Origin of "Mathematics"
Bill
I guess it comes from greek ?
Thanks,Bill
Sebastian Hew
> What is the origin of the word "Mathematics" ?
> I guess it comes from greek ?
An etymological dictionary would be the reference to consult, but, in the
absence of one:
Yes, it does indeed come from the Greek μαθηματικός, probably via Latin
and/or French.
Sebastian.
steve
Dictionaries give mathematics < L mathemalicus < Gk mathema (learning)
but surely that raises the question who did the Greeks and Romans learn
their mathematics from?
Egyptian: [ma3't] true [mh] (cubit measure); [ma3't mh] (true measure)
If you go by the fact that the Greeks and Romans used Egyptian unit fractions
to perform their calculations you might want to consider the Egyptian words
[mh] (cubit measure); [ma3't mh] (true measure) as the Gk etymology of mathema
[ma3't] (accurate, correct, straight, plumb, level, upright)
[gm ma3't] (you have found the answer correctly)
>Sebastian.
regards,
steve
Gary Vellenzer
whi...@shore.net says...
What we call mathematics was considered a subfield of astrology.
Gary
Uwe Hercksen
steve schrieb:
>
> Dictionaries give mathematics < L mathemalicus < Gk mathema (learning)
> but surely that raises the question who did the Greeks and Romans learn
> their mathematics from?
Hello,
look here:
http://www-history.mcs.st-andrews.ac.uk/history/Indexes/HistoryTopics.html
Babylonian, Egyptian and Greek matematics, but nothing about
Romans.
Centuries later, there were italian mathematicans in the
16th Century.
Bye
Uwe Hercksen
Gary Vellenzer schrieb:
>
> In late antiquity and the Middle Ages, "mathematicus" meant astrologer.
> What we call mathematics was considered a subfield of astrology.
Hello,
you should not confuse astronomy, astrology and mathematics.
Bye
Mike Cleven
In ancient times "people did"; actually they just didn't make the
separation, as people post-1700 or so tend to.....
My own bit on this: what's the possibility of a Babylonian/Chaldean root
behind Gr. mathema; the Egyptian suggestion is OK, but mathematics (and
astronomy/astrology) came to Greece from Babylon, not from Egypt.
--
Mike Cleven
http://www.cayoosh.net (Bridge River Lillooet history)
http://www.hiyu.net (Chinook Jargon phrasebook/history)
steve
In the Middle Ages, the university curriculum was modelled
on a division of the Seven Liberal Arts into Trivium
(for bachelor's degree) and Quadrivium (for master's degree).
Trivium Consisted of Grammar, Dialectic, and Rhetoric and
Quadrivium of Geometry, Arithmetic, Music and Astronomy.
In alchemy (the analysis of transformations of elements or fluxions)
there was similar wordplay in the question "what is hard as stone and
maleable as wax" with the answer being mathematics.
In Platos philosophy the seven standards of the dialectic process
chaos, mythos, eros, holos, logos, chronos and cosmos were code for
the different philosophical approaches to mathematical relationships,
similarity, difference, motion, rest, number, sequence and consequence.
In natural philosophy air, earth, fire, water, quintessence, time and space
represent the essential form of the same seven standards
The seven elements gold, silver, bronze, copper, tin, iron and lead
also refer to the same mathematical relationships in an alchemical
sense of transforming the rules of the operations.
Mathematical counterparts of thaumaturgy, divination, alchemy,
necromancy, wizardry sorcery, and magic can also be found in
the alchemical processes Calcination, Congelation, Solution,
Multiplication, Fermentation, Fixation, Ceration; along with
Separation, Sublimation, Distillation, Projection, and Digestion.
There should be no confusion of astronomy, astrology and mathematics
because essentially they are all different approaches to the same thing.
>Bye
regards,
steve
Brian M. Scott
<gvell...@nyc.nospam.rr.com> wrote:
[...]
>In late antiquity and the Middle Ages, "mathematicus" meant astrologer.
As a noun it could mean 'magician'; as an adjective, 'abstract,
theoretical; magical'. <Mathematica>, however, meant 'mathematics'.
>What we call mathematics was considered a subfield of astrology.
No, it wasn't. Arithmetic and geometry, the two branches of
mathematics recognized at the time, were two of the four branches of
the quadrivium.
Brian
Brian M. Scott
<Herc...@mew.uni-erlangen.de> wrote:
[...]
>Centuries later, there were italian mathematicans in the
>16th Century.
Don't forget Leonardo Pisano (Fibonacci) ca.1200.
Brian
Brian M. Scott
>In article <3ce0b24e$0$4696$afc3...@news.optusnet.com.au>, rada...@hotmail.com says...
>>"Bill" <bill...@my-deja.com> wrote in message
>>> What is the origin of the word "Mathematics" ?
>>> I guess it comes from greek ?
>>An etymological dictionary would be the reference to consult, but, in the
>>absence of one:
>>Yes, it does indeed come from the Greek μαθηματικός, probably via Latin
>>and/or French.
>Dictionaries give mathematics < L mathemalicus < Gk mathema (learning)
There is no <mathemalicus>. <Mathematics> is from Middle English
<mathematik>, from Old French <mathematique>, from Latin
<mathe:matica>, from Greek <mathe:matike: (tekhne:)> 'mathematical
(science)', feminine of <mathe:matikos> 'mathematical'. This
adjective is a derivative of <mathe:ma> 'that which is learnt;
learning, knowledge', from the verb <manthano:> 'learn by inquiry,
ascertain; understand, comprehend'.
>but surely that raises the question who did the Greeks and Romans learn
>their mathematics from?
No, it doesn't. The word and the thing named obviously need not have
the same source. In any case we know that the Romans learned most of
their mathematics from the Greeks, and that the Greeks discovered (or
invented, depending on one's point of view) most of theirs.
>Egyptian: [ma3't] true [mh] (cubit measure); [ma3't mh] (true measure)
>If you go by the fact that the Greeks and Romans used Egyptian unit fractions
>to perform their calculations
They didn't.
[...]
BMS
steve
>
>Uwe Hercksen wrote:
>> Gary Vellenzer schrieb:
>>
>>>In late antiquity and the Middle Ages, "mathematicus" meant astrologer.
>>>What we call mathematics was considered a subfield of astrology.
>>
>>
>> Hello,
>>
>> you should not confuse astronomy, astrology and mathematics.
>
>In ancient times "people did"; actually they just didn't make the
>separation, as people post-1700 or so tend to.....
>
>My own bit on this: what's the possibility of a Babylonian/Chaldean root
>behind Gr. mathema; the Egyptian suggestion is OK, but mathematics (and
>astronomy/astrology) came to Greece from Babylon, not from Egypt.
The names and standards of units of measure include
acre < F are< L area <Gk are < Eg 3kr < Sum.iku acre
There are a lot of math terms that go back to Sumerian/Akkadian
They came to Greece and Rome first c 600 BC from Sumeria/Akkadia
through Egypt in a Pythagorean form that went back to the Hyksos
and then came again to Greece in a later revised form through
a Persian empire that included the combined influences of Egypt,
Phoenicia, Babylon and India.
Balance <bala
dub-bi...bala: to go over the account
(with -da-)('tablet' + 'its' + 'to pass through').
Tabulate < tab
daţ, taţ: n., substitute, replacement [DAH archaic frequency: 21].
v., to add; to multiply; to repeat; to say further;
to help (motion into numerousness).
Set < $ita5, $č
$ár, sár: n., totality, all; world; horizon; ball, counter, token;
the number 3600 = 602 (many, much + ŕr, 'ring, coil').
v., to be many; to multiply or mix (with -da-); to make abundant;
to slaughter; to request, implore (reduplication class).
$ita5, $it, $id, $ed: n., measure; number ($č, 'portion', + ta, dá, 'nature, character').
v., to count; to consider; to calculate, figure out; to memorize; to recite; to read aloud.
cube <L cubitus <Ak ka ba < Sum kab
káb...dug4: to measure or count commodities for accounting or taxation ('string' ? + 'to do').
(dug)káb-dug4-ga: a measuring jar with a capacity of 20 sěla.
Manage < L manus hand manipulate < Sum ma-na
ma-na: a unit of weight measure, mina = ca. 500 grams = 60 gín
(since Akkad period, 2 ma-na = 1 sěla of water) (Akk., manűm, 'to count').
Origin, Original OF origine < L ordinus < Sum igi-ńál
igi: reciprocal of a number (= the multiplier that will give 60; the igi of 5 is 0;12)
(abbreviation of igi-ńál, 'that which is opposite').
Order, Ordinal < Ordre < L ordo inus (row) < Sum dir
Direct < L dirigere to arrange < Sum dir
dirig, diri, dir [SI.A]: n., addition; excess; overdraft; trouble;
amount by which credits of an account tablet exceed debits -
appears in the credits section of the succeeding period's
account tablet; intercalary month after either 11th month
or 12th month (based as much on whether the winter crop
will be ready for the harvest month as on the need to
reconcile the lunar year with the solar year, which
required an average of 7 intercalary months in 19 years)
(cf., (gi)u$ub).
Account:
níń-kas7/ka9[$ID]: account; accounting; result
(of a mathematical operation or calculation)
(from Akk. nikkassu, 'deduction', from nakaasu, 'to cut off').
kas7, ka9: deduction; settlement of accounts; possession (back-formation from níń-kas7/ka9).
níń-im-ba: loss ('thing' + 'the paid out').
níń-ka-bi ba-ak: account settled ('account' + 'its' + conjugation prefix + 'to make').
níń-kal-la: precious ('thing' + 'to value, esteem' + nominative).
níń-kal-kal(-la): everything valuable ('things' + reduplicated 'to value, esteem' + nominative).
níń-kas7/ka9[ŠID]: account; accounting; result (of a mathematical operation or calculation) (from Akk. nikkassu, 'deduction', from nakaasu, 'to cut off').
níń-ka9-ak: balanced account ('account' + 'made').
>--
>Mike Cleven
regards,
steve
wugi
> This
> adjective is a derivative of <mathe:ma> 'that which is learnt;
> learning, knowledge', from the verb <manthano:> 'learn by inquiry,
> ascertain; understand, comprehend'.
According to my D. etymo-source, related to D. monter (lively), Goth. mundon
(pay attention), OEng. mundian (help, protect).
My questions: no links with groups like mental-mind? man? mood-moral?
Thanks
--
Guido
www.ping.be/wugi
steve
>>Egyptian: [ma3't] true [mh] (cubit measure); [ma3't mh] (true measure)
>
>>If you go by the fact that the Greeks and Romans used Egyptian unit fractions
>>to perform their calculations
>
>They didn't.
Baloney.
Egyptian unit fractions were in common use by the Greeks and Romans
and in Europe as late as Medieval times.
http://asgle.classics.unc.edu/numerals/greek_numerals.html
"Fractions:
By Tom Elliott
Fractions were expressed as sums of unit fractions
(e.g., 1/2 + 1/3 would be used to express 5/6).
The unit fractions were expressed using the same characters
as integers, with the addition of a diacritical mark to
indicate the fractional nature of that value.
Usage of these marks seems to have varied,
but often an acute accent was used immediately
after the character (or sometimes after a sum)
to mark the numeral or sum as a fraction.
Integers were sometimes differentiated from fractions
by placing a bar, a dot, or another symbol over the integer."
--------------------------------------------------------------------------------
Bibliography:
Pingree, David. "Numbers," in The Oxford Dictionary of Byzantium.
Richardson, W.F. Numbering and Measuring in the Classical World, Auckland 1985.
Tod, M.N. "The Alphabetic Numeral System in Attica," BSA 45 (1950), 126-139; reprinted in Ancient Greek Numerical Systems: Six Studies. Chicago: Ares Publishers, 1979.
"How did the Romans express fractions?
Answer
In scientific work, which was always written in Greek,
the Romans used sexagesimal fractions, like those used for angles and time,
expressed by Greek literal numbers and positional notation.
For everyday uses, common fractions were always used, often spelled out,
such as tribus duas partes (with thirds two parts) for 2/3. The solidus
(the line in a fraction between the two numerals), or any implied division,
was never used. However, abbreviations were often used if necessary.
The most common were S or SK (semisque, or "and a half") for 1/2,
and T or TK for 1/3; 11/2 could be written ISK.
A symbol for the sestertius (a unit of money worth 21/2 bronze asses),
was IIS, later written HS. F, Z or FZ was used for 2/3 while 1/4 was
represented by the usual modern division symbol ÷, or :- -, or G, or
a backward C, the scilicus.
=============
An overhead horizontal bar meant either 1/12 or 1/16, and could be combined
with dots and other symbols. *Common fractions were often expressed as sums
of simpler fractions, for example 9/16 = 1/2 + 1/16, written S- -.*"
That Brian, is an example of the Roman use of Egyptian unit fractions.
========================
A good place to see such fractions is Book X of Vitruvius's De Architectura,
where they're used in connection with the construction of military machines.
However, ignorant medieval (and modern) copyists have corrupted many fractions
in existing texts because they did not understand the unfamiliar symbols.
There are also a few examples of fractions in inscriptions but evidence
is scanty and, as classical scholars usually pay little attention to numbers,
science or mathematics, the usual reference works provide no enlightenment.
Roman practical calculations were done on the abacus, which used a decimal
notation for whole numbers, but not for fractions (which were usually
monetary fractions), and these had special columns of beads. Incidentally,
the notation for large numbers was different from that used in today's
Roman numerals, and more convenient. Except for I, V and X,
Roman numerals were not the usual alphabetical letters we see today,
but symbols derived from Etruscan and other sources. L, C, D and M
evolved from these, but many of the more unusual symbols remained
for fractions. Even Greek letters are sometimes found.
X was also used for 1/6.
So, except for the simpler fractions, there was little standardisation.
Roman engineers relied more on analogue and graphical methods of
calculation than we do today, and numerical calculations were
avoided as far as possible
Jim Calvert, Exeter Devon
"Answer
The Egyptians used fractions and evidence survives in a few papyri,
notably the Rhind papyrus, bought in Luxor in 1858 by Henry Rhind--
now in the British Museum. It dates from 1650 BC and was probably
copied from a text written two centuries earlier. It shows methods
of calculation, problems, exercises and puzzles involving fractions.
There was an Egyptian symbol denoting fractions and the numerator
was always 1, except for 2/3 and 3/4. Even these could be derived
by subtracting 1/3 and 1/4 from the whole.
Intermediate values could be expressed as the sum of unit fractions,
for example 3/5 = 1/3 + 1/5 + 1/15.
Abstract fractions, as we know them today, were probably invented
by Hindu mathematicians in about AD 500, and the horizontal bar
(the solidus) was introduced by the Arabs around 1200."
John Richmond, Worcester Park Surrey
Problems involving Egyptian unit fractions are still
considered an interesting topic by modern mathematicians.
http://mtcs.truman.edu/~thammond/history/NumberTheory.html
Rees, Charles S. Egyptian fractions. Math.
Chronicle 10 (1981), no. 1-2, 13--30.
(Reviewer: Bruno Poizat.) SC: 10A30 (01A15), MR: 82m:10016.
This article uses the Egyptian preference for dealing with unit fractions
(except in the case of 2/3) as a starting point for some interesting problems
in number theory. There are several proofs that every fraction can be represented
as a sum of unit fractions, and these vary in the number of fractions produced and
the maximum size of the denominators (these proofs are given as Fibonacci-Sylvester,
Erdös (1950), Golomb (1962), Bleicher (1968, using Farey series), and Bleicher
(1972, using continued fractions)).
He also discusses various conjectures about unit fractions.
For example, Erdös and Strauss conjectured that 4/n can always
be written as the sum of three or less Egyptian fractions, and
Sierpinski made the same conjecture for numbers of the form 5/n.
The author also discusses some interesting results by R. L. Graham (1963).
As an example, Graham proves some interesting theorems where the denominators
of the unit fractions are required to be squares, or to be cubes, or to be
square free. Closely related topics: Ancient Egypt and Arithmetic.
>BMS
steve
Brian M. Scott
[...]
>There should be no confusion of astronomy, astrology and mathematics
>because essentially they are all different approaches to the same thing.
No, they're not.
Bobby D. Bryant
> In article <3ce0b24e$0$4696$afc3...@news.optusnet.com.au>, rada...@hotmail.com says...
>>
>>"Bill" <bill...@my-deja.com> wrote in message
>>
>>> What is the origin of the word "Mathematics" ?
>>> I guess it comes from greek ?
>>
>>An etymological dictionary would be the reference to consult, but, in the
>>absence of one:
>>
>>Yes, it does indeed come from the Greek μαθηματικός, probably via Latin
>>and/or French.
>
> Dictionaries give mathematics < L mathemalicus < Gk mathema (learning)
> but surely that raises the question who did the Greeks and Romans learn
> their mathematics from?
>
> Egyptian: [ma3't] true [mh] (cubit measure); [ma3't mh] (true measure)
Surely it was ancient Bogon instead?
mat - "unity"
he - "copulating with" (participle)
ik - "reveals"
os - "duality"
Usually translated by the vulgar colloquialism, "one and one is two",
but actually part of a mystical mantra explaining the origin of their
dualist universe.
Bobby Bryant
Austin, Texas
p.s. - See, I can make this stuff up too.
Bobby D. Bryant
My Webster's says the Greek is from PIE *mendh, "pay attention",
"be alert", cf. G. _munter_, "cheerful" and Av. _mazda:_, "memory".
However, I don't know whether *mendh is akin to *men. It certainly
looks similar and has a similar meaning, but I'd rather have an
informed opinion rather than a simple "it looks like it, so it must
be".
Bobby Bryant
Austin, Texas
Αλέξανδρος Διαμαντίδης
> >and/or French.
>
> Dictionaries give mathematics < L mathemalicus < Gk mathema (learning)
> but surely that raises the question who did the Greeks and Romans learn
> their mathematics from?
>
> Egyptian: [ma3't] true [mh] (cubit measure); [ma3't mh] (true measure)
>
> If you go by the fact that the Greeks and Romans used Egyptian unit fractions
> to perform their calculations you might want to consider the Egyptian words
> [mh] (cubit measure); [ma3't mh] (true measure) as the Gk etymology of mathema
> [ma3't] (accurate, correct, straight, plumb, level, upright)
> [gm ma3't] (you have found the answer correctly)
I don't think so... «μάθημα» (mathema) doesn't stand alone, it comes
from «έμαθα» (ematha), the aorist of «μανθάνω» (manthano, "to learn").
Alexandros
--
Αλέξανδρος Διαμαντίδης * ad...@hellug.gr
Brian M. Scott
>"Brian M. Scott" schreef :
Watkins (2000) takes them back to distinct PIE roots: */mendh-/ 'to
learn', */men-/ 'to think', */man-/, and */me:-/, respectively. A
connection between the first two seems quite reasonable, though.
Brian
Brian M. Scott
>>>Egyptian: [ma3't] true [mh] (cubit measure); [ma3't mh] (true measure)
>>>If you go by the fact that the Greeks and Romans used Egyptian unit fractions
>>>to perform their calculations
>>They didn't.
>Baloney.
As usual, you don't know what you're talking about. For starters,
you're confusing calculation with representation. As we know from
numerous pictures (among other sources), the Greeks and Romans did
most of their *calculation* with the functional equivalent of the
abacus. (Indeed, two Roman abaci about the size of a modern pocket
calculator still survive.) How they *recorded* the results of these
calculations is another matter.
>Egyptian unit fractions were in common use by the Greeks and Romans
>and in Europe as late as Medieval times.
In *common* use? No. The Romans *occasionally* used unit fractions
in the Egyptian fashion, but as a rule they simply used duodecimal
fractions, either approximating if necessary (e.g., representing 5/9
as ~7 unciae, or septunx), or translating into even smaller units
(e.g., 2/3 unciae = 16 scruples).
[...]
>"How did the Romans express fractions?
>Answer
>In scientific work, which was always written in Greek,
>the Romans used sexagesimal fractions, like those used for angles and time,
>expressed by Greek literal numbers and positional notation.
Exactly. And this system continued in use into the Middle Ages for
astronomical work.
[snip more ill-digested web gleanings]
BMS
steve
Who did the Greeks and Romans learn their mathematics from?
The ancient Greeks commonly took existing words and phrases, toponyms,
proper names, etc; put them in a Greek form and then assigned them
a Greek meaning. Apollo, Zeus, Hercules, Athena, Venus, were all
taken from Egyptian gods; Neferhotep=Aesclepios, etc.
The Romans did the same to the Greeks as the Greeks did to the Egyptians
sky father=Jupiter=Zeus-pitar=Nu-Ptah etc;
Thoth = Hermes
www.championtrees.org/yarrow/phi/phi5.htm
Aphrodite=Astarte
www-irma.u-strasbg.fr/~foata/ anne/papers/Aphrodite.html
Chochmah= Sophia
www.awakenedwoman.com/goddesses_older_women.htm
Arsinoe=Crocodilopolis (because of its god Sobek)
www.touregypt.net/featurestories/sobek.htm
Syut=Lycopolis
www.touregypt.net/Asyut.htm
citharis=lyre
library.thinkquest.org/16088/greece.html
Mesopotamia, Erythrian, Phoenician etc;
>
>Alexandros
regards,
steve
Henry Polard
http://www.geocities.com/etymonline/ gives:
mathematic(s) - 1387 as singular, 1581 as plural, from L. mathematica
(pl.), from Gk. mathematike tekhne "mathematical science," fem. sing. of
mathematikos "relating to mathematics," from mathema (gen. mathematos)
"science, knowledge, mathematical knowledge," related to manthanein "to
learn," from I.E. base *mn-/*men-/*mon- "think." Math is a 19c.
shortening in Amer.Eng.
This site looks like a valuable resource; any comments as to its
accuracy? Are there other good free etymological dictionaries and
resources online?
--
Henry Polard || Grant me the company of those who seek truth, and
protect me from those who have found it.
steve
>
>On Tue, 14 May 2002 17:35:13 GMT, whi...@shore.net (steve) wrote:
>
>>>>Egyptian: [ma3't] true [mh] (cubit measure); [ma3't mh] (true measure)
>
>>>>If you go by the fact that the Greeks and Romans used Egyptian unit fractions
>>>>to perform their calculations
>
>>>They didn't.
>
Baloney.
"The earliest Egyptian and Greek fractions were usually unit fractions
(having a numerator of 1), so that the fraction was shown simply by writing
a numeral with a mark above or to the right indicating that the numeral
was the denominator of a fraction."
http://members.aol.com/jeff570/fractions.html
>
>As usual, you don't know what you're talking about.
Baloney on Rye.
http://www.mathpages.com/home/whyunits.htm
"Why did the ancient Egyptians (and others) persist in their use
of Egyptian fractions for so many centuries? Was it a conceptual
limitation, or simply a matter of notation? Some scholars contrast
the _exactness_ of Egyptian expansions with the approximate nature
of fixed-base expansions such as in decimal system and the Babylonian
sexigesimal system. This contrast is interesting, although it
takes some effort for modern readers (accustomed to fixed-base
representations) to imagine the intellectual difficulties involved
in this paradigm shift.
The Egyptian preference for exact expansions reminds me of the Greek
preference for geometry over symbolic arithmetic. *When the Greeks
discovered irrational numbers they realized that rational arithmetic
can only approximate the values of most real numbers. As a result, not
wanting to deal with approximations, they devoted themselves mainly to
geometry. Even within geometry, their insistence on being able to give
_exact_ constructions using straight-edge and compass is similar to the
Egyptian insistence on giving exact expansions using unit fractions.*
There are at least two separate aspects to Egyptian fraction expansions
that makes them puzzling to modern people. One is the variable "base",
e.g., rather than expanding a fraction into a sum of fractions with the
denominators equal to powers of a single base number (such as 10 or 60),
they freely chose denominators to give an exact identity. Thus, while
the Babylonians might have expressed 1/7 as (approximately)
1/7 = 8/60 + 34/60^2 + 17/60^3
the Egyptians would have preferred the exact expansion
1/7 = 1/14 + 1/21 + 1/42
This also highlights the other puzzling aspect of Egyptian fractions,
namely, their preference for unit numerators. This might have
derived from their "binary" approach to integer arithmetic, in which
successive doublings of the operands were used to multiply numbers,
so that effectively their numbers were expressed in the form
N = c0*2^0 + c1*2^1 + c2*2^2 + ...
where the coefficients ci are either 0 or 1. When they expanded their
arithmetic to include fractions, they expressed all numbers in the form
p/q = n1*A^-1 + n2*B^-2 + n3*C^-3 + ... where again the coefficients
are either 0 or 1, but realizing that using A=B=C=...=2 would not allow
exact expansions, they used independently variable denominators A,B,C.. "
>For starters, you're confusing calculation with representation.
Baloney.
Brian you have no interest in or knowledge of the Egyptians
Greeks and Romans use of unit fractions
http://www.mathpages.com/home/kmath340.htm
http://www.mathpages.com/home/whyunits.htm
or of the modern mathematicians
who are working on them.
http://www.mathpages.com/home/kmath315.htm
http://www.mathpages.com/mobius/mobius.htm
http://www.ics.uci.edu/~eppstein/numth/egypt/
>As we know from
>numerous pictures (among other sources), the Greeks and Romans did
>most of their *calculation* with the functional equivalent of the abacus.
Baloney.
Show me how the Greeks would use an abacus to generate the
well known architectual proportions used in the various orders
of architecture
"Suppose we wish to generate integer solutions of the harmonic equation
1 1 1
--- + --- = ---
x y z
This can be regarded as a special case of a more general expansion
related to the Fibonacci numbers. Let s[j], j=0,1,2,... be a sequence
of integers that satisfy the recurrence s[k] = s[k-1] + s[k-2] with
arbitrary initial values s[0] and s[1]. It can be shown that for
any integers m,n with m>n we have
1 1 m 1
----------- = ----------- + SUM ------------- (1)
s[n-1] s[n] s[m] s[m+1] j=n s[j-1] s[j+1]
For example, setting s[0]=s[1]=1 and n=5, m=10 gives
1 1 1 1 1 1 1 1
--- = --- + --- + --- + ---- + ---- + ---- + -----
40 65 168 442 1155 3026 7920 12816
In general, to expand 1/D into a sum of unit fractions, the method
is to split D into two factors, D = pq. Then we can set s[0]=p and
s[1]=q and generate the s sequences as follows
k s[k] s[k] s[k-1] s[k] s[k-2]
--- ------- ----------- -----------
0 p
1 q pq
2 p+q q(p+q) p(p+q)
3 p+2q (p+q)(p+2q) q(p+2q)
4 2p+3q (p+2q)(2p+3q) (p+q)(2p+3q)
5 3p+5q (2p+3q)(3p+5q) (p+2q)(3p+5q)
6 5p+8q (3p+5q)(5p+8q) (2p+3q)(5p+8q)
7 8p+13q (5p+8q)(8p+13q) (3p+5q)(8p+13q)
etc etc etc
We can now express 1/pq as the sum of the inverses of the numbers
in the third column down to the mth row, plus the inverse of the mth
number in the second column. Thus we have
1/pq = 1/p(p+q) + 1/q(p+q)
= 1/p(p+q) + 1/q(p+2q) + 1/(p+q)(p+2q)
= 1/p(p+q) + 1/q(p+2q) + 1/(p+q)(2p+3q) + 1/(p+2q)(2p+3q)
etc.
Of course, we can let m in equation (1) go to infinity, giving the
infinite unit fraction expansion
1 inf 1
----------- = SUM ------------- (2)
s[n-1] s[n] j=n s[j-1] s[j+1]
This can also be generalized to higher order recurrences. For
example, if we define the sequence s[j] to satisfy the 3rd order
recurrence s[k] = s[k-2] + s[k-3] with the initial values a,b,c,
then we can generate the following sequences
k s[k] s[k]s[k-1]s[k-2] s[k]s[k-1]s[k-3]
--- ------ -------------------- ----------------------
0 a
1 b
2 c abc
3 a+b bc(a+b) ac(a+b)
4 b+c c(a+b)(b+c) b(a+b)(b+c)
5 a+b+c (a+b)(b+c)(a+b+c) c(b+c)(a+b+c)
6 a+2b+c (b+c)(a+b+c)(a+2b+c) (a+b)(a+b+c)(a+2b+c)
etc etc etc
so we have
1/abc = 1/ac(a+b) + 1/bc(a+b)
= 1/ac(a+b) + 1/b(a+b)(b+c) + 1/c(a+b)(b+c)
= 1/ac(a+b) + 1/b(a+b)(b+c) + 1/c(b+c)(a+b+c) + 1/(a+b)(b+c)(a+b+c)
and so on. To illustrate, with a=3,b=7,c=11 this last formula gives
1/231 = 1/330 + 1/770
= 1/330 + 1/1260 + 1/1980
= 1/330 + 1/1260 + 1/3780 + 1/4158
and with a=23,b=c=1 it gives
1/23 = 1/24 + 1/552
= 1/48 + 1/50 + 1/552 + 1/1200"
Tell us why the Greeks would use an abacus for this. The Greeks based their
mathematics on geometry rather than numerical analysis.
> (Indeed, two Roman abaci about the size of a modern pocket
>calculator still survive.) How they *recorded* the results of these
>calculations is another matter.
Baloney.
The calculation is dependant on unit fractions not decimals
As to how they recorded their fractions, go look up gematria
http://www.cs.utk.edu/~mclennan/OM/BA/Iso-gen.html
>
>>Egyptian unit fractions were in common use by the Greeks and Romans
>>and in Europe as late as Medieval times.
>
>In *common* use? No.
In common use yes! First in the Attic and then in the Ionian system.
"The Greeks used fractions, as did earlier civilizations. Their notation,
however, was ambiguous and context was crucial for the correct reading
a fraction. A diacritical mark was placed after the denominator of the
(unit) fraction"
http://www.math.tamu.edu/~dallen/history/gr_count/gr_count.html
>The Romans *occasionally* used unit fractions
>in the Egyptian fashion, but as a rule they simply used duodecimal
>fractions, either approximating if necessary (e.g., representing 5/9
>as ~7 unciae, or septunx), or translating into even smaller units
>(e.g., 2/3 unciae = 16 scruples).
Baloney.
The Romans used factor rich decimal, hexadecimal and octal systems
to make the use of unit fractions easier. Look at their hexadecimal
standards of measure Their pes or foot had sixteen digitus. They
could divide it into 4 palmus with 1 palmus = '4 pes
Rather than write 5/16 in roman numerals they would write 'IV 'XVI
>
>[...]
>
>>"How did the Romans express fractions?
>
>>Answer
>>In scientific work, which was always written in Greek,
>>the Romans used sexagesimal fractions, like those used for angles and time,
>>expressed by Greek literal numbers and positional notation.
This snipped quotation is taken from
http://www.newscientist.com/lastword/answers/656numbers.jsp?tp=numbers1
it continues
"Common fractions were often expressed as sums of simpler fractions,
for example 9/16 = 1/2 + 1/16, written S- -."
That Brian, is an example of the Romans using Egyptian unit fractions.
>Exactly. And this system continued in use into the Middle Ages for
>astronomical work.
Yes Brian the Egyptian astronomical calculations were copied by the Greeks
http://www.leidenuniv.nl/nino/aeb98/aeb98_8.html
98.1042
DEPUYDT, Leo, The demotic mathematical astronomical papyrus Carlsberg 9
reinterpreted, in: Egyptian Religion. Studies Quaegebeur, 1277-1297. (tables).
In BA 14720 and 69000 Neugebauer established that the Demotic Mathematical
Astronomical Pap. Carlsberg 9 describes a version of the 25-year lunar cycle,
which cycle involves the observation that 309 lunar months are just about as
long as 25 Egyptian wandering years of 365 days, or 9125 days. ...
98.1041
DEPUYDT, Leo, Ancient Egyptian Star Clocks and their Theory, BiOr 55 (1998),
5-44. (fig.). Review article inspired by AEB 95.1149. After brief remarks
in section I on the place of Egypt in the early history of astronomy,
the author analyzes in section II star clocks,...
If Brian knew more about unit fractions he wouldn't go on like this.
>BMS
steve
Bobby D. Bryant
> The ancient Greeks commonly took existing words and phrases, toponyms,
> proper names, etc; put them in a Greek form and then assigned them
> a Greek meaning. Apollo, Zeus, Hercules, Athena, Venus, were all
> taken from Egyptian gods
*ding* *ding* *ding* Factual Error Alert! *ding* *ding* *ding*
Zeus, for example, is an I-E god with a PIE-derived name.
Bobby Bryant
Austin, Texas
Brian M. Scott
[...]
>Who did the Greeks and Romans learn their mathematics from?
>The ancient Greeks commonly took existing words and phrases, toponyms,
>proper names, etc; put them in a Greek form and then assigned them
>a Greek meaning. Apollo, Zeus, Hercules, Athena, Venus, were all
>taken from Egyptian gods; Neferhotep=Aesclepios, etc.
No, they weren't. <Zeus> is from PIE */dyeu-/ 'to shine'. <Venus> is
Latin, not Greek, and is from PIE */wen-/ 'to desire, strive for'.
These are clearly not borrowings Egyptian.
>The Romans did the same to the Greeks as the Greeks did to the Egyptians
>sky father=Jupiter=Zeus-pitar=Nu-Ptah etc;
More confusion. The Latin is <Iu:piter>, the Greek, <Zeus pate:r>,
from PIE */dyeu-p@ter-/; nothing to do with Egyptian.
[flush]
BMS
Brian M. Scott
<hpo...@mindspring.com> wrote:
>In article <3ce151e9....@enews.newsguy.com>,
> b.s...@csuohio.edu (Brian M. Scott) wrote:
>> On Tue, 14 May 2002 19:10:29 +0200, "wugi" <wu...@ping.be> wrote:
>> >"Brian M. Scott" schreef :
>> >> This
>> >> adjective is a derivative of <mathe:ma> 'that which is learnt;
>> >> learning, knowledge', from the verb <manthano:> 'learn by inquiry,
>> >> ascertain; understand, comprehend'.
>> >According to my D. etymo-source, related to D. monter (lively), Goth. mundon
>> >(pay attention), OEng. mundian (help, protect).
>> >My questions: no links with groups like mental-mind? man? mood-moral?
>> Watkins (2000) takes them back to distinct PIE roots: */mendh-/ 'to
>> learn', */men-/ 'to think', */man-/, and */me:-/, respectively. A
>> connection between the first two seems quite reasonable, though.
>http://www.geocities.com/etymonline/ gives:
>mathematic(s) - 1387 as singular, 1581 as plural, from L. mathematica
>(pl.), from Gk. mathematike tekhne "mathematical science," fem. sing. of
>mathematikos "relating to mathematics," from mathema (gen. mathematos)
>"science, knowledge, mathematical knowledge," related to manthanein "to
>learn," from I.E. base *mn-/*men-/*mon- "think." [...]
Here he's made a choice to follow one of his sources rather than
another, though I shouldn't be surprised if there were indeed a
connection.
>This site looks like a valuable resource; any comments as to its
>accuracy? Are there other good free etymological dictionaries and
>resources online?
He's used reasonable sources, at any rate. You can also get some
English etymological information from Merriam-Webster On-line
(www.m-w.com) and the on-line 4th edition of the American Heritage
Dictionary, which includes Watkins' supplement on PIE roots
(www.bartleby.com/61/). Let's see; Svenska Akademiens ordbok (SAOB)
is on-line through <sälta>; I imagine that some of the etymologies are
dated, but it's certainly not to be sneezed at. There's also some
etymological information in the bokmålsordbok and nynorskordbok at
<http://www.dokpro.uio.no/ordboeker.html>. *Very* dated but perhaps
not wholly useless is _Wörterbuch der Indogermanischen Sprachen:
Dritter Teil: Wortschatz der Germanischen Spracheinheit_ (Dictionary
of the Indo-European Languages: Third Part: Vocabulary of the Germanic
Language Unity) by August Fick with contributions by Hjalmar Falk,
entirely revised by Alf Torp in 1909, available online in both scanned
images and uncorrected, OCRed text at
<http://www.ling.upenn.edu/~kurisuto/germanic/pgmc_torp_about.html>,
courtesy of Sean Crist.
Brian
Bobby D. Bryant
> Show me how the Greeks would use an abacus to generate the
> well known architectual proportions used in the various orders
> of architecture
AIUI, they didn't use an abacus or Egyptian arithemetic either;
they used 1:1 or foreshortened scale geometric constructions on the
walls of the cella, and removed them during the finishing. These
have been discovered on at least one temple that was never
finished.
Bobby Bryant
Austin, Texas
steve
I'm not talking about the layout by the tekton. I'm talking about
the design of the system by the arch tekton or master builder.
See Normands "Parallel of the Orders of Architecture"
Drawings to scale were made by the Egyptians and used for construction in the OK.
Though determination of which proportions are pleasing to the eye is often
linked to the fibonacci series, they occur naturally out of a septenary
system of standards of measure that uses unit fractions...
>
>Bobby Bryant
>Austin, Texas
regards,
steve
Brian M. Scott
>In article <3ce153de....@enews.newsguy.com>, b.s...@csuohio.edu says...
>>On Tue, 14 May 2002 17:35:13 GMT, whi...@shore.net (steve) wrote:
>>>>>Egyptian: [ma3't] true [mh] (cubit measure); [ma3't mh] (true measure)
>>>>>If you go by the fact that the Greeks and Romans used Egyptian unit fractions
>>>>>to perform their calculations
>>>>They didn't.
[...]
>>As usual, you don't know what you're talking about.
>Baloney on Rye.
>http://www.mathpages.com/home/whyunits.htm
Bad site: no references, and no indication of authorship.
[...]
>>For starters, you're confusing calculation with representation.
>Baloney.
>Brian you have no interest in or knowledge of the Egyptians
>Greeks and Romans use of unit fractions
>http://www.mathpages.com/home/kmath340.htm
>http://www.mathpages.com/home/whyunits.htm
>or of the modern mathematicians
>who are working on them.
Wrong on all counts. As usual. Not only do I know rather more about
the history of calculation and numeration systems than you do, I have
the advantage of actually understanding some mathematics.
>http://www.mathpages.com/home/kmath315.htm
>http://www.mathpages.com/mobius/mobius.htm
Irrelevant.
>http://www.ics.uci.edu/~eppstein/numth/egypt/
And if you knew anything about real mathematics at all, you'd
recognize that most of this is puzzles; the rest is cute, but not of
any great mathematical significance.
>>As we know from
>>numerous pictures (among other sources), the Greeks and Romans did
>>most of their *calculation* with the functional equivalent of the abacus.
>Baloney.
>Show me how the Greeks would use an abacus to generate the
>well known architectual proportions used in the various orders
>of architecture
You really haven't a clue about early uses of calculation, have you?
[snip unit fractions and Fibonacci numbers, a modern connection
unknown to the Greeks]
>Tell us why the Greeks would use an abacus for this. The Greeks based their
>mathematics on geometry rather than numerical analysis.
Not true. It's quite clear from the sophistication of the
_Arithmetica_ of Diophantus that they must have had a fairly strong
non-geometric tradition, albeit almost nothing of it survives. But
all of this is also irrelevant, since most serious computation was
done in connection with mercantile activities, and most non-mercantile
computation was astronomical, not purely mathematical.
>> (Indeed, two Roman abaci about the size of a modern pocket
>>calculator still survive.) How they *recorded* the results of these
>>calculations is another matter.
>Baloney.
The abaci do indeed survive. So does knowledge of how the results of
computations were recorded.
>The calculation is dependant on unit fractions not decimals
No one said anything about decimals. They *did* in fact use
positional notation for astronomical purposes, but it was sexagesimal,
not decimal.
[...]
>>>Egyptian unit fractions were in common use by the Greeks and Romans
>>>and in Europe as late as Medieval times.
>>In *common* use? No.
>In common use yes! First in the Attic and then in the Ionian system.
Your claim was that unit fractions were in common use by Greeks, by
Romans, and in the European Middle Ages. Taken as a whole the
statement is false.
[...]
>>The Romans *occasionally* used unit fractions
>>in the Egyptian fashion, but as a rule they simply used duodecimal
>>fractions, either approximating if necessary (e.g., representing 5/9
>>as ~7 unciae, or septunx), or translating into even smaller units
>>(e.g., 2/3 unciae = 16 scruples).
>Baloney.
>The Romans used factor rich decimal, hexadecimal and octal systems
>to make the use of unit fractions easier.
No, child. Sixteen and eight are *not* conveniently divisible by a
variety of smaller integers, and as I pointed out above, they dealt
quite handily with non-unit fractions like 7/12 'septunx'.
[...]
>>>"How did the Romans express fractions?
>>>Answer
>>>In scientific work, which was always written in Greek,
>>>the Romans used sexagesimal fractions, like those used for angles and time,
>>>expressed by Greek literal numbers and positional notation.
>This snipped quotation is taken from
>http://www.newscientist.com/lastword/answers/656numbers.jsp?tp=numbers1
It's a pity that you didn't understand it.
[...]
>>Exactly. And this system continued in use into the Middle Ages for
>>astronomical work.
>Yes Brian the Egyptian astronomical calculations were copied by the Greeks
The subject is notational systems used for astronomical calculations,
not the calculations themselves, and the system in question is
Babylonian, not Egyptian.
[snip irrelevant references]
BMS
steve
>
>On Tue, 14 May 2002 19:10:02 GMT, whi...@shore.net (steve) wrote:
>
>[...]
>
>>Who did the Greeks and Romans learn their mathematics from?
>
>>The ancient Greeks commonly took existing words and phrases, toponyms,
>>proper names, etc; put them in a Greek form and then assigned them
>>a Greek meaning. Apollo, Zeus, Hercules, Athena, Venus, were all
>>taken from Egyptian gods; Neferhotep=Aesclepios, etc.
>
>No, they weren't.
Of course they were. I gave you a long list of cites
not just to the Egyptian gods renamed by the Greeks
but to the other existing words and phrases, toponyms,
proper names, etc; that the Greeks adopted, put in a
Greek form and then assigned a Greek meaning.
> <Zeus> is from PIE */dyeu-/ 'to shine'.
deus or deity is also proposed, but as you go on to write
Zeus pate:r you should admit the meaning is sky father.
As for the word for father<peter<pater<pitar<ptah
As for the word for sky Egyptian nu
http://www.abcgallery.com/C/correggio/correggio5.html
<Venus> is Latin, not Greek,
Gee Brian, where do you think the Latin names came from?
Look in any common dictionary. The Romans adopted the
entire Greek pantheon just as the Greeks adopted the
Egyptian and the Egyptians adopted gods and goddesses
from Mesopotamia and points beyond.
http://www.seds.org/nineplanets/nineplanets/venus.html
"Venus (Greek: Aphrodite; Babylonian: Ishtar)
is the goddess of love and beauty."
If you want to you can trace her origins all the way back to India.
> and is from PIE */wen-/ 'to desire, strive for'.
No, not even close.
>These are clearly not borrowings Egyptian.
You are clearly not very knowledgable about pantheons.
Try reading Budge "Gods of the Egyptians" 2 vol
or look at any of the on line material, its no secret.
>
>>The Romans did the same to the Greeks as the Greeks did to the Egyptians
>>sky father=Jupiter=Zeus-pitar=Nu-Ptah etc;
>
>More confusion. The Latin is <Iu:piter>, the Greek, <Zeus pate:r>,
>from PIE */dyeu-p@ter-/; nothing to do with Egyptian.
from
http://www.bartleby.com/61/25/Z0012500.html
Zeus
NOUN: Greek Mythology The principal god of the Greek pantheon,
ruler of the heavens, and father of other gods and mortal heroes.
ETYMOLOGY: Greek. See dyeu- in Appendix I.
WORD HISTORY: Homer's Iliad calls him "Zeus who thunders on high"
and Milton's Paradise Lost, "the Thunderer,"
so it is surprising to learn that the Indo-European ancestor of Zeus
was a god of the bright daytime *sky*. [Egyptian nu-ptah, sky father
(Nu is the sky and Ptah, whose head is blue, is its creator)]
Zeus is a somewhat unusual noun in Greek,
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
having both a stem Zn- (as in the philosopher Zeno's name) and
a stem Di-(earlier Diw-). In the Iliad prayers to Zeus begin with
the vocative form Zeu pater, "o *father* Zeus."
Father Zeus was the head of the Greek pantheon; another ancient
Indo-European society, the Romans, called the head of their pantheon
Ipiter or Iuppiter-Jupiter. *The -piter part of his name is just a
reduced form of pater, "father,"* and Iov corresponds to the Zeu in Greek:
Ipiter is therefore precisely equivalent to Zeu pater and could be translated
"father Jove." Jove itself is from Latin Iov", the stem form of Ipiter, an older
version of which in Latin was Diov", showing that the word once had a d as in Greek Diw-.
An exact parallel to Zeus and Jupiter is found in the Sanskrit god addressed as Dyau pitar:
pitar is "father," and dyau means "sky." We can equate Greek Zeu pater, Latin I-piter,
and Sanskrit dyau pitar and reconstruct an Indo-European deity, *Dyus pter, who was
associated with the sky and addressed as "father."
Comparative philology has revealed that the "sky" word refers specifically
to the bright daytime sky, as it is derived from the root meaning "to shine."
This root also shows up in Latin dis "day," borrowed into English in words
like diurnal. "Closely related to these words is Indo-European *deiwos "god,"
which shows up, among other places, in the name of the Old English god Tw
in Modern English Tuesday, "Tiw's day." *Deiwos is also the source of Latin
dvus "pertaining to the gods," whence English divine and the Italian operatic
diva, and deus, "god," whence deity."
Next you will tell me that the Hittites had no knowledge of Egyptian gods
and the Egyptians and Greeks no knowledge of Hittite gods
>BMS
steve
Harlan Messinger
>In article <3ce153de....@enews.newsguy.com>, b.s...@csuohio.edu says...
>>
>>On Tue, 14 May 2002 17:35:13 GMT, whi...@shore.net (steve) wrote:
>>
>>>>>Egyptian: [ma3't] true [mh] (cubit measure); [ma3't mh] (true measure)
>>
>>>>>If you go by the fact that the Greeks and Romans used Egyptian unit fractions
>>>>>to perform their calculations
>>
>>>>They didn't.
>>
>Baloney.
>
>"The earliest Egyptian and Greek fractions were usually unit fractions
>(having a numerator of 1), so that the fraction was shown simply by writing
>a numeral with a mark above or to the right indicating that the numeral
>was the denominator of a fraction."
>http://members.aol.com/jeff570/fractions.html
Jeff 570 of prestigious AOL University? Do you know the *source* of
his information? You can't just point to any old page on the Internet
and call it "corroboration".
--
Harlan Messinger
Remove the first dot from my e-mail address.
Veuillez ôter le premier point de mon adresse de courriel.
Bobby D. Bryant
> In article <3ce16c4e....@enews.newsguy.com>,
> b.s...@csuohio.edu says...
>> <Zeus> is from PIE */dyeu-/ 'to shine'.
>
> deus or deity is also proposed,
Be aware that multiple words can be derived from the same word in a
proto-language. Be aware also that Greek and Latin are different
languages, although related.
> but as you go on to write
> Zeus pate:r you should admit the meaning is sky father.
That's is indeed what it means. But it's derived from PIE morphemes
(and shows up _independently_ in Greek, Latin, Sanskrit, and maybe
some others).
> As for the word for father<peter<pater<pitar<ptah
Bogus etymology detected. "pitar" is the specifically Sanskrit
variant, and derives from a form almost identical to the Greek
"pate:r", except that the 'a' was a laryngeal rather than an
ordinary vowel.
> As for the word for sky Egyptian nu
> http://www.abcgallery.com/C/correggio/correggio5.html
True or not, it's completely irrelevant to the IE etymology.
> <Venus> is Latin, not Greek,
>
> Gee Brian, where do you think the Latin names came from?
>
> Look in any common dictionary. The Romans adopted the entire Greek
> pantheon
No, the Romans already had their own pantheon, which they mapped
onto the Greek while preserving the original names. They _did_
borrow a few from the Greeks (sometimes via the Etruscans, as with
Herakles), and in the later period they borrowed exotic gods from
all over the Middle East. But the basic pantheon that you learn in
gradeschool is almost entirely native.
> just as the Greeks adopted the Egyptian
Not in general. Some of their pantheon is very obviously derived
from the IE tradition. Others have unknown origins, presumably
adopted from the aborigines. I don't think any of the gods from the
main pantheon can be derived from Egyptian sources, though like the
Romans they adopted all manner of exotica in the later period.
> and the Egyptians adopted gods and goddesses from Mesopotamia and
> points beyond.
IANAEgyptologist, but I don't think this is well established either.
> http://www.seds.org/nineplanets/nineplanets/venus.html "Venus
> (Greek: Aphrodite; Babylonian: Ishtar) is the goddess of love and
> beauty."
Yes, the ancients _associated_ the gods of the various pantheons
together as best they could (sometimes poorly), but that is not the
same as saying that the gods had common origins.
Some are so similar as to raise suggestions of influence if not
outright borrowing, but there's not the faintest support for the
mass borrowings you believe in.
> If you want to you can trace her origins all the way back to
> India.
>
>> and is from PIE */wen-/ 'to desire, strive for'.
>
> No, not even close.
And you're an authority who can dispute with the experts, eh?
>>These are clearly not borrowings Egyptian.
>
> You are clearly not very knowledgable about pantheons. Try reading
> Budge "Gods of the Egyptians" 2 vol or look at any of the on line
> material, its no secret.
Most on-line material is rubbish. Budge appears not to be much
better, as witness these reviews on Amazon:
"""
As it happens with many of Budge's books, this two-volumes set is
quite out-dated and, moreover, it is highly-speculative (but without
warning one that what he says is just that: speculation). ...
Another criticism, which can be extended over to any of his other
titles, is the lack or meagre references to the bibliography or
documents from which he extracted his quotations. So that, BEGINNERS
BEWARE!
"""
I think that last sentence was directed at you, Steve.
Here's another:
"""
The most frustraing thing about E.A. Wallis Budge's books is that
it's often impossible to tell when he's using conjecture and when
he's actually stating a fact. Far too often he'll make a statement
that today we know to be false -- for example, that the name of
"Bast" and "Sekhmet" derive from words for "fire", which they don't
as they mean (respectively) "Devouring/Ointment Lady" and "Powerful
Lady" (nothing at all to do with fire) -- and then make a statement
that actually has some basis in fact. For BEGINNERS, I would say:
STAY AWAY from this book until you have a very firm grasp of
Egyptian society and culture. ... For ADVANCED USERS, I would say:
Yes, you should probably read this, but be sure that when Budge
makes a statement that there's some way to verify what he's saying,
or your research could be seriously skewed.
"""
That one had a sentence for you too, Steve. But not the last one.
And here's another review:
"""
Budge's works are generally considered a bit of an Egyptological
embarrassment; his intentions were noble but he seemed to favor
quantity over quality when it came to research ... This book, like
all of his others, is rife with errors, contradictions,
mistranslations of the ancient texts and sadly void of references
for Budge's countless "scientific" assertions. ... The amateur
Egyptolgist may use this book with a grain of salt and opt instead
for scholarly recent books by Meeks or Hornung.
"""
The last sentence of that one would be good advice for you, Steve.
Remember, believe half of what you read, none of what you hear, and
the opposite of what you see on the Web.
>>>The Romans did the same to the Greeks as the Greeks did to the
>>>Egyptians sky father=Jupiter=Zeus-pitar=Nu-Ptah etc;
>>
>>More confusion. The Latin is <Iu:piter>, the Greek, <Zeus
>>pate:r>, from PIE */dyeu-p@ter-/; nothing to do with Egyptian.
>
> from
> http://www.bartleby.com/61/25/Z0012500.html
>
> Zeus
> NOUN: Greek Mythology The principal god of the Greek pantheon,
> ruler of the heavens, and father of other gods and mortal heroes.
> ETYMOLOGY: Greek. See dyeu- in Appendix I. WORD HISTORY: Homer's
> Iliad calls him "Zeus who thunders on high" and Milton's Paradise
> Lost, "the Thunderer,"
>
> so it is surprising to learn that the Indo-European ancestor of
> Zeus was a god of the bright daytime *sky*.
Funny, scholars who actually know something about it don't find it
surprising. In fact it makes a great deal of sense in the
primitive IE pantheon, as best we can reconstruct it.
> [Egyptian nu-ptah, sky
> father (Nu is the sky and Ptah, whose head is blue, is its
> creator)]
>
> Zeus is a somewhat unusual noun in Greek,
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ having both a stem Zn-
> (as in the philosopher Zeno's name) and a stem Di-(earlier Diw-).
It's not rare for Greek (or any other IE language) to have
variations where different _stems_ are built from a single _root_.
> In the Iliad prayers to Zeus begin with the vocative form Zeu
> pater, "o *father* Zeus."
Yes, that's the expected vocative form of "Zeus".
You're quoting a lot of reasonably accurate material as if it
supports your case, but unfortunately it doesn't have any bearing
on your claims whatsoever.
> Father Zeus was the head of the Greek pantheon; another ancient
> Indo-European society, the Romans, called the head of their
> pantheon Ipiter or Iuppiter-Jupiter. *The -piter part of his name
> is just a reduced form of pater, "father,"* and Iov corresponds to
> the Zeu in Greek: Ipiter is therefore precisely equivalent to Zeu
> pater and could be translated "father Jove." Jove itself is from
> Latin Iov", the stem form of Ipiter, an older version of which in
> Latin was Diov", showing that the word once had a d as in Greek
> Diw-.
None of which indicates any derivation from Egyptian...
> An exact parallel to Zeus and Jupiter is found in the Sanskrit god
> addressed as Dyau pitar: pitar is "father," and dyau means "sky."
> We can equate Greek Zeu pater, Latin I-piter, and Sanskrit dyau
> pitar and reconstruct an Indo-European deity, *Dyus pter, who was
> associated with the sky and addressed as "father."
Indeedie. Are you going to claim that the speakers of Sanskrit
also borrowed the name from the Egyptians?
> Comparative philology has revealed that the "sky" word refers
> specifically to the bright daytime sky, as it is derived from the
> root meaning "to shine." This root also shows up in Latin dis
> "day," borrowed into English in words like diurnal. "Closely
> related to these words is Indo-European *deiwos "god," which shows
> up, among other places, in the name of the Old English god Tw in
> Modern English Tuesday, "Tiw's day." *Deiwos is also the source of
> Latin dvus "pertaining to the gods," whence English divine and the
> Italian operatic diva, and deus, "god," whence deity."
None of which has anything to do with Egyptian...
> Next you will tell me that the Hittites had no knowledge of
> Egyptian gods and the Egyptians and Greeks no knowledge of Hittite
> gods
Completely irrelevant to your claims. The word "Zeus" and the god
it referred to, and their cognates in the other IE languages, come
from the PIE language and the culture that spoke it. Do you claim
that Egyptian cultural imperialism dominated southeast Europe and
the Eurasian steppes in 4000 BCE?
Bobby Bryant
Austin, Texas
Brian M. Scott
>In article <3ce16c4e....@enews.newsguy.com>, b.s...@csuohio.edu says...
>>On Tue, 14 May 2002 19:10:02 GMT, whi...@shore.net (steve) wrote:
>>[...]
>>>Who did the Greeks and Romans learn their mathematics from?
>>>The ancient Greeks commonly took existing words and phrases, toponyms,
>>>proper names, etc; put them in a Greek form and then assigned them
>>>a Greek meaning. Apollo, Zeus, Hercules, Athena, Venus, were all
>>>taken from Egyptian gods; Neferhotep=Aesclepios, etc.
>>No, they weren't.
>Of course they were. I gave you a long list of cites
>not just to the Egyptian gods renamed by the Greeks
>but to the other existing words and phrases, toponyms,
>proper names, etc; that the Greeks adopted, put in a
>Greek form and then assigned a Greek meaning.
No, you didn't. You gave three Greek names of gods (<Apollo>, <Zeus>,
<Athena>), at least one of which is definitely not borrowed from
Egyptian; a Latin form of a Greek name (<Hercules>); a Latin goddess
name (<Venus>) that definitely isn't borrowed from Egyptian; a partly
Latinized form of a Greek name <Askle:pios> that very obviously isn't
*linguistically* related to <Neferhotep>, whatever *cultural*
connections they may have; and the following pointless list:
>Thoth = Hermes
>www.championtrees.org/yarrow/phi/phi5.htm
As usual, you fail to understand what you read: not even the author of
that rather loony site actually equates the names linguistically.
Indeed, he says 'Thoth, ... who[sic] the Greeks renamed Hermes'. The
well-known equivalence between Thoth and Hermes is one of function and
has nothing to do with their names.
>Aphrodite=Astarte
>www-irma.u-strasbg.fr/~foata/ anne/papers/Aphrodite.html
Useless: 'the requested URL was not found on this server'. Moreover,
the server turns out to be that of the Institut de Recherche
Mathématique Avancée, Strasbourg, an unlikely place to find
information on an etymological connection between <Aphrodite> and
<Astarte>, though in this case I believe that there may actually be
one. Of course <Astarte> isn't Egyptian.
>Chochmah= Sophia
>www.awakenedwoman.com/goddesses_older_women.htm
You can't even copy accurately, can you? The article gives <Chokmah>,
not <Chochmah>, though the latter is probably more accurate, and says
that she was *renamed* <Sophia> by the Greeks. In other words,
<Sophia> and <Chokmah> are not claimed here to be *linguistically*
related. What's more, no evidence is offered for a goddess Chokmah,
merely a reviewer's report of an assertion made by a feminist
psychotherapist (so described in the review). What's more, a little
searching makes it clear that none of this has anything to do with
Egypt: <chokmah> appears to be a transliteration (possibly bad --
better sources suggest that it should be <khokhmah>) of a Hebrew word
for 'wisdom'. Greek <sophia> 'wisdom' is related only by its meaning,
not by its etymology.
>Arsinoe=Crocodilopolis (because of its god Sobek)
>www.touregypt.net/featurestories/sobek.htm
Another case of *renaming*, not of etymological relationship.
>Syut=Lycopolis
>www.touregypt.net/Asyut.htm
And again.
>citharis=lyre
>library.thinkquest.org/16088/greece.html
This last is particularly humorous and shows yet again how little
attention you pay to the sites that you dig up (or perhaps just how
poorly you understand what you read there): whatever their ultimate
origin, both <lyra> and <kithara> are Greek.
>> <Zeus> is from PIE */dyeu-/ 'to shine'.
>deus or deity is also proposed,
No, these two simply go back to the same PIE root.
>but as you go on to write
>Zeus pate:r you should admit the meaning is sky father.
What's to admit? It's well known.
>As for the word for father<peter<pater<pitar<ptah
No. The chain is from modern English <father> to Old English <fæder>
to Gmc. */fadar/ to PIE */p@ter-/. Latin <pater>, Greek <pate:r>, and
Sanskrit <pitar-> are not in the chain from PIE to English; they are
separate offshoots of PIE. And Egyptian <ptah> has nothing to do with
any of it.
>As for the word for sky Egyptian nu
>http://www.abcgallery.com/C/correggio/correggio5.html
Which shows Correggio's 'Zeus and Io', a 16th c. painting wholly
irrelevant to any of this.
><Venus> is Latin, not Greek,
>Gee Brian, where do you think the Latin names came from?
Not, in this case, from Greek -- which is why I mentioned it.
>Look in any common dictionary. The Romans adopted the
>entire Greek pantheon just as the Greeks adopted the
>Egyptian and the Egyptians adopted gods and goddesses
>from Mesopotamia and points beyond.
Idiot. The Greek goddess most nearly corresponding to Roman Venus is
Aphrodite, whose name is wholly unrelated. The Romans may have
adopted some of her mythological characteristics, but they used their
own, home-grown name.
>http://www.seds.org/nineplanets/nineplanets/venus.html
>"Venus (Greek: Aphrodite; Babylonian: Ishtar)
>is the goddess of love and beauty."
>If you want to you can trace her origins all the way back to India.
I don't give a flying fuck how far back you can trace a goddess with
similar attributes. In case you hadn't realized it, the subject is
the *name*, not the *goddess*.
>> and is from PIE */wen-/ 'to desire, strive for'.
>No, not even close.
The sky will be full of pigs before you learn enough to justify even
an ill-informed opinion on any matter relating to language. By the
way, this information is from the same source that you quote below on
the word <Zeus>.
>>These are clearly not borrowings Egyptian.
>You are clearly not very knowledgable about pantheons.
Actually, I probably know rather more about them than you do. But
don't let your ignorance get you down: the subject is the *names* of
the gods, not their functions.
>Try reading Budge "Gods of the Egyptians" 2 vol
>or look at any of the on line material, its no secret.
If I wanted to learn more about Egyptian gods and goddesses, I'd
certainly choose a better source than Budge.
>>>The Romans did the same to the Greeks as the Greeks did to the Egyptians
>>>sky father=Jupiter=Zeus-pitar=Nu-Ptah etc;
>>More confusion. The Latin is <Iu:piter>, the Greek, <Zeus pate:r>,
>>from PIE */dyeu-p@ter-/; nothing to do with Egyptian.
>from
>http://www.bartleby.com/61/25/Z0012500.html
Which is the AHD4 entry for <Zeus> and says nothing to the point that
I haven't already said. In particular, it of course says nothing
about a non-existent Egyptian linguistic connection.
[...]
BMS
Brian M. Scott
<h.mes...@comcast.net> wrote:
>whi...@shore.net (steve) wrote:
>>In article <3ce153de....@enews.newsguy.com>, b.s...@csuohio.edu says...
>>>On Tue, 14 May 2002 17:35:13 GMT, whi...@shore.net (steve) wrote:
>>>>>>Egyptian: [ma3't] true [mh] (cubit measure); [ma3't mh] (true measure)
>>>>>>If you go by the fact that the Greeks and Romans used Egyptian unit fractions
>>>>>>to perform their calculations
>>>>>They didn't.
>>Baloney.
>>"The earliest Egyptian and Greek fractions were usually unit fractions
>>(having a numerator of 1), so that the fraction was shown simply by writing
>>a numeral with a mark above or to the right indicating that the numeral
>>was the denominator of a fraction."
>>http://members.aol.com/jeff570/fractions.html
>Jeff 570 of prestigious AOL University? Do you know the *source* of
>his information? You can't just point to any old page on the Internet
>and call it "corroboration".
Sure he can; for Steve it's SOP. In this case he actually did better
than usual, since the author does in fact cite his sources for most
assertions. He doesn't offer a reference for this one, but it's
pretty well-known. He does, however, provide a reference for his
information on Roman representation of fractions, information that to
a considerable extent contradicts Steve's claim. (His sources are
pretty decent, too.)
Brian
Bobby D. Bryant
> In article <abrv66$d3t$1...@geraldo.cc.utexas.edu>,
> bdbr...@mail.utexas.edu says...
>>
>>On Tue, 14 May 2002 14:23:44 -0600, steve wrote:
>>
>>> Show me how the Greeks would use an abacus to generate the well
>>> known architectual proportions used in the various orders of
>>> architecture
>>
>>AIUI, they didn't use an abacus or Egyptian arithemetic either;
>>they used 1:1 or foreshortened scale geometric constructions on
>>the walls of the cella, and removed them during the finishing.
>>These have been discovered on at least one temple that was never
>>finished.
>
> I'm not talking about the layout by the tekton. I'm talking about
> the design of the system by the arch tekton or master builder. See
> Normands "Parallel of the Orders of Architecture"
What precisely does this book say to support your claims? Give a
short quote and a page number, please. By chance I'll be on campus
tomorrow, and not far from the Classics Library.
> Drawings to scale were made by the Egyptians and used for
> construction in the OK.
And this supports your claim, how?
> Though determination of which proportions are pleasing to the eye
> is often linked to the fibonacci series, they occur naturally out
> of a septenary system of standards of measure that uses unit
> fractions...
Enough with the obfuscation. Got any peer-reviewed publications that
you can cite to support your claim about the origin of the word
"mathematics"?
Bobby Bryant
Austin, Texas
steve
>
>On Tue, 14 May 2002 20:23:44 GMT, whi...@shore.net (steve) wrote:
>
>>In article <3ce153de....@enews.newsguy.com>, b.s...@csuohio.edu says...
>
>>>On Tue, 14 May 2002 17:35:13 GMT, whi...@shore.net (steve) wrote:
>
>>>>>>Egyptian: [ma3't] true [mh] (cubit measure); [ma3't mh] (true measure)
>
>>>>>>If you go by the fact that the Greeks and Romans used Egyptian unit fractions
>>>>>>to perform their calculations
>
>>>>>They didn't.
Baloney.
"The earliest Egyptian and Greek fractions were *usually unit fractions*
(having a numerator of 1), so that the fraction was shown simply by writing
a numeral with a mark above or to the right indicating that the numeral
was the denominator of a fraction."
http://members.aol.com/jeff570/fractions.html
>
>[...]
>
>>>As usual, you don't know what you're talking about.
>
>>Baloney on Rye.
>
>>http://www.mathpages.com/home/whyunits.htm
>
>Bad site: no references, and no indication of authorship.
Bad Site? really??? Kevin Brown?? Stanford??? means nothing to you?
no references? What do you call this?
http://www.mathpages.com/rr/bibliog/bibliog.htm
perhaps you would have to be a mathematician to enjoy it.
>
>[...]
>
>>>For starters, you're confusing calculation with representation.
>
>>Baloney.
>
>>Brian you have no interest in or knowledge of the Egyptians
>>Greeks and Romans use of unit fractions
>
>>http://www.mathpages.com/home/kmath340.htm
>>http://www.mathpages.com/home/whyunits.htm
>
>>or of the modern mathematicians
>>who are working on them.
>
>Wrong on all counts. As usual.
You just proved me right.
>Not only do I know rather more about
>the history of calculation and numeration systems than you do, I have
>the advantage of actually understanding some mathematics.
Tell us what you know about Kevin Brown and unit fractions Brian
>>http://www.mathpages.com/home/kmath315.htm
>>http://www.mathpages.com/mobius/mobius.htm
>
>Irrelevant.
That you don't understand the relevence doesn't make it irrelevant.
>
>>http://www.ics.uci.edu/~eppstein/numth/egypt/
>
>And if you knew anything about real mathematics at all, you'd
>recognize that most of this is puzzles; the rest is cute, but not of
>any great mathematical significance.
!!!
Brian(the mathematician)
dismisses as "puzzles of no great mathematical significance"
!!!
http://www.mathpages.com
Number Theory
Combinatorics
Geometry
Algebra
Calculus & Diff Eqs
Probability & Statistics
Set Theory & Foundations
History of Mathematics
Physics
Reflections on Relativity
Symmetric Pseudoprimes
Linear Fractional Transformations
Lead-Lag Algorithms
Animated (Java) Illustrations
Combined List of Articles
Albro Swift
Quotations
Music
!!!
>>>As we know from
>>>numerous pictures (among other sources), the Greeks and Romans did
>>>most of their *calculation* with the functional equivalent of the abacus.
>
>>Baloney.
>
>>Show me how the Greeks would use an abacus to generate the
>>well known architectual proportions used in the various orders
>>of architecture
>
>You really haven't a clue about early uses of calculation, have you?
Null response; if you can't do it why not just say so.
>
>[snip unit fractions and Fibonacci numbers, a modern connection
>unknown to the Greeks]
!!!
unknown to the Greek mathematicians, but known to the Egyptian architects?
http://www.bath.ac.uk/brlsi/egypt.htm
http://mtcs.truman.edu/~thammond/history/Fibonacci.html
"Technical Analysis from A to Z"
By Steven B. Achelis
"Leonardo Fibonacci was a mathematician who was born in Italy
around the year 1170. It is believed that Mr. Fibonacci discovered
the relationship of what are now referred to as Fibonacci numbers
while studying the Great Pyramid of Gizeh in Egypt.
Fibonacci numbers are a sequence of numbers in which each
successive number is the sum of the two previous numbers:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 610, etc.
These numbers possess an intriguing number of interrelationships,
such as the fact that any given number is approximately 1.618 times
the preceding number and any given number is approximately 0.618 times
the following number. The booklet Understanding Fibonacci Numbers
by Edward Dobson contains a good discussion of these interrelationships."
http://www.equis.com/free/taaz/fibonacci.html
>
>>Tell us why the Greeks would use an abacus for this. The Greeks based their
>>mathematics on geometry rather than numerical analysis.
>
>Not true.
False. The Greeks did not use numerical analysis
It's quite clear from the sophistication of the
>_Arithmetica_ of Diophantus that they must have had a fairly strong
>non-geometric tradition, albeit almost *nothing of it survives*.
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Diophantus.html
"The most details we have of Diophantus's life come from the Greek Anthology,
compiled by Metrodorus around 500 AD. This collection of puzzles contain
one about Diophantus which says:-
... his boyhood lasted 1/6th of his life; he married after 1/7th more;
his beard grew after 1/12th more, and his son was born 5 years later;
the son lived to half his father's age, and the father died 4 years
after the son. "
This anecdote about Diophantus is actually an example of how the Greeks
used unit fractions to solve their equations.
>But all of this is also irrelevant, since most serious computation was
>done in connection with mercantile activities, and most non-mercantile
>computation was astronomical, not purely mathematical.
Baloney.
The achievements of Greek geometry amount to nothing more than
the ability to calculate how to double a talent in the Agora?
>
>>> (Indeed, two Roman abaci about the size of a modern pocket
>>>calculator still survive.) How they *recorded* the results of these
>>>calculations is another matter.
>
>>Baloney.
>
>The abaci do indeed survive. So does knowledge of how the results of
>computations were recorded.
>>>As we know from
>>>numerous pictures (among other sources), the Greeks and Romans did
>>>most of their *calculation* with the functional equivalent of the abacus.
Show me the abacus the Greeks used to determine how to formulate their
classical mathematical problems. They wouldn't have allowed it was a proof
if someone did work out how to square a circle, double a cube and trisect
an angle with an abacus.
>
>>The calculation is dependant on unit fractions not decimals
>
>No one said anything about decimals.
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Greek_numbers.html
http://pespmc1.vub.ac.be/POS/Turchap9.html
Decimals are among the the number bases the Egyptians and the Greeks used.
>They *did* in fact use positional notation for astronomical purposes,
>but it was sexagesimal, not decimal.
bssst
try sexagesimal and decimal...plus unit fractions
Mesopotamia used a factor rich sexigesimal notation keyed to measures
For astronomical purposes its convenient to know how many degrees
equate to a given unit measure a given distance away
The Egyptian bases were decimal, septenary and sexigesimal
The Greek bases were decimal, octal, sexigesimal...whatever was required.
To divide 360 evenly into prime factors like '7, '11, '13, '17 and '19
unit fractions work a lot better than an abacus.
Try determining by naked eye observation when a planet has moved 3/19
of a degree along the ecliptic. Using unit fractions you can calculate
that 3/19 degree is '7 '70 '1330 of a unit measure at a unit distance
Besides, its precise. The way we use fractions requires a round off.
>[...]
>
>>>>Egyptian unit fractions were in common use by the Greeks and Romans
>>>>and in Europe as late as Medieval times.
>
>>>In *common* use? No.
>
>>In common use yes! First in the Attic and then in the Ionian system.
>
>Your claim was that unit fractions were in common use by Greeks, by
>Romans, and in the European Middle Ages. Taken as a whole the
>statement is false.
No its not. You use "Egyptian unit fractions" nearly every day
in "making change in commercial transactions". Thus, a penny = $1/100;
a nickel = $1/20; a dime = $1/10; a quarter = $1/4; a fifty-cent piece = $1/2
>[...]
>
>>>The Romans *occasionally* used unit fractions
>>>in the Egyptian fashion, but as a rule they simply used duodecimal
>>>fractions, either approximating if necessary (e.g., representing 5/9
>>>as ~7 unciae, or septunx), or translating into even smaller units
>>>(e.g., 2/3 unciae = 16 scruples).
>
>>Baloney.
>
>>The Romans used factor rich decimal, hexadecimal and octal systems
>>to make the use of unit fractions easier.
>
>No, child. Sixteen and eight are *not* conveniently divisible by a
>variety of smaller integers,
You forget their standards of measure were based on a pes of 16 digitus
The Roman stadium was the same length as the Greek stadion and eight of
them made a milliare of 1000 pasus or 80,000 digitus with 6,000,000
digitus equal to a degree. Now what makes this convienient is that
its part of a doubling system, ie powers of 2 which is how you
work with unit fractions
...
>>>Exactly. And this system continued in use into the Middle Ages for
>>>astronomical work.
>
>>Yes Brian the Egyptian astronomical calculations were copied by the Greeks
>
>The subject is notational systems used for astronomical calculations,
>not the calculations themselves, and the system in question is
>Babylonian, not Egyptian.
>
>[snip irrelevant references]
Brian you can snip things that refute you without response if you like
but you certainly aren't going to make your case by ignoring the facts.
>
>BMS
steve
steve
>
>whi...@shore.net (steve) wrote:
>
>>In article <3ce153de....@enews.newsguy.com>, b.s...@csuohio.edu says...
>>>
>>>On Tue, 14 May 2002 17:35:13 GMT, whi...@shore.net (steve) wrote:
>>>
>>>>>>Egyptian: [ma3't] true [mh] (cubit measure); [ma3't mh] (true measure)
>>>
>>>>>>If you go by the fact that the Greeks and Romans used Egyptian unit fractions
>>>>>>to perform their calculations
>>>
>>>>>They didn't.
>>>
>>Baloney.
>>
>>"The earliest Egyptian and Greek fractions were usually unit fractions
>>(having a numerator of 1), so that the fraction was shown simply by writing
>>a numeral with a mark above or to the right indicating that the numeral
>>was the denominator of a fraction."
>>http://members.aol.com/jeff570/fractions.html
>
>Jeff 570 of prestigious AOL University? Do you know the *source* of
>his information? You can't just point to any old page on the Internet
>and call it "corroboration".
What you should take away from this page is that what I'm trying
to explain to Brian would be common knowledge to most reasonably
bright high school students.
Assistance for this page has been provided by Julio González Cabillón,
John Aldrich, Avinoam Mann, Eddie Mizzi, Fred E. Wadley, Giovanni Ferraro,
Judy Ann Brown, Len Berggren, Manoel Almeida, Michael Closs, Milo Gardner,
Paul Pollack, and Samuel S. Kutler. The page is maintained by Jeff Miller,
a teacher at Gulf High School in New Port Richey, Florida.
While admittedly, using AOL as a provider would tend to indicate
a lack of internet sophistication on the teachers part it doesn't
necessarily label the entire group as mathematically unsophisticated.
Cabillón, Julio González (1959- ) is the author of numerous mathematics
textbooks. He currently teaches Real Analysis at the German Institute DSM
(Deutsche Schule Montevideo) in Uruguay. His main subject in mathematics
is "q-Gaussian coefficients."
http://members.aol.com/jeff570/sources.html
>--
>Harlan Messinger
regards,
steve
steve
>
>On Tue, 14 May 2002 16:52:44 -0600, steve wrote:
>
>> In article <3ce16c4e....@enews.newsguy.com>,
>> b.s...@csuohio.edu says...
>
>>> <Zeus> is from PIE */dyeu-/ 'to shine'.
>>
>> deus or deity is also proposed,
>
>Be aware that multiple words can be derived from the same word in a
>proto-language. Be aware also that Greek and Latin are different
>languages, although related.
Perhaps more to the point are these links
http://ccat.sas.upenn.edu/~jfarrell/courses/spring96/myth/feb12.html
http://www.geocities.com/geenath_2000/greek1.html
>
>
>> but as you go on to write
>> Zeus pate:r you should admit the meaning is sky father.
>
>That's is indeed what it means. But it's derived from PIE morphemes
>(and shows up _independently_ in Greek, Latin, Sanskrit, and maybe
>some others).
That is one theory.
"One of the central characteristics of both Zeus and Jupiter
is that they are considered to be the "fathers" of many of
the other gods, and to be the symbolic "fathers" of the
universe as a whole. Jupiter's name actually shows this:
the Romans also called him "Diespiter" and understood this
name to mean "Dies pater" = "Father of the Day" or "Sky Father".
"Pater" (="Father") is also a common epithet of the Greek Zeus,
who is frequently addressed as "Zeus pater" (="Father Zeus").
Now, the similarity of the names "Jupiter" and "Zeus pater"
is noticeable, and anyone conversant with the Indo-European
hypothesis might well wonder whether the names were related.
If one then learns that there is a a sky god in the ancient
Indian pantheon named "Dyaus-pitar" and that this god shows
many of the same characteristics ascribed to Zeus and Jupiter,
it becomes difficult not to see the same pattern at work in
mythology that we have observed in the case of languages."
Another is that of the Greeks themselves.
"Linguistically, these cultures were outside the Indo-European family,
and the general shape of their religious systems too differs from that
of the Greeks. Nevertheless, Herodotus did not shrink from tracing
certain Greek institutions to the Egyptians in particular, and from
identifying certain Greek gods and goddesses with Egyptian counterparts.
There is, moreover, the myth of Io and her descendants Io was the
daughter of the King of Argos. Seduced by Zeus, she wandered to Egypt
and gave birth to a child, Epaphus. Epaphus became the father of Libya
-- the name of a large part of northern Africa -- and of Belus, who in
turn became the father of Danaus and Aegyptus. Danaus returned to his
ancestral Argos, while Aegyptus became king of Egypt.
(A portion of this myth is the subject of Aeschylus' Suppliants
or Suppliant Maidens.) Thus, acconrding to this myth, the Greeks
and the Egyptians were actually related through their ancestors
Danaus and Aegyptus, two brothers descended from the Argive heroine Io."
>> As for the word for father<peter<pater<pitar<ptah
>
>Bogus etymology detected. "pitar" is the specifically Sanskrit
>variant, and derives from a form almost identical to the Greek
>"pate:r", except that the 'a' was a laryngeal rather than an
>ordinary vowel.
Sanskrit and Greek came along a bit later than ancient Egyptian.
If the Greek Herodotus is correct certain Greek gods and goddesses
had Egyptian counterparts. If you accept that Lapis Lazuli and
Carnelian came to Egypt in the predynastic Naqada II from India
and Afghanistan by whatever routes and chains of middleman you
might allow that by Greek times the Egyptians had a cultural
sphere of influence that probably equaled or exceeded that of PIE.
>
>
>> As for the word for sky Egyptian nu
>> http://www.abcgallery.com/C/correggio/correggio5.html
>
>True or not, it's completely irrelevant to the IE etymology.
Not necessarily. Sure Egyptian is Afroasiatic but that wouldn't
prevent the Greeks from borrowing the Egyptian mythology along with
certain Greek institutions from the Egyptians in particular, and from
identifying certain Greek gods and goddesses with Egyptian counterparts
>
>
>> <Venus> is Latin, not Greek,
>>
>> Gee Brian, where do you think the Latin names came from?
>>
>> Look in any common dictionary. The Romans adopted the entire Greek
>> pantheon
>
>No, the Romans already had their own pantheon, which they mapped
>onto the Greek while preserving the original names. They _did_
>borrow a few from the Greeks (sometimes via the Etruscans, as with
>Herakles), and in the later period they borrowed exotic gods from
>all over the Middle East. But the basic pantheon that you learn in
>gradeschool is almost entirely native.
Which Roman gods predated Rome? Keep in mind that everybody borrowed
everything from everyone else and tell me which Roman gods you think
originated with the Romans and when their mythos dates to.
>
>> just as the Greeks adopted the Egyptian
>
>Not in general. Some of their pantheon is very obviously derived
>from the IE tradition.
Some of it goes back long before any IE tradition. Some of it
is derived from Mesopotamia. Try picking a specific god you think
is IE and lets see what that gods antecedents are.
>Others have unknown origins, presumably adopted from the aborigines.
What aboriginees? Australian aboriginees? Trace the origins back as
far as what you are familiar with and lets see where it goes from there.
>I don't think any of the gods from the
>main pantheon can be derived from Egyptian sources, though like the
>Romans they adopted all manner of exotica in the later period.
So is Herodotus mistaken or just misinformed?
>
>> and the Egyptians adopted gods and goddesses from Mesopotamia and
>> points beyond.
>
>IANAEgyptologist, but I don't think this is well established either.
Study up on it and then let me know what you think.
>
>> http://www.seds.org/nineplanets/nineplanets/venus.html "Venus
>> (Greek: Aphrodite; Babylonian: Ishtar) is the goddess of love and
>> beauty."
>
>Yes, the ancients _associated_ the gods of the various pantheons
>together as best they could (sometimes poorly), but that is not the
>same as saying that the gods had common origins.
Try this. Pick a particular god or goddess and collect images and
descriptions of that god or goddesses attributes. Take for example
an Indian Goddess with 10 arms. If you see another goddess with
8 arms and two wings and the same attributes would you suspect
a relationship? How about the set of goddesses who stand on lions?
>
>Some are so similar as to raise suggestions of influence if not
>outright borrowing, but there's not the faintest support for the
>mass borrowings you believe in.
Searched the web for "the same goddess".
Results 1 - 10 of about 1,050.
http://members.tripod.com/Dragonrest/ishtar.html
"Her name varied from place to place, but it was the same goddess
who was known as Inanna, Innin, Astarte, Ashtar, and Aphrodite
among other names. Ishtar first arose among the Sumerians sometime
in the third millennium. They created an entire pantheon of gods
who were like humans - only better. The gods of Sumer reflected
the general pessimism of the Sumerians, but also their belief that
the human mind could divine the minds of gods by observing perceived
supernatural activity.
The Sumerians' views were a major influence on their contemporaries
(especially the early Semites) as well as on their successors, the
Babylonians. They also influenced the Hittites, Assyrians, Elamites,
and those living in Palestine. Certain Sumerian gods made the leap
to Greece and later to Rome, and Ishtar was such a deity. She became
Aphrodite to the Greeks. They stripped her of her war-making aspect
and focused almost solely on her nature as goddess of love (especially
sexual) and beauty. From the Greeks, the Romans adopted this goddess
as their own under the name of Venus. All forms of Ishtar under all
of their different names were associated with the planet we now know
as Venus and which was first known as the morning and evening stars.
Thus we are able to see how the worship of this goddess has reached
across the void of time and touched us in some small way."
Campbell, Joseph. The Masks of God: Creative Mythology. New York: The Viking Press, 1974.
Frazer, Sir James George. The Golden Bough: A Study in Magic and Religion, Volume II Abridged Edition. New York: Macmilian Company, 1951.
Goodrich, Norma Lorre. Ancient Myths. New York:New American Library, 1960.
Harding, M. Esther. Woman's Mysteries: Ancient and Modern. New York: Perennial Library, 1976.
Hawkes, Jacquetta. Dawn of the Gods. New York: Random House, 1968.
Hawkes, Jacquetta. The First Great Civilizations:Life in Mesopotamia, the Indus Valley, and Egypt. New York: Alfred A. Knopf, 1973.
Kramer, Samuel Noah. Cradle of Civilization. New York: Time Incorporated, 1967.
Moscati, Sabatino. Ancient Semitic Civilizations. New York:Capricorn Books, 1960.
Oppenheim, A. Leo. Ancient Mesopotamia: Portrait of a Dead Civilization. Chicago: The University of Chicago Press, 1965.
Parrider, Geoffrey, Editor. World Religions:From Ancient History to the Present. New York:Facts on File Publications, 1983.
Preston, James J., Editor. Mother Worship:Themes and Variations. Chapel Hill, North Carolina:The University of North Carolina Press, 1983.
Reinhold, Meyer. Past and Present: The Continuity of Classical Myths. Toronto, Canada: A. M. Hakkert Ltd., 1972.
>> If you want to you can trace her origins all the way back to
>> India.
>>
>>> and is from PIE */wen-/ 'to desire, strive for'.
>>
>> No, not even close.
>
>And you're an authority who can dispute with the experts, eh?
Experts don't have to dispute.
>
>>>These are clearly not borrowings Egyptian.
>>
>> You are clearly not very knowledgable about pantheons. Try reading
>> Budge "Gods of the Egyptians" 2 vol or look at any of the on line
>> material, its no secret.
>
>Most on-line material is rubbish. Budge appears not to be much
>better, as witness these reviews on Amazon:
Your knowledge of Egyptology is derived from Amazon abstracts?
If it is true that you have never read Budge, and have no idea
why he was knighted for his work it might be worth your while
to check him out.
He may be of some use to people like you who are interested beginners,
his work includes the cartouches of all the kings listed by dynasty,
the names of gods broken down into nome gods, foreign gods, gods of
the hours of the day and night,etc with lots of cross referencing
plus a number of books about Egypt in general, "The Nile", "The Mummy",
Cleopatra's Needle,...Many of the Books Budge wrote Amazon gives five stars.
Later you will find he's useful when you are trying to read an inscription
and want to see how the names of the gods were spelled and what the various
forms of the titles and formulas were. To use him effectively you need Gardiner,
Faulkner, Baines and Mal'ek, Loprieno and Wilkenson at a minimum.
>As it happens with many of Budge's books, this two-volumes set is
>quite out-dated and, moreover, it is highly-speculative (but without
>warning one that what he says is just that: speculation). ...
>Another criticism, which can be extended over to any of his other
>titles, is the lack or meagre references to the bibliography or
>documents from which he extracted his quotations. So that, BEGINNERS
>BEWARE!
>"""
>
>I think that last sentence was directed at you, Steve.
When you finally do get around to wanting to read something about Egypt
be sure and let Amazon be your guide.
>Here's another:
>
>"""
> The most frustraing thing about E.A. Wallis Budge's books is that
> it's often impossible to tell when he's using conjecture and when
> he's actually stating a fact. Far too often he'll make a statement
> that today we know to be false -- for example, that the name of
> "Bast" and "Sekhmet" derive from words for "fire", which they don't
> as they mean (respectively) "Devouring/Ointment Lady" and "Powerful
> Lady" (nothing at all to do with fire) -- and then make a statement
> that actually has some basis in fact.
"Devