surprising coincidence.
I would like to say that although your logic isn't too bad, and of
course your right about cognates, you seem to be ignoring or
overlooking a number of possibilities. First of all there is the
possibility of the words being truly cognate as per the Nostratic
hypotheses. (I said possibility, not likelihood) Second of all, the
likelihood that farming in very early Greece would have been
introduced, after arrival into the Mediterranean from the north, by
influencial neighbours. Thirdly, that it could be a mutation of the
theoretically borrowed Egyptian word "aroura", having an early meaning
of roughly "farm-plot" or "farm-division" and then verbized (is that a
verb?) as "farm" became "farming". I think the verb will more often
come from the noun, don't you? Furthur into that conjecture, it could
be postulated that the Greeks abandoned the noun upon throwing off a
foreign influence, reverting to their native IE word for farm. I
believe you were too liberal with the words "only other possibility".
You are probably objecting to the last two numbered points based on
your asserted Indo-European common origin for aroura and arvum. Well,
I give two reasons why I think that root might not be the case. One,
the IE form is well known, and is akr-- and not ar--, and seems
otherwise unprecedented in IE. But the better point is to look at the
Greek and Roman pronounciations. Greek "aroura": picture it being
loudly orated in Greek, in the dramatic Homerian fashion with the
strong semi-rolling "R" sound. For the Roman, let's first look at
what you wrote:
>I haven't the resources handy that would let me make
>certain, but it appears from the congruence of form and meaning that
>Greek <aroura> and Latin <aruum> are related. This, if true, suggests
>that the Greek word is of Indo-European rather than Egyptian origin.
The term is "arvum" not "aruum". It is pronounced "arwum". I am
suggesting that the w sound derives from the strong Greek r sound.
Indeed this part of the word could sound identical. The m ending in
the nominative could have come from excessive use of the accusative
form, perhaps being read aloud in the context of taxes. (ie. So-and-so
has one farmplot, three cattle, etc.) and could maybe even indicate it
was a borrowed word, though that is heavily just a guess.
How to explain the early transmission of this term from Greece to
Rome? The migrating Greeks could have passed it on when they were
orating to natives of the Iberian peninsula in pre-Roman times.
Now if the ancient Greeks had aroura (farm, land, plot, etc.) and
there is a word in neighbouring Egypt that was intrinsic to their
culture (What was more important to an Egyptian than his equally
alotted plot of measured land?) (and one that meant, most commonly,
"measured farmplot of Ra")... What causes you, Brian, to object to a
derivation from Egypt? Citing inconclusive rules of linguistics
cannot prove that the Greeks did not borrow the term from Egypt.
I see problems with the scenario too, as well as Steve's seeming
methodology, but nothing to rule it out completely, as you do, and
quite a few reasons to consider it carefully.
Hmmm. To continue my first paragraph, I see a fourth possibility.
Namely that early Etruscans, Latins, or other IEs in neolithic
Anatolia, could have somehow contributed to the Egyptians adopting the
term from them as a concept of measured plots of land...
Please reply, if only to say "Horsefeathers, you loon!"
Peter Szabo.
Realms of Archaea--------> http://users.uniserve.com/~peters5/zoomquk4.html
zoomQuake!---------------> http://users.uniserve.com/~peters5/
"The fool doth think he is wise, but the wise man knows himself to be a fool."
Paul Murray
On Wed, 10 Sep 1997 20:57:24 -0400, Richard Carr <ca...@math.columbia.edu> wrote:
>Paul Murray wrote:
>> >In article <5v430n$4...@fridge-nf0.shore.net>, Steve Whittet
>> ><whi...@shore.net> writes
>> >>Are SI units easier to work with. I would have to say no, not at all.
>> Speaking as a Brit, by the time I went to school we were not even
>> taught most of what you call the English system (we call it the Imperial
>> system), and having grown up using the metric system for calculations in
>> my maths, physics and chemistry courses the idea of wanting to switch to
>> using the Imperial one seems incomprehensible.
>> The pint tends to be used now only to refer beer, anything else is
>> in litres, and while I still think of weight in stones and pounds, apart
>> from that I, and most of my generation, are metric to the core. To say that
>> the metric system will pass and the Imperial make a comeback is ignoring the
>> fact that entire generations will have grown up with the metric system and
>> wouldn't even know how to use the Imperial one if they wanted to.
>milkman- as opposed to cartons). I wouldn't know 1st hand about beer,
>but it's fairly likely you get 5 pounds of potatoes rather than 2
>kilograms. I'd also be inclined to think that you know your height in
>feet and inches as well as in metres.
>Incomprehensible seems a bit odd too, after all, many of the
>transformations from Imperial to metric are affine.
Milk - especially within cities the local milkman is a dying trade, more
and more people are buying milk from supermarkets, in cartons, and as of a
year or so ago all volumes must be listed in litres. (Although to be honest,
for milk all that has happened is that stores list the exact litre
equivalent of x pints, so you have a point) However fruit juices, wines,
bottled water, soft drinks, etc.. all in litres.
Potatoes - I have to admit that I've absolutely no idea, on the few
occasions I've bought bags of potatoes I just pick up a bag, without looking
at the size.
Height - Point, I do indeed think of my height in feet, I should have listed
that as one of the exceptions.
Incomprehensible - I find it much easier, and more obvious, to work in a
system with constant factors of powers of ten between different units, rather
than one with 12,14,16,etc.. used for different measures. It's probably just
the case of whatever you have been brought up with seeming obvious, but that
is precisely my point, more and more people are being brought up understanding
only the metric system, and once these people become the next generation of
parents and teachers, the change will be almost irreversable.
-Paul
PS: In another thread, Steve askes 'Is there still not an English Pound?'
Well indeed there is, but it is a decimalised pound of 100 pence, not the
old Imperial pound. (And it's been quite a while since the name 'Pound' had
any relevance to units of weight!)
PPS: Just thought of another exception, at least when I was last buying
sweets in shops (a while ago now:) they were still weighed in quarters of a
pound, not in grammes.
Steve Whittet
In article <Bt65H3A9...@chrism.demon.co.uk>, ch...@chrism.demon.co.uk says...
>
>In article <5v66vh$8...@fridge-nf0.shore.net>, Steve Whittet
><whi...@shore.net> writes
>>Actually any system can be simple if you know the system. Do you
>>divide a circle into grades or do you use degrees?
>
>As a scientist, I nearly always measure angles in radians. Most "common"
>angles are simple factors of "pi" in that system. "Degrees" are a rather
>awkward system to work with, since whenever you want to actually *use*
>an angle for a practical purpose, the first thing you normally do is
>convert to radians anyway!
My point was really that the metric "grade" used to make the measurements
upon which the metric system is based didn't really survive much beyond
the period during which the measurements were being made.
As an architect I usually measure in degrees, and in fact use them
with Autocad to draw lines. Line enter 0,0 enter @48<0 enter
@36<90 enter @60<217 enter; works reasonably well, though I admit
I often snap to endpoints cause its faster.
>> Some parts of the
>>metric system never have and never will catch on. Do you tell time
>>in hours, minutes and seconds? What about your position? Are your
>>maps still using meridians of longitude which pass through Greenwich?
>
>You are of course perfectly correct in what you say - such things are
>such a fundamental part of our culture, that they probably never will be
>made metric. For units of length, mass, energy, power, etc, though I
>find the SI system *hugely* simpler to work with.
I suppose I am something of a sentimental romantic.
The idea of a truly beautiful and very sophisticated system
of subtly interwoven naturally commensurate proportions
which lasted unchanged for 5 millenia simply being discarded
bothers me.
It comes across in about the same way as people burning books
because its easier to find stuff on the web.
Its like a beautiful old building with intricate carvings
and proud roof lines being torn down to make room for a parking lot
in the name of progress. You may have seen a bit of that in Europe,
We certainly have in the States.
The subtle harmonies of this mathmatical symphony of proportions
stand to be lost forever because educators were too lazy
to study it in depth before teaching it, or too dissmissive of
the capabilities of their predecessors to comprehend it
>"Imperial" units of length - inches, feet, yards, chains, furlongs,
>miles, etc are a nightmare; consider the simple problem of multiplying
>lengths - 1.53 metres multiplied by 10 is a trivial calculation; 1 yd 2
>ft 3.5" multiplied by 10 is not.
Its a trivial calculation in feet and inches also. Though it
sounds a bit longer because of the way you wrote it, in pracice
its the sort of thing you would do instantly in your head.
First off, measures of yards and feet are rarely mixed, most
distances are given in rough estimates as yards, for example
the distance a pass is thrown in football or the length of
a drive in golf; The game of football uses a surveyors chain.
to measure the actual distance in feet and inches.
Strings or multiple measures are usually taken in inches.
63.5" x 10 is 635"
Converting between feet and inches is just the same degree
of difficulty as converting between meters and mm except one
is base 10 and the other base 12.
53' is 636" the answer is 52'-11"
The beauty of the English system is that if you understand it
properly, its really a binary, septenary, octal, decimal
unidecimal and sexigesimal system which converts easily to almost
any other system within a practical round off.
Its works like a vernier scale, you just choose the closest
appropriate base.
>
>>
>>Is there no longer an English Pound?
>
>If you're talking about weights, then everyday life in the UK uses kg
>virtually exclusively. *Everything* in shops in marked in, and sold by,
>the kilogram, not by the pound. If you're talking about our currency,
>then that's been "decimal" for some 25-odd years now.
Don't you still call it the English Pound? Just cause it divides up
decimally doesn't mean it isn't essentially the same measure.
>
>> Are Horses no longer measured in hands?
>
>Actually, they aren't, no. "Hands" officially went out of use about a
>year ago.
That's a good metaphor for what has been lost in my view,
measuring a horse in hands involves touching the living animal
using a ruler makes a horse something we no longer have the same
feeling for.
>
>> Do they no longer race on courses measured in furlongs?
>
>Yes, they do, and a cricket pitch is 1 chain long. Traditions die hard.
As well they should. Traditions are like ancestors, they connect
you to your roots.
>
>With the noteable exception of road distances (which are still measured
>in miles), again, the UK is almost totally metric. Lengths and distances
>are measured in metres, not inches, feet, and yards.
>
>> Have you given up your pint of Guiness?
>
>Can't stand the stuff personally. Virtually all liquids are now measured
>in and sold by the litre, eg garages sell petrol (gasoline) by the
>litre, not by the gallon. The 3 exceptions to this I can think of are
>milk, beer, and blood, which are still measured in pints!
Maybe that should tell you something about the degree to which
people have kept the English measures close to their hearts...
Gasoline by the liter, milk, blood and beer by the pint
is a nice metaphor for the inhumanity of the metric system
petrol guzzling cars and scientists love it, humanity doesn't
>
>Chris
steve
Brian M. Scott
On Wed, 10 Sep 1997 11:20:15 GMT, pet...@uniserve.com (Peter Szabo)
wrote:
>Brian M. Scott wrote:
>>On 9 Sep 1997 04:12:52 GMT, whi...@shore.net (Steve Whittet) wrote
>>>He claims it can't be a cognate even though
>>>the spelling, pronunciation and meaning are virtually identical because
>>>Egyptian isn't an Indo European language. That is simply foolish.
>>No, it's not foolish; it's a matter of the definitions. A native
>>Egyptian word and a native Greek word cannot have common ancestry,
>>simply because the languages aren't related. Therefore they cannot be
>>cognate. The only ways an Egyptian and a Greek word can be related
>>are for one of them to be a borrowing from the other or for both to be
>>borrowed from a third language. I take it that <arura> is native
>>Egyptian. I could be wrong, but it appears to me that <aroura> is
>>native Greek. (Liddell-Scott-Jones appears to agree.) If that's the
>>case, the words are unrelated, and their similarity is indeed
>>coincidence. The only other possibility is that <aroura> is a Greek
>>borrowing, but in that case its apparent kinship with the Greek verb
>>'to plow' is an equally surprising coincidence.
>I would like to say that although your logic isn't too bad, and of
>course your right about cognates, you seem to be ignoring or
>overlooking a number of possibilities. First of all there is the
>possibility of the words being truly cognate as per the Nostratic
>hypotheses. (I said possibility, not likelihood)
Agreed. I intentionally omitted mention of the possibility on the
grounds that a relationship at so great a time depth wasn't relevant
to the use of the term(s) as unit(s) of measure.
>I think the verb will more often
>come from the noun, don't you?
I have no idea; both types of derivation seem to be quite common.
>>I haven't the resources handy that would let me make
>>certain, but it appears from the congruence of form and meaning that
>>Greek <aroura> and Latin <aruum> are related. This, if true, suggests
>>that the Greek word is of Indo-European rather than Egyptian origin.
>The term is "arvum" not "aruum". It is pronounced "arwum".
I know. (That's what happens when you've been staring at accurate
transcriptions of names from medieval Latin rolls. When I'm in a
hurry, I tend to write <v> initially and <u> everywhere else.)
> I am
>suggesting that the w sound derives from the strong Greek r sound.
>Indeed this part of the word could sound identical. The m ending in
>the nominative could have come from excessive use of the accusative
>form, perhaps being read aloud in the context of taxes.
Eh? It's just the neuter adjective <arvus, -a, -um> 'ploughed' used
as a substantive. I'm no Latinist, but I believe that the adjective
is a straightforward verbal adjective in -vus/-uus, like <pascuus>
'for pasture' from <pascere> 'to feed, lead to pasture'. This seems
to be a regular formation; there's no need for an ad hoc explanation.
>How to explain the early transmission of this term from Greece to
>Rome? The migrating Greeks could have passed it on when they were
>orating to natives of the Iberian peninsula in pre-Roman times.
Iberian?
>What causes you, Brian, to object to a
>derivation from Egypt? Citing inconclusive rules of linguistics
>cannot prove that the Greeks did not borrow the term from Egypt.
Nor have I claimed proof. I've explained why I think it unlikely.
(And I'm not sure why you single out the linguistic evidence as
'inconclusive', especially in connection with a question that is
primarily linguistic.)
Brian M. Scott
Steve Whittet
>>>
>>>>>>>...demonstrate common weights and volumes.
>>>>>>>...standardization across countries was introduced by Rome
>>>>>>>...to facilitate commerce.
>>>
>>>>standardization across countries was introduced by Egypt, and Mesopotamia
>>>
>>>>>>...based on cubes and cylinders of the unit lengths.
>>>>>>... Compare the cube of a foot to the gallon
>>>>>>...the cube an ordinary cubit of 17.698 inches on a side
>>>>>>...a royal cubit of 20.628 inches on a side
>>Egyptian units of length came first. Measures of volume were cubes
>>on the sides of the units of length.
>If you have some other basis for your claim, fine. But it can NOT
>be derived from the two measures you give. Only something with a
>volume the equivalent of two gallons can be supported.
One Minah, the 1/60 of a talent, is a pint
>
>>but you should find that most units of volume for dry measure are
>>defined as cubes and liquid measures are cylinders, barrels, casks,
>>niperkins, etc. Our gallon of 231 cubic inches came to us as a wine
>>gallon, but the English did not invent wine, nor for that matter
>>beer. At the wedding at Cana a Hebrew rabi provides wine for the
>>guests in units of a mettrette.
>
> 231 per gallon is a US gallon, not a british gallon. It is
>unclear why an Egyptian measure would skip England and come directly
>to the US.
The wine gallon, which had existed for a long time previously
was first made an official English measure by the decree of
Queen Elizabeth at about the same time she changed the length
of the mile to 5280 feet.
>>Liquid measures generally run a little over the dry measures. You
>>might want to compare the Biblical bath and epath of 12 gallons.
>
>>The Hebrews got their liquid measures from the Egyptians who had
>>a fondness for beer. The most common small liguid measure used by
>>the Egyptians was the Hinu.
>
> When did archaeologists uncover these measuring devices?
The first studies began around 1680, and have been more or less
continuous since then.
>
>>>Second, without checking your calculations, a mark down to the
>>>throusandths of an inch borders upon ridiculous. Over lengths that
>>>great they would change more than a 1/1000th of an inch with only a
>>>few degrees of temperature change.
>
>>You can round them off to the nearest 1/16" if you like, how many
>>decimals will you use use to express even 1/8" of an inch (.125")
>>let alone 1/16" (.0625")?
>
>Inless you are not claiming the "inch" existed, whose known
>origin is three barleycorns, fractions of an inch are not admissable.
The Egyptians used an inch of 1 1/3 finger and indeed had
tables of 1/3 and 2/3 their standard units
unit 1 1/3 unit 2 2/3 unit 5 1/3
finger inch 2 inches palm
nail palm fist 3 quarters
palm hand link 4 hands
fist 2 palms foot 2 feet
quarter foot 2 feet 4 feet
cubit 2 feet 4 feet 8 feet
3 quarters yard 6 feet 12 feet
>>>Thus the absolutely even "gallon" measures appear to be the
>>>result of reverse estimating the length of the cubit.
>>There are a number of sources which give us a fair range for the royal cubit
>>20.62" is favored by some archaeologists, IES Edwards, among them
>>20.59" is given by Gillings favoring Gardiner
>>Klein gives a range of cubits from all over the ancient world
>>whose fingers average about.735", giving 20.58"
>>Petrie chose 524 mm which is 20.6299..."
>>Stechinni makes a case for 525 mm 20.669"
>>Coles survey gives an average of 523.55 mm for the length of the
>>royal cubits used to make the great Pyramid. 20.61"
>
>>I generally use 20.6" as a round number unless I'm trying to show
>>at which end of the range of values a correlation falls.
>
>>20.628" is well within the range
>
>>>Finally, it is unclear how, without great effort in those days
>>>and to no apparent value, one would manufacture a cubic measuring
>>>device for a standard. Does on hollow out a stone? Create a cubic clay
>>>pot?
>
>>The Egyptians made wooden boxes with great skill. Grain
>>was stored in rooms made of clay bricks. As it happens
>>they did hollow out stones,
>
> These would not hold liquid.
Sure they did
>
>>thousands of alabaster vases
>>have been found with walls so thin you can see through them.
>
>Making them useless for commerce. Without commerce there is no
>value in a standard measure.
Do we find glassware useless for commerce? By the way, the
Egyptians began making glass c 4,000 BC.
They also made boxes, cloth and leather sacks, clay pots,
jugs, vases, jars, baskets, amphorae, barrels, casks, kegs,
and a wide range of other containers too numerous to mention.
>>As to making pots, amphora and clay vessels of a given capacity,
>>If you layout a sheet of clay to a length which is 22/7 the
>>unit length of a standard of measure and roll it into a cylinder
>>which you fashion into a jug or jar and it happens that your units
>>of measure are multiples of Pi, then conversions are a piece of cake.
>
>This is a method of pot making that is otherwise unsupported. Not
>until physics got into angular velocity did pi have a value in measure.
The Egyptian ruler was divided into 28 fingers
It had a division marked with the glyph for Isis to the
right of the 22nd division from the left and to the left of the
7th division from the right, effectively dividing the ruler
into portions proportionate to Pi taken as 3 + 1/7
>
>>> And where to we find people able to pick it up and pour out the
>>>contents? I mean, filled with water, that is going to be heavy and
>>>clearly very inconvenient.
>>^^^^^^^^^^^^^^^^^^^^^^^^^^
>
>>You are talking about a people who built pyramids,
>
> I do not see the relevance.
It seems really strange to talk about a people who lug 2 1/2 million
stone blocks averaging about three tones apiece up to the top of
a pyramid 481 feet off the ground as finding it inconvenient to
pick up a bucket of water. What point were you trying to make here?
>
>>but aside from
>>that, if the standards of measure are defined as the cube of a length
>>you just measure your granary and determine what proportion of its
>>capacity has been used.
>
>There are clearly many ways to do that which are much simpler and
>convenient than what you suggest.
Ok, you have just completed the harvest, your cylindrical
grainery measures 9 royal cubits in diameter and is filled
to a height of 1 rod of 10 royal cubits.
How would you determine how many cubic khar of grain that is?
The Egyptians tell us how they did it in their mathematical
papyri.
>
>>> Water is what, seven pounds per gallon?
>
>>sea water is 64 lb per cu'
>>ice water is 56 lb per cu'
>>alcohol is 49 lb cu'
>>olive oil is 58 lb cu'
>>
>>there are about 7 1/2 gallons to an English cubic foot
>>
>>>That is 168 and 266
>>>pounds respectively exclusive of container weight.
>>
>>For what container? With what inside it?
>
>As for a gallon we are talking a liquid measure, water will do.
A container which holds 168 pounds of water of 28.875 cu" to a
pound has a side of 17" and holds exactly 21 gallons
A container which holds 266 pounds of water of 28.875 cu" to a
pound has a side of 19 1/2" and holds 33 1/4 gallons, just
over 1 standard barrel.
I have no idea where you get those weights from or what
significance you think they have.
===============================
...
>
> Second if you are talking liquid shipping containers, fine. A lot
>of them must have been found by know. What is their volume?
Typically 12 gallons or multiples thereof.
>
>>> So we have several problems here, starting with we can't say the
>>>basic unit is anything other than two gallons, going through the quite
>>>questionable accuracy of the cubit and finally to an impractically
>>>sized measurement.
>
>>The basic unit is a linear measure taken as the side of a cube to
>>calculate volumes. For a gallon we have a liquid measure so instead
>>of a cube its a cylinder. 1 Hekat was 8 English pints (dry measure)
>
>>take a cylinder of diameter 2 palms (5.8") and height 3 palms (8.8")
>>It has a volume of PI r^2 h = 232.5 cubic inches
>>our gallon is 231 cu inches; not a bad correlation for 5000 years.
>
> You are back to force fitting a linear measure that you have not
>supported. Your claim is the gallon. That is not supported. If
>anything is supported, it is something two gallons in size.
The cube of side 2 palms was 1 gallon
One cubic quarter yard was aproximately Pi gallons
One cubic foot was 7.5 gallons
The epath or bath was 12 gallons
One cubic cubit was 24 gallons
There is no measure of which I know which is the cube
of a standard measure on a side that gives 2 gallons
it comes out to about 10.3 fingers
however a cylinder of diameter 7" and 12" high
or a span dia by a foot height does hold 2 gallons
>
>>>>>>You should find "a pint's a pound the world around"
>>>>>
>>>>>Only in the British Empire, a touch late for this arguement.
>>>
>>>>We still use some English measures in the US. Whats interesting
>>>>is that they represent three millenia of reasonably stable standards
>>>>which are now being ignorrantly elbowed aside by the metric system.
>
>>>The metric system is approaching two hundred years old. There are
>>>very few holdouts and then only in theory.
People just don't really realise what they are losing and
how the religion of science finds it necessary to eradicate
any vestiges of ancient natural philosophy in order to make
a place for itself as guardian of the truth.
>
>>In the long run the present fad for the metric system will become
>>an historical curiosity, a great anachronism. It has about as much
>>chance of surviving the next millenium as organized religion.
>
>Until such time as their is evidence of that trend, I will file
>that prediction away along with things from the psychic hotline.
The only really dependable thing in all of human history has
been change. If you don't think measures will evolve through
the metric system just as political systems finally have begun
to emerge from their fascination with the communism that came
out of the French Revolution you are misguided.
...
>>>
>>>>Generally I was first impressed by the correspondence between the Egyptians
>>>>linear measures and our own. later I became aware that most measures
>>>>of weight and volume are defined as the cube whose side is a unit of
>>>>length. Thus the correspondence between the linear measures led to
>>>>a correspondence between measures of volume and weight.
>>>
>>>>The talent for example was the cube of the foot. The foot was Egyptian
>>>>in origin.
>
>>> Excuse me but there are references to a "talent of gold."
>
>>Sure, there were also talents of silver. Essentially the talent was
>>one cubic foot; The hekat was 4 quarts, the khar was 2/3 of a cubic
>>cubit or about 20 hekats, the hinu was 1/10 hekat.
>
>>>Without it being poured in in liquid form it is not an accurate measure.
>
>>Where does that bit of weirdness come from? The talent was a dry measure.
>
>There are air spaces unless liquid. Thus it is not nearly
>accurate enough.
When measuring something like grain, which does have air spaces, a bulk
measure which takes the weight of a standard volume is wholly appropriate.
>
>>>It would also be unliftable if the container weighed nothing. And no one
>>>has ever measured gold save by weight. It appears here the talent is
>>>in fact a measure of weight.
>
>>I don't know how you can on the one hand assert that gold was measured by
>>a measure of volume,
>
>It is your assertion that a talent is a volume measure based upon
>a cubic foot.
No, its just a fact. Look it up in a good dictionary or encycopedia
My cite was (Klein page 88)
>
>>the talent, and on the other hand assert it was
>>never measured other than by weight. Of course the amount of gold
>>which filled a cubic foot (1205 pounds)
>
> Which pound are you referring to?
The pound of 16 ounces avoirdupis or 453.5924g, .453592 kg
7000 grains = 256 drams = 16oz = 1 pound
>
>>was also a known value
>>but gold was more commonly measured by the minah, sheckel, drachma,
>>bekah, rebah, gerah, quedat and grain which were weights defined
>>as volumes by being fractions of the talent..
>
> It is not clear how you are getting to weights being defined by
>volumes? That is a very "metric" concept.
Heck no, Its an Egyptian concept. The French savants who defined the
metric system learned about it by studying the works of ancient authors.
>>>If a talent of gold is in fact a cubic foot of gold we have here
>>>a proverbial king's ransom. Yet references to a talent of gold
>>>indicate it was more on the order of an ounce of gold.
>
>>A Hebrew talent or kikkor was 60 minahs 29,900 grams.
>>The Greek talent was 25,900 grams
>
> By those measures we are talking on the order of a talent being
>worth $250,000 or so and roughly the size of today's 1000 ounce ingot
>which is no where near a cubic foot.
Our foot is 12" giving 1728" cubic inches, or 27,215.55392 g
but at the time the talent was established the foot in use
was 11.42", the Roman pes
>
>Clearly there are different measures referred to as a talent
>which complicates things once more.
Yes and No. There was a profane and sacred system of measures
developed by the Hebrews which essentially included a tithe
or tax to the temple of 1 part in 13.
>>... the subject is measurements. Weights were defined as volumes
>>and volumes were defined as cubes with sides of a given length.
>
>....coincidence at best and then rather dubious.
This is a common response when confronted by facts which
contradict long cherished beliefs, its called cognative
dissonace.
The way science procedes is to produce a testable
hypothesis and then test it. In this case we see that indeed
units of length do give rise to units of volume which are the
cube of their sides.
>
>>>>I find the easiest way to compare units of volume is in cubic inches.
>>>>a bushel is 2219.3 cubic inches and a gallon is 231 cubic inches.
>
>>>>To find an Egyptian measure of volume which contains an even number
>>>>of English gallons is not likely to be a coincidence. To find two
>>>>such measures reduces the possibility that much further
>
>>>>231 x 24 = 5544 cu" this is the side of the cube
>>>>of the ordinary cubit, 17.69"
>>>>321 x 38 = 8778 cu" this is the side of the cube of royal cubit, 20.628"
>>>
>>> The "even" number of gallons is quite what is against you as the
>>>largest common divisor is two gallons. BTW: You are talking British
>>>gallons or do you mean American gallons? It is the difference between
>>>five and four quarts respectively. Not a trivial difference.
>
>>I am talking wine gallons, we can take it down to quarts or pints, gills,
>>ounces, whatever you like.
>
> What is a wine gallon?
231 cubic inches as defined by Queen Elizabeth.
>It traditionally came in quite large containers, later casks, bottling
>be a relatively recent development. And even now wine by the gallon
>isn't that common. However it still does not tell whether it is British
>or American gallon or if this "wine" gallon is either of them.
It goes back to the Egyptians, was used by the Hebrews, Greeks and Romans
and institutionalized as law by Queen Elizabeth for the British which is
how it came to be adopted by the Americans.
>
>>> I further point out that between the Roman Empire and the metric
>>>system, there was no standardization in weights and measures in
>>>Europe. There were many systems even in the same country.
>
>>Just because you don't yet know the systems of conversion doesn't mean
>>there was no standardization. Actually all the measures Egyptian,
>>Hebrew, Greek, Roman, English and American are amazingly consistent
>>with one another. Where there are variations there is usually a
>>discernable reason. For example a cubic measure with a side 5/4
>>the side of another cubic measure was taken as its double.
>
> May I point out the driving factor of the metric system was
>commerce which is what lead to its adoption in Europe? People in
>Europe agreed standardization was needed. It was quite obviously their
>opinion that "amazingly consistant" was not good enough.
The ancient measures were actually much more consistent. In the
Middle Ages much knowledge was lost. The more that was lost the
more people tried to standardise things by redefining the wheel.
Eventually things got so bad they had to go back to antiquity
to try and determine what the original standards had been.
Despite that, after 5 millenia, we vary less from the original
Egyptian standard than the variation between European countries
which existed in the Middle Ages.
>
>>>Your assertion depends upon a one to one correspondance between
>>>Egyptian and British whereas there was no correspondance between
>>>British and other European systems.
Actually the correspondance is better between the British and
Egyptian systems than some other European systems. You need to
take into account that most of Europe was so ravaged by the plauge
during the middle ages that very little survived.
The British happened at this time to become infatuated with
the Classical Architecture of Greece and Rome and through it
with the classic works of the writers of antiquity. This helped
to anchor them because they could read about systems of proportion
in Vitruvious.
>>> Thus you are claiming not only a
>>>unique but highly unlikely connection. You will have to explain this
>>>also.
>
>>You can read all about it for yourself in the cited reference material.
>>There was excellent correspondence between the English and other European
>>systems. The russians for example used a measure called an arshin
>>egual in length to the English foot.
>
>
>
steve
Chris Marriott
In article <5v90p3$4...@fridge-nf0.shore.net>, Steve Whittet
<whi...@shore.net> writes
>In article <Bt65H3A9...@chrism.demon.co.uk>, ch...@chrism.demon.co.uk
>says...
>>
>>In article <5v66vh$8...@fridge-nf0.shore.net>, Steve Whittet
>><whi...@shore.net> writes
>>>Actually any system can be simple if you know the system. Do you
>>>divide a circle into grades or do you use degrees?
>>
>>As a scientist, I nearly always measure angles in radians. Most "common"
>>angles are simple factors of "pi" in that system. "Degrees" are a rather
>>awkward system to work with, since whenever you want to actually *use*
>>an angle for a practical purpose, the first thing you normally do is
>>convert to radians anyway!
>
>My point was really that the metric "grade" used to make the measurements
>upon which the metric system is based didn't really survive much beyond
>the period during which the measurements were being made.
The "grad" is NOT a part of the SI system, Steve. The SI unit of angular
measure is the radian ("pi" radians = 180 degrees).
Every scientific calculator I've ever owned has offered degrees,
radians, and grads as units of angular measure, but equally I've never
actually come across a situation in which grads are used. I have a vague
memory that they're used in surveying - can anyone confirm or deny this.
In the "real world", scientists and mathematicians measure angles in
radians, almost everyone else uses degrees. Radian measure is much more
useful for practical calculations.
>>> Some parts of the
>>>metric system never have and never will catch on. Do you tell time
>>>in hours, minutes and seconds? What about your position? Are your
>>>maps still using meridians of longitude which pass through Greenwich?
>>
>>You are of course perfectly correct in what you say - such things are
>>such a fundamental part of our culture, that they probably never will be
>>made metric. For units of length, mass, energy, power, etc, though I
>>find the SI system *hugely* simpler to work with.
>
>I suppose I am something of a sentimental romantic.
>
>The idea of a truly beautiful and very sophisticated system
>of subtly interwoven naturally commensurate proportions
>which lasted unchanged for 5 millenia simply being discarded
>bothers me.
It wasn't "simply discarded", Steve. The SI system was VERY carefully
thought out and defined over many years by international agreement. As
you've pointed out yourself in previous posts, there are lots of
DIFFERENT definitions for units such as "pint"; in order for science and
engineering to have "solid foundations", PRECISE definitions are
required for the fundamental physical units - definitions which everyone
can agree on.
The beauty of the SI system is that with one exception - the definition
of the kilogram - SI units are defined in terms of fundamental physical
quantities which can be independently measured and refined. For example,
the "second" is defined in terms of units of the period of natural
vibration of a Caesium atom, the "metre" is defined in terms of the
speed of light, and so on. All these are universal physical "realities"
which don't depend on human interpretation. That's VITAL for science.
>Converting between feet and inches is just the same degree
>of difficulty as converting between meters and mm except one
>is base 10 and the other base 12.
>
>53' is 636" the answer is 52'-11"
>
>The beauty of the English system is that if you understand it
>properly, its really a binary, septenary, octal, decimal
>unidecimal and sexigesimal system which converts easily to almost
>any other system within a practical round off.
I'm afraid I don't agree, Steve. The benefit of the SI system is that
you can use the SAME unit of measure - the metre - for measuring
everything from the size of atomic nuclei to the size of galaxies with
simple "powers of 3" prefixes - micro, milli, kilo, mega, giga, tera,
etc. and conversions are trivial. Multiplying or dividing by powers of
10 is *hugely* simpler than using powers of 12 or 60, simply because our
number system uses 10 as its base.
>>>Is there no longer an English Pound?
>>
>>If you're talking about weights, then everyday life in the UK uses kg
>>virtually exclusively. *Everything* in shops in marked in, and sold by,
>>the kilogram, not by the pound. If you're talking about our currency,
>>then that's been "decimal" for some 25-odd years now.
>
>Don't you still call it the English Pound? Just cause it divides up
>decimally doesn't mean it isn't essentially the same measure.
I'm not sure I follow you, Steve. The "pound" is just a word we use for
our currency unit. 1 pound = 100 pence. I'm not sure what you mean when
you ask "isn't it essentially the same measure". It has no "historical
significance" for me personally - I'd be just as happy using the
proposed single European currency - the "Euro".
>That's a good metaphor for what has been lost in my view,
>measuring a horse in hands involves touching the living animal
>using a ruler makes a horse something we no longer have the same
>feeling for.
Why does it? A "hand" is four inches if I remember correctly. You still
have to measure the horse with a ruler (or whatever) to find its height
in "hands"; you can't actually USE your hands since everyone's are a
different size!
William Wallace
On 11 Sep 1997 19:13:38 GMT, whi...@shore.net (Steve Whittet) wrote:
>>If you have some other basis for your claim, fine. But it can NOT
>>be derived from the two measures you give. Only something with a
>>volume the equivalent of two gallons can be supported.
>One Minah, the 1/60 of a talent, is a pint
Imperial or US?
>>>but you should find that most units of volume for dry measure are
>>>defined as cubes and liquid measures are cylinders, barrels, casks,
>>>niperkins, etc. Our gallon of 231 cubic inches came to us as a wine
>>>gallon, but the English did not invent wine, nor for that matter
>>>beer. At the wedding at Cana a Hebrew rabi provides wine for the
>>>guests in units of a mettrette.
>> 231 per gallon is a US gallon, not a british gallon. It is
>>unclear why an Egyptian measure would skip England and come directly
>>to the US.
>The wine gallon, which had existed for a long time previously
>was first made an official English measure by the decree of
>Queen Elizabeth at about the same time she changed the length
>of the mile to 5280 feet.
And what size might it be and how did she learn Egyptian? And how
does it relate to the other two gallons?
>>>Liquid measures generally run a little over the dry measures. You
>>>might want to compare the Biblical bath and epath of 12 gallons.
>>>The Hebrews got their liquid measures from the Egyptians who had
>>>a fondness for beer. The most common small liguid measure used by
>>>the Egyptians was the Hinu.
>> When did archaeologists uncover these measuring devices?
>The first studies began around 1680, and have been more or less
>continuous since then.
Please cite any studies prior to Naplean.
>>>>Second, without checking your calculations, a mark down to the
>>>>throusandths of an inch borders upon ridiculous. Over lengths that
>>>>great they would change more than a 1/1000th of an inch with only a
>>>>few degrees of temperature change.
>>>You can round them off to the nearest 1/16" if you like, how many
>>>decimals will you use use to express even 1/8" of an inch (.125")
>>>let alone 1/16" (.0625")?
>>Inless you are not claiming the "inch" existed, whose known
>>origin is three barleycorns, fractions of an inch are not admissable.
>The Egyptians used an inch of 1 1/3 finger and indeed had
>tables of 1/3 and 2/3 their standard units
>
>unit 1 1/3 unit 2 2/3 unit 5 1/3
>
>finger inch 2 inches palm
>nail palm fist 3 quarters
>palm hand link 4 hands
>fist 2 palms foot 2 feet
>quarter foot 2 feet 4 feet
>cubit 2 feet 4 feet 8 feet
>3 quarters yard 6 feet 12 feet
The origin of the inch remains three barleycorns. This is well
known. It has no relation to Egypt.
>>>The Egyptians made wooden boxes with great skill. Grain
>>>was stored in rooms made of clay bricks. As it happens
>>>they did hollow out stones,
>> These would not hold liquid.
>Sure they did
You have cited only that research started in 1680. That does not
make wooden boxes or clay brick hold water. Please tell me where I can
find verification of waterproof wooden boxes of Egyptian origin of the
correct period.
>>>thousands of alabaster vases
>>>have been found with walls so thin you can see through them.
>>Making them useless for commerce. Without commerce there is no
>>value in a standard measure.
>Do we find glassware useless for commerce? By the way, the
>Egyptians began making glass c 4,000 BC.
That is not alabaster.
>They also made boxes, cloth and leather sacks, clay pots,
>jugs, vases, jars, baskets, amphorae, barrels, casks, kegs,
>and a wide range of other containers too numerous to mention.
And their volumes are?
>>>As to making pots, amphora and clay vessels of a given capacity,
>>>If you layout a sheet of clay to a length which is 22/7 the
>>>unit length of a standard of measure and roll it into a cylinder
>>>which you fashion into a jug or jar and it happens that your units
>>>of measure are multiples of Pi, then conversions are a piece of cake.
>>This is a method of pot making that is otherwise unsupported. Not
>>until physics got into angular velocity did pi have a value in measure.
>The Egyptian ruler was divided into 28 fingers
>It had a division marked with the glyph for Isis to the
>right of the 22nd division from the left and to the left of the
>7th division from the right, effectively dividing the ruler
>into portions proportionate to Pi taken as 3 + 1/7
This method of making clay pots is still unsupported in the
literature.
>>>> And where to we find people able to pick it up and pour out the
>>>>contents? I mean, filled with water, that is going to be heavy and
>>>>clearly very inconvenient.
>>>^^^^^^^^^^^^^^^^^^^^^^^^^^
>>
>>>You are talking about a people who built pyramids,
>> I do not see the relevance.
>It seems really strange to talk about a people who lug 2 1/2 million
>stone blocks averaging about three tones apiece up to the top of
>a pyramid 481 feet off the ground as finding it inconvenient to
>pick up a bucket of water. What point were you trying to make here?
The point is that if you want a standard measure by which people
measure things you make it convenient for people to use as a measure.
What you do not do is claim that a measure much to large for
convenience is explained by the pyramids. That is not responsive.
>>>but aside from
>>>that, if the standards of measure are defined as the cube of a length
>>>you just measure your granary and determine what proportion of its
>>>capacity has been used.
>>There are clearly many ways to do that which are much simpler and
>>convenient than what you suggest.
>Ok, you have just completed the harvest, your cylindrical
>grainery measures 9 royal cubits in diameter and is filled
>to a height of 1 rod of 10 royal cubits.
>How would you determine how many cubic khar of grain that is?
You count the number of measures that are put into it. You do not
need any other measure.
>The Egyptians tell us how they did it in their mathematical
>papyri.
Counting is not that difficult.
>>>> Water is what, seven pounds per gallon?
>>>sea water is 64 lb per cu'
>>>ice water is 56 lb per cu'
>>>alcohol is 49 lb cu'
>>>olive oil is 58 lb cu'
>>>there are about 7 1/2 gallons to an English cubic foot
>>>>That is 168 and 266
>>>>pounds respectively exclusive of container weight.
>>>For what container? With what inside it?
>>As for a gallon we are talking a liquid measure, water will do.
>A container which holds 168 pounds of water of 28.875 cu" to a
>pound has a side of 17" and holds exactly 21 gallons
>A container which holds 266 pounds of water of 28.875 cu" to a
>pound has a side of 19 1/2" and holds 33 1/4 gallons, just
>over 1 standard barrel.
>I have no idea where you get those weights from or what
>significance you think they have.
I am pointing out that your length measures have nothing to do
with weight and volume measures. We now have three different gallons
under discussion and you insist the Egyptian measure bypassed England
and came straight to the US. I do not accept that.
You gave them to me when here.
>>>The weights and volumes are also common, based on cubes and cylinders
>>>of the unit lengths. They have already been discussed at some length
>>>in the thread. Compare the cube of a foot to the gallon for example
>>>You will find that the cube an ordinary cubit of 17.698 inches on a
>>>side holds 24 gallons, a royal cubit of 20.628 inches on a side
>>>holds 38 gallons.
24 and 38 gallons. Only a measure equivalent to two US gallons
fits both. That give 12 and 19 of them respectively. Saying the basic
measure is one half of these is no different from saying it is 1/3 or
1/5 or 1/90 of it as they all fit equally. You have no basis for
claiming it is 1/2 instead of the other possibilities.
>>>>The metric system is approaching two hundred years old. There are
>>>>very few holdouts and then only in theory.
>People just don't really realise what they are losing and
>how the religion of science finds it necessary to eradicate
>any vestiges of ancient natural philosophy in order to make
>a place for itself as guardian of the truth.
There is no necessity to eradicate it when the only knowledge of
value it produced that was of value is indistinguishable from chance.
And since the value of "ancient natural philosophy" is bound up
in the length of the forearm of so long dead civil ruler it is unclear
what anyone would expect to gain from it.
>>>In the long run the present fad for the metric system will become
>>>an historical curiosity, a great anachronism. It has about as much
>>>chance of surviving the next millenium as organized religion.
>>Until such time as their is evidence of that trend, I will file
>>that prediction away along with things from the psychic hotline.
>The only really dependable thing in all of human history has
>been change. If you don't think measures will evolve through
>the metric system just as political systems finally have begun
>to emerge from their fascination with the communism that came
>out of the French Revolution you are misguided.
As I said, UNTIL there is evidence of that, your prediction is in
the same category of the Psychic Hotline.
>...
>>>>>Generally I was first impressed by the correspondence between the Egyptians
>>>>>linear measures and our own. later I became aware that most measures
>>>>>of weight and volume are defined as the cube whose side is a unit of
>>>>>length. Thus the correspondence between the linear measures led to
>>>>>a correspondence between measures of volume and weight.
>>>>>The talent for example was the cube of the foot. The foot was Egyptian
>>>>>in origin.
>>>> Excuse me but there are references to a "talent of gold."
>>>Sure, there were also talents of silver. Essentially the talent was
>>>one cubic foot; The hekat was 4 quarts, the khar was 2/3 of a cubic
>>>cubit or about 20 hekats, the hinu was 1/10 hekat.
>>>>Without it being poured in in liquid form it is not an accurate measure.
>>>Where does that bit of weirdness come from? The talent was a dry measure.
>>There are air spaces unless liquid. Thus it is not nearly
>>accurate enough.
>When measuring something like grain, which does have air spaces, a bulk
>measure which takes the weight of a standard volume is wholly appropriate.
Gold is measure by weight, period. You are claiming there is a
volume measure. There is no way to make a weight to volume conversion
without knowing the concept of specific gravity, rather clearly
discovered by the Greeks. There is no other way, period.
>>>>It would also be unliftable if the container weighed nothing. And no one
>>>>has ever measured gold save by weight. It appears here the talent is
>>>>in fact a measure of weight.
>>>I don't know how you can on the one hand assert that gold was measured by
>>>a measure of volume,
>>It is your assertion that a talent is a volume measure based upon
>>a cubic foot.
>No, its just a fact. Look it up in a good dictionary or encycopedia
>My cite was (Klein page 88)
To hell with your cite, your statement is that it is a volume
measure.
>>>the talent, and on the other hand assert it was
>>>never measured other than by weight. Of course the amount of gold
>>>which filled a cubic foot (1205 pounds)
>> Which pound are you referring to?
>
>The pound of 16 ounces avoirdupis or 453.5924g, .453592 kg
>7000 grains = 256 drams = 16oz = 1 pound
Since gold is measured in troy ounces and troy pounds your basis
is clearly in error.
Have you seriously looked into or are you just playing games on a
calculator?
>>>was also a known value
>>>but gold was more commonly measured by the minah, sheckel, drachma,
>>>bekah, rebah, gerah, quedat and grain which were weights defined
>>>as volumes by being fractions of the talent..
>> It is not clear how you are getting to weights being defined by
>>volumes? That is a very "metric" concept.
>Heck no, Its an Egyptian concept. The French savants who defined the
>metric system learned about it by studying the works of ancient authors.
Not in the least. The timing is all wrong. That is quite
impossible.
>>>>If a talent of gold is in fact a cubic foot of gold we have here
>>>>a proverbial king's ransom. Yet references to a talent of gold
>>>>indicate it was more on the order of an ounce of gold.
>>>A Hebrew talent or kikkor was 60 minahs 29,900 grams.
>>>The Greek talent was 25,900 grams
>> By those measures we are talking on the order of a talent being
>>worth $250,000 or so and roughly the size of today's 1000 ounce ingot
>>which is no where near a cubic foot.
>Our foot is 12" giving 1728" cubic inches, or 27,215.55392 g
>but at the time the talent was established the foot in use
>was 11.42", the Roman pes
That does not significantly change what I posted. However it does
shoot your "perfect" measures all to shit.
>>Clearly there are different measures referred to as a talent
>>which complicates things once more.
>Yes and No. There was a profane and sacred system of measures
>developed by the Hebrews which essentially included a tithe
>or tax to the temple of 1 part in 13.
Please, let me put this in perspective. The Israelites were a
generally primitive people who made not one contribution to the
culture of the world in any regard. They only claim to fame was a
short period in which they were the meanest rapers and pillagers in
the valley.
The mythical hebrews were illiterate goat herders even according
to the myth.
Pointing the rapists or the myth is completely irrelevent.
>>>... the subject is measurements. Weights were defined as volumes
>>>and volumes were defined as cubes with sides of a given length.
>>....coincidence at best and then rather dubious.
>This is a common response when confronted by facts which
>contradict long cherished beliefs, its called cognative
>dissonace.
I have no cherished beliefs. Most measurement systems can be
traced back to legal proclamations in which the basis is given in the
proclamation. It is simply that claiming US measure came from Egypt
while bypassing Britain is laughable.
>The way science procedes is to produce a testable
>hypothesis and then test it. In this case we see that indeed
>units of length do give rise to units of volume which are the
>cube of their sides.
What I have seen that you have not in the least researched your
material beyond what is in an almanac and even then missing the
obvious as in gold measure and which gallon. You have concentrated
upon measures so old that there is no certainty regarding them yet you
give them to the thousandths of three british barleycorns.
>>>I am talking wine gallons, we can take it down to quarts or pints, gills,
>>>ounces, whatever you like.
>> What is a wine gallon?
>231 cubic inches as defined by Queen Elizabeth.
Then that is neither the US or imperial gallon.
>>It traditionally came in quite large containers, later casks, bottling
>>be a relatively recent development. And even now wine by the gallon
>>isn't that common. However it still does not tell whether it is British
>>or American gallon or if this "wine" gallon is either of them.
>It goes back to the Egyptians, was used by the Hebrews, Greeks and Romans
>and institutionalized as law by Queen Elizabeth for the British which is
>how it came to be adopted by the Americans.
It was NOT adopted by the Americans nor by the British as you
have demonstrated.
>> May I point out the driving factor of the metric system was
>>commerce which is what lead to its adoption in Europe? People in
>>Europe agreed standardization was needed. It was quite obviously their
>>opinion that "amazingly consistant" was not good enough.
>The ancient measures were actually much more consistent. In the
>Middle Ages much knowledge was lost. The more that was lost the
>more people tried to standardise things by redefining the wheel.
>Eventually things got so bad they had to go back to antiquity
>to try and determine what the original standards had been.
Unless you can produce actual standards from pre-Dark Ages times
you have no basis for this claim.
>Despite that, after 5 millenia, we vary less from the original
>Egyptian standard than the variation between European countries
>which existed in the Middle Ages.
Then you are saying again that the measures of Egypt not only
bypassed Britain but all of Europe to arrive in the US. You are
becoming a touch absurd.
>>>>Your assertion depends upon a one to one correspondance between
>>>>Egyptian and British whereas there was no correspondance between
>>>>British and other European systems.
>Actually the correspondance is better between the British and
>Egyptian systems than some other European systems. You need to
>take into account that most of Europe was so ravaged by the plauge
>during the middle ages that very little survived.
In case you missed it, Britain was on the hind teat of Europe
until the war with Spain and was more than equally ravaged.
>The British happened at this time to become infatuated with
>the Classical Architecture of Greece and Rome and through it
>with the classic works of the writers of antiquity. This helped
>to anchor them because they could read about systems of proportion
>in Vitruvious.
You are several centuries off.
>>>> Thus you are claiming not only a
>>>>unique but highly unlikely connection. You will have to explain this
>>>>also.
>>>You can read all about it for yourself in the cited reference material.
>>>There was excellent correspondence between the English and other European
>>>systems. The russians for example used a measure called an arshin
>>>egual in length to the English foot.
As a summary, you have a mixture of wishful thinking, guessing
about basics where they are unknown, and a host of improbabilities in
addition to being flat out wrong on many matters such as the gallon
and the troy ounce.
I have no idea how you can salvage this mess.
Brian M. Scott
On 11 Sep 1997 19:13:38 GMT, whi...@shore.net (Steve Whittet) wrote:
>The Egyptian ruler was divided into 28 fingers
>It had a division marked with the glyph for Isis to the
>right of the 22nd division from the left and to the left of the
>7th division from the right, effectively dividing the ruler
>into portions proportionate to Pi taken as 3 + 1/7
It's not clear whether you're using 'division' for the marks on the
ruler - is more than one specimen known, by the way? - or for the
intervals between them. You've previously said that the glyph lies in
one of the intervals. The phrase 'a division marked with the glyph'
therefore suggests that by 'division' you mean 'interval between
marks'. In that case your description implies that the glyph is in
the 23rd interval from the left and the 8th interval from the right,
i.e., that these two intervals are equal. Unfortunately, that would
mean that the ruler was divided into 30 intervals, not 28.
You've previously indicated that the glyph falls in the 22nd segment
from the left, which is the 7th segment from the right. Not counting
the ends of the ruler as marks, this places it between the 21st and
22nd marks from the left-hand end. At that point it is about 21.5
fingers from the left-hand end and therefore divides the ruler approx.
in the ratio 21.5 : 6.5, or 43:13, not 22:7.
=====
>>It is your assertion that a talent is a volume measure based upon
>>a cubic foot.
>No, its just a fact. Look it up in a good dictionary or encycopedia
The OED is a good dictionary. It says that the talent is an ancient
weight and money of account. It says that the Royal Babylonian talent
averaged about 29.87 kg and mentions an Old AEginetan talent of 40.3
kg, a later AEginetan talent of 36.4, and a Solonian talent of 25.8
kg. It also says that the word is related to a Greek verbal root
<tal-, tla-> 'to bear', which supports (!) the notion that it was
originally a weight.
>My cite was (Klein page 88)
I believe that Klein also gives it as a weight, namely, the weight of
a cu. cubit of water.
=====
>Actually the correspondance is better between the British and
>Egyptian systems than some other European systems. You need to
>take into account that most of Europe was so ravaged by the plauge
>during the middle ages that very little survived.
This doesn't square with the facts. The plague actually came rather
late, after much of the past had been recovered. The real loss had
occurred many centuries earlier after the western Roman empire fell
apart. Look at some of the names associated with the century or so
after the arrival of the plague in Europe; these include Chaucer,
Petrarch, Boccaccio in literature; Dunstable and Machaut in music; Fra
Angelico and the van Eycks in painting; the founding of the
universities of Prague, Vienna, Heidelberg, Koeln, Leipzig, and St.
Andrews (Scotland), Louvain, Caen, Poitiers, several colleges at
Oxford and Cambridge; the discovery of the Azores; and Gutenberg. In
mathematics Nichole Oresme dealt with infinite series with
considerable competence, giving the first proof that the harmonic
series diverges. For all that it probably reduced the European
population by about a third, the plague does not seem to have had a
devastating effect on learning.
>The British happened at this time to become infatuated with
>the Classical Architecture of Greece and Rome and through it
>with the classic works of the writers of antiquity. This helped
>to anchor them because they could read about systems of proportion
>in Vitruvious.
At exactly what time do you have in mind? And how do you account for
the fact that it was in Italy and France that the first 'modern'
editions of Vitruvius were published?
=====
>>>The russians for example used a measure called an arshin
>>>egual in length to the English foot.
The Russian <arshin> before Peter the Great was about 28" according to
Nicholson.
Brian M. Scott
J. B. Stephen (Buck)
Steve,
Whats the Egyptian word for "mathematician"?
Buck
J Stephen
Dept Math Sci
NIU
J. B. Stephen (Buck)
In article <5vbokd$r...@fridge-nf0.shore.net>,
Steve Whittet <whi...@shore.net> wrote:
>In article <5vahqn$lhk$1...@gannett.math.niu.edu>, bu...@shuksan.math.niu.edu says...
>>
>>
>>Steve,
>>Whats the Egyptian word for "mathematician"?
>
>unless you had already come up dry, so I began looking
>forewarned with that.
>
Not quite. I don't believe that you will find
any Egyptian term equivalent to mathematician.
About the best you are going to do is "accountant".
Steve Whittet
In article <5vahqn$lhk$1...@gannett.math.niu.edu>, bu...@shuksan.math.niu.edu says...
>
>
>Steve,
>Whats the Egyptian word for "mathematician"?
A very good question. Certainly you wouldn't have asked it
unless you had already come up dry, so I began looking
forewarned with that.
I know they are generally refered to as 'rope stretchers"
and there is a Greek word for that. Archaeologists refer
to Egyptians with the ability to read and write and do sums
in English as scribes; but it seemed likely there should be
a specific Egyptian word that perhaps gives some additional
insight into their role.
First I checked out the usual quick references.
I didn't find it in Gillings.I didn't find it in IES Edwards.
I didn't find it in Baines and Ma'lek.I didn't find it in Rossini.
I didn't find it in Gardiners A list as a profession though
there are words to describe the tools and implements of the
profession. I know that in Arabic an equivalent word is
"Mohandis", more specifically "Mohandis Mahri"
Gardiner Y3-4 gives "mnhd" (scribes outfit[palette])
"h3" (measure), "pss" (divide)
"ssw" writings.
Gardiner Y5 (draught[drawing]board)"znt" "mn"
(remain)"mnh" wax [Coptic Amoun] a wax tablet on which
the amounts of transactions were kept.
If I am going to have to go page by page in Faulkner
Gardiner at least provides some clues as to where to look.
Generally the Egyptians use more specific terms than
the general catagory "mathematician". The role apears to be
that of both the wise man or savant and the master craftsman,
a trained scribe, a man who can measure, weigh, judge, evaluate,
keep accounts, keep records, make reports, distribute goods, survey,
draw, paint, illustrate, layout, build, register, record, put in order,
teach, instruct, guide, divide correctly, govern, administer, work out,
prove and understand, as the Greeks would put it, an "arch techtos".
Faulkner
p97
"pd" stretch out, measure (foundation)
p 109
"mnhd" scribes. pallette
p 115
"mh3t" balance, keeper of the balance
"mh3" match, equal, adjust, make level
p 124
"mdh" builder, carpenter, [engineer]
p 170
"hmww" craftsman, 'wr-hrp-hm-wt' master craftsman
p183
"h3i", measure
"h3yw, measurements
"h3y" plumb line
"h3t3" land measure
p 201
"h''w" measure
p208
"s3t" prudence, wisdom
"s33" wise man
p209
"s3b" dignitary of unknown rank, senior, scribe,
superintendent of documents, govenor, chief justice
"s3rt" wisdom, understanding
p 212
"siptywr" inventory
p213
"sinw" ropes
p 219
"sb3" teach, teaching, instructions, pupil, surveying instrument
p 227
"sm3'" put in order, correct
p 233
"snhy" register, record
p 234
"snt" measure out land
p 246 (with the determinitive for the tools of the scribe)
"ss" write, inscribe, paint, enroll troops, writing, depiction,
record, papyrus roll, letter, document, painter, draftsman
p 247
"ssm" lead, guide, rule, govern, show the way
quidence, procedure, conduct, business, expenditure
state of affairs
"ssmt" working out, proof (math)
"ssmw" ruler, leader
p 248
"sss3" make wise
"sst3" make secret, mysterious, inaccessible, confidential, secret
p 261
"s3'" container for corn, space, volume
"s3w" weight, worth, value
"n-s3w-n" in the capacity of
p 264
"sbsb" adjust, divide correctly
"spnt" a measure of beer
p 268
"snw" circuit, circumference (the same word as rope{English sinew})
[The Egyptian cartouche is a "snw"]
"snwt" granary
p314
"dni" scribe of distribution
"dniw" share portion
"dns" heavy, weighty, massive
"dnsw" weights
>
>Buck
>
>J Stephen
>
steve
Steve Whittet
In article <5vbrro$t18$1...@gannett.math.niu.edu>, bu...@shuksan.math.niu.edu says...
>s...
>>>
>>>
>>>Steve,
>>>Whats the Egyptian word for "mathematician"?
>>
>>A very good question. Certainly you wouldn't have asked it
>>unless you had already come up dry, so I began looking
>>forewarned with that.
>>
>
>any Egyptian term equivalent to mathematician.
>About the best you are going to do is "accountant".
No, as should have been evident I checked pretty carefully
and said about what I wanted to say...
"Generally the Egyptians use more specific terms than
the general catagory "mathematician". The role apears to be
that of both the wise man or savant and the master craftsman, "
There is none of this ivory tower intellectual,
stuck in the office behind a desk publish or perish, stuff.
The guy is out there in the "sht" (field) getting his boots muddy,
he is also...
"a trained scribe, a man who can measure, weigh, judge, evaluate,
keep accounts, keep records, make reports, distribute goods, survey,"
willing to do some drudge work, but possessed of an artistic
tempermant, as a draftsman he can...
"draw, paint, illustrate,"
accurately enough that someone can build what he has drawn
"layout, build,"
I would include engineer; he can run the numbers and see if the
beam he wants to use will work for the span he has in mind....
register, record, put in order,
He can handle the paper work to make sure the blocks show up
on the jobsite the same time as the crew that's going to move
them around...
"teach, instruct, guide, divide correctly, govern, administer, work out,
prove and understand, "
he is someone whose opinion is valued
"as the Greeks would put it, an "arch techtos"."
Arch Techtos is closer than accountant.
>
>Buck
>
>J Stephen
steve
William Wallace
>Every scientific calculator I've ever owned has offered degrees,
>radians, and grads as units of angular measure, but equally I've never
>actually come across a situation in which grads are used. I have a vague
>memory that they're used in surveying - can anyone confirm or deny this.
All I remember from the HP-45 manual was a short mention that it
was used in Europe.
Steve Whittet
In article <3418c296...@news.csuohio.edu>, sc...@math.csuohio.eduŻ says...
>
>On 11 Sep 1997 19:13:38 GMT, whi...@shore.net (Steve Whittet) wrote:
>
>>The Egyptian ruler was divided into 28 fingers
>>It had a division marked with the glyph for Isis to the
>>right of the 22nd division from the left and to the left of the
>>7th division from the right, effectively dividing the ruler
>>into portions proportionate to Pi taken as 3 + 1/7
>
>ruler - is more than one specimen known, by the way? - or for the
>intervals between them. You've previously said that the glyph lies in
>one of the intervals. The phrase 'a division marked with the glyph'
>therefore suggests that by 'division' you mean 'interval between
>marks'. In that case your description implies that the glyph is in
>the 23rd interval from the left and the 8th interval from the right,
>i.e., that these two intervals are equal. Unfortunately, that would
>mean that the ruler was divided into 30 intervals, not 28.
We have discussed this before. There is a sting of 22 increments
running from left to right marked at its right end with a glyph
to the left of the last division.
There is a sting of 7 increments running from right to left marked
at its left end with a glyph to the right of the last division.
22 fingers is also 3 + 1/7 spans
>
>You've previously indicated that the glyph falls in the 22nd segment
>from the left, which is the 7th segment from the right. Not counting
>the ends of the ruler as marks, this places it between the 21st and
>22nd marks from the left-hand end. At that point it is about 21.5
>fingers from the left-hand end and therefore divides the ruler approx.
>in the ratio 21.5 : 6.5, or 43:13, not 22:7.
The glyph itself is the label for a range, not the increment
which divides it up.
>
One single glyph serves to divide the ruler of 28 fingers into
a measure of 22 parts and a measure of 7 parts. Modern folding
rules and tape measures do the same thing by putting the number
associated with an increment beside it instead of below it.
>=====
>
>>>It is your assertion that a talent is a volume measure based upon
>>>a cubic foot.
>
>>No, its just a fact. Look it up in a good dictionary or encycopedia
>
>The OED is a good dictionary. It says that the talent is an ancient
>weight and money of account. It says that the Royal Babylonian talent
>averaged about 29.87 kg and mentions an Old AEginetan talent of 40.3
>kg, a later AEginetan talent of 36.4, and a Solonian talent of 25.8 kg.
That's pretty close. Klein gives 29,900 and 25,900. Now compare that
to the value of a foot. You should find the Pes is pretty close.
A modern foot is 28316.85 grams
A foot of 29,900 grams is 12.22", is a geographic foot of 310 mm
A foot of 25,900 grams is 11.65", the pes
>It also says that the word is related to a Greek verbal root
><tal-, tla-> 'to bear', which supports (!) the notion that it was
>originally a weight.
Yes, all the ancient volume measures were taken as weights.
>
>>My cite was (Klein page 88)
>
>I believe that Klein also gives it as a weight, namely, the weight of
>a cu. cubit of water.
Its a cubic foot of water. A cubic cubit (17.575") is PI times
the weight of a cubic foot of 12".
There is also a substantial difference between the weight of a cubic foot
of different liquids; ice water is 56 lbs, sea water is 64 pounds
water at 100 degree centigrade is 59.83 pounds
alcohol is 49 pounds.
Interestingly enough the minah reflected this discrepancy, dividing
the Talent into both 50 and 60 parts.
>
>=====
>
>>Actually the correspondance is better between the British and
>>Egyptian systems than some other European systems. You need to
>>take into account that most of Europe was so ravaged by the plauge
>>during the middle ages that very little survived.
>
>This doesn't square with the facts. The plague actually came rather
>late, after much of the past had been recovered.
First you have the Dark Ages, then the Crusades (which were actually
still being pursued by some factions into this century). In 1493
Byzantiums library is burned. We are told that Columbus (1492)
actually has to convince people the world is round.
It is true that people who came in contact with the arabs
during the crusades learned something about how much
knowledge had been lost, (or suppressed) but in the time
of Sir Issac Newton people still were trying to figure out
exactly what the science of the ancients had been like.
>The real loss had occurred many centuries earlier after the
>western Roman empire fell apart.
No, the real loss occured when the church discouraged the
teaching of anything which disagreed with its tenets. During
the Middle Ages most people were confirmed Ludites. Science
was equated with witchcraft, alchemy, sorcery, thaumaturgy,
necromancy or worse. You could get burned at the stake
just for knowing how to read.
Trade guilds jealously guarded their secrets of building technology
and industry. Sea Captains hid away their charts and People took
a doctorate at Oxford to learn how to do fractions.
>Look at some of the names associated with the century or so
>after the arrival of the plague in Europe; these include Chaucer,
>Petrarch, Boccaccio in literature; Dunstable and Machaut in music; Fra
>Angelico and the van Eycks in painting; the founding of the
>universities of Prague, Vienna, Heidelberg, Koeln, Leipzig, and St.
>Andrews (Scotland), Louvain, Caen, Poitiers, several colleges at
>Oxford and Cambridge; the discovery of the Azores; and Gutenberg.
Ok, Chaucer is so scientifically enlightened as to make fun of
alchemists as being basically nothing more than puffers and con men.
Boccaccio is getting a rude laugh out of telling ribald stories of
cukoldry, Hubert and Jan Van Eyck and the Flemish composers are so
egotisticaly ignorant of the wonders of antiquity as to be famed
for saying that "nothing worth painting (or composing) had been
done before their time."
The Universities you mention were granting doctorates to wealthy
young noblemen if they could write their name and do fractions.
As to the discovery of the Azores that was done by the Phoenicians
c 200 BC, (Check out the recent thread in sci.archeology on hoardes
of Phoenician and Carthaginean coins there.)
Movable type was not first used by Gutenberg but rather by the makers
of the Phaistos Disk, c 1700 BC in Crete.
In mathematics Nichole Oresme dealt with infinite series with
>considerable competence, giving the first proof that the harmonic
>series diverges.
You have been reading Boyer, talk to Milo about the Egyptians
work with harmonic series...:)
>For all that it probably reduced the European
>population by about a third, the plague does not seem to have had a
>devastating effect on learning.
That should tell you something,
The Plauge had virtually no effect at all...
because 2/3 of know nothing is still know nothing.
>
>>The British happened at this time to become infatuated with
>>the Classical Architecture of Greece and Rome and through it
>>with the classic works of the writers of antiquity. This helped
>>to anchor them because they could read about systems of proportion
>>in Vitruvious.
>
>At exactly what time do you have in mind?
8:30 PM the 11th of August, 1490
The High Rennaisance begins with Leonardo Da Vinci,... why?...
because he troubled himself to wonder what the ancients had actually known
and endeavored to find out. In concert with the architect Donato Bramante
after 1490 he begins to reintroduce Europe to systematic proportions.
Michalangelo's vestibule of the laurentian Library in Florence was designed
between 1558 and 1559
Andrea Palladio, (1518-80) Inigo Jones, Christopher Wren, Thomas Jefferson
following in his footsteps.
>And how do you account for the fact that it was in Italy and France
>that the first 'modern' editions of Vitruvius were published?
There is no question that the continental Europeans had every opportunity
to get with the program, but in Italy, Spain and France they were too
closely tied to the church.
>
>=====
>
>>>>The russians for example used a measure called an arshin
>>>>egual in length to the English foot.
>
>The Russian <arshin> before Peter the Great was about 28" according to
>Nicholson.
Yes, Russia had a very Egyptian septanary system and even after Peter
westernized his measures they still kept a unit of 7 feet.
>
>Brian M. Scott
steve
J. B. Stephen (Buck)
Steve has given us his perceptions on the role of
a scribe in ancient Egypt. I sugessted that the
closest term would be accountant, but the scribe is
the person who did practical mathematics.
I agree that the scribe
was a servant who appears to have had considerable
privilege and that
>[Steve] he is someone whose opinion is valued
But I don't see the evidence for the scribe as
universalist, as he does.
As for your claim that
"Arch Techtos is closer than accountant"
well, not really, it's not egyptian.
Steve Whittet
In article <34187fce....@news.mindspring.com>, WWal...@freedom.orgв says...>>>...basis for your claim,...can NOT be derived
>>>...from the two measures you give.
>>>...Only something with a volume
>>>...the equivalent of two gallons can be supported.
>>One Minah, the 1/60 of a talent, is a pint
>
> Imperial or US?
"spnt", Egyptian...
>
>>>>but you should find that most units of volume for dry measure are
>>>>defined as cubes and liquid measures are cylinders, barrels, casks,
>>>>niperkins, etc. Our gallon of 231 cubic inches came to us as a wine
>>>>gallon, but the English did not invent wine, nor for that matter
>>>>beer. At the wedding at Cana a Hebrew rabi provides wine for the
>>>>guests in units of a mettrette.
>
>>>...231 per gallon is a US gallon, not a british gallon....
>
>>The wine gallon, which had existed for a long time previously
>>was first made an official English measure by the decree of
>>Queen Elizabeth at about the same time she changed the length
>>of the mile to 5280 feet.
>
> And what size might it be
8 stadia of 600 feet (the distance between Roman mileposts)
The Greek mile of 4840 feet from which the Roman mile
of 4800 feet (they liked multiples of 16) was derived
became a British mile of 5000 feet when the Romans took
the stadia as 125 paces of 5 feet making it 625 feet
where it had been 600.
.
Queen Elizabeth increased it to 5280 feet so that
it would contain 640 acres.
>and how did she learn Egyptian?
Why would she need to? She probably read the report of John Greaves.
>And how does it relate to the other two gallons?
As I have explained to you, linear measures are taken
as the sides of cubes which define volumes.
>
>>>>Liquid measures generally run a little over the dry measures. You
>>>>might want to compare the Biblical bath and epath of 12 gallons.
>
>>>>The Hebrews got their liquid measures from the Egyptians who had
>>>>a fondness for beer. The most common small liguid measure used by
>>>>the Egyptians was the Hinu.
>
>>> When did archaeologists uncover these measuring devices?
>
>>The first studies began around 1680, and have been more or less
>>continuous since then.
>
> Please cite any studies prior to Naplean.
"~Well we could begin with the Classical Greeks, Agatharchydes of Cygnus,
Herodotus, Diodorus Siculus have come down to us; Euhemerus,
Duris of Samoa, Aristagorus, Antisthenes, Demetrius of Phaleron,
Dionysius of Phaleron, Demotles, Artemidorus of Ephesus,
Alexander Polyhistor, Butorides and Apion are fragmentary or lost
and survive only in quotation.
Strabo studied them in depth but the 47 books of his History are lost,
all that survives is a geographical Aappendix
Al Mamun went so far as to cause the Great Pyramid to be opened
and subsequently its casing was removed.
In the intervening years between Al Mamun and John Greaves
there were many visitors but no serious explorers
In 1638 John Greaves a 36 year old mathematician who had taught at Oxford
went to the Great Pyramid as part of a survey of ancient buildings in
hopes of restablishing the value of the Roman foot. In the Vatican gardens
he had found the staue of a yound architect with his architectural
implements incuding a ruler of 1 Roman foot.
Greaves measurements were used by Newton to compute that the Egyptian cubit
had been 20.63"
Greaves left his measuring instruments with Burrattini
In 1765 Davison began exploring
On May 19, 1798 a 29 year old Bonaparte set sail from Toulon with a force of
35,000 soldiers and 175 "savants" or scholars.~"
You can read more about this in
Peter Tompkins book "Secrets of the Great Pyramid" (excerpted above.)
which does a good job of presenting the history of the explorations
>>>Inless you are not claiming the "inch" existed, whose known
>>>origin is three barleycorns, fractions of an inch are not admissable.
Since you claim to "know" this, please be so good as to tell me
how you know, and how you explain away previously existing measures of 1"?
For example King David I of Scotllands "thoums", Greek "onych,
"ungis" and "unglia" in Italian, Latin "uncia" meaning 1/12 (pes)
>>The Egyptians used an inch of 1 1/3 finger and indeed had
>>tables of 1/3 and 2/3 their standard units
>>unit 1 1/3 unit 2 2/3 unit 5 1/3
>>finger inch 2 inches palm
>>nail palm fist 3 quarters
>>palm hand link 4 hands
>>fist 2 palms foot 2 feet
>>quarter foot 2 feet 4 feet
>>cubit 2 feet 4 feet 8 feet
>>3 quarters yard 6 feet 12 feet
>The origin of the inch remains three barleycorns. ...
That's a conclusion which is unsupported by the data.
(Even the Greek had an "oynch" and the Roman had an "uncia" of .97")
but instead refers to king Athelsthanes girth which I have
previously discussed.
>
>>>>The Egyptians made wooden boxes with great skill. Grain
>>>>was stored in rooms made of clay bricks. As it happens
>>>>they did hollow out stones,
>
>>> These would not hold liquid.
>
>>Sure they did
>
>..cited only that research started in 1680. That does not
>make wooden boxes or clay brick hold water.
What is a wooden boat? ...:) Actually, better yet, what is your point?
Liquids such as wine, oil and water were stored in clay pots, amphora,
and yes, stone bowls filled with oil and used as lamps.
>...verification of waterproof
>wooden boxes of Egyptian origin of the correct period.
Just in case you are interested any tightly joined wooden box
will hold water unless the wood is very porous, so will some baskets.
Even without waterproofing them.
...
>
>>They also made boxes, cloth and leather sacks, clay pots,
>>jugs, vases, jars, baskets, amphorae, barrels, casks, kegs,
>>and a wide range of other containers too numerous to mention.
>
> And their volumes are?
Generally in hinu, hekats, talents, khar, cubic cubits, artaba,
and quedet.
>
>>>>As to making pots, amphora and clay vessels of a given capacity
...
>
>This method of making clay pots is still unsupported in the literature.
What literature have you read? Stechinni detailed it in his Appendix,
and S Gideon has pointed out that artifacts indicate a line under the
rim was used to mark the measure. How do you think the Egyptians
made their water clocks?
=========
>>...What point were you trying to make here?
>
>The point is that if you want a standard measure by which people
>measure things you make it convenient for people to use as a measure.
>What you do not do is claim that a measure much to large for
>convenience is explained by the pyramids. That is not responsive.
A convenient size measure for dry measure was the hekat, about
20 pints of 282 cu", this was multiplied and divided by doubling
The Egyptians also used multiples of 3/4, 2/3, 1/2, 1/3, 1/4, ...,
down to the ro of 1/320 hekat.
>
>>>>but aside from
>>>>that, if the standards of measure are defined as the cube of a length
>>>>you just measure your granary and determine what proportion of its
>>>>capacity has been used.
>
>>>There are clearly many ways to do that which are much simpler and
>>>convenient than what you suggest.
>
>>Ok, you have just completed the harvest, your cylindrical
>>grainery measures 9 royal cubits in diameter and is filled
>>to a height of 1 rod of 10 royal cubits.
>
>>How would you determine how many cubic khar of grain that is?
>
> You count the number of measures that are put into it. You do not
>need any other measure.
You have been putting grain in and taking it out for years,
now its time to take the inventory, how do you do it?
>
>>The Egyptians tell us how they did it in their mathematical
>>papyri.
>
> Counting is not that difficult.
That isn't the method they give.
>
>>>>> Water is what, seven pounds per gallon?
>
>>>>sea water is 64 lb per cu'
>>>>ice water is 56 lb per cu'
>>>>alcohol is 49 lb cu'
>>>>olive oil is 58 lb cu'
>
>>>>there are about 7 1/2 gallons to an English cubic foot
>
>>>>>That is 168 and 266
>>>>>pounds respectively exclusive of container weight.
>
>>>>For what container? With what inside it?
>
>>>As for a gallon we are talking a liquid measure, water will do.
>
>>A container which holds 168 pounds of water of 28.875 cu" to a
>>pound has a side of 17" and holds exactly 21 gallons
>
>>A container which holds 266 pounds of water of 28.875 cu" to a
>>pound has a side of 19 1/2" and holds 33 1/4 gallons, just
>>over 1 standard barrel.
>
>>I have no idea where you get those weights from or what
>>significance you think they have.
>
>I am pointing out that your length measures have nothing to do
>with weight and volume measures. We now have three different gallons
>under discussion and you insist the Egyptian measure bypassed England
>and came straight to the US. I do not accept that.
We have one gallon under discussion, a wine gallon of 231 cu"
>
>>===============================
>>...
>>>
>>> Second if you are talking liquid shipping containers, fine. A lot
>>>of them must have been found by know. What is their volume?
>>
>>Typically 12 gallons or multiples thereof.
>>>
>>>>The basic unit is a linear measure taken as the side of a cube to
>>>>calculate volumes. For a gallon we have a liquid measure so instead
>>>>of a cube its a cylinder. 1 Hekat was 8 English pints (dry measure)
>>>
>>>>take a cylinder of diameter 2 palms (5.8") and height 3 palms (8.8")
>>>>It has a volume of PI r^2 h = 232.5 cubic inches
>>>>our gallon is 231 cu inches; not a bad correlation for 5000 years.
...
>>
>>The cube of side 2 palms was 1 gallon
>>One cubic quarter yard was aproximately Pi gallons
>>One cubic foot was 7.5 gallons
>>The epath or bath was 12 gallons
>>One cubic cubit was 24 gallons
>>
>>There is no measure of which I know which is the cube
>>of a standard measure on a side that gives 2 gallons
>>it comes out to about 10.3 fingers
>>however a cylinder of diameter 7" and 12" high
>>or a span dia by a foot height does hold 2 gallons
>
> You gave them to me when here.
>
>>>>The weights and volumes are also common, based on cubes and cylinders
>>>>of the unit lengths. They have already been discussed at some length
>>>>in the thread. Compare the cube of a foot to the gallon for example
>>>>You will find that the cube an ordinary cubit of 17.698 inches on a
>>>>side holds 24 gallons, a royal cubit of 20.628 inches on a side
>>>>holds 38 gallons.
>
>24 and 38 gallons. Only a measure equivalent to two US gallons fits both.
38/24 = The Egyptian value for Pi/2, this makes converting between
a dry measure stored in a cubic container and a liquid measure
stored in a cylindrical container easier.
>That give 12 and 19 of them respectively. Saying the basic
>measure is one half of these is no different from saying it is 1/3 or
>1/5 or 1/90 of it as they all fit equally. You have no basis for
>claiming it is 1/2 instead of the other possibilities.
see above
>
>>>>>The metric system is approaching two hundred years old. There are
>>>>>very few holdouts and then only in theory.
>
>>People just don't really realise what they are losing and
>>how the religion of science finds it necessary to eradicate
>>any vestiges of ancient natural philosophy in order to make
>>a place for itself as guardian of the truth.
>
> There is no necessity to eradicate it when the only knowledge of
>value it produced that was of value is indistinguishable from chance.
If you look a little more carefully you will find that the foundations
of what you consider science are resting on the experiments of alchemists.
>
> And since the value of "ancient natural philosophy" is bound up
>in the length of the forearm of so long dead civil ruler it is unclear
>what anyone would expect to gain from it.
>
>>>>In the long run the present fad for the metric system will become
>>>>an historical curiosity, a great anachronism. It has about as much
>>>>chance of surviving the next millenium as organized religion.
>
>>>Until such time as their is evidence of that trend, I will file
>>>that prediction away along with things from the psychic hotline.
>
>>The only really dependable thing in all of human history has
>>been change. If you don't think measures will evolve through
>>the metric system just as political systems finally have begun
>>to emerge from their fascination with the communism that came
...
>>>>>>The talent for example was the cube of the foot. The foot was Egyptian
>>>>>>in origin.
>
>>>>> Excuse me but there are references to a "talent of gold."
>
>>>>Sure, there were also talents of silver. Essentially the talent was
>>>>one cubic foot; The hekat was 4 quarts, the khar was 2/3 of a cubic
>>>>cubit or about 20 hekats, the hinu was 1/10 hekat.
...
>
> Gold is measure by weight, period.
...
>
>>>It is your assertion that a talent is a volume measure based upon
>>>a cubic foot.
>
>>No, its just a fact. Look it up in a good dictionary or encycopedia
>>My cite was (Klein page 88)
>
> To hell with your cite, your statement is that it is a volume
>measure.
>
>>>>the talent, and on the other hand assert it was
>>>>never measured other than by weight. Of course the amount of gold
>>>>which filled a cubic foot (1205 pounds)
>
>>> Which pound are you referring to?
>>
>>The pound of 16 ounces avoirdupis or 453.5924g, .453592 kg
>
>>7000 grains = 256 drams = 16oz = 1 pound
>
> Since gold is measured in troy ounces and troy pounds your basis
>is clearly in error.
When do you think the troy or apothecaries ounce originated? Before or
after the talent? Its 12 ounces to the pound is derived from the Greek
drachma and that the drachma was 1/6000 the Greek talent which derived
originally from a measure of wine whereas the Hebrews used oil.
The abreviation for the pound (lb) actually comes from the Roman
libra each of whose fractions, 1, 11/12, 5/6, 3/4, 2/3 etc was named
individually in the Egyptian manner.
>
>Have you seriously looked into or are you just playing games on a
>calculator?
I just read a lot...,
>
>>>>was also a known value
>>>>but gold was more commonly measured by the minah, sheckel, drachma,
>>>>bekah, rebah, gerah, quedat and grain which were weights defined
>>>>as volumes by being fractions of the talent..
>
>>> It is not clear how you are getting to weights being defined by
>>>volumes? That is a very "metric" concept.
>
>>Heck no, Its an Egyptian concept. The French savants who defined the
>>metric system learned about it by studying the works of ancient authors.
>
>Not in the least. The timing is all wrong. That is quite impossible.
wrong again.
>
>>>>>If a talent of gold is in fact a cubic foot of gold we have here
>>>>>a proverbial king's ransom. Yet references to a talent of gold
>>>>>indicate it was more on the order of an ounce of gold.
>
>>>>A Hebrew talent or kikkor was 60 minahs 29,900 grams.
>>>>The Greek talent was 25,900 grams
>
>>> By those measures we are talking on the order of a talent being
>>>worth $250,000 or so and roughly the size of today's 1000 ounce ingot
>>>which is no where near a cubic foot.
>
>>Our foot is 12" giving 1728" cubic inches, or 27,215.55392 g
>>but at the time the talent was established the foot in use
>>was 11.42", the Roman pes
>
> That does not significantly change what I posted. However it does
>shoot your "perfect" measures all to shit.
Not at all. My point is that the system originated with the
Egyptians, and has remained essentially the same system for
about 5 millenia. The Egyptian foot was 300 mm, The Roman foot
was 296 mm The Greek foot was 308.4 mm and ours is 304.8 mm
The Egyptians divided their foot into both 12 and 16 parts.
The Greeks picked up on the Egyptians idea of making it geocommensurate
The Romans followed the Greeks but divided their foot into 16 parts.
We divide ours into 12
>
>>>Clearly there are different measures referred to as a talent
>>>which complicates things once more.
>
>>Yes and No. There was a profane and sacred system of measures
>>developed by the Hebrews which essentially included a tithe
>>or tax to the temple of 1 part in 13.
>
===============
>Please, let me put this in perspective. The Israelites were a
>generally primitive people who made not one contribution to the
>culture of the world in any regard.
===================
Whew!!! You are gonna get some nasty mail on that one
=================
> They only claim to fame was a short period in which they
>were the meanest rapers and pillagers in the valley.
==============
>The mythical hebrews were illiterate goat herders even according
>to the myth.
=============================
>
>Pointing the rapists or the myth is completely irrelevent.
=================
Well its nice to see where your true colors lie,
Hows the weather in Idaho this time of year?
>
>>>>... the subject is measurements. Weights were defined as volumes
>>>>and volumes were defined as cubes with sides of a given length.
>
>>>....coincidence at best and then rather dubious.
>
>>This is a common response when confronted by facts which
>>contradict long cherished beliefs, its called cognative
>>dissonace.
>
> I have no cherished beliefs.
see above
Most measurement systems can be
>traced back to legal proclamations in which the basis is given in the
>proclamation. It is simply that claiming US measure came from Egypt
>while bypassing Britain is laughable.
>
>>The way science procedes is to produce a testable
>>hypothesis and then test it. In this case we see that indeed
>>units of length do give rise to units of volume which are the
>>cube of their sides.
>
> What I have seen that you have not in the least researched your
>material beyond what is in an almanac and even then missing the
>obvious as in gold measure and which gallon. You have concentrated
>upon measures so old that there is no certainty regarding them yet you
>give them to the thousandths of three british barleycorns.
>
>>>>I am talking wine gallons, we can take it down to quarts or pints, gills,
>>>>ounces, whatever you like.
>
>>> What is a wine gallon?
>
>>231 cubic inches as defined by Queen Elizabeth.
>
> Then that is neither the US or imperial gallon.
It has becoame the US gallon
>
>>>It traditionally came in quite large containers, later casks, bottling
>>>be a relatively recent development. And even now wine by the gallon
>>>isn't that common. However it still does not tell whether it is British
>>>or American gallon or if this "wine" gallon is either of them.
>
>>It goes back to the Egyptians, was used by the Hebrews, Greeks and Romans
>>and institutionalized as law by Queen Elizabeth for the British which is
>>how it came to be adopted by the Americans.
>
> It was NOT adopted by the Americans nor by the British as you
>have demonstrated.
wrong again.
>
>>> May I point out the driving factor of the metric system was
>>>commerce which is what lead to its adoption in Europe? People in
>>>Europe agreed standardization was needed.
Some people did, those people tried to take all the people
who weren't "standard" or who disgareed with them and
put them in ovens, a perspective with which I can see
you agree.
It was quite obviously their
>>>opinion that "amazingly consistant" was not good enough.
>
>>The ancient measures were actually much more consistent. In the
>>Middle Ages much knowledge was lost. The more that was lost the
>>more people tried to standardise things by redefining the wheel.
>>Eventually things got so bad they had to go back to antiquity
>>to try and determine what the original standards had been.
>
> Unless you can produce actual standards from pre-Dark Ages times
>you have no basis for this claim.
Of course we can, thats what we have been discussing
>
>>Despite that, after 5 millenia, we vary less from the original
>>Egyptian standard than the variation between European countries
>>which existed in the Middle Ages.
>
> Then you are saying again that the measures of Egypt not only
>bypassed Britain but all of Europe to arrive in the US. You are
>becoming a touch absurd.
>
>>>>>Your assertion depends upon a one to one correspondance between
>>>>>Egyptian and British whereas there was no correspondance between
>>>>>British and other European systems.
>
>>Actually the correspondance is better between the British and
>>Egyptian systems than some other European systems. You need to
>>take into account that most of Europe was so ravaged by the plauge
>>during the middle ages that very little survived.
>
>In case you missed it, Britain was on the hind teat of Europe
>until the war with Spain and was more than equally ravaged.
You don't like anybody very much do you?
>
>>The British happened at this time to become infatuated with
>>the Classical Architecture of Greece and Rome and through it
>>with the classic works of the writers of antiquity. This helped
>>to anchor them because they could read about systems of proportion
>>in Vitruvious.
>
> You are several centuries off.
Off from what? Do you know what date I have in mind?
>
>>>>>...a unique but highly unlikely connection.
>>>>You can read all about it for yourself in the cited reference material.
>>>>There was excellent correspondence between the English and other European
>>>>systems. The russians for example used a measure called an arshin
>>>>egual in length to the English foot.
>
> ...wishful thinking, guessing...
>...a host of improbabilities ...flat out wrong ...
>
> I have no idea how you can salvage this mess.
No that you have shown us what you are and where you are coming from
why would I want to continue giving you information you don't
appreciate anyway?
steve
Brian M. Scott
On 12 Sep 1997 22:01:26 GMT, bu...@shuksan.math.niu.edu (J. B. Stephen
(Buck)) wrote:
>As for your claim that
> "Arch Techtos is closer than accountant"
>well, not really, it's not egyptian.
It's not even Greek. The word is <arkhitekto^n> 'master builder'.
What Steve described is a combination of the medieval professions of
clerk and master builder.
Brian M. Scott
Steve Whittet
In article <3419d7d9...@news.csuohio.edu>, sc...@math.csuohio.eduï says...
>
>On 12 Sep 1997 22:01:26 GMT, bu...@shuksan.math.niu.edu (J. B. Stephen
>(Buck)) wrote:
>
>>As for your claim that
>> "Arch Techtos is closer than accountant"
>>well, not really, it's not egyptian.
>
>It's not even Greek. The word is <arkhitekto^n> 'master builder'.
The phrases I gave you are the Egyptian. They are not purely
the description of a mere mathematician
>What Steve described is a combination of the medieval professions of
>clerk and master builder.
What I described is just what it sounds like I described. Actually
though, it isn't my description, Its what Faulkner and Gardiner
are telling us the Egyptians allocated to the scribes for work.
The position requires quite a generalist. The scribe as "master builder"
isn't just a carpenter or mason though he may have some experience in
those trades. He is also formally educated, trained in engineering
business and contract law rather than just pure mathematics.
The scribe "Imhotep" (I am thankful), our Egyptian arch tectos
is in the vein of Archimedes, Leonardo Da Vinci Galileo and Newton.
Whether you call him arch techtos, mohandis mahri or scribe
would make no more difference to him than it does to me.
He experiments and finds out what works by trial and error.
He has to be careful because, from the time of Hamurrabi, if the
builder builds a building which doesn't work his life is forfeit.
To get around that he trys out his ideas on models. He makes
mistakes and learns from them. He defines experience as having
already made all those mistakes before.
He is expected to know something about the strength of materials
and to be something of an inventor, but frequently finds himself
going back to the drawing board as with the bent pyramid of Dashur.
He probably begins his education learning to read by studying history
and natural philosophy, gaining a vocabulary of what has been done before
and being encouraged to put that aside and try something different.
The scribe may learn how to work with numbers by acting as
a clerk of the works for roads and dams and quarries.
He learns to draw drafting layouts for inscriptions, drawing columns,
and the facades of buildings covered with hieroglyphics laid out
on a grid.
He may spend some time in the army learning how to give orders,
overseeing the distribution of land and surveying fields,
He spends a long apprenticeship working with tools, carving inscriptions,
painting tombs, building furniture, first working himself to
learn the trade and then instructing others as he oversees the work.
The Phoenician, Greek, Roman and Medieval models are not greatly
different, except that by medieval times the arts have become
carefully guarded secrets.
>Brian M. Scott
steve
Brian M. Scott
On 12 Sep 1997 20:59:02 GMT, whi...@shore.net (Steve Whittet) wrote:
>One single glyph serves to divide the ruler of 28 fingers into
>a measure of 22 parts and a measure of 7 parts.
I can live with this; it's technically correct, albeit misleading to
anyone who hasn't read a clear description of the ruler. (Is more
than one exemplar known?) It would be clearer if you noted that the
measures overlap by one part.
=====
>>>>It is your assertion that a talent is a volume measure based upon
>>>>a cubic foot.
>>>No, its just a fact. Look it up in a good dictionary or encycopedia
>>The OED is a good dictionary. It says that the talent is an ancient
>>weight and money of account.
>>It also says that the word is related to a Greek verbal root
>><tal-, tla-> 'to bear', which supports (!) the notion that it was
>>originally a weight.
>Yes, all the ancient volume measures were taken as weights.
You miss the point, Steve. The talent is a unit of WEIGHT. It is not
a unit of volume, though at least one version of it was apparently
defined in terms of a volume OF WATER, not just a volume. It's
essential to distinguish the type of unit from the nature of its
definition.
=====
>>>Actually the correspondance is better between the British and
>>>Egyptian systems than some other European systems. You need to
>>>take into account that most of Europe was so ravaged by the plauge
>>>during the middle ages that very little survived.
>>This doesn't square with the facts. The plague actually came rather
>>late, after much of the past had been recovered.
>First you have the Dark Ages, then the Crusades (which were actually
>still being pursued by some factions into this century). In 1493
>Byzantiums library is burned. We are told that Columbus (1492)
>actually has to convince people the world is round.
I thought that by now that myth had been eradicated even from grade
school texts. No *educated* person in late-15th c. Europe doubted
that the world was round. As I recall, Columbus's problem was to
convince those whose opinions mattered that the earth was small enough
in diameter to justify trying to reach the Far East by sailing west.
He was still using a value some 25% too small, based on Strabo's
misunderstanding of Poseidonios's figure; by his day that figure was
suspect.
>It is true that people who came in contact with the arabs
>during the crusades learned something about how much
>knowledge had been lost, (or suppressed)
On the contrary, it was through Spain that most of what the Arabs had
preserved came to Europe. It's well known that in 12th c. Toledo the
translation of scientific works from Arabic and Greek into Latin was
almost an industry.
>but in the time
>of Sir Issac Newton people still were trying to figure out
>exactly what the science of the ancients had been like.
This is altogether wrong. By Newton's day Euclid's 'Elements',
Ptolemy's 'Almagest', and al-Khowarizmi's 'Algebra', to name but three
of the most important mathematical works, had been available to
European scholars for five centuries.
>>The real loss had occurred many centuries earlier after the
>>western Roman empire fell apart.
>No, the real loss occured when the church discouraged the
>teaching of anything which disagreed with its tenets.
From John H. Mundy, _Europe in the High Middle Ages, 1150/1309_:
'Because most thinkers of [the 13th c.] assumed that man's natural
reason was capable of comprehending some part of the cosmos and even
of glimpsing the nature of the divine principle itself, knowledge was
almost idolized. It enabled the Latins to plunder the wealth of
ancient and Islamic thought, breathing the heady air of intellectual
exploration.' (473) 'The *magistri* or *divini* of the thirteenth
century enjoyed a real measure of autonomy and rarely had their
opinions suppressed by the rest of the Church and society.' (481)
>During
>the Middle Ages most people were confirmed Ludites.
Most people were subsistance peasants who probably didn't care. And
the term 'Luddite' makes no sense in a non-industrial era.
> Science
>was equated with witchcraft, alchemy, sorcery, thaumaturgy,
>necromancy or worse. You could get burned at the stake
>just for knowing how to read.
Comic-book history. It appears that in late-14th and 15th c. London
about 40% of the male witnesses who gave evidence in the consistory
court had some ability to read Latin. These included braziers,
cappers, grocers, pewterers, shearmen, and tailors, among others. The
percentage would doubtless have been higher had the group included any
lawyers, physicians, scriveners, or lay schoolmasters. [Sylvia
Thrupp, _The Merchant Class of Medieval London_, 156ff.] Rather
earlier, the early 14th c. Florentine chronicle of John Villani
reported that 8,000 to 10,000 boys and girls were learning to read and
write in Florence; 1000 to 1200 students, he says, attended 6 abacus
schools to learn arithmetic and business; and 4 great grammar schools
housed 550-600 students of Latin and logic. His specific numbers may
be questioned, but he's obviously not describing a culture in which
reading was unusual. Bonvesino of Riva, a teacher, says that Milan
had about 70 teachers of elementary letters and 8 professors of
grammar in 1288. Earlier yet, a residential college for poor students
was founded in Paris in 1180. (Mundy, 464-5)
John Harvey, _Mediaeval Craftsmen_, Ch. 3, points out that '[t]he
number of schools *above primary level* was immense', a fact that
implies that primary schooling was very widely available. Skilled
craftsmen were almost always freemen - in some guilds they had to be -
and 'there is good reason to suppose that among freemen living towns
the proportion of literates was high from the thirteenth century
onwards'.
>Trade guilds jealously guarded their secrets of building technology
>and industry.
Of course. In this they were protecting their livelihoods. They were
also following an ancient model. Harvey mentions a cuneiform tablet
(17th c. BCE) that was eventually found to contain the formula for an
excellent glaze for earthenware: it was hidden in an elaborate
cryptogram. The secret was apparently kept pretty well, since it
isn't until 1000 years later that knowledge of the glaze seems to be
widespread.
>Sea Captains hid away their charts and People took
>a doctorate at Oxford to learn how to do fractions.
The ordinary fractions associated with commerce were widely taught,
not just in formal schools but also to apprentices in a number of
occupations.
>>Look at some of the names associated with the century or so
>>after the arrival of the plague in Europe; these include Chaucer,
>>Petrarch, Boccaccio in literature; Dunstable and Machaut in music; Fra
>>Angelico and the van Eycks in painting; the founding of the
>>universities of Prague, Vienna, Heidelberg, Koeln, Leipzig, and St.
>>Andrews (Scotland), Louvain, Caen, Poitiers, several colleges at
>>Oxford and Cambridge; the discovery of the Azores; and Gutenberg.
>Ok, Chaucer is so scientifically enlightened as to make fun of
>alchemists as being basically nothing more than puffers and con men.
He was correct: most of them in his day were. He was also so
scientifically enlightened that he wrote a useful treatise on the
astrolabe.
>Boccaccio is getting a rude laugh out of telling ribald stories of
>cukoldry,
Boccaccio was one of the great early stylists in the Italian
vernacular, along with Dante and Petrarch; as such he had a hand in
the creation of modern Italian. (And if that's all that you get from
Boccaccio, you have my sympathy. In the same vein you could describe
Shakespeare as a plagiarist of shop-worn tales.)
>Hubert and Jan Van Eyck and the Flemish composers are so
>egotisticaly ignorant of the wonders of antiquity as to be famed
>for saying that "nothing worth painting (or composing) had been
>done before their time."
If this is in fact a quotation, what is its source? And how is this
relevant? The point is that Europe boasted brilliant painters and
composers at a time when according to you European culture was
non-existent.
>The Universities you mention were granting doctorates to wealthy
>young noblemen if they could write their name and do fractions.
Perhaps you should take a look at what it actually took to get a
doctorate in the Middle Ages. You might also take a look at the
student population. 'A very large percentage had their studies paid
for by someone else, a wealthy relative or patron, an important cleric
or some student foundation. Many were very poor.' [Friedrich Heer,
_The Medieval World_, 257.]
>As to the discovery of the Azores that was done by the Phoenicians
>c 200 BC, (Check out the recent thread in sci.archeology on hoardes
>of Phoenician and Carthaginean coins there.)
They may have been discovered a number of times; that isn't the point
(unless your name is Guinness). The point is that there was a great
deal of European intellectual activity in the century or so following
the arrival of the Black Death; your notion that it left Europe an
intellectual wasteland is untenable.
>Movable type was not first used by Gutenberg but rather by the makers
>of the Phaistos Disk, c 1700 BC in Crete.
This misses the point in the same way. I might add that neither the
Cretans nor, somewhat later, the Chinese produced a print revolution.
(And if you really want to understand the significance of the latter,
I strongly recommend the 2-vol. work by E. (I think) Eisenstein.)
>In mathematics Nichole Oresme dealt with infinite series with
>>considerable competence, giving the first proof that the harmonic
>>series diverges.
>You have been reading Boyer, talk to Milo about the Egyptians
>work with harmonic series...:)
(I've been reading a number of sources.) The Egyptians are entirely
beside the point, which is that during the years after the plague,
Europe was anything but an intellectual wasteland. (And if they did
anything with the infinite harmonic series, no trace of it seems to
remain.)
>>For all that it probably reduced the European
>>population by about a third, the plague does not seem to have had a
>>devastating effect on learning.
>That should tell you something,
>The Plauge had virtually no effect at all...
>because 2/3 of know nothing is still know nothing.
You have a wonderful capacity for denial: I explicitly list a number
of intellectual achievements of the period in question, and you
pretend that they don't exist.
>>>The British happened at this time to become infatuated with
>>>the Classical Architecture of Greece and Rome and through it
>>>with the classic works of the writers of antiquity. This helped
>>>to anchor them because they could read about systems of proportion
>>>in Vitruvious.
>>At exactly what time do you have in mind?
>8:30 PM the 11th of August, 1490
>The High Rennaisance begins with Leonardo Da Vinci,... why?...
>because he troubled himself to wonder what the ancients had actually known
>and endeavored to find out. In concert with the architect Donato Bramante
>after 1490 he begins to reintroduce Europe to systematic proportions.
Oh, my. I thought that you were an architect; aren't you familiar
with Leon Battista Alberti (1404-1472), the 'Florentine Vitruvius'?
His 'De re aedificatori', published in 1485, was an interpretation of
Vitruvius in terms of Renaissance thought and became the Renaissance
architectural bible.
=====
>>>>>The russians for example used a measure called an arshin
>>>>>egual in length to the English foot.
>>The Russian <arshin> before Peter the Great was about 28" according to
>>Nicholson.
>Yes, Russia had a very Egyptian septanary system and even after Peter
>westernized his measures they still kept a unit of 7 feet.
In other words, you were wrong about the size of the <arshin>. Your
willingness to admit to obvious error is one of your more endearing
traits.
Brian M. Scott
Brian M. Scott
On 12 Sep 1997 23:41:23 GMT, whi...@shore.net (Steve Whittet) wrote:
>In article <34187fce....@news.mindspring.com>, WWal...@freedom.orgв says...
>>On 11 Sep 1997 19:13:38 GMT, whi...@shore.net (Steve Whittet) wrote:
>>>The wine gallon, which had existed for a long time previously
>>>was first made an official English measure by the decree of
>>>Queen Elizabeth at about the same time she changed the length
>>>of the mile to 5280 feet.
>> And what size might it be
>8 stadia of 600 feet (the distance between Roman mileposts)
I suspect that Mr. Wallace was asking about the wine gallon, but I'll
leave that to him. I like the next bit.
>>and how did [Elizabeth] learn Egyptian?
>Why would she need to? She probably read the report of John Greaves.
[snip]
>In 1638 John Greaves a 36 year old mathematician who had taught at Oxford
>went to the Great Pyramid as part of a survey of ancient buildings in
>hopes of restablishing the value of the Roman foot.
Elizabeth I died on 24 March 1603 (N.S.). She was quite a lady, but I
suspect that reading Greaves's report was a bit beyond her, or vice
versa.
=====
>You can read more about this in
>Peter Tompkins book "Secrets of the Great Pyramid" (excerpted above.)
>which does a good job of presenting the history of the explorations
You can read brief but pointed comments on this book and its author in
Bernard Ortiz de Montellano's recent post 'primary sources' in
sci.archaeology.
Brian M. Scott
Steve Whittet
In article <341a40d1...@news.csuohio.edu>, sc...@math.csuohio.eduŻ says...
>
>On 12 Sep 1997 20:59:02 GMT, whi...@shore.net (Steve Whittet) wrote:
>
>>One single glyph serves to divide the ruler of 28 fingers into
>>a measure of 22 parts and a measure of 7 parts.
>
>I can live with this; it's technically correct, albeit misleading to
>anyone who hasn't read a clear description of the ruler. (Is more
>than one exemplar known?)
Yes, I have seen three or four royal rulers which differ among other things,
in the number of fingers which are subdivided. I don't know how many
there are total but my quess would be its somewhere in the hundreds
though most are nowhere near as fancy.
>It would be clearer if you noted that the
>measures overlap by one part.
>
>=====
>
>>>>>It is your assertion that a talent is a volume measure based upon
>>>>>a cubic foot.
>
>>>>No, its just a fact. Look it up in a good dictionary or encycopedia
>
>>>The OED is a good dictionary. It says that the talent is an ancient
>>>weight and money of account.
>
>>>It also says that the word is related to a Greek verbal root
>>><tal-, tla-> 'to bear', which supports (!) the notion that it was
>>>originally a weight.
>
>>Yes, all the ancient volume measures were taken as weights.
>
>You miss the point, Steve. The talent is a unit of WEIGHT. It is not
>a unit of volume, though at least one version of it was apparently
>defined in terms of a volume OF WATER, not just a volume. It's
>essential to distinguish the type of unit from the nature of its
>definition.
There is a talent of alcohol and one of either oil or water which
are different sizes and contain different weights, so your point
is a good one.
I don't see it as conflicting with what I said earlier. There are
enough linear measures to make enough different size cubes to
make a set of weights which as they are doubled in size double
in weight.
Designed to be used with a set of scales such sets have been found
in Egypt Mesopotamia and the IVC in consistant proportion to one
another.
Think how convenient it was to have units of length related to
units of volume and weight. Think about what was being weighed.
The largest bulk cargos would be grain, olive oil and wine.
Trade was good; there weren't as many people then as there are now
to share the available wealth, so trading families made a bundle.
The measure of gold was in drachma, 1/6000 the talent. When
the Hebrews walked out of Egypt carying 70 talents of gold
and 60 of silver split up amongst perhaps 162,500 people
it suggests they were all, man, woman and child, carrying
about a pound of precious metal apiece.
Keep in mind that while the measure of gold was in drachma,
1/6000 the talent, the geodetic foot representing 1/6000
of a minute of arc was the side of the talent.(309 mm)
This linear measure existed in antiquity as the Foot of Athens
which was responsible for creating the drachma as a unit of
measure.
>
>=====
>
>>>>Actually the correspondance is better between the British and
>>>>Egyptian systems than some other European systems. You need to
>>>>take into account that most of Europe was so ravaged by the plauge
>>>>during the middle ages that very little survived.
>
>>>This doesn't square with the facts. The plague actually came rather
>>>late, after much of the past had been recovered.
>
>>First you have the Dark Ages, then the Crusades (which were actually
>>still being pursued by some factions into this century). In 1493
>>Byzantiums library is burned. We are told that Columbus (1492)
>>actually has to convince people the world is round.
>
>I thought that by now that myth had been eradicated even from grade
>school texts. No *educated* person in late-15th c. Europe doubted
>that the world was round.
We are agreed on that, but no the myth has not been eradicated,
probably because then as now there were a lot of people who
could care less about looking beyond the simple answers, myths,
legends,etc; The frivolous explanations we are given as children
have a tendency to be repeated from one generation to the next.
By the way, what would you say the proportion of "educated"
people to uneducated illiterate believers was in late-15th c. Europe?
>As I recall, Columbus's problem was to convince those whose
>opinions mattered that the earth was small enough in diameter
>to justify trying to reach the Far East by sailing west.
>He was still using a value some 25% too small, based on Strabo's
>misunderstanding of Poseidonios's figure; by his day that figure was
>suspect.
How is it that that figure came to be "suspect" do you suppose?
Unless it conflicted with some other figure what reason would
there be to doubt it? Could it possibly be that c 1490 the ideas
of Girolamo Cardano the Millanese Physician and mathematician
had through the influence of his friend Leonardo da Vinci begun
to be heard?
Cardano maintained that a body of exact science must have prexisted
the Greeks. He suspected that a degree of meridien (far more exact
than that of Eratosthenes or Ptolemy) could be found in Egypt.
He cited Pythagoras as having claimed that the measures of antiquity
were derived from Egyptian standards, copied from an invariable
prototype taken from nature.
Cardano thought that perhaps the pyramids had been built to record the
dimensions of the earth and furnish an imperishable standard of linear
measure.
He was presenting these ideas as a friend of Leonardo Da Vinci
in the same circles of "educated" Europeans that Columbus was
frequenting trying to get money at the same time. (c 1490)
>
>>It is true that people who came in contact with the arabs
>>during the crusades learned something about how much
>>knowledge had been lost, (or suppressed)
>
>On the contrary, it was through Spain that most of what the Arabs had
>preserved came to Europe. It's well known that in 12th c. Toledo the
>translation of scientific works from Arabic and Greek into Latin was
>almost an industry.
What? Spain wasn't a participant in the Crusades? Spain had been
fighting against and learning from the infidel longer than anyone.
The leading proponents of making the translations were alchemists
closely followed by gnostics, cathars and heretics; people the
Spanish made serious efforts to exterminate in their inquisition.
>
>>but in the time of Sir Issac Newton people still were trying to
>>figure out exactly what the science of the ancients had been like.
>
>This is altogether wrong. By Newton's day Euclid's 'Elements',
>Ptolemy's 'Almagest', and al-Khowarizmi's 'Algebra', to name but three
>of the most important mathematical works, had been available to
>European scholars for five centuries.
You need to read more than just Boyer.
Greaves, a mathematician who had discussed the problem with Newton
at Oxford went to Egypt in 1638 as part of a tour of ancient sites
where he hoped to find a datum that might help establish the true
dimensions of the planet which Newton needed to complete his
general theory of gravitation.
On Greaves return Newton wrote a paper entitled
"A dissertation upon the sacred cubit of the jews and the cubits
of several nations" In which from the dimensions of the Greatest Pyramid.
as taken by Mr John Greaves, the ancient cubit of Memphis is determined."
(Newton found it to be 20.63")
>
>>>The real loss had occurred many centuries earlier after the
>>>western Roman empire fell apart.
>
>>No, the real loss occured when the church discouraged the
>>teaching of anything which disagreed with its tenets.
>
>From John H. Mundy, _Europe in the High Middle Ages, 1150/1309_:
>'Because most thinkers of [the 13th c.] assumed that man's natural
>reason was capable of comprehending some part of the cosmos and even
>of glimpsing the nature of the divine principle itself, knowledge was
>almost idolized.
Note that the phrase "most thinkers" limits the set to the range
of cathers, gnostics, infidels and heretics as far as the church
was concerned. At the time Newton sent Greaves to Egypt, Galileo
was being tried and imprisoned by the church for supporting the
Copernican belief that the earth revolved around the sun.
>It enabled the Latins to plunder the wealth of
>ancient and Islamic thought, breathing the heady air of intellectual
>exploration.' (473) 'The *magistri* or *divini* of the thirteenth
>century enjoyed a real measure of autonomy and rarely had their
>opinions suppressed by the rest of the Church and society.' (481)
That was true so long as the Templars wielded influence with the church
The crusades meant several centuries of constant warfare in Europe as well
as the Middle East.
The Crusades were declared in 1095
The Templars were founded in 1118
The Mongols captured northern China in 1211
Ukraine fell to the Mongols in 1240
The Mongols defeated the mameluks at Homs 1299
The Templars were arrested in France in 1307
Jaques De Molay burned at the stake 1314
Outbreak of the Hundred Years war 1337
The Black Death 1348-1350
The Great Schism divides the Catholic Church 1378-1417
Granada surrenders to the Spanish 1492
In that period from 1095 to 1492 most people thought about
little else besides staying alive. Between 1314 and 1417
and especially between 1378 and 1417 during the Schism the
Catholic Church grew increasingly intolerant of divisive ideas.
>>During the Middle Ages most people were confirmed Ludites.
>
>Most people were subsistance peasants who probably didn't care. And
>the term 'Luddite' makes no sense in a non-industrial era.
What makes you think it was a "non-industrial era" Read
Jean Gimples "The Medieval Machine". The problem was that
if a man built a mill and didn't ask his Bishops permission first
the Bishop would have it torn down.
>
>> Science was equated with witchcraft, alchemy, sorcery, thaumaturgy,
>>necromancy or worse. You could get burned at the stake
>>just for knowing how to read.
>
>Comic-book history. It appears that in late-14th and 15th c. London
>about 40% of the male witnesses who gave evidence in the consistory
>court had some ability to read Latin. These included braziers,
>cappers, grocers, pewterers, shearmen, and tailors, among others.
Late 14th century is after the time of troubles is over. a 40 %
litteracy rate means a 60% illiteracy rate, and the test was
whether you could read and write your own name which was
something a witness could be rather easily taught by a lawyer.
Your representative sample of the population appears to include
only townspeople. Skilled workman who were probably taught some
ciphers by their guilds and small businessmen who were probably
required to keep accounts for tax purposes.
I don't see a large number of agrarian farm workers on your list
even the shearman was more of a self employed businessman than
a serf.
>The percentage would doubtless have been higher had the group
>included any lawyers, physicians, scriveners, or lay schoolmasters.
>[Sylvia Thrupp, _The Merchant Class of Medieval London_, 156ff.]
^^^^^^^^^^^^^^^^^^
>Rather earlier, the early 14th c. Florentine chronicle of John Villani
>reported that 8,000 to 10,000 boys and girls were learning to read and
>write in Florence; 1000 to 1200 students, he says, attended 6 abacus
>schools to learn arithmetic and business; and 4 great grammar schools
>housed 550-600 students of Latin and logic.
So at its most prosperous, Florence with a population in the
hundreds of thousands provided for the chindren of its 500
most wealthy and influential merchant families to be tutored
for a year. Of those perhaps 1 in 10 went on to study business
an additional year and 1 in a 1000 of the cities population
actually learned to read Latin at the grammar school level.
Compare this to ancient Egypt where a large part of the population
was literate, able at the very least to read the inscriptions
proclaiming the attributes of the gods and glory of the rulers,
considered it of critical importance for their children to get an
education, and gave over their children willingly to be trained
as scribes knowing the scribes training could last a lifetime.
>His specific numbers may be questioned, but he's obviously not
>describing a culture in which reading was unusual.
I would disagree. If only 1 in 1000 of the citizens in Europes
most prosperous and culturally aware city could read at the
grammar school level, what does that tell us about litteracy
gennerally?
> Bonvesino of Riva, a teacher, says that Milan
>had about 70 teachers of elementary letters and 8 professors of
>grammar in 1288. Earlier yet, a residential college for poor students
>was founded in Paris in 1180. (Mundy, 464-5)
70 teachers with perhaps twelve students each gives us 840 students
in Milan, another extremely rich city with a large population.
What this is telling us is that only the children of the
most privledged upper classes were being taught anything.
>
>John Harvey, _Mediaeval Craftsmen_, Ch. 3, points out that '[t]he
>number of schools *above primary level* was immense', a fact that
>implies that primary schooling was very widely available. Skilled
>craftsmen were almost always freemen - in some guilds they had to be -
>and 'there is good reason to suppose that among freemen living towns
>the proportion of literates was high from the thirteenth century
>onwards'.
Trade guilds taught their apprentices considerably more than the
average person could hope to learn. Thats one reason people were
willing to be apprenticed. An apprenticeship amounted to perhaps
1/3 to 1/2 a lifetime of involuntary servitude so it was almost
as serious a commitment as marriage, and for that matter of a
similar nature.
>
>>Trade guilds jealously guarded their secrets of building technology
>>and industry.
>
>Of course. In this they were protecting their livelihoods. They were
>also following an ancient model. Harvey mentions a cuneiform tablet
>(17th c. BCE) that was eventually found to contain the formula for an
>excellent glaze for earthenware: it was hidden in an elaborate
>cryptogram. The secret was apparently kept pretty well, since it
>isn't until 1000 years later that knowledge of the glaze seems to be
>widespread.
Yes, we are agreed; that knowledge during the middle ages was
not considered the provence of the masses, was limited to
business and profesional skills, was considered complete
when a person could read their own name or count to ten,
and even that amount of education was considered a
dangerous secret to be kept to oneself on pain of death.
>>Sea Captains hid away their charts and People took
>>a doctorate at Oxford to learn how to do fractions.
>
>The ordinary fractions associated with commerce were widely taught,
>not just in formal schools but also to apprentices in a number of
>occupations.
Gillings says that "in English speaking countries as late as the
sixteenth century it was not part of the school curriculum to
learn any multiplication tables at all."
"Samuel Pepys, the famous diarist, educated at St Pauls School,
and at Magdalen College, Cambridge University,
' an able man of business' was secretary to the British Admiralty,
and in that position must surely have needed to know how to calculate
but note this entry:
July 4,1662...Up by 5 O'clock...Comes M Cooper of whom
I intend to learn mathematiques and do being with him today.
After an hours being with him at arithmatique, my first attempt
was made to learn the multiplication table."
I am familiar with Alberti, that's why I skipped past him.
The first breaks with the Romanesque and Gothic traditions which
indicate the emergence of the Rennaisance from the Dark Ages
are sometimes taken as dating from"Filippo Brunescheli (1379-1446)
who in 1406 proposed to vault the central octagon of the cathedral
of Florence with a dome.", but "there was little in his solution
which was not medieval in inspiration except the boldness of the span"
The followers of Brunescelli in Florence independently reinvent some
classical forms which had been in use by the Romans such as
composition about a central vertical axis (symetry)
In Rome Alberti "paganized" the church of San Francesco at Rimini (1447)
by using Ronan piers and arches. He doesn't get to Florence until 1470
where he essentially copies the facades of classic Roman Buildings onto
the Church of the Annunziatta and the Palazzo Rucellai.
At San Sebastino at Mantua (1459) and in Saint Andrea at Mantua (1470)
he used a "triumphal arch motive in the porch and the interior walls
of the nave"
"Other monuments under Alberti's influence, such as the Palazzo Venezia
and the vestibule of the church of San Marco in Rome include
some of the *most literal reproductions of the antique yet attempted*"
Laurana, who developed Albertis ideas more imaginatively, is known
for the Palazzo Cancelleria in Rome completed in 1495
"About 1490 began a change under the leadership of Donato Bramante
(1444-1514) Inspired by the works of Alberti and Laurana
(more Laurana) he took up the main thread of development"
"Bramante was the moving spirit in the new Roman school of architecture"
(Bramante, Raphael, Leonardo da Vinci and Michaelangelo.
"A History of Architecture" Fiske , Kimball, Edgell
>
>=====
>
>>>>>>The Russians for example used a measure called an arshin
>>>>>>egual in length to the English foot.
>
>>>The Russian <arshin> before Peter the Great was about 28" according to
>>>Nicholson.
>
>>Yes, Russia had a very Egyptian septanary system and even after Peter
>>westernized his measures they still kept a unit of 7 feet.
>
>In other words, you were wrong about the size of the <arshin>.
sheesh Brian, at the time in question, after Peter the Great,
the foot was equal to the English foot, prior to that it was even
more directly connected to the Egyptian measures.
>Your willingness to admit to obvious error is one of your
>more endearing traits.
One mans ceiling is another man's floor...
>
>Brian M. Scott
steve
Steve Whittet
...
>>>and how did [Elizabeth] learn Egyptian?
>>Why would she need to? She probably read the report of John Greaves.
>
>
>>In 1638 John Greaves a 36 year old mathematician who had taught at Oxford
>>went to the Great Pyramid as part of a survey of ancient buildings in
>>hopes of restablishing the value of the Roman foot.
>
>suspect that reading Greaves's report was a bit beyond her, or vice
>versa.
Thats true, the government actually began to regulate commerce and
Industry in 1560, so the report which influenced all three and the
dramatic shift to Renaissance architecture is more likely to have
been the report of Cardano c 1490.
>
>
>Brian M. Scott
steve
Alan M. Dunsmuir
In article <5vecpm$c...@fridge-nf0.shore.net>, Steve Whittet
<whi...@shore.net> writes
>Cardano maintained that a body of exact science must have prexisted
>the Greeks. He suspected that a degree of meridien (far more exact
>than that of Eratosthenes or Ptolemy) could be found in Egypt.
>
>He cited Pythagoras as having claimed that the measures of antiquity
>were derived from Egyptian standards, copied from an invariable
>prototype taken from nature.
>
>Cardano thought that perhaps the pyramids had been built to record the
>dimensions of the earth and furnish an imperishable standard of linear
>measure.
>
>He was presenting these ideas as a friend of Leonardo Da Vinci
>in the same circles of "educated" Europeans that Columbus was
>frequenting trying to get money at the same time. (c 1490)
And in making these suppositions, he had precisely as much supporting
evidence as you have repeating them today. "Suspecting" that an accurate
measurement of a degree of latitude might be found in Egypt is not QUITE
the same thing as having actually unearthed an Egyptian reference to one
and interpreted its significance. (Or did he too have a mysteriously-
acquired comprehension of Egyptian hieroglyphs?)
I refer you to the annotation Einstein inscribed in Velikovski's book,
when he returned to V. the complimentary (and unsolicited) copy V. had
sent to him. "Very interesting theories" <g>
--
Alan M. Dunsmuir
Were diu werlt alle min von deme mere unze an den Rijn
des wolt ih mih darben,
daz diu chunigen von Engellant lege an minen armen!
J. B. Stephen (Buck)
In article <5vecpm$c...@fridge-nf0.shore.net>,
Steve Whittet <whi...@shore.net> wrote:
>
>Yes, I have seen three or four royal rulers which differ among other things,
>in the number of fingers which are subdivided. I don't know how many
>there are total but my quess would be its somewhere in the hundreds
>though most are nowhere near as fancy.
>
I was just about to ask a related question:
1) Where can I find the best examples of Egyptian
rulers.
2) Are there any known counting boards with
good provenece from the Babylonians, Egyptians,
Greeks or Romans. Any good quality reproductions
or detailed descriptions with photographs?
I have seen light discussions of these topics,
and remember that Roman counting boards were
grooved.
Anyone know of a good reference?
Thanks,
Buck
J Stephen
Dept Math Sci
NIU
J. B. Stephen (Buck)
>Cardano thought that perhaps the pyramids had been built to record the
>dimensions of the earth and furnish an imperishable standard of linear
>measure.
>He was presenting these ideas as a friend of Leonardo Da Vinci
>in the same circles of "educated" Europeans that Columbus was
>frequenting trying to get money at the same time. (c 1490)
Again we have a problem. Cardano was 18 when Da Vinci died.
Buck
J Stephen
Math Sci
NIU
J. B. Stephen (Buck)
In article <5vedcs$c...@fridge-nf0.shore.net>,
Steve Whittet <whi...@shore.net> wrote:
>Thats true, the government actually began to regulate commerce and
>Industry in 1560, so the report which influenced all three and the
>dramatic shift to Renaissance architecture is more likely to have
>been the report of Cardano c 1490.
Who do you mean here?
It's not Girolamo Cadano, he lived 1501-1576.
Steve Whittet
...
>Referring to the notion that such ostensibly anatomical measures as
>the palm and foot 'did not originate with the parts of the body' but
>'were mapped to the body as a grid', Steve says:
>>Actually its the subject of Vitruvious "Ten Books on Architecture".
>
>Vitruvius is hardly an authority on the history of these units. You
>mistake after-the-fact theorizing for history.
Vituvious is one of the best authorities we have.
Reporting at that early period he is far closer to the action
than we are.
His observation that the Roman measures came from the ancients
is accompanied by a discussion of where the ancients came up with their
standards and he discounts the idea that they came originally from
parts of the body. He does this by telling us where Greek and Roman
measures come from and what the Egyptians have told the Greeks and Romans
about the basis of their standards.
>>>>>(And definitions based directly on body parts occur
>>>>>remarkably late. In the 16th c. Master Koebel, a surveyor, wrote: 'On
>>>>>a certain Sunday as they happen to come out of church, bid sixteen men
>>>>>to stop, tall ones and short ones, .... 16 men shall stand in line
>>>>>with the left feet touching, one behind the other. This distance
>>>>>shall be the right and lawfull Rood and one-sixteenth of it shall be
>>>>>the foot.')
>
>>>>The Europeans of the Dark Ages and even some modern people tend not to
>>>>give much thought to what a standard of measure is and just how long
>>>>they have been around in essentially the same form.
>
>>>What on earth do the so-called Dark Ages have to do with 16th c.
>>>England?
>
>>By the 16th century much had been lost. People knew it and tried to
>>reconstruct things as best they could. "A Canticle for Leibowitz"
>>comes to mind.
>
>I burst out laughing when I read this. Please, Steve, take the time
>to read a little about at least the last 1000 years or so of Western
>European history. You seem to think that the 16th c. was part of what
>you are pleased to miscall the Dark Ages.
What I am saying is that when someone in the 16th century goes
looking for a standard of measure he doesn't find it because
it was lost in the Dark Ages between say 1095 and 1417.
After 1490 people begin trying to restablish what the standards
of measure were, but at first the best they can do is copy them.
They had no idea of the scientific principles which underly
them and indeed if you were to tell them what those principles are
in the most straightforward way imaginable they would simply have
been incredulous.
It isn't until the 17th and 18th century that people begin to think
about restablishing standards of measure based on invariable
natural constants.
> The term, which has for some time been out of favour amongst
>historians, traditionally covers no more than the period c.500 - c.1000.
That's One perspective, (based on the breakup of the Holy Roman Empire
after the death of Charlemagne). Another perspective considers that
Europe in terms of the degree of disruption was even worse off during
the period of the crusades, the black death, the hundred years war,
the invasion of the Mongols and the inquisition.
>In fact, by the end of the 16th c. most of what we know of Greek
>mathematics had already been recovered, and algebra had been taken
>further than ever before.
By the end of the 16th century European science was aproaching
comparable levels of sophistication to the science of the
ancient Greeks and Romans but had yet to catch up with some
of the details of the ancient Egyptian methodology.
One of my favorite texts on alchemy as science was published
around the time of the American Civil war. Chemistry and Physics
still rest their foundations and much of their terminology on the
work of medieval alchemists like Sir Isaac Newton.
Todays high school dropout, better educated than all but the most erudite
scholars of the middle ages, probably has a little less appreciation
of scientific principles than the average 16th century "puffer".
Carrying that backward, the most erudite scholars of the middle ages
probably had about the same appreciation of scientific principles as
the average Greek philosopher studying at the library in Alexandria.
Carrying that backward and comparing the Greeks of Alexandria to the
Egyptian scribes, I have to admit I find the scribes hold their own.
>=====
>
>>why would you measure a foot in palms?
>
>For the reason already given: to make large units integral multiples
>of smaller ones. (Don't try to tell me that you don't recognize the
>usefulness of such an arrangement: you've appealed to it in the past.)
>
>=====
>
>[Steve claimed '24835.36 miles' as a Greek value for the equatorial
>circumference of the earth.]
>
>>>Sheer silliness. They hadn't the instrumentation to measure the
>>>earth's circumference to the nearest 0.01 mile.
You have to deal with the data, you can't just blow it off.
The Greeks claim that 600 stadia of 600 feet are a degree.
That makes the claim that their foot = 1/29,600,000 the earths eq circ.
They make that claim so you can't say they are unaware of the concept.
Their foot used to define their talent and drachma is 308.4 mm
run the numbers for yourself.
The correct value is a foot of 309.24 mm, (24902.727 mi)
>
>>Suppose I stand on top of a pyramid and have two assistants stand
>>at the eastern and western horizon . I adjust their position with
>>signals until I can see one on the backsight of my observation of
>>the other.
>
>>Each uncovers a torch when he observes the sun rise and I call out
>>when I see the torches for another assistant to note the
>>difference in time with a water clock or sundial. My assistant
>>informs me it took 8 minutes
>
>You haven't persuaded me that this was possible. Remember, your view
>of history requires this determination at a very early date in order
>to set the sizes of linear measures. At such dates the Egyptian hours
>weren't constant, since they divided real day and night into 12 hours
>each, so any assumption that they were using constant minutes need a
>*lot* of justification.
I wouldn't expect you to ask for anything less.
>
>>I then have the distance between the two observers measured.
>>it works out that they were about 138 miles apart.
>
>You're assuming that a tangent 1 degree around the earth from your
>position passes through the top of your pyramid. The secant of 1
>degree exceeds 1.00015, and the radius of the earth exceeds 20,000,000
>ft., so your pyramid must exceed 3000 ft. in height. (This is over 6
>times the height of the GP.) At the very early date that your theory
>requires, where in Egypt are you going to find a tall enough tower?
I was simplifying, The Egyptians noted the rising and setting of the sun
in the mountains where differences in elevations exceed 3000 feet.
Had they wished they could have measured a shorter distance
from a lower elevation. basically the method is simple, accurate
and requires little in the way of technology.
>
>From a 500 ft. tower - a little more than the height of the Great
>Pyramid - the horizon should be about 27 mi. away. That makes them
>about 0.8 degrees apart, and you'd actually have to be able to measure
>an interval of 3.2 min.
They used both water clocks and sundials (The Great Pyramid was a big one)
Measurements of small divisions of time are really not that difficult to find,
The human pulse, pendulums, the drip of water or sand, musical rhythms, chants...
>
>=====
>
>>>Speaking of the fact that the earth is more nearly an ellipsoid than a
>>>sphere, Steve said:
>>>>You are assuming, I guess,that because Europeans didn't become aware
>>>>of this again until the late 17th century, the well documented
>>>>knowledge of this in antiquity can be dismissed.
>
>>>Produce the documentation.
>
>>Pythias measured the degree of latitude all the way from Marseilles
>>up to Iceland and noted how it decreased as he went north. You can read
>>about his studies in the commentaries of Strabo and Pliny.
>
>...I suspect that what Pytheas measured - if anything - was the size
>of a degree of *longitude*.
Latitude is an angular distance on the earths surface northward
or southward of the equator measured in degrees along a meridian.
The Equator is 0 degrees of latitude. On a map its a horizontal line
Longitude is vertical
Longitude was not measured by Pythias. His method was to time the
length of a day with an accurate sundial. As the days grew shorter
so did the circumference of each degree of latitude (even as the
angle of the degree of latitude from the equator increased)
Longitude is measured east and west from the prime meridian
through Greenwich. Since the earth is an oblate spheroid as
you approach the poles the radius of the arc of the circumference
of the degree of longitude inceases
>Its shrinkage would merely tend to confirm a spherical
>model. This has nothing to do with measuring the flattening at the
>poles, which is far too small to be measured by any instrumentation
>available to Pytheas.
A.) He was measuring Latitude, not Longitude
B.) He had constructed a highly accurrate sundial fully capable of
detecting the difference in the length of a day.
>
>=====
>
>[Steve claims that all of these features were intentionally
>incorporated in the dimensions of the GP:
>
>(A) the slope of 14/11, which is approx. 4/pi; (B) the amicable
>numbers 220 and 284; (C) the fact that the slant height was approx. 1
>stadion.]
>
>As I pointed out before, (A) and (C) together completely determine the
>dimensions of the pyramid. Once you settle on them, you have no
>choice about the size.
Except of course if you use a pyramidion to truncate the pyramid.
Then you have two sets of data to work with. This is what
Agarthachydes of Cygnus tells us the Egyptians did.
>At that point the height and half-side are
>given: either they give you a pair of amicable numbers, or they don't.
In this case they give a pair of amicable numbers 284 and 220
>The fact that they do (after you add an extra 4 cubits at the top) is
>a slightly fudged mathematical coincidence.
How do you fudge a coincidence?
The Egyptians built their pyramids with a pyramidion. We know from
their mathematical papyri that the worked with and calculated the
properties of truncated pyramids. We know from Agatharchydes that
the length of the Pyramid was 4'. (Other pyramids whose pyramidions
have been preserved show that they were indeed this size)
>In other words, while you might set out to accomplish all three goals,
>it's only an accidental peculiarity of the integers, helped along by
>those extra 4 cubits and the ratio of stadion to cubit, that allows
>you to do so.
Is that a coincidence?... or was their inclusion of the
pyramidion intentional do you think?
>There's no guarantee ahead of time that after you've accomplished
>(A) and (C), (B) will even be possible.
You miss the point. It was possible because it was accomplished.
To claim that as a mathematician you don't know how to set up the
"think of a number" problem which the Egyptians used to get all
these variables to align suggests they could do something you can't.
>If you wanted a different slope, or if the ratio of stadion
>to cubit were different, you couldn't achieve both
>(B) and (C) (along with your desired slope).
What you are saying is that not only did the Egyptians happen on
the only size and shape which would futhfill all these conditions,
they did it all by coincidence with no idea of what they were doing.
>
>It's clear from your response to my previous attempt that you didn't
>understand the point at all; if you show as little comprehension after
>this attempt, we might as well drop the matter, which I suspect falls
>in your intellectual blind spot.
My blind spot?
How many coincidences are we up to now? Lets see, we have Pi, Phi,
A face of 8 khet, the face equal to the square of the height,
an apothem 1 stadium in length, the stadium 1/600 degree,
amicable numbers, the base perimeter of the pyramidion equals
Pi royal cubits, its perimeter 4 2/3 English furlongs,
its height the length of an Egyptian year ...
>
>=====
>
>>>>>>>>The Greeks had an acre of 40,000 Greek feet
>
>>>>>>>You've made this unsupported assertion before. If they had such a
>>>>>>>measure, what did they call it?
>
>>>>The Ptolomaic Greeks used a term "schoenia" and or "aroura"
>>>>for the Egyptian arura, an area with a side of 100 cubits.
>
>>>Which isn't even close to the acre and does not measure 40,000 sq.
>>>ft., Greek or otherwise.
The acre = 43,560 English feet of 304.8 mm
The acre = 40,000 Greek feet of 332 mm
comparing to the Old English foot of 331 mm
and the Belgic foot of 332 mm (Greek aroura)
They are the same area
The 1/2 acre = 21780 English feet of 304.8 mm
The arura = 100 ordinary cubits of 17.71" on a side (1770/12")
>
>>It is 1/2 acre. In antiquity fields were associated in pairs
>>one of which was left fallow. The acre simply considers the
>>pair as one field and the measure remains the same.
>
>Even this contrived explanation fails.
Whats contrived about it?
>The Greek <aroura> was approx. equal to the Roman <iugerum>,
>and both were about 2/3 of an acre.
First off we are talking the Egyptian arura. Its value is 1/2 acre.
Any common multiple of that would show some likely association
Secondly I would like to see your cite for the value of the
Greek aroura. (I would be interested to see if your sources
trace back to Gardiner) Then I would like to know what makes
you think it was equal to the Roman jugerum.
>This is well-known and easily substantiated from a variety of sources.
>You still have not produced a Greek 'acre' of approx. 40,000 sq. ft.
Actually I have done so several times.
>
>>>(And you're confusing lengths and areas again.
>>> The 'schoenia' was a length, not an area, so it obviously was
>>>NOT a Ptolemaic Greek term for the Egyptian <arura>.
>
>>It is the length of the side of the arura...sheesh... Brian
>
>Then it isn't a term for the <arura>, which is what you originally
>said: 'The Ptolomaic Greeks used a term "schoenia" ... for the
>Egyptian arura'. Don't blame me for your verbal incompetence.
Brian, the Ptolomaic Greeks used the term 'Schoenia" to refer
to the side of the Egyptian arura. Why pretend you don't
understand this?
>
>=====
>
>>>[Steve made the hilarious claim that '(English) acre comes from
>>>(Latin)are or area which comes from (Greek)aroura which comes from
>>>(Egyptian) "a r u ra"'. I pointed out that <are> is a modern French
>>>neologism based on Latin <area> and that the other postulated
>>>derivations are simply wrong. Most of Steve's response merely
>>>confirms his ignorance of the subject (e.g., confusion of cognates
>>>with borrowings) and isn't worth comment, but some bits caught my
>>>attention.]
>
>>Brian admits the acre was borrowed
>
>Liar.
"Most of Steve's response merely confirms his ignorance of the subject
(e.g., confusion of cognates with borrowings)"
^^^^^^^^^^
>>but wants to weasel away
>>with another quibble. He claims it can't be a cognate even though
>>the spelling, pronunciation and meaning are virtually identical because
>>Egyptian isn't an Indo European language. That is simply foolish.
>
>No, it's not foolish; it's a matter of the definitions. A native
>Egyptian word and a native Greek word cannot have common ancestry,
>simply because the languages aren't related.
Who says its a native Greek word? A native Egyptian word "borrowed"
by the Greeks and made a part of their vocabulary is what we are
talking about here. The Greeks may have slightly Helenicized the
spelling and pronounciation but its anticedents remain quite
recognizable. It may be that it is more properly refered to as
code switching but where there is full integration as was the
case with the Greeks the element can be regarded as a borrowing.
>Therefore they cannot be cognate.
The word "cognate from Latin "cognatus"(born together) meaning
related by descent. "Unrelated languages may also have cognate items."
"Oxford Companion" p 289
>The only ways an Egyptian and a Greek word can be related
>are for one of them to be a borrowing from the other or for both to be
>borrowed from a third language. I take it that <arura> is native
>Egyptian.
Yes
> I could be wrong, but it appears to me that <aroura> is native Greek.
If what you wish to maintain is that the Greeks independently
invented the same word for the same thing, that flies in the face
of what the archaeologists have told us. (That the Ptolemaic
Greeks borrowed the word from the Egyptians) I think you are quite wrong.
>(Liddell-Scott-Jones appears to agree.) If that's the
>case, the words are unrelated, and their similarity is indeed
>coincidence.
Don't you ever get tired of using that word?
>The only other possibility is that <aroura> is a Greek
>borrowing, but in that case its apparent kinship with the Greek verb
>'to plow' is an equally surprising coincidence.
There is no coincidence involved. The Greeks simply took
the Egyptian word and its meaning together, lock stock and barrel.
Why does that suprise you?
>
>>He goes so far as to argue that if the Greeks had the same word
>>as the Egyptians the Egyptians must have got the word from the Greeks !!!!!
>
>No, Steve, that's not what I said. Only you could have so badly
>misunderstood. Go back and try again; I'll wait.
>derived from a Proto-Germanic *akraz,
>which in turn corresponds regularly to IE *agros, which is also
>represented by Latin <ager>, Greek <agros>, and Sanskrit <ajras>.
>(This is evidently a very old Indo-European word.)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Explain why Latin <ager>, Greek <agros>, and Sanskrit <ajras>
None of which is documented earlier than c 500 BC couldn't all
have been borrowed from Egyptian arura for which we have a
hieroglyphic going back to c 1800 BC
>
>I will not deal further with the word 'acre'. I've given you the
>correct information, which you could verify if you'd bother to learn a
>little historical linguistics. From this discussion and others in
>sci.lang it's apparent that you choose to remain ignorant, in effect
>denying that there is such a subject, so further discussion is a
>complete waste of time.
I will take it then that you accept the English acre is derived
from the Egyptian arura as I have demonstrated.
>
>=====
>
>>>>It wouldn't be hard to list several
>>>>dozen Egyptian or for that matter Sumarian words
>>>>which have come into English virtually unchanged.
>
>>>By all means do so, being sure to indicate when they entered English
>>>and in precisely what form.
>
>>Why not just go back and look at Saida list of tree words, there was
>>a whole thread on this some months ago Brian.
>
>It's your improbable claim, so the onus is on you to produce the
>evidence. Don't bother with Saida's compost.
I have since posted a number of these words, which we can deal with
as a separate thread if you wish. They really are not to hard to find.
>
>=====
>
>>>>>>The Greeks
>>>>>>tell us there are 600 feet in a stadium and 600 stadia in a degree.
>>>>>>Why isn't that a geocommensurate standard of measure?
>
>>>>>'The Greeks' isn't very specific. Eratosthenes reckoned 700 stades to
>>>>>a degree, and he was certainly Greek. A figure mentioned by Strabo,
>>>>>apparently accepted by Ptolemy, and still known (and influential) in
>>>>>the 15th c. corresponds to a value of 500 stades to a degree.
>
>>>>As I mentioned before, they took 600 stadia to a degree of latitude
>>>>and 500 stadia to a degree of longitude.
>
>>>So they thought that the earth was a prolate spheroid with its long
>>>axis through the poles, like an upright American football? I doubt it
>>>very much.
>
>>No, they used two different length feet !!!
>
>It must have been very awkward to have to use two sets of rulers, one
>for north-south dimensions and the other for east-west dimensions.
We still use the nautical mile in order to deal with longitude.
It is taken as 1/60 degree regardless of latitude.
The nautical mile at 8 stadia to a mile works out to
480 stadia to a degree and at 600 feet to a stadia
would have a foot the length of the Greek cubit.
>=====
>
>>The Egyptians welcomed the Greeks into their libraries as children
>>and attempted to teach them, as they would any young scribe, the
>>accumulated observations of several millenia. They taught the Greeks
>>medicine, law, philosophy, history, science, art, music and a respect
>>for the wisdom of the ages.
>
...snip
>
>Brian M. Scott
steve
Brian M. Scott
On 13 Sep 1997 21:15:22 GMT, bu...@shuksan.math.niu.edu (J. B. Stephen
(Buck)) wrote:
>2) Are there any known counting boards with
>good provenece from the Babylonians, Egyptians,
>Greeks or Romans. Any good quality reproductions
>or detailed descriptions with photographs?
>Anyone know of a good reference?
Try the Karl Menninger book on number words and symbols that I
mentioned in the number words thread. It has a long discussion of the
counting board and abacus in a variety of cultures. For obvious
reasons the most detailed information is on medieval use and design,
but I seem to remember some good pictures and discussion of Roman and
possibly Greek versions.
Brian M. Scott
William Wallace
On 12 Sep 1997 23:41:23 GMT, whi...@shore.net (Steve Whittet) wrote:
>In article <34187fce....@news.mindspring.com>, WWal...@freedom.orgв says...
>>>The wine gallon, which had existed for a long time previously
>>>was first made an official English measure by the decree of
>>>Queen Elizabeth at about the same time she changed the length
>>>of the mile to 5280 feet.
>> And what size might it be
>8 stadia of 600 feet (the distance between Roman mileposts)
Which of the three different gallons are you talking about?
Alan M. Dunsmuir
In article <5vf3ei$3...@fridge-nf0.shore.net>, Steve Whittet
<whi...@shore.net> writes
>We still use the nautical mile in order to deal with longitude.
>It is taken as 1/60 degree regardless of latitude.
>The nautical mile at 8 stadia to a mile works out to
>480 stadia to a degree and at 600 feet to a stadia
>would have a foot the length of the Greek cubit.
This is the utmust rubbish. (I say this as an active aviator, who uses
nautical miles, and their relationship to degrees of latitude and
longitude, every day.)
1 nautical mile is defined as one minute of LATITUDE, measured along a
great circle. Because of the non-sphericalness of the earth, this
measure actually varies by up to 62 feet, depending on the latitude at
which it is taken, and so was 'standardised' by the Admiralty to be
6080ft. For most practical navigational purposes a nautical mile equates
to 1 minute of latitude anywhere, but the length of 1 minute of
LONGITUDE is strongly dependent on the latitude in question (it shrinks
to zero at the poles) and is related to the nautical mile by the
equation:
1 minute of longitude = 1 nautical mile x cos(latitude)
Brian M. Scott
[Follow-ups set to soc.history.medieval.]
On 13 Sep 1997 15:51:18 GMT, whi...@shore.net (Steve Whittet) wrote:
>>>We are told that Columbus (1492)
>>>actually has to convince people the world is round.
>>I thought that by now that myth had been eradicated even from grade
>>school texts. No *educated* person in late-15th c. Europe doubted
>>that the world was round.
>By the way, what would you say the proportion of "educated"
>people to uneducated illiterate believers was in late-15th c. Europe?
Not particularly germane to Columbus's efforts to win support for his
scheme. He wasn't dealing with the uneducated.
=====
>>>It is true that people who came in contact with the arabs
>>>during the crusades learned something about how much
>>>knowledge had been lost, (or suppressed)
>>On the contrary, it was through Spain that most of what the Arabs had
>>preserved came to Europe. It's well known that in 12th c. Toledo the
>>translation of scientific works from Arabic and Greek into Latin was
>>almost an industry.
>What? Spain wasn't a participant in the Crusades? Spain had been
>fighting against and learning from the infidel longer than anyone.
'At Toledo Arabs, Jews and Greeks worked with Spaniards, Frenchmen and
Germans, with Slavs from the Balkans and, last but not least, with
Englishmen.' (F. Heer, _The Medieval World_) This was a genuinely
cosmopolitan community, irrespective of what may have been going on to
the south and east.
>The leading proponents of making the translations were alchemists
>closely followed by gnostics, cathars and heretics; people the
>Spanish made serious efforts to exterminate in their inquisition.
The leading patron of the Toledan school of translators was Don
Raimundo, who was Archbishop of Toledo and primate of Spain for the
second quarter of the 12th c.; so important was his support that he is
often credited with founding it. His chief assistant was the
archdeacon of Segovia. Catharism didn't appear in Western Europe
until c.1140.
>>>>The real loss had occurred many centuries earlier after the
>>>>western Roman empire fell apart.
>>>No, the real loss occured when the church discouraged the
>>>teaching of anything which disagreed with its tenets.
>>From John H. Mundy, _Europe in the High Middle Ages, 1150/1309_:
>>'Because most thinkers of [the 13th c.] assumed that man's natural
>>reason was capable of comprehending some part of the cosmos and even
>>of glimpsing the nature of the divine principle itself, knowledge was
>>almost idolized.
>Note that the phrase "most thinkers" limits the set to the range
>of cathers, gnostics, infidels and heretics as far as the church
>was concerned.
More comic-book history. The quotation was in reference to CLERICAL
intellectuals. Aquinas himself had taught that 'it is impossible that
those things which are of philosophy can be contrary to those things
which are of the faith'. I repeat the quotation from Mundy: 'The
*magistri* or *divini* of the thirteenth century enjoyed a real
measure of autonomy and rarely had their opinions suppressed by the
REST of the Church and society.' [The * indicates his italics; u.c.
emphasis is mine.]
>That was true so long as the Templars wielded influence with the church
The Templars were, more or less in chronological order, a military
force, a diplomatic and political force, and an economic force (as
international bankers); why do you imagine that they took significant
interest in the 13th c. magistri?
>In that period from 1095 to 1492 most people thought about
>little else besides staying alive.
I imagine that one could safely make the same statement about the
entire period in which the human race has existed.
>>>During the Middle Ages most people were confirmed Ludites.
>>Most people were subsistance peasants who probably didn't care. And
>>the term 'Luddite' makes no sense in a non-industrial era.
>What makes you think it was a "non-industrial era"
The fact that it was. Medieval use of certain kinds of machinery does
not qualify the English Middle Ages as an industrial era (unless, of
course you have your own definition of 'industrial era' to go with
your definition of 'Dark Ages').
> The problem was that
>if a man built a mill and didn't ask his Bishops permission first
>the Bishop would have it torn down.
What kind of man? When? Where? (And why bishop? On a 13th c.
English manor, say, the issue was one of manorial economics: the mill
was a significant source of revenue, so it's natural that the lord
would not have wanted competition, but it's also true that in general
only the lord had the resources necessary for the mill's continuous
upkeep. The Church had nothing to do with the matter unless the manor
happens to be Church property.)
=====
>>> Science was equated with witchcraft, alchemy, sorcery, thaumaturgy,
>>>necromancy or worse. You could get burned at the stake
>>>just for knowing how to read.
>>Comic-book history. It appears that in late-14th and 15th c. London
>>about 40% of the male witnesses who gave evidence in the consistory
>>court had some ability to read Latin. These included braziers,
>>cappers, grocers, pewterers, shearmen, and tailors, among others.
>Late 14th century is after the time of troubles is over.
This simply isn't true. For starters, the Hundred Years War was still
in progress. Population would continue to decline for another
half-century or more.
>Your representative sample of the population appears to include
>only townspeople.
I don't believe that I suggested that it was representative; it
obviously was not, since it fails to include clergy, lawyers, lay
schoolmasters, physicians, etc. It is also an urban sample, so of
course it excludes the rural population. But it doesn't need to be
representative to refute your contention: it's obvious that a great
many people knew how to read and were in no danger of being burned at
the stake on that account. It's also obvious that many of these
people were not of the aristocracy.
>>Rather earlier, the early 14th c. Florentine chronicle of John Villani
>>reported that 8,000 to 10,000 boys and girls were learning to read and
>>write in Florence; 1000 to 1200 students, he says, attended 6 abacus
>>schools to learn arithmetic and business; and 4 great grammar schools
>>housed 550-600 students of Latin and logic.
>So at its most prosperous, Florence with a population in the
>hundreds of thousands provided for the chindren of its 500
>most wealthy and influential merchant families to be tutored
>for a year.
The same chronicler estimated the population of Florence at 90,000
before the plague; this is probably a bit of an over-estimate. There
wasn't a city in Europe with a population of 'hundreds of thousands'
in the early 14th c.; I doubt that any even reached 100,000.
>Compare this to ancient Egypt where a large part of the population
>was literate, able at the very least to read the inscriptions
>proclaiming the attributes of the gods and glory of the rulers,
>considered it of critical importance for their children to get an
>education, and gave over their children willingly to be trained
>as scribes knowing the scribes training could last a lifetime.
With some reservations about the actual level of literacy this accords
reasonably well with what I've read about the Middle Kingdom; the Old
Kingdom is another matter.
>>His specific numbers may be questioned, but he's obviously not
>>describing a culture in which reading was unusual.
>I would disagree. If only 1 in 1000 of the citizens in Europes
>most prosperous and culturally aware city could read at the
>grammar school level, what does that tell us about litteracy
>gennerally?
Your hypothesis is obviously false: 1/1000 of 90,000 is 90, which
probably barely accounts for the teachers alone. You may also be
misunderstanding 'grammar school', which meant something quite
different from what it means today: the term refers to a secondary
school whose curriculum overlapped with that of the university.
=====
>> Bonvesino of Riva, a teacher, says that Milan
>>had about 70 teachers of elementary letters and 8 professors of
>>grammar in 1288. Earlier yet, a residential college for poor students
>>was founded in Paris in 1180. (Mundy, 464-5)
>70 teachers with perhaps twelve students each gives us 840 students
>in Milan, another extremely rich city with a large population.
>What this is telling us is that only the children of the
>most privledged upper classes were being taught anything.
Then how do you explain the colleges founded specifically for POOR
students and the fact that a great many students were extremely poor?
Obviously the children of the upper classes were likelier to receive
more education, but the idea that no one else had access to education
is demonstrably false.
=====
>>>Trade guilds jealously guarded their secrets of building technology
>>>and industry.
>>Of course. In this they were protecting their livelihoods. They were
>>also following an ancient model. Harvey mentions a cuneiform tablet
>>(17th c. BCE) that was eventually found to contain the formula for an
>>excellent glaze for earthenware: it was hidden in an elaborate
>>cryptogram. The secret was apparently kept pretty well, since it
>>isn't until 1000 years later that knowledge of the glaze seems to be
>>widespread.
>Yes, we are agreed; that knowledge during the middle ages was
>not considered the provence of the masses, was limited to
>business and profesional skills, was considered complete
>when a person could read their own name or count to ten,
>and even that amount of education was considered a
>dangerous secret to be kept to oneself on pain of death.
No, we are not agreed. Knowledge of this kind has rarely been the
province of the masses; the Middle Ages weren't unusual in this
respect. It's quite obvious from the facts of medieval commerce that
business and professional skills in many businesses and professions
went far beyond your limited notion of literacy. Primary education at
least to the level you describe, far from being a dangerous secret,
was widely available, very often from clerics.
=====
>>>Sea Captains hid away their charts and People took
>>>a doctorate at Oxford to learn how to do fractions.
>>The ordinary fractions associated with commerce were widely taught,
>>not just in formal schools but also to apprentices in a number of
>>occupations.
>Gillings says that "in English speaking countries as late as the
>sixteenth century it was not part of the school curriculum to
>learn any multiplication tables at all."
Multiplication tables aren't fractions. There was no need to learn
multiplication tables: the counting board was still in widespread use.
It's an extremely effective computational device whose use does not
require memorization of the multiplication tables. With just a little
practice it is as fast as the usual pencil and paper algorithms; in
the hands of an experienced user it's on a par with the pocket
calculator.
Brian M. Scott
Brian M. Scott
On 13 Sep 1997 22:17:54 GMT, whi...@shore.net (Steve Whittet) wrote:
>What I am saying is that when someone in the 16th century goes
>looking for a standard of measure he doesn't find it because
>it was lost in the Dark Ages between say 1095 and 1417.
This is contradicted by the existence of royal edicts setting
standards of measure during that period. In 14th c. England standard
measures were available for purchase. Building contracts often
contained rather precise specifications of the required dimensions.
=====
>> The term [Dark Ages], which has for some time been out of favour amongst
>>historians, traditionally covers no more than the period c.500 - c.1000.
>That's One perspective, (based on the breakup of the Holy Roman Empire
>after the death of Charlemagne). Another perspective considers that
>Europe in terms of the degree of disruption was even worse off during
>the period of the crusades, the black death, the hundred years war,
>the invasion of the Mongols and the inquisition.
The fact remains that the term does not refer to the 14th c. If you
use it with that meaning, you will be misunderstood unless you go on
to explain yourself. It's easier to use it correctly, if you must use
it at all.
=====
[Steve claimed '24835.36 miles' as a Greek value for the equatorial
circumference of the earth.]
>>>>Sheer silliness. They hadn't the instrumentation to measure the
>>>>earth's circumference to the nearest 0.01 mile.
>>>Suppose I stand on top of a pyramid and have two assistants stand
>>>at the eastern and western horizon . I adjust their position with
>>>signals until I can see one on the backsight of my observation of
>>>the other.
>>>Each uncovers a torch when he observes the sun rise and I call out
>>>when I see the torches for another assistant to note the
>>>difference in time with a water clock or sundial. My assistant
>>>informs me it took 8 minutes
>>You haven't persuaded me that this was possible. Remember, your view
>>of history requires this determination at a very early date in order
>>to set the sizes of linear measures. At such dates the Egyptian hours
>>weren't constant, since they divided real day and night into 12 hours
>>each, so any assumption that they were using constant minutes need a
>>*lot* of justification.
>I wouldn't expect you to ask for anything less.
Are you going to offer any?
>>>I then have the distance between the two observers measured.
>>>it works out that they were about 138 miles apart.
[I pointed out that this would require a tower over 3000 ft. tall.]
>I was simplifying, The Egyptians noted the rising and setting of the sun
>in the mountains where differences in elevations exceed 3000 feet.
So you need an elevation of at least 3000 ft. from which the eastern
and western horizons are visible and lie at sea level. Where?
You've also neglected to account for latitude.
=====
Speaking of the fact that the earth is more nearly an ellipsoid than a
sphere, Steve said:
>>>>>You are assuming, I guess,that because Europeans didn't become aware
>>>>>of this again until the late 17th century, the well documented
>>>>>knowledge of this in antiquity can be dismissed.
>>>>Produce the documentation.
>>>Pythias measured the degree of latitude all the way from Marseilles
>>>up to Iceland and noted how it decreased as he went north. You can read
>>>about his studies in the commentaries of Strabo and Pliny.
>>...I suspect that what Pytheas measured - if anything - was the size
>>of a degree of *longitude*.
>Latitude is an angular distance on the earths surface northward
>or southward of the equator measured in degrees along a meridian.
>The Equator is 0 degrees of latitude. On a map its a horizontal line
>Longitude is vertical
This is true. In your last post, however, you were confused,
explicitly identifying latitude as longitude ('Moving north from the
equator As we increase our Longitude the value of a degree of Latitude
decreases'). That is one reason I doubted your statement.
>Longitude was not measured by Pythias. His method was to time the
>length of a day with an accurate sundial. As the days grew shorter
>so did the circumference of each degree of latitude (even as the
>angle of the degree of latitude from the equator increased)
The phrase 'circumference of each degree of latitude' makes no sense.
I suspect that you're trying to say that as he went north, the circles
of constant latitude got smaller. That is certainly true; and what it
means is - as I said - that a degree of longitude is shorter at higher
latitudes.
Knowing the number of hours of daylight at midsummer allows one to
determine one's latitude, though you've inverted the relationship: at
higher latitudes the maximum number of hours of daylight *increases*.
Using the nr. of hrs. of daylight to estimate one's latitude at any
time of year except midsummer or midwinter would be a much more
difficult mathematical problem, and doing so at either equinox would
be impossible. Observations of the altitude of the sun at noon would
be much more useful in determining latitude.
It's not clear just what method you're proposing, since you seem to be
describing a phenomenon that doesn't exist. Perhaps a sample
calculation showing how you think that Pytheas might have obtained the
length of a degree of latitude would clarify matters.
=====
>>>>>>>>>The Greeks had an acre of 40,000 Greek feet
>>>>>>>>You've made this unsupported assertion before. If they had such a
>>>>>>>>measure, what did they call it?
>>>>>The Ptolomaic Greeks used a term "schoenia" and or "aroura"
>>>>>for the Egyptian arura, an area with a side of 100 cubits.
You have quoted Gillings as follows: 'The linear length of 100 royal
cubits was called a schoenia in the time of the Ptolomies.') You have
also said: 'The same relationship as existed between khet and setat
existed between schoenia and arura. The length of the side is the khet
or schoenia; the area is the setat or arura.' A square 1 schoenia -
100 *royal* cubits - on a side has an area of about 2/3 of an acre.
=====
>>>Brian admits the acre was borrowed
>>Liar.
>"Most of Steve's response merely confirms his ignorance of the subject
>(e.g., confusion of cognates with borrowings)"
> ^^^^^^^^^^
I have no idea what you think you're getting at here. If you will
re-read what I have said about the word <acre>, you will not find any
statement that it was borrowed. (To be completely accurate, I did say
that the English word was borrowed *into* medieval Latin as <acra>; I
did not say that the English word was borrowed *from* anywhere.)
Indeed, I have several times pointed out that <acre> is cognate with
Lat. <ager> and Gk. <agros> but *not* a borrowing of either.
=====
>I will take it then that you accept the English acre is derived
>from the Egyptian arura as I have demonstrated.
As you like; it's not the first demonstrable falsehood that you've
accepted.
Brian M. Scott
Steve Whittet
In article <341b411f....@news.mindspring.com>, WWal...@freedom.org/ says...
>
>On 12 Sep 1997 23:41:23 GMT, whi...@shore.net (Steve Whittet) wrote:
>
>>In article <34187fce....@news.mindspring.com>, WWal...@freedom.orgв sa
>ys...
>
>>>>was first made an official English measure by the decree of
>>>>Queen Elizabeth at about the same time she changed the length
>>>>of the mile to 5280 feet.
>
>>> And what size might it be
>
>>8 stadia of 600 feet (the distance between Roman mileposts)
>
First off liquid measures of alcohol revolve around the pint. They are
part of a doubling system listed in the Barley Mow (a drinking song)
The gallon of 231 cu" is just 8 wet pints
The pint is 20 ounces 28.875 cu"
The 1/2 pint 10 ounces
The 1/4 pint or Jack is 5 ounces
The 1/8 pint or Jock is 2 1/2 ounces
The 1/16 pint or Joey is a shot of 1 1/4 ounces
The ounce goes back to the Greek and Roman division by 1/16 ths
of the Libra, a pound of 16 oz, 16/20 of the pound based on the foot
because it was based on the volume whose side was the linear measure
of the pes.
The pint comes in both dry and liquid measure
Double the wet pint is the guart 57.5 cu"
quadruple the quart is the gallon 321 cu"
=========================================
The Imperial gallon is a division of the bushel
1 bushel is 4 buckets, 16 Imperial gallons, 66 dry pints
1 bucket is 4 Imperial gallons
1 Imperial gallon is 277.42 cu " making it the Egyptian
Hekat or corn measure which has a side of the royal cubit/Pi
using a recognized Egyptian value of 256/81 for Pi
this gives a value of 20.613" for the Royal cubit
The Biblical homer is 120 US or 100 Imperial gallons
a volume with a side of 1/2 pace or 30"
The Biblical lethech is 60 US or 50 Imperial gallons
a volume with a side of 2 feet or 24"
A cubic royal Egyptian cubit is 38 US gallons or 31 2/3 Imperial gallons
a volume with a side of 1 royal Egyptian cubit of 20.63"
A cubic remen is 30 US gallons or 25 Imperial gallons
a volume of with a side of 19"
A cubic cubit of 24 US gallons is 20 Imperial gallons
a volume with a side of 1 ordinary Egyptian cubit of 17.7"
A Roman remen of 15 US gallons is 12 1/2 Imperial gallons
a volume with a side of 1 Egyptian remen of 15.13"
A Biblical bath or epath is 12 US gallons or 10 Imperial gallons.
A Biblical metrette is 10 4/5 US gallons 9 Imperial gallons making
it the cube with a side twice the side of the Hekat, 13 9/16"
A measure of 7.5 US gallons is 6 1/4 Imperial gallons
a volume with a side of 1 foot of 12"
A measure of 7 US gallons is 5 6/7 Imperial gallons
a volume with a side of 1 pes of 11.7"
The Biblical seah is 4 US or 3 1/3 Imperial gallons.
a volume with a side of 1 guarter (yard) 9.13"
The measures all agree in length and volume so its
fair to say its all part of one consistent system
with the volumes the cube of unit lengths
==================
1 quartern is 1/2 imperial gallon
1 quartern is 16 noggins
2 bushels is a strike
3 bushels is a sock (Egyptian sack)
4 bushels is a coomb
1 barrel is 36 Imperial gallons
1 seam is 8 bushels
1 butt is 126 Imperial gallons
1 chaldron is 32 bushels
1 wey is the cube 26 royal cubits or 30 ordinary cubits on a side
1 puncheon is 70 Imperial gallons
1 register ton is 100 cubic feet
1 last is 80 bushels
1 rod is 1000 cu feet.
Basically what we have is a system used by farmers to measure
units of bread and beer which is the same today as it was
five millenia earlier, and is based on essentially the same
naturaly invariant standard, the circumference of the earth,
as was adopted by the French for the metric system.
steve
Steve Whittet
In article <5vf09c$h36$1...@gannett.math.niu.edu>, bu...@shuksan.math.niu.edu says...
Good catch.
The Girolamo Cardano in question, did live 1501 -1576
a Milanese physician and Mathematician, he was a close
friend of Leonardo Da Vinci (1452-1519) apparently when
he was a young man and Leonardo was getting on in years.
That would mean that his reference to ancient traditions
as indicating the Great Pyramid incorporated an
earth commensurate unit of measure would have come
later than I expected, after Columbus but shortly
before the English government began doing away with the ancient
guild standards in favor of a geocommensurate redefinition c 1560
>
>Buck
>
>J Stephen
steve
Steve Whittet
In article <5vevpa$h13$1...@gannett.math.niu.edu>, bu...@shuksan.math.niu.edu says...
>
>In article <5vecpm$c...@fridge-nf0.shore.net>,
>Steve Whittet <whi...@shore.net> wrote:
>>
>>Yes, I have seen three or four royal rulers which differ among other things,
>>in the number of fingers which are subdivided. I don't know how many
>>there are total but my quess would be its somewhere in the hundreds
>>though most are nowhere near as fancy.
>>
>
>
>1) Where can I find the best examples of Egyptian
>rulers.
One of the better ones is presently at the Museum of Turin.
I believe some are listed in Flinder Petries Book
"Ancient Weights and Measures", London, University College, 1926
>
>2) Are there any known counting boards with
>good provenece from the Babylonians, Egyptians,
>Greeks or Romans. Any good quality reproductions
>or detailed descriptions with photographs?
A number of counting boards seem to have developed
into board games such as senet, cribbage, chess and go.
There is an interesting illustration on page 129 of
The Atlas of Cultural Mesopotamia showing a round
disk divided into 13 parts by a series of crenalated
castles around the perimeter. Each castle has 4 holes.
Inside the outer ring of holes there is an additional
ring of 52 holes. The circle is divided into 4 quadrants
with illustrations of the activities associated with
the different seasons.
Perhaps a calander of 13 months with 4 weeks of seven days
totaling 52 weeks it comes from the palace of Asherbanipal
dating c 883-859 BC
Another possible system of calculation involving unit
fractions was the set of weights and scales.
>I have seen light discussions of these topics,
>and remember that Roman counting boards were
>grooved.
>
>Anyone know of a good reference?
>
>
>Thanks,
>
>Buck
>
>J Stephen
steve
Steve Whittet
In article <5vf0lv$h58$1...@gannett.math.niu.edu>, bu...@shuksan.math.niu.edu says...><whi...@shore.net> writes
>>Cardano thought that perhaps the pyramids had been built to record the
>>dimensions of the earth and furnish an imperishable standard of linear
>>measure.
>
>>He was presenting these ideas as a friend of Leonardo Da Vinci
>>in the same circles of "educated" Europeans that Columbus was
>>frequenting trying to get money at the same time. (c 1490)
>
Yes, you are correct and I was mistaken. His ideas would not have
influenced Columbus although the ideas which did influence Columbus
might have influenced him as well.
>
>Buck
>
>J Stephen
steve
William Wallace
On 14 Sep 1997 13:49:47 GMT, whi...@shore.net (Steve Whittet) wrote:
>In article <341b411f....@news.mindspring.com>, WWal...@freedom.org/ says...
>>
>>On 12 Sep 1997 23:41:23 GMT, whi...@shore.net (Steve Whittet) wrote:
>>
>>>In article <34187fce....@news.mindspring.com>, WWal...@freedom.orgв sa
>>ys...
>>
>>>>>The wine gallon, which had existed for a long time previously
>>>>>was first made an official English measure by the decree of
>>>>>Queen Elizabeth at about the same time she changed the length
>>>>>of the mile to 5280 feet.
>>
>>>> And what size might it be
>>
>>>8 stadia of 600 feet (the distance between Roman mileposts)
>>
>> Which of the three different gallons are you talking about?
>
>First off liquid measures of alcohol revolve around the pint. They are
>part of a doubling system listed in the Barley Mow (a drinking song)
>The gallon of 231 cu" is just 8 wet pints
Which of the three different gallons are you talking about?
=====
D. Spencer Hines
Alan M. Dunsmuir wrote:
>
> In article <5vi7mv$3...@fridge-nf0.shore.net>, Steve Whittet
> <whi...@shore.net> writes
> >As we move north from the Equator the earth flattens increasing
> >the radius of the arc of longitude. As we increase the radius
> >of the arc of the degree of longitude the radius of the degree
> >of latitude decreases, though not in a linear way.
>
> Sheer meaningless and brain-dead nonsense. (Steve really ought to
> consider investing in a remedial numeracy course.)
> --
> Alan M. Dunsmuir
>
> Were diu werlt alle min von deme mere unze an den Rijn
> des wolt ih mih darben,
> daz diu chunigen von Engellant lege an minen armen!
>
You do have a way with the Queen's English.
--
D. Spencer Hines --- "Non nobis, Domine, non nobis, sed Nomini Tuo da
gloriam, propter misericordiam Tuam et veritatem Tuam." Henry V,
[1387-1422] King of England --- Ordered it to be sung by his prelates
and chaplains --- after the Battle of Agincourt, 25 Oct 1415, --- while
every able-bodied man in his victorious army knelt, on the ground.
[Psalm CXV, Verse I]
Peter Szabo
Brian M. Scott wrote:
>On Wed, 10 Sep 1997 11:20:15 GMT, pet...@uniserve.com (Peter Szabo)
>wrote:
>>Brian M. Scott wrote:
>>The term is "arvum" not "aruum". It is pronounced "arwum".
>
>I know. (That's what happens when you've been staring at accurate
>transcriptions of names from medieval Latin rolls. When I'm in a
>hurry, I tend to write <v> initially and <u> everywhere else.)
I can see it. :) I wish I had that good of an excuse for writing
"Iberian Peninsula" earlier.
>> I am
>>suggesting that the w sound derives from the strong Greek r sound.
>>Indeed this part of the word could sound identical. The m ending in
>>the nominative could have come from excessive use of the accusative
>>form, perhaps being read aloud in the context of taxes.
>
>Eh? It's just the neuter adjective <arvus, -a, -um> 'ploughed' used
>as a substantive. I'm no Latinist, but I believe that the adjective
>is a straightforward verbal adjective in -vus/-uus, like <pascuus>
>'for pasture' from <pascere> 'to feed, lead to pasture'. This seems
>to be a regular formation; there's no need for an ad hoc explanation.
I was referring to the noun Arvum, -i nt field, land, country, plain
It ends in -um in the nominative, which seems irregular to me but I
could be wrong.
Peter Szabo.
Realms of Archaea--------> http://users.uniserve.com/~peters5/zoomquk4.html
zoomQuake!---------------> http://users.uniserve.com/~peters5/
"The fool doth think he is wise, but the wise man knows himself to be a fool."
Steve Whittet
In article <341bbdeb...@news.csuohio.edu>, sc...@math.csuohio.eduв says...
>
>On 13 Sep 1997 22:17:54 GMT, whi...@shore.net (Steve Whittet) wrote:
>
>>What I am saying is that when someone in the 16th century goes
>>looking for a standard of measure he doesn't find it because
>>it was lost in the Dark Ages between say 1095 and 1417.
>
>This is contradicted by the existence of royal edicts setting
>standards of measure during that period.
Thats just it. The Royal edicts can be anything from the
shoes sizes of the first 16 men out of church in the morning
to king Athelsthanes girth. barley corns are not geocommensurate.
>In 14th c. England standard measures were available for purchase.
Yes, the guild halls kept pretty good standards for a while
In England by 1560 they were all lost.
>Building contracts often contained rather precise specifications
>of the required dimensions.
That's why people measure buildings to determine what value was used
for the foot or pes or cubit they were built with.
>
>=====
>
>>> The term [Dark Ages], which has for some time been out of favour amongst
>>>historians, traditionally covers no more than the period c.500 - c.1000.
>
>>That's One perspective, (based on the breakup of the Holy Roman Empire
>>after the death of Charlemagne).
"The History of Art" has a similar definition but notes that that
the length of the period has been generally decreasing in recent
years. Now that we have aquired a somewhat belated appreciation
of Gothic art and architecture that may be the case in those areas.
From a scientific perspective things are a little different.
> Another perspective considers that
>>Europe in terms of the degree of disruption was even worse off during
>>the period of the crusades, the black death, the hundred years war,
>>the invasion of the Mongols and the inquisition.
>
>The fact remains that the term does not refer to the 14th c.
I would still carry it forward to include the schism of the
catholic Church in 1417. The political paranoia of the clergy
as the schism approached must have made the slightest deviation
in thinking suspect.
>If you use it with that meaning, you will be misunderstood unless
>you go on to explain yourself. It's easier to use it correctly,
>if you must use it at all.
I have never considered myself constrained by what's easier.
>
>=====
>
>[Steve claimed '24835.36 miles' as a Greek value for the equatorial
>circumference of the earth.]
>
>>>>>Sheer silliness. They hadn't the instrumentation to measure the
>>>>>earth's circumference to the nearest 0.01 mile.
>
>>>>Suppose I stand on top of a pyramid and have two assistants stand
>>>>at the eastern and western horizon . I adjust their position with
>>>>signals until I can see one on the backsight of my observation of
>>>>the other.
>
>>>>Each uncovers a torch when he observes the sun rise and I call out
>>>>when I see the torches for another assistant to note the
>>>>difference in time with a water clock or sundial. My assistant
>>>>informs me it took 8 minutes
>
>>>You haven't persuaded me that this was possible. Remember, your view
>>>of history requires this determination at a very early date in order
>>>to set the sizes of linear measures. At such dates the Egyptian hours
>>>weren't constant, since they divided real day and night into 12 hours
>>>each, so any assumption that they were using constant minutes need a
>>>*lot* of justification.
>
>>I wouldn't expect you to ask for anything less.
>
>Are you going to offer any?
As I pointed out small increments of time can be counted with
a human pulse, a water clock, a sand timer, a sundial, even
a rhythmic chant, "one thousand one, one thousand two..."
>
>>>>I then have the distance between the two observers measured.
>>>>it works out that they were about 138 miles apart.
>
>[I pointed out that this would require a tower over 3000 ft. tall.]
>
>>I was simplifying, The Egyptians noted the rising and setting of the sun
>>in the mountains where differences in elevations exceed 3000 feet.
>
>So you need an elevation of at least 3000 ft. from which the eastern
>and western horizons are visible and lie at sea level. Where?
Only if you want to measure a full two degrees at one hit.
Suppose, just for the sake of argument that I stand on top of Mt Sinai
(Gebel Musa is 2285 meters or 7497 feet)and look across the Red sea
to Ras Garib and across the mouth of the Gulf of Aquaba to Al Bad
both of which are beaches 138 miles apart on an east-west line
along latitude 27.5 degrees.
>
>You've also neglected to account for latitude.
Latitude 27.5 degrees, about the same as Al Minya on the Nile
>
>=====
>
>Speaking of the fact that the earth is more nearly an ellipsoid than a
>sphere, Steve said:
>>>>>>You are assuming, I guess,that because Europeans didn't become aware
>>>>>>of this again until the late 17th century, the well documented
>>>>>>knowledge of this in antiquity can be dismissed.
>
>>>>>Produce the documentation.
>
>>>>Pythias measured the degree of latitude all the way from Marseilles
>>>>up to Iceland and noted how it decreased as he went north. You can read
>>>>about his studies in the commentaries of Strabo and Pliny.
>
>>>...I suspect that what Pytheas measured - if anything - was the size
>>>of a degree of *longitude*.
>
>>Latitude is an angular distance on the earths surface northward
>>or southward of the equator measured in degrees along a meridian.
>>The Equator is 0 degrees of latitude. On a map its a horizontal line
>>Longitude is vertical
>
>This is true. In your last post, however, you were confused,
>explicitly identifying latitude as longitude ('Moving north from the
>equator As we increase our Longitude the value of a degree of Latitude
>decreases'). That is one reason I doubted your statement.
As we move north from the Equator the earth flattens increasing
the radius of the arc of longitude. As we increase the radius
of the arc of the degree of longitude the radius of the degree
of latitude decreases, though not in a linear way.
>
>>Longitude was not measured by Pythias. His method was to time the
>>length of a day with an accurate sundial. As the days grew shorter
>>so did the circumference of each degree of latitude (even as the
>>angle of the degree of latitude from the equator increased)
>
>The phrase 'circumference of each degree of latitude' makes no sense.
>I suspect that you're trying to say that as he went north, the circles
>of constant latitude got smaller. That is certainly true; and what it
>means is - as I said - that a degree of longitude is shorter at higher
>latitudes.
The distance between meridiens is less.
>Knowing the number of hours of daylight at midsummer allows one to
>determine one's latitude, though you've inverted the relationship: at
>higher latitudes the maximum number of hours of daylight *increases*.
Yes, however the length of a day also varies with the time of year.
Moving north as the day decreased in length due to the seasons
Pythias was able to observe the increase in length due to the
change in latuitude.
>Using the nr. of hrs. of daylight to estimate one's latitude at any
>time of year except midsummer or midwinter would be a much more
>difficult mathematical problem,
It was a difficult mathematical problem, however Pythias not only
solved it in theory he put it to the test by building a very accurate
sundial and sailing north.
>and doing so at either equinox would be impossible. Observations of
>the altitude of the sun at noon would be much more useful in determining latitude.
Perhaps, Pythias made a lot of observations, charting coastlines
and describing the people and places he visited. To be honest I
don't remember if he shot the sun at noon with his astrolab or not.
Its invention didn't much precede him as I recall.
>It's not clear just what method you're proposing, since you seem to be
>describing a phenomenon that doesn't exist. Perhaps a sample
>calculation showing how you think that Pytheas might have obtained the
>length of a degree of latitude would clarify matters.
As I recall he noted the time of the rising and the setting of the sun
at the latitude of Marseilles for a year, then compared the time of day
the sun rose and set for each day of the year as he went north and he
also took note of how far he had travelled according to his ships log.
>
>=====
>
>>>>>>>>>>The Greeks had an acre of 40,000 Greek feet
>
>>>>>>>>>You've made this unsupported assertion before. If they had such a
>>>>>>>>>measure, what did they call it?
>
>>>>>>The Ptolomaic Greeks used a term "schoenia" and or "aroura"
>>>>>>for the Egyptian arura, an area with a side of 100 cubits.
>
>You have quoted Gillings as follows: 'The linear length of 100 royal
>cubits was called a schoenia in the time of the Ptolomies.') You have
>also said: 'The same relationship as existed between khet and setat
>existed between schoenia and arura. The length of the side is the khet
>or schoenia; the area is the setat or arura.' A square 1 schoenia -
>100 *royal* cubits - on a side has an area of about 2/3 of an acre.
"itrw" river (river measure)
"itrw" measure of length, schoenus
"itrw" season
True, and an area 100 ordinary cubits on a side has an area of
exactly 1/2 acre as close as we can establish the value of that
unit. Taking into account the Egyptians use of doubling to multiply
and divide and their fondness for the multiple of 2/3 it seems
likely that both were used, the one becoming the jugerum and the
other the acre.
>
>=====
>
>>>>Brian admits the acre was borrowed
>
>>>Liar.
>
>>"Most of Steve's response merely confirms his ignorance of the subject
>>(e.g., confusion of cognates with borrowings)"
>> ^^^^^^^^^^
>
>I have no idea what you think you're getting at here. If you will
>re-read what I have said about the word <acre>, you will not find any
>statement that it was borrowed.
In saying that I called it a cognate and was confusing cognates
with borrowing it seemed evident you prefered to say it was borrowed.
>(To be completely accurate, I did say
>that the English word was borrowed *into* medieval Latin as <acra>; I
>did not say that the English word was borrowed *from* anywhere.)
>Indeed, I have several times pointed out that <acre> is cognate with
>Lat. <ager> and Gk. <agros> but *not* a borrowing of either.
This is silly Brian, The Egyptian use of the word preceedes the Greek
use by a millenia. Just in case you are interested the Egyptian word
for "the land itself" was "3kr" prounounced acre. The "arura"
was a measure of "the land itself" or acre. It was a plowed field,
its area was 1/2 acre. It was 1/2 of a pair of fields one of which
was left fallow. The pair of fields was eventually taken as one
"measure of the land itself" or acre. One arura of the acre.
>
>=====
>
>>I will take it then that you accept the English acre is derived
>>from the Egyptian arura as I have demonstrated.
>
>As you like; it's not the first demonstrable falsehood that you've
>accepted.
No. Nor is it the first time you have rejected a demonstrable truth as false.
>
>Brian M. Scott
steve
Alan M. Dunsmuir
>the radius of the arc of longitude. As we increase the radius
>of the arc of the degree of longitude the radius of the degree
>of latitude decreases, though not in a linear way.
Sheer meaningless and brain-dead nonsense. (Steve really ought to
Brian M. Scott
On Sun, 14 Sep 1997 06:57:45 GMT, pet...@uniserve.com (Peter Szabo)
wrote:
>I was referring to the noun Arvum, -i nt field, land, country, plain
>It ends in -um in the nominative, which seems irregular to me but I
>could be wrong.
It's a substantivization of the neuter adjective. I believe that the
formation is not uncommon, e.g., <album> 'white color; a white
writing-tablet' from <albus> 'white; shining'.
Brian M. Scott
Dik T. Winter
In article <341c48e7....@news.mindspring.com> WWal...@freedom.org (William Wallace) writes:
> >>>>>The wine gallon, which had existed for a long time previously
> >>>>>was first made an official English measure by the decree of
> >>>>>Queen Elizabeth at about the same time she changed the length
> >>>>>of the mile to 5280 feet.
> Which of the three different gallons are you talking about?
Obviously the wine gallon which is 6 reputed quarts, each quart
being 0.56 Imperial quarts. (And we have of course in addition
the US liquid quart, the US dry quart and the Winchester quart.
It appears that the Winchester quart of about 0.99 Imperial
quarts is the oldest.)
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
Dik T. Winter
In article <KiGLEYAD...@chrism.demon.co.uk> Chris Marriott <ch...@chrism.demon.co.uk> writes:
> >My point was really that the metric "grade" used to make the measurements
> >upon which the metric system is based didn't really survive much beyond
> >the period during which the measurements were being made.
>
> The "grad" is NOT a part of the SI system, Steve. The SI unit of angular
> measure is the radian ("pi" radians = 180 degrees).
Some confusion here I think. Steve intended with "metric system" the
metric system as sanctioned by the French revolution, and the grade
was part of it. SI is based on the metric system as sanctioned by
the French revolution, and the grade is not part of that. The grade
did not survive the French revolution, except that it may still be
used in France on very rare occasions.
Brian M. Scott
[Steve claimed '24835.36 miles' as a Greek value for the equatorial
circumference of the earth.]
>>>>>>Sheer silliness. They hadn't the instrumentation to measure the
>>>>>>earth's circumference to the nearest 0.01 mile.
>>>>>Suppose I stand on top of a pyramid and have two assistants stand
>>>>>at the eastern and western horizon . I adjust their position with
>>>>>signals until I can see one on the backsight of my observation of
>>>>>the other.
>>>>>Each uncovers a torch when he observes the sun rise and I call out
>>>>>when I see the torches for another assistant to note the
>>>>>difference in time with a water clock or sundial. My assistant
>>>>>informs me it took 8 minutes
>>>>You haven't persuaded me that this was possible. Remember, your view
>>>>of history requires this determination at a very early date in order
>>>>to set the sizes of linear measures. At such dates the Egyptian hours
>>>>weren't constant, since they divided real day and night into 12 hours
>>>>each, so any assumption that they were using constant minutes need a
>>>>*lot* of justification.
>As I pointed out small increments of time can be counted with
>a human pulse, a water clock, a sand timer, a sundial, even
>a rhythmic chant, "one thousand one, one thousand two..."
Only *after* a small unit of time has been defined. You've given no
evidence of such a definition.
>>>>>I then have the distance between the two observers measured.
>>>>>it works out that they were about 138 miles apart.
[I pointed out that this would require a tower over 3000 ft. tall.]
>>>I was simplifying, The Egyptians noted the rising and setting of the sun
>>>in the mountains where differences in elevations exceed 3000 feet.
>>You've also neglected to account for latitude.
>Latitude 27.5 degrees, about the same as Al Minya on the Nile
Yes, but do you have any idea why the latitude matters and what effect
it has on the calculation? If you mean seriously to propose a method,
give the details. And since you claimed a value to the nearest 0.01
mile, I expect an analysis of the possible accuracy and precision of
the method.
=====
Speaking of the fact that the earth is more nearly an ellipsoid than a
sphere, Steve said:
>>>>>>>You are assuming, I guess,that because Europeans didn't become aware
>>>>>>>of this again until the late 17th century, the well documented
>>>>>>>knowledge of this in antiquity can be dismissed.
>>>>>>Produce the documentation.
>>>>>Pythias measured the degree of latitude all the way from Marseilles
>>>>>up to Iceland and noted how it decreased as he went north. You can read
>>>>>about his studies in the commentaries of Strabo and Pliny.
>>>His method was to time the
>>>length of a day with an accurate sundial. As the days grew shorter
>>>so did the circumference of each degree of latitude (even as the
>>>angle of the degree of latitude from the equator increased)
[Steve means that the circles of constant latitude got smaller.]
>>Using the nr. of hrs. of daylight to estimate one's latitude at any
>>time of year except midsummer or midwinter would be a much more
>>difficult mathematical problem,
>It was a difficult mathematical problem, however Pythias not only
>solved it in theory he put it to the test by building a very accurate
>sundial and sailing north.
>As I recall he noted the time of the rising and the setting of the sun
>at the latitude of Marseilles for a year, then compared the time of day
>the sun rose and set for each day of the year as he went north and he
>also took note of how far he had travelled according to his ships log.
And just how, from this, is he supposed to have detected the
flattening of the earth at the pole? How accurate was his log? How
accurate was his sundial? How big was it? Did he use it at sea or on
land?
=====
>>>>>>>>>>>The Greeks had an acre of 40,000 Greek feet
>>>>>>>>>>You've made this unsupported assertion before. If they had such a
>>>>>>>>>>measure, what did they call it?
>>>>>>>The Ptolomaic Greeks used a term "schoenia" and or "aroura"
>>>>>>>for the Egyptian arura, an area with a side of 100 cubits.
>>You have quoted Gillings as follows: 'The linear length of 100 royal
>>cubits was called a schoenia in the time of the Ptolomies.') You have
>>also said: 'The same relationship as existed between khet and setat
>>existed between schoenia and arura. The length of the side is the khet
>>or schoenia; the area is the setat or arura.' A square 1 schoenia -
>>100 *royal* cubits - on a side has an area of about 2/3 of an acre.
>True, and an area 100 ordinary cubits on a side has an area of
>exactly 1/2 acre as close as we can establish the value of that
>unit. Taking into account the Egyptians use of doubling to multiply
>and divide and their fondness for the multiple of 2/3 it seems
>likely that both were used, the one becoming the jugerum and the
>other the acre.
So after all this we finally establish that you have no evidence for
an Egyptian unit of area 100 ordinary cubits on a side (and thus about
half of a modern acre); you simply think that 'it seems likely' that
such a unit was used. Why didn't you say so in the first place
instead of insisting that such a unit unquestionably existed?
Permit me to quote you from another recent post:
>There is a difference between "could have" and "did" which regular
>readers of sci.archaeology are well aware of.
When are you going to start practising what you preach? I've been
trying for weeks to get you to make this distinction in your own
posts, but you habitually refuse to do so until backed up against a
wall by a contradiction too glaring to be ignored.
=====
>>>>>Brian admits the acre was borrowed
>>>>Liar.
>>>"Most of Steve's response merely confirms his ignorance of the subject
>>>(e.g., confusion of cognates with borrowings)"
>>> ^^^^^^^^^^
>>I have no idea what you think you're getting at here. If you will
>>re-read what I have said about the word <acre>, you will not find any
>>statement that it was borrowed.
>In saying that I called it a cognate and was confusing cognates
>with borrowing it seemed evident you prefered to say it was borrowed.
You are completely confused about the course of the conversation.
Compared with your confusion about language, however, it hardly
matters.
=====
>>>I will take it then that you accept the English acre is derived
>>>from the Egyptian arura as I have demonstrated.
>>As you like; it's not the first demonstrable falsehood that you've
>>accepted.
>No. Nor is it the first time you have rejected a demonstrable truth as false.
Even you should recognize that the demonstrable falsehood to which I
was referring was the assertion that I accept your crackpot notion.
Brian M. Scott
Dik T. Winter
In article <5v66vh$8...@fridge-nf0.shore.net> whi...@shore.net (Steve Whittet) writes:
> >Since you obviously KNOW how "English" measures work, Steve, how could
> >you possible make a statement as ludicrous as:
> >
> >"A pint's a pound the world around"
I have heard it as "a pint of water is a pound and a quarter" ;-).
> The English attempted to spread the pint around their Empire only
> to find the measure or a close equivalent already in use in many places
> because it is a convenient conversion between weight, volume and length.
Oh well, let's see. Amsterdam around 1630: 1 pint beer: 0.6 l,
1 pint milk: 0.9 l, and there was an official ruling for four
different pounds (depending on what was measured): 469.09 g,
467.09 g, 369.12 g and 492.16 g. We were not part of the Empire
of course, but especially the pints do not really provide a close
equivalent, although they are based on the same original. And I
do not see at all a convenient conversion between weight and volume.
Dik T. Winter
In article <5v90p3$4...@fridge-nf0.shore.net> whi...@shore.net (Steve Whittet) writes:
> The idea of a truly beautiful and very sophisticated system
> of subtly interwoven naturally commensurate proportions
> which lasted unchanged for 5 millenia simply being discarded
> bothers me.
Unchanged? Only due to very early standardization in England the
system was virtually unchanged for many centuries (since medieval
time?). In the Netherlands approximately the same system was
in use, but it had deteriorated much more due to lack of common
legislation. At one time over 50 different "feet" were in use,
ranging from 0.258 m to 0.395 m. Also many different "rods" were
in use, were the number of "feet" in a "rod" varied from 7 to 21.
For instance, in Uitgeest (try to find that on your map) two
different "feet" and two different "rods" were in use, one "rod"
had 12 "feet" of 0.283 m, the other had 14 "feet" of 0.296 m.
That surveyors at one stage used "rods" containing 10 "feet"
tells much about the convenience.
J. B. Stephen (Buck)
In article <5vmcqj$n...@fridge-nf0.shore.net>,
Steve Whittet <whi...@shore.net> wrote:
>In article <341e1b42...@news.csuohio.edu>, sc...@math.csuohio.eduĒ says...
>>
>>
>>[Steve claimed '24835.36 miles' as a Greek value for the equatorial
>>circumference of the earth.]
>>
>>>>>>>>...the earth's circumference to the nearest 0.01 mile.
>>>>>>>Suppose I stand on top of a pyramid and have two assistants stand
>>>>>>>at the eastern and western horizon . I adjust their position with
>>>>>>>signals until I can see one on the backsight of my observation of
>>>>>>>the other.
>>
>>>>>>>Each uncovers a torch when he observes the sun rise and I call out
>>>>>>>when I see the torches for another assistant to note the
>>>>>>>difference in time with a water clock or sundial. My assistant
>>>>>>>informs me it took 8 minutes
>>
>>>>>>You haven't persuaded me that this was possible.
>
>instrumentation than a torch and for time the human pulse.
Then you are not discussing what the record shows,
you are discussing your perceptions of what *could* have
happened. For a scholar, this is a starting point, and
all the work remains.
Please move to alt.arch.what-if
Steve Whittet
In article <341e1b42...@news.csuohio.edu>, sc...@math.csuohio.eduÇ says...
>
>
>[Steve claimed '24835.36 miles' as a Greek value for the equatorial
>circumference of the earth.]
>
>>>>>>>...They hadn't the instrumentation to measure
>>>>>>>...the earth's circumference to the nearest 0.01 mile.
>
>>>>>>Suppose I stand on top of a pyramid and have two assistants stand
>>>>>>at the eastern and western horizon . I adjust their position with
>>>>>>signals until I can see one on the backsight of my observation of
>>>>>>the other.
>
>>>>>>Each uncovers a torch when he observes the sun rise and I call out
>>>>>>when I see the torches for another assistant to note the
>>>>>>difference in time with a water clock or sundial. My assistant
>>>>>>informs me it took 8 minutes
>
>>>>>You haven't persuaded me that this was possible.
I showed you that its possible and requires no more complex
instrumentation than a torch and for time the human pulse.
...
>>As I pointed out small increments of time can be counted with
>>a human pulse, a water clock, a sand timer, a sundial, even
>>a rhythmic chant, "one thousand one, one thousand two..."
>
>Only *after* a small unit of time has been defined. You've given no
>evidence of such a definition.
A number of pulses is counted equal to 8 minutes. I have shown
that the Egyptians had hours and minutes (Gardiner) and that a
pyramid serves itself as a huge sundial.
>>>>>>I then have the distance between the two observers measured.
>>>>>>it works out that they were about 138 miles apart.
>
>[I pointed out that this would require a tower over 3000 ft. tall.]
>
>>>>I was simplifying, The Egyptians noted the rising and setting of the sun
>>>>in the mountains where differences in elevations exceed 3000 feet.
Brian asked me to name a place where this could occur. When I did
he snipped it without comment.
>
>>>You've also neglected to account for latitude.
>
>>Latitude 27.5 degrees, about the same as Al Minya on the Nile
>
>Yes, but do you have any idea why the latitude matters and what effect
>it has on the calculation?
The value for the degree of latitude changes as you go north
taking the initial value at 211,000 cubits you can add cubits
according to the series 1,3,6,10,15,21 to each degree as you
go north up to 36 degrees, then for the next 6 degrees you add
a constant 38 cubits then for the next 6 degrees you add a
constant 37 cubits for the remaining 36 degrees the amount
added is the same as that applied to the first 36 degrees
but in the reverse order.
>If you mean seriously to propose a method,
>give the details. And since you claimed a value to the nearest 0.01
>mile, I expect an analysis of the possible accuracy and precision of
>the method.
This is off by about 7 parts in 1000
>
>=====
>...
>
>>It was a difficult mathematical problem, however Pythias not only
>>solved it in theory he put it to the test by building a very accurate
>>sundial and sailing north.
>
>>As I recall he noted the time of the rising and the setting of the sun
>>at the latitude of Marseilles for a year, then compared the time of day
>>the sun rose and set for each day of the year as he went north and he
>>also took note of how far he had travelled according to his ships log.
>
>And just how, from this, is he supposed to have detected the
>flattening of the earth at the pole? How accurate was his log?
He took measurements several times a day for 8 years.
>How accurate was his sundial? How big was it? Did he use it at sea or on
>land?
I don't know exactly how accurate his sundial was. Most ancient
historians simply refer to it as "very accurate" Its size was
probably less than 20 feet in diameter. He apparently had it
mounted on gymbals so he could use it on both sea and land.
>
>=====
...
>>>You have quoted Gillings as follows: 'The linear length of 100 royal
>>>cubits was called a schoenia in the time of the Ptolomies.') You have
>>>also said: 'The same relationship as existed between khet and setat
>>>existed between schoenia and arura. The length of the side is the khet
>>>or schoenia; the area is the setat or arura.' A square 1 schoenia -
>>>100 *royal* cubits - on a side has an area of about 2/3 of an acre.
>
>>True, and an area 100 ordinary cubits on a side has an area of
>>exactly 1/2 acre as close as we can establish the value of that
>>unit. Taking into account the Egyptians use of doubling to multiply
>>and divide and their fondness for the multiple of 2/3 it seems
>>likely that both were used, the one becoming the jugerum and the
>>other the acre.
>
>So after all this we finally establish that you have no evidence for
>an Egyptian unit of area 100 ordinary cubits on a side (and thus about
>half of a modern acre); you simply think that 'it seems likely' that
>such a unit was used.
No, what I said was it was likely they used both units; they
certainly used at least one but it is likely they used both.
>>There is a difference between "could have" and "did" which regular
>>readers of sci.archaeology are well aware of.
>
>When are you going to start practising what you preach? I've been
>trying for weeks to get you to make this distinction in your own
>posts, but you habitually refuse to do so until backed up against a
>wall by a contradiction too glaring to be ignored.
I make the distinction Brian, it sometimes takes a while to make
my point, I have to go over and over even very minor details with
you until you eventually understand them.
As for example with the acre. The Egyptian measure "arura"
of "the land itself "3kr" has a value of 1/2 the English acre
and 2/3 the Roman jugerum. It means plowed field. The Egyptians
associated fields in pairs with one planted and one left fallow.
The English took this pair as one unit and called it the acre.
The Ptolomaic Greeks preserved the word arura as aroura. For you
to continue to argue about this makes me suspect you have no interest
in finding out the true state of affairs and just like to argue.
>
>=====
>
...
>
>Brian M. Scott
steve
Brian M. Scott
On 16 Sep 1997 16:40:51 GMT, whi...@shore.net (Steve Whittet) wrote:
[Steve claimed '24835.36 miles' as a Greek value for the equatorial
circumference of the earth. When I pointed out that the hadn't the
instrumentation to measure the earth's circumference to the nearest
0.01 mile, he proposed the following method.]
'Suppose I stand on top of a pyramid and have two assistants stand at
the eastern and western horizon . I adjust their position with signals
until I can see one on the backsight of my observation of the other.
'Each uncovers a torch when he observes the sun rise and I call out
when I see the torches for another assistant to note the difference in
time with a water clock or sundial. My assistant informs me it took 8
minutes'
[I doubted whether the elapsed interval could be measured with
sufficient accuracy.]
>I showed you that its possible and requires no more complex
>instrumentation than a torch and for time the human pulse.
You SHOWED me nothing; you merely ASSERTED that it was possible.
Since you haven't yet shown that Old Kingdom Egyptians even divided
the day into equal hours, let alone minutes, your assertion lacks
substance.
>>>As I pointed out small increments of time can be counted with
>>>a human pulse, a water clock, a sand timer, a sundial, even
>>>a rhythmic chant, "one thousand one, one thousand two..."
>>Only *after* a small unit of time has been defined. You've given no
>>evidence of such a definition.
>A number of pulses is counted equal to 8 minutes. I have shown
>that the Egyptians had hours and minutes (Gardiner) and that a
>pyramid serves itself as a huge sundial.
You have shown nothing of the kind.
[Steve's proposed method continues:]
'I then have the distance between the two observers measured.it works
out that they were about 138 miles apart.'
[He then calculated from this a degree of 69 miles.]
>>>>You've also neglected to account for latitude.
>>>Latitude 27.5 degrees, about the same as Al Minya on the Nile
>>Yes, but do you have any idea why the latitude matters and what effect
>>it has on the calculation?
>The value for the degree of latitude changes as you go north
>taking the initial value at 211,000 cubits you can add cubits
>according to the series 1,3,6,10,15,21 to each degree as you
>go north up to 36 degrees, then for the next 6 degrees you add
>a constant 38 cubits then for the next 6 degrees you add a
>constant 37 cubits for the remaining 36 degrees the amount
>added is the same as that applied to the first 36 degrees
>but in the reverse order.
How do you know this? How would an Old Kingdom Egyptian know this?
And what does it have to do with determining the circumference of the
earth, which is what your experiment was supposed to do?
>>If you mean seriously to propose a method,
>>give the details. And since you claimed a value to the nearest 0.01
>>mile, I expect an analysis of the possible accuracy and precision of
>>the method.
>This is off by about 7 parts in 1000
This is worthless. I want an analysis of the sources of error in your
experiment and how they affect the result. Remember, you're claiming
1/100 mile accuracy for the circumference; how do you justify it from
the experimental design?
=====
>>>It was a difficult mathematical problem, however Pythias not only
>>>solved it in theory he put it to the test by building a very accurate
>>>sundial and sailing north.
>>>As I recall he noted the time of the rising and the setting of the sun
>>>at the latitude of Marseilles for a year, then compared the time of day
>>>the sun rose and set for each day of the year as he went north and he
>>>also took note of how far he had travelled according to his ships log.
>>And just how, from this, is he supposed to have detected the
>>flattening of the earth at the pole? How accurate was his log?
>He took measurements several times a day for 8 years.
This is almost meaningless. Details, please. What did he measure?
What kinds of calculations did he make?
>>How accurate was his sundial? How big was it? Did he use it at sea or on
>>land?
>I don't know exactly how accurate his sundial was.
Then you have no idea how accurately he could estimate his latitude.
> Most ancient
>historians simply refer to it as "very accurate" Its size was
>probably less than 20 feet in diameter. He apparently had it
>mounted on gymbals so he could use it on both sea and land.
=====
>>>>You have quoted Gillings as follows: 'The linear length of 100 royal
>>>>cubits was called a schoenia in the time of the Ptolomies.') You have
>>>>also said: 'The same relationship as existed between khet and setat
>>>>existed between schoenia and arura. The length of the side is the khet
>>>>or schoenia; the area is the setat or arura.' A square 1 schoenia -
>>>>100 *royal* cubits - on a side has an area of about 2/3 of an acre.
>>>True, and an area 100 ordinary cubits on a side has an area of
>>>exactly 1/2 acre as close as we can establish the value of that
>>>unit. Taking into account the Egyptians use of doubling to multiply
>>>and divide and their fondness for the multiple of 2/3 it seems
>>>likely that both were used, the one becoming the jugerum and the
>>>other the acre.
>>So after all this we finally establish that you have no evidence for
>>an Egyptian unit of area 100 ordinary cubits on a side (and thus about
>>half of a modern acre); you simply think that 'it seems likely' that
>>such a unit was used.
>No, what I said was it was likely they used both units; they
>certainly used at least one but it is likely they used both.
What do you mean, 'No'? We know that they used the larger unit, and
you think it likely that they used both, but you have no concrete
evidence that they used the smaller one.
>As for example with the acre. The Egyptian measure "arura"
>of "the land itself "3kr" has a value of 1/2 the English acre
Your own evidence, quoted above, shows this to be false.
Brian M. Scott
Steve Whittet
In article <5vmgp3$pm$1...@gannett.math.niu.edu>, bu...@shuksan.math.niu.edu says...
>
>In article <5vmcqj$n...@fridge-nf0.shore.net>,
>Steve Whittet <whi...@shore.net> wrote:
>>In article <341e1b42...@news.csuohio.edu>, sc...@math.csuohio.eduĒ says
>...
>>>
>>>
>>>circumference of the earth.]
>>>
>>>>>>>>>...They hadn't the instrumentation to measure
>>>>>>>>>...the earth's circumference to the nearest 0.01 mile.
>>>
>>>>>>>>Suppose I stand on top of a pyramid and have two assistants stand
>>>>>>>>at the eastern and western horizon . I adjust their position with
>>>>>>>>signals until I can see one on the backsight of my observation of
>>>>>>>>the other.
>>>
>>>>>>>>Each uncovers a torch when he observes the sun rise and I call out
>>>>>>>>when I see the torches for another assistant to note the
>>>>>>>>difference in time with a water clock or sundial. My assistant
>>>>>>>>informs me it took 8 minutes
>>>
>>>>>>>You haven't persuaded me that this was possible.
>>
>>I showed you that its possible and requires no more complex
>>instrumentation than a torch and for time the human pulse.
>
>you are discussing your perceptions of what *could* have
>happened. For a scholar, this is a starting point, and
>all the work remains.
>
>Please move to alt.arch.what-if
We began by showing it was done. What the record includes
is both written and artifactual evidence that the Egyptians
created standards of measure, incorporated these standards
in artifacts such as rulers and used them in constructing
artifacts such as pyramids.
The record both written and artifactual shows that the Greeks,
Romans, Israelites, and English borrowed these standards of
measure from the Egyptians.
Further it has been shown that they are geocommensurate to a
high degree of accuracy.
Brian was incredulous that these primative africans working in the
middle bronze age had the technology to make any such measurements;
after all that is contrary to what he has been taught. He raised
the objection that the technology didn't exist.
Here it is demonstrated that no great degree of technology was required.
Further the record both written and artifactual shows that the Egyptians
were in the places indicated making observation of the sun on the
horizon.
The name Ramesses literally (Ra mes ses)means
The sun, its birth, guard (observe)
Their hieroglyphic for the sun rising and setting is a notch
between two mountains. On Gebel Musa they have left inscriptions
and monuments indicating that they observed the sun rising and
setting there.
For a discussion of the Egyptians surveying instruments, the mekhert
and the bey with which they made such observations refer to IES Edwards
"The Pyramids of Egypt.
>
>Buck
>
>J Stephen
steve
Steve Whittet
In article <341ef412...@news.csuohio.edu>, sc...@math.csuohio.edu says...
>
>On 16 Sep 1997 16:40:51 GMT, whi...@shore.net (Steve Whittet) wrote:
>
>...
>Since you haven't yet shown that Old Kingdom Egyptians even divided
>the day into equal hours, let alone minutes, your assertion lacks
>substance.
The Egyptians divided the day and night not only into hours but also
into minutes. They assigned a deity to each. Further the Egyptians
were above all else carefully proportionate. They did nothing which
was not measured, precise and rational.
The Egyptian year "rmpt"was divided into 12 months "3bd"
of 30 days "hrw", completed to 365 days by the addition of the
five so called epagomenal or added days. (5 hryw rnpt)
The year was further divided into three seasons "tr" of four months each.
"3ht" (inundation), "prt" winter (emergence), "smw" summer (deficiency)
of water
The Egyptians were the first to divide the day into hours "wnwt"
there were twelve hours in the day and 12 hours in the night.
also "m dw3" (in the morning),"nw n sty-r"(noon meal)
"myst" (supper), tr n h3wy (night time)and "3t" (minute)
Though Gardiner claims the Egyptians "had no very precise
instruments for measuring the hours of the day" other writers have
shown that they used sundials and waterclocks which are quite
precise.
Baines and Ma'lek "The Atlas of Ancient Egypt" illustrate a large
gnomen fixed in a court on a raised platform with a pavement divided
up into increments which appears to have been used as a very large
and accurate sundial at Abu Ghurab p 154.
"The rulers of the 5th Dynasty, with the exception of the last two,
expressed their preference for the Heliopolitan sun god Re by
building special temples *designed for his worship*"
"The dominent feature of the upper temple was a large open court
with an altar and masonry built (not monolithic) obelisk, the
symbol of the sun god"
>>>>As I pointed out small increments of time can be counted with
>>>>a human pulse, a water clock, a sand timer, a sundial, even
>>>>a rhythmic chant, "one thousand one, one thousand two..."
>
>>>Only *after* a small unit of time has been defined. You've given no
>>>evidence of such a definition.
>
>>A number of pulses is counted equal to 8 minutes. I have shown
>>that the Egyptians had hours and minutes (Gardiner) and that a
>>pyramid serves itself as a huge sundial.
>
>You have shown nothing of the kind.
Why don't you go and check out some of the sources I have cited
for you; maybe then you will get the idea.
Budge, "The Gods of the Egyptians" Vol 1 p 176-258 discusses the
divisions of the underworld (the sky under the world or night sky)
into 12 parts and also the subdivisions of the hours of the day and night.
illustrated on p 179
>
>[Steve's proposed method continues:]
>'I then have the distance between the two observers measured.it works
>out that they were about 138 miles apart.'
>
>[He then calculated from this a degree of 69 miles.]
>
>>>>>You've also neglected to account for latitude.
>
>>>>Latitude 27.5 degrees, about the same as Al Minya on the Nile
>
>>>Yes, but do you have any idea why the latitude matters and what effect
>>>it has on the calculation?
>
>>The value for the degree of latitude changes as you go north
>>taking the initial value at 211,000 cubits you can add cubits
>>according to the series 1,3,6,10,15,21 to each degree as you
>>go north up to 36 degrees, then for the next 6 degrees you add
>>a constant 38 cubits then for the next 6 degrees you add a
>>constant 37 cubits for the remaining 36 degrees the amount
>>added is the same as that applied to the first 36 degrees
>>but in the reverse order.
>
>How do you know this?
Its from one of Stecchinis tables
>How would an Old Kingdom Egyptian know this?
By measuring the degrees of latitude along the meridien which runs
through Egypt,
>And what does it have to do with determining the circumference of the
>earth, which is what your experiment was supposed to do?
I was just answering your question about latitude.
You asked me "do you have any idea why the latitude matters and
what effect it has on the calculation? "
>
>>>If you mean seriously to propose a method,
>>>give the details. And since you claimed a value to the nearest 0.01
>>>mile, I expect an analysis of the possible accuracy and precision of
>>>the method.
>
>>This is off by about 7 parts in 1000
>
>This is worthless. I want an analysis of the sources of error in your
>experiment and how they affect the result. Remember, you're claiming
>1/100 mile accuracy for the circumference; how do you justify it from
>the experimental design?
That is incorrect. The actual equatorial circumference of the earth
is 24,902.727 mi I said the Egyptians got a value of about 69 miles
to a degree. Thats 24,840 miles, a difference of almost 1 degree
in 360 degrees or 62.727 mi.
ok we put two observers as far away from eachother on an east west line
as we could and still see them and asked them to signal us with a torch
when they observed the sunrise.
Lets say it takes +/- 4 seconds to determine the sun has dawned
Mullahs sounding prayer call in the morning use the moment at
which they can distinguish a white thread from a black thread
in the palm of their hand. They were usually within seconds
of the jets taking off at Dahran so I would say this is reasonable.
If the torch is already lit and shrouded they need only uncover it
lets say that takes 1/2 second, the speed of light is instantaneous
but lets say the recorder takes another 1 second to react and begin
timing. You would be off something like 10 seconds in 8 minutes.
The second source of error is in the measurement of their distance
apart. We have previously agreed that the Egyptians were fairly
accurate measurers. Stecchini cites Borchardt to the effect that
they triangulated their measurements using a right triangle
12' x 16'-6". If they were as accurate with this as modern
surveyors they would be off 1 foot in 1,000', or about 728.64'
(The builders of the Great Pyramid were off 6" in 755'-4")
This is a total maximum error of 1728.64' in 2 degrees, they would be
off about 58.93 miles working to this tolerance
One would expect that if they repeated the experiment a few times
they would get better results
>
>=====
>
>>>>It was a difficult mathematical problem, however Pythias not only
>>>>solved it in theory he put it to the test by building a very accurate
>>>>sundial and sailing north.
>
>>>>As I recall he noted the time of the rising and the setting of the sun
>>>>at the latitude of Marseilles for a year, then compared the time of day
>>>>the sun rose and set for each day of the year as he went north and he
>>>>also took note of how far he had travelled according to his ships log.
>
>>>And just how, from this, is he supposed to have detected the
>>>flattening of the earth at the pole? How accurate was his log?
>
>>He took measurements several times a day for 8 years.
>
>This is almost meaningless. Details, please. What did he measure?
>What kinds of calculations did he make?
Dawn, Noon and Dusk. When the sun rose, when it reached its zenith
when it set.
>
>>>How accurate was his sundial? How big was it? Did he use it at sea or on
>>>land?
>
>>I don't know exactly how accurate his sundial was.
>
>Then you have no idea how accurately he could estimate his latitude.
That doesn't follow. Even garden sundials can cut a 1 minute line.
A large sundial could be accurate to fractions of a second, I would
say 1 second is a fair estimate.
No. They used the larger one *in the time of the Ptolemies*.
They used the smaller one during the middle kingdom, so the
question is were they using both at the same time when the
Ptolemies came to power.
>
>>As for example with the acre. The Egyptian measure "arura"
>>of "the land itself "3kr" has a value of 1/2 the English acre
>
>Your own evidence, quoted above, shows this to be false.
No Brian, you just don't seem to read carefully. Why do I have
to tell you everything about 12 times before you finally get it?
>
>Brian M. Scott
steve
Alan M. Dunsmuir
>The value for the degree of latitude changes as you go north
>taking the initial value at 211,000 cubits you can add cubits
>according to the series 1,3,6,10,15,21 to each degree as you
>go north up to 36 degrees, then for the next 6 degrees you add
>a constant 38 cubits then for the next 6 degrees you add a
>constant 37 cubits for the remaining 36 degrees the amount
>added is the same as that applied to the first 36 degrees
>but in the reverse order.
Absolute gibberish!
The distance on the earth's surface subtended by successive degrees of
latitude, measured along a parallel of longitude, DECREASES
MONOTONICALLY as one moves from the Equator towards the Poles, due to
the oblateness of the earth. It varies around its average value of
364,800 feet (69.1 statute miles) by +/- 1.860 feet (0.35 statute miles)
William Wallace
On 17 Sep 1997 04:29:18 GMT, whi...@shore.net (Steve Whittet) wrote:
>In article <341ef412...@news.csuohio.edu>, sc...@math.csuohio.edu says...
>>
>>On 16 Sep 1997 16:40:51 GMT, whi...@shore.net (Steve Whittet) wrote:
>>
>>...
>>Since you haven't yet shown that Old Kingdom Egyptians even divided
>>the day into equal hours, let alone minutes, your assertion lacks
>>substance.
>
>The Egyptians divided the day and night not only into hours but also
>into minutes. They assigned a deity to each. Further the Egyptians
>were above all else carefully proportionate. They did nothing which
>was not measured, precise and rational.
Minutes?
In abense of any evidence of minutes you may politely put your
hypothesis where the sun don't shine.
Lisbeth Andersson
Unfortunately I don't know who wrote the following, I missed the
original post and I haven't been able to find it.
[...]
> >
> >>Suppose I stand on top of a pyramid and have two assistants stand
> >>at the eastern and western horizon . I adjust their position with
> >>signals until I can see one on the backsight of my observation of
> >>the other.
> >
> >>Each uncovers a torch when he observes the sun rise and I call out
> >>when I see the torches for another assistant to note the
> >>difference in time with a water clock or sundial. My assistant
> >>informs me it took 8 minutes
> >
[......]
<ROTFLMAO>
What really set me off was the suggestion that the assistant,
could use a sundial to measure the time *in this experiment*. Then
I started to think about the other practial problems (the
assistant has switched to his water clock), would it be possible
to see the western torch at a distance of over 40 kilometers when
you are standing in the sunlight, is it possible to get the
assistants in position at that distance, is the pyramid big
enough to get in the way when the western assistant observes the
sunrise and how flat does the ground have to be for this to work?
I was starting to do some calculations on this when I started to
wonder: Why would they bother? (Then I stopped the calculations.)
They could measure the distance of the horizon from a known
height. That is all that is needed to calculate the earths
diameter. Why bother with the rest of the stuff?
Lisbeth.
--
I know I said something about "Correct me if I'm wrong",
but I didn't expect you guys to follow orders that well.
Lisbeth Andersson, Sweden
Lisbeth....@xt.etx.ericsson.se
Brian M. Scott
On 17 Sep 1997 04:29:18 GMT, whi...@shore.net (Steve Whittet) wrote
more of the usual.
Steve, I'll just let your last post in this subthread stand as a
monument to blinkered credulity.
Brian M. Scott
Alan M. Dunsmuir
In article <341FAA...@xt.etx.ericsson.se>, Lisbeth Andersson
<Lisbeth....@xt.etx.ericsson.se> writes
>Unfortunately I don't know who wrote the following, I missed the
>original post and I haven't been able to find it.
You've just stumbled across one of the gentler Whittetisms, in which
phenomena this NewsGroup has been bathed over the last three or four
years.
If you really think you can cope with some of the wilder examples, do a
dejanews search for 'Steve Whittet'.
Steve Whittet
In article <341FAA...@xt.etx.ericsson.se>, Lisbeth....@xt.etx.ericsson.se says...
>
>Unfortunately I don't know who wrote the following, I missed the
>original post and I haven't been able to find it.
Its part of a long thread on measurements which should be archived
in deja news.
>
>[...]
>> >
>> >>Suppose I stand on top of a pyramid and have two assistants stand
>> >>at the eastern and western horizon . I adjust their position with
>> >>signals until I can see one on the backsight of my observation of
>> >>the other.
>> >
>> >>Each uncovers a torch when he observes the sun rise and I call out
>> >>when I see the torches for another assistant to note the
>> >>difference in time with a water clock or sundial. My assistant
>> >>informs me it took 8 minutes
>> >
>[......]
>
><ROTFLMAO>
>
>What really set me off was the suggestion that the assistant,
>could use a sundial to measure the time *in this experiment*.
Is it that you don't think the Egyptians were capable
of making a sundial?
The Egyptians built obelisks surrounded by pavements to
aid them in observing the sun (Ra) which they worshipped
from predynastic times.
There are many different ways to measure time which don't require
a high degree of technology. Drum beats were used in Galleys to
time the stroke of the oars, rhythmic chanting helped sailors
pull in unison when raising sail. A human pulse can be used.
Sundials and water clocks also date back to the ancient Egyptians,
The initial suggestion was that the Egyptians were incapable
of measuring the circumference of the earth because they
didn't have the technology and probably didn't even know the
earth was round.
This raises the question just how much technology does it take.
You can observe the earth is round just by standing on top of a hill.
>Then I started to think about the other practial problems (the
>assistant has switched to his water clock), would it be possible
>to see the western torch at a distance of over 40 kilometers when
>you are standing in the sunlight,
When the western torch is lit the observer to the east has the sun
behind him and very low on the horizon. At the moment the eastern
torch is lit a point almost seventy miles to the east is still in
the dark.
>is it possible to get the assistants in position at that distance,
Using a backsite on a mekhert it is possible to align them
very accurately. The point where the sun appeared to rise
and set on the horizon as viewed from a solar temple on
each day of the year was observed very carefully by the
Egyptians over a period of millenia and became what we
would call a geodetic benchmark, sometimes marked by
a small pyramid.
>is the pyramid big enough to get in the way when the western
>assistant observes the sunrise and how flat does the ground
>have to be for this to work?
It works best if the two torches are at sea level.
To the observers the central point is tangent to the
curvature of the earth. Indeed as Brian points out,
at a distance of 70 miles you need about 3000 feet
of altitude for the observer in the center to see
the torches. I proposed that
The observer was standing on Gebel Musa with the torch
bearers at sea level on the shores of the Red Sea and the
Gulf of Aquaba.
>I was starting to do some calculations on this when I started to
>wonder: Why would they bother?
The question is a good one. Why would someone want to know the
measured distance between the points at which the sun rose and set
badly enough to make an organized effort to find out in the
middle bronze age.
The Egyptians culture had some characteristics that might help us
answer that question. The worshipped both the sun (Ra) and accuracy
im measures (Ma'at) Their worship of the sun involved observing
and measuring all its properties, the length of its shadow
included. They made particular note of its passage through the sky
in the Sekhert boat and assigned hours of the day and night to
mark its passage.
Secondly, because of their annual flood the Egyptians used
surveyors or "cord stretchers" to restablish the boundaries
of fields taking the "arura" (land measure) of the "3kr"
(the land itself) using a "mekhert" and "bay"
(surveying instruments) and a "mr" survey right triangle
with legs 12' x 16'-6".
The Egyptians created standards of measure we still use today
based on 600 stadia to a degree and 600 feet to a stadia.
(Then I stopped the calculations.)
>They could measure the distance of the horizon from a known
>height. That is all that is needed to calculate the earths
>diameter.
You mean because that indicates the point of tangency?
Why bother with the rest of the stuff?
The question would be how do you know exactly where the
horizon lies? You could easily measure a distance but
how do you relate the distance to the exact point of
the horizon to establish the curvature of the earth?
>
>
>Lisbeth.
steve
Xcott Craver
Steve Whittet:
>>> >>Suppose I stand on top of a pyramid and have two assistants stand
>>> >>at the eastern and western horizon . I adjust their position with
>>> >>signals until I can see one on the backsight of my observation of
>>> >>the other.
>>> >
>>> >>Each uncovers a torch when he observes the sun rise and I call out
>>> >>when I see the torches for another assistant to note the
>>> >>difference in time with a water clock or sundial. My assistant
>>> >>informs me it took 8 minutes
Lisbeth....@xt.etx.ericsson.se:
>>What really set me off was the suggestion that the assistant,
>>could use a sundial to measure the time *in this experiment*.
Steve Whittet:
>Is it that you don't think the Egyptians were capable
>of making a sundial?
BWAHAHAHAHAHAHAAAA!!!
Steve, you whimsically ignorant goob.
If someone all the way off on the East horizon (with respect to
you) just notices the sun rise, *YOU CAN'T USE A SUNDIAL TO CHECK THE TIME*.
The sun isn't even up yet, as far as your assistant can tell.
I can imagine Steve the Pyramidologist attempting this experiment:
Steve: There it is! What does the sundial say?
Assistant: That it's dark.
*SIGH* So what happened to your claim that 28/9 = 22/7?
-Caj
Milo Gardner
One problem with Steve's post is -- pyramids were built over
1,000 years before water clocks came into use. The dates
when specific technologies have been confirmed to have come
into use needed to be stated --- and not continually ignored.
Regards to all,
Milo Gardner
On 17 Sep 1997, Steve Whittet wrote:
> In article <341FAA...@xt.etx.ericsson.se>, Lisbeth....@xt.etx.ericsson.se says...
> >
> >Unfortunately I don't know who wrote the following, I missed the
> >original post and I haven't been able to find it.
>
> Its part of a long thread on measurements which should be archived
> in deja news.
> >
> >[...]
> >> >
> >> >>Suppose I stand on top of a pyramid and have two assistants stand
> >> >>at the eastern and western horizon . I adjust their position with
> >> >>signals until I can see one on the backsight of my observation of
> >> >>the other.
> >> >
> >> >>Each uncovers a torch when he observes the sun rise and I call out
> >> >>when I see the torches for another assistant to note the
> >> >>difference in time with a water clock or sundial. My assistant
> >> >>informs me it took 8 minutes
> >> >
> >[......]
> >
> ><ROTFLMAO>
> >
> >What really set me off was the suggestion that the assistant,
> >could use a sundial to measure the time *in this experiment*.
>
> Is it that you don't think the Egyptians were capable
> of making a sundial?
>
Steve Whittet
In article <5vpn5v$j6a$1...@gannett.math.niu.edu>, c...@baker.math.niu.edu says...
>
>Steve Whittet:
>
>>>> >>Suppose I stand on top of a pyramid and have two assistants stand
>>>> >>at the eastern and western horizon . I adjust their position with
>>>> >>signals until I can see one on the backsight of my observation of
>>>> >>the other.
>>>> >
>>>> >>Each uncovers a torch when he observes the sun rise and I call out
>>>> >>when I see the torches for another assistant to note the
>>>> >>difference in time with a water clock or sundial. My assistant
>>>> >>informs me it took 8 minutes
>
>
>>>What really set me off was the suggestion that the assistant,
>>>could use a sundial to measure the time *in this experiment*.
>
>
>>Is it that you don't think the Egyptians were capable
>>of making a sundial?
>
>
> Steve, you whimsically ignorant goob.
>
> If someone all the way off on the East horizon (with respect to
>you) just notices the sun rise, *YOU CAN'T USE A SUNDIAL TO CHECK THE TIME*.
>The sun isn't even up yet, as far as your assistant can tell.
For a suposedly intelligent person this is a pretty weird statement to make.
The suns rays first hit the Earths atmosphere at a height of about 3 miles
and begin to light the morning sky quite a while before the sun actually
"dawns" relative to the horizon. Apparently you have never actually
arisen early enough in your entire life to observe this.
> -Caj
steve
Xcott Craver
Steve Whittet <whi...@shore.net> wrote:
>c...@baker.math.niu.edu wrote:
>>
>> Steve, you whimsically ignorant goob.
>>
>> If someone all the way off on the East horizon (with respect to
>>you) just notices the sun rise, *YOU CAN'T USE A SUNDIAL TO CHECK THE TIME*.
>>The sun isn't even up yet, as far as your assistant can tell.
>The suns rays first hit the Earths atmosphere at a height of about 3 miles
>and begin to light the morning sky quite a while before the sun actually
>"dawns" relative to the horizon. Apparently you have never actually
>arisen early enough in your entire life to observe this.
The pre-dawn glow in the sky can not be used by a sundial to
accurately determine the time of day. Unlike the sun, which is
a light source in a specific location in the sky, the pre-dawn glow
is smeared across the eastern horizon, and does not cast a distinct
shadow pointing in a distinct direction. Remember, you're talking
about measuring a time interval on the order of *minutes*.
You also haven't addressed other problems with your experiment,
such as the question of the pyramid getting in the way of the line
of sight of the western observer! "I think our western observer
is shouting that he can see the dawn!" "No, I think he's just shouting
`DOWN IN FRONT.'"
And I still haven't received any real explanation of your
claim that 28/9 = 22/7, the famous last step in your clever proof that
the Egyptians used 22/7 for Pi instead of 28/9. Must I pester you
forever? At least you took back your claim that a cubic foot was
31 gallons.
-Caj
Steve Whittet
In article <5vs0ab$2o7$1...@gannett.math.niu.edu>, c...@baker.math.niu.eduż says...
>
>Steve Whittet <whi...@shore.net> wrote:
>>c...@baker.math.niu.edu wrote:
>>>
>>> Steve, you whimsically ignorant goob.
>>>
>>> If someone all the way off on the East horizon (with respect to
>>>you) just notices the sun rise, *YOU CAN'T USE A SUNDIAL TO CHECK THE TIME*.
>>>The sun isn't even up yet, as far as your assistant can tell.
>
>>The suns rays first hit the Earths atmosphere at a height of about 3 miles
>>and begin to light the morning sky quite a while before the sun actually
>>"dawns" relative to the horizon. Apparently you have never actually
>>arisen early enough in your entire life to observe this.
>
> The pre-dawn glow in the sky can not be used by a sundial to
>accurately determine the time of day. Unlike the sun, which is
>a light source in a specific location in the sky, the pre-dawn glow
>is smeared across the eastern horizon, and does not cast a distinct
>shadow pointing in a distinct direction.
I'm sorry but I have to disagree. As the sun gets closer and closer to
sunrise a distinct beam of sunlight intensifies its focus. by the time you
are four minutes short of sunrise the shadows are quite sharp. If you want
I can email you some photos taken just before dawn which clearly show this.
>Remember, you're talking about measuring a time interval on the order
>of *minutes*.
The measurements precision isn't a function of the lights
intensity just its presence.
>
> You also haven't addressed other problems with your experiment,
>such as the question of the pyramid getting in the way of the line
>of sight of the western observer!
As Brian pointed out when measuring a full two degrees at a hit
the middle position needs to be at an elevation of 3000' to be seen
because of the curvature of the earth so it is not going to be in
the way of the observation.
> "I think our western observer is shouting that he can see the dawn!"
>"No, I think he's just shouting`DOWN IN FRONT.'"
Whats the matter, Caj do you still think the earth is flat?
> -Caj
>
steve
Alan M. Dunsmuir
In article <34260475...@news.uniserve.com>, Peter Szabo
<pet...@uniserve.com> writes
>Please tell me, where do you get these words from?
>
>numeracy
>subtend
>monotonically
>
I'm not sure whether to take this as a troll or not. I'll give you the
benefit of the doubt and assume your questions are intended seriously.
I give you the Oxford English Dictionary -
numeracy: The quality or state of being numerate; ability with or
knowledge of numbers.
("Numeracy" is used in relation to numerical or mathematical skills
exactly as "literacy" is used with language skills.)
subtend: To stretch or extend under, or be opposite to: said esp. of a
line or side of a figure opposite an angle; also, of a chord or angle
opposite an arc.
(e.g. "The two roads running on from the Y-junction subtend an angle of
60 degrees")
monotonically: In the manner of a monotonic function, i.e. either
without ever increasing or without ever decreasing.
(This term is VERY common in mathematics. A monotonic function is one
which either is always going up (or staying the same), or always coming
down (or staying the same), over the area of interest. For example the
parabola
y = x^2 (i.e. "y equals x squared")
is monotonically decreasing with increasing x for all x <= 0, and
monotonically increasing with increasing x for all x >= 0. Considered
over the entire range from x = - infinity to x = + infinity it is not a
monotonic function of x because of its minimum at x = 0.)
Peter Szabo
Alan M. Dunsmuir wrote:
>Absolute gibberish!
>
>The distance on the earth's surface subtended by successive degrees of
>latitude, measured along a parallel of longitude, DECREASES
>MONOTONICALLY as one moves from the Equator towards the Poles, due to
>the oblateness of the earth. It varies around its average value of
>364,800 feet (69.1 statute miles) by +/- 1.860 feet (0.35 statute miles)
Good to see you contributing, Alan. I knew I should hold off on the
killfile for a while.
Please tell me, where do you get these words from?
numeracy
subtend
monotonically
I won't pretend omniscience and assume you are making them up. I'm
sure you can explain. Maybe your vocabulary exceeds the 59,000 words
in my Webster's. P'raps i need an Oxford, wot?
Peter Szabo.
Realms of Archaea--------> http://users.uniserve.com/~peters5/zoomquk4.html
zoomQuake!---------------> http://users.uniserve.com/~peters5/
"The fool doth think he is wise, but the wise man knows himself to be a fool."
Peter Szabo
Alan M. Dunsmuir wrote:
>In article <34260475...@news.uniserve.com>, Peter Szabo
><pet...@uniserve.com> writes
>>Please tell me, where do you get these words from?
>>
>>numeracy
>>subtend
>>monotonically
>>
>I'm not sure whether to take this as a troll or not. I'll give you the
>benefit of the doubt and assume your questions are intended seriously.
Intentions? Kind of fishing, really. I figured either you knew what
you were talking about (more likely) or you were extrapolating English
a bit like Shakespeare. As I mentioned my Webster (of the American
language) (I know! the shame of it. I'm Canadian.) didn't list any of
those words. It still doesn't. I'll check again tomorrow.
>I give you the Oxford English Dictionary -
Gack! I knew I needed one of those damn things.
>numeracy: The quality or state of being numerate; ability with or
>knowledge of numbers.
>
>("Numeracy" is used in relation to numerical or mathematical skills
>exactly as "literacy" is used with language skills.)
>
>subtend: To stretch or extend under, or be opposite to: said esp. of a
>line or side of a figure opposite an angle; also, of a chord or angle
>opposite an arc.
>
>(e.g. "The two roads running on from the Y-junction subtend an angle of
>60 degrees")
>
>monotonically: In the manner of a monotonic function, i.e. either
>without ever increasing or without ever decreasing.
I think I have betrayed my level of mathematical scholastic
achievment, no? (that was rhetorical)
>(This term is VERY common in mathematics. A monotonic function is one
>which either is always going up (or staying the same), or always coming
>down (or staying the same), over the area of interest. For example the
>parabola
>
> y = x^2 (i.e. "y equals x squared")
>
>is monotonically decreasing with increasing x for all x <= 0, and
>monotonically increasing with increasing x for all x >= 0. Considered
>over the entire range from x = - infinity to x = + infinity it is not a
>monotonic function of x because of its minimum at x = 0.)
I appreciated this answer a lot in that as my questions formed they
were nextly answered. (nextly? must be my Shakespearean blood)
Thanks Alan. Peace. (I'll try not to flame your flames, as long as
they seem to be informative...)
Brian M. Scott
On 23 Sep 1997 15:39:43 GMT, bu...@shuksan.math.niu.edu (J. B. Stephen
(Buck)) wrote:
>Contents: Brief comment on dictionaries, &
>request for info. Where did the greeks get the
>word "gnomon"?
According to my dictionary of Classical Greek, it's literally 'one who
knows; judge'. It's related to the verb <gigno^sko^> 'to perceive,
know, determine', reduplicated from a hypothetical *<gnoeo^>. There
is a Latin cognate, <noscere> 'to become acquainted with, get to
know', apparently from an earlier *<gnosc->. There's a corresponding
Sanskrit root <jn~a^->. Following the usual correspondences, <know>
should be an English cognate, and indeed the OED confirms the
relationship. So the answer would appear to be that it's from a PIE
root *<gno^-> connected with knowing.
Brian M. Scott
J. B. Stephen (Buck)
Contents: Brief comment on dictionaries, &
request for info. Where did the greeks get the
word "gnomon"?
RE: Definitions of words used in mathematical
context. Several recent posts have used mathematical
terms, and some have wondered about their meanings.
1) There are dictionaries of mathematical terms, such
as The Harper Collins Dictionary of Mathematics.
It's not great, but it would have explained "subtend"
"monotonically", etc, well.
2) One must be careful with the use of mathematical terms;
their meaning is not consistent over time, and common
notions of today may not have an easily explained
parallel in an historical context.
a) "ratio" - a rather modern idea, but one in
which many explanations of proportion are couched.
b) "gnomon" - used mainly in current math in
the same way that it was used (geometrically)
by the greeks, but there are plenty of other
mathematical meanings. (The OED has a good
discussion of this word since the greeks. I
would like to know where the greeks got it.)
Buck
J Stephen
Dept Math Sci
NIU
Steve Whittet
In article <608nrv$ik7$1...@gannett.math.niu.edu>, bu...@shuksan.math.niu.edu says...
>
>Contents: Brief comment on dictionaries, &
>request for info. Where did the greeks get the
>word "gnomon"?
You ask good questions. I would first compare Greek words
like gnostic, gnome, gnosis, and gnosiology. "Gnomon" appears
to be related to the stem of gignoskein (to know)
It has the sense of indicator,as in pithy sayings, maxims,
and little old men living in caves guarding secret treasures,
with a special knowledge of spiritual mysteries. It is also the
parallelogram which remains after a parallelogram has been
removed from the corner of a similar but larger parallelogram
You can learn a lot looking things up in dictionaries.
Faulkner p 108 gives "mnw" (kind of stone, thread, pigeons),
[a symbol for a measured straight line; ie as the crow flies]
p 109 gives "mnmn" (move about, move quickly)
p 137 gives "nhmn" (surely, assuredly)
also p 290 he gives "gnwt" (records, annals)
I can just hear you saying to yourself "knew it"!?
there he goes again....:)
>
>RE: Definitions of words used in mathematical
>context. Several recent posts have used mathematical
>terms, and some have wondered about their meanings.
>
>1) There are dictionaries of mathematical terms, such
>as The Harper Collins Dictionary of Mathematics.
>It's not great, but it would have explained "subtend"
>"monotonically", etc, well.
I use the McGraw Hill "Dictionary of Mathematics and Physics"
as well as a number of other standard reference works. Unfortunately
"numeracy" is not given as a word in any dictionary which I possess.
It seems that either the words numerical or numeration are taken as
providing a better usage.
Where some might claim that there is a word "numeracy" of a sense
comparable to the word literacy, my dictionaries inform me that the
word literacy actually encompasses "numeracy" in that sense, ie the
state or condition of being knowledgable, learned, educated, and cultured.
subtend: [math] A line segment or an arc of a circle subtends an angle
with vertex at a specified point if the end points of the line segment
or arc lie on the sides of the angle. Those who would define subtend
as the stretching or extending of a line opposite an angle or an arc
would thus apparently be missing the point that the extension must be
to the line segment opposite the angle
The word monotonically is used only in reference to a monotone function
It may be either a monotone nondecreasing function
or a monotone nonincreasing function,
>
> a) "ratio" - a rather modern idea, but one in
> which many explanations of proportion are couched.
>
> b) "gnomon" - used mainly in current math in
> the same way that it was used (geometrically)
> by the greeks, but there are plenty of other
> mathematical meanings. (The OED has a good
> discussion of this word since the greeks. I
> would like to know where the greeks got it.)
My best guess is that the Greeks got gnomen from
the stem of gignoskein (to know)
>Buck
>
>J Stephen
steve
Alan M. Dunsmuir
In article <6094lh$p...@fridge.shore.net>, Steve Whittet
<whi...@shore.net> writes
>It has the sense of indicator,as in pithy sayings, maxims,
>and little old men living in caves guarding secret treasures,
>with a special knowledge of spiritual mysteries.
Or, as the Oxford English Dictionary tells us under the entry 'gnome'
associated with the meaning 'goblin, or dwarf': " ... The connexion
commonly assumed with Gr. gnome (see prec.) or gnomon (cf. gnomon) seems
unlikely."
I'm only surprised that Steve doesn't link it all the way back to the
Egyptian mrkt (pronounced 'go-no-may') which 'in all probability' meant
"small man, beloved of Ptah, who lives in a cave."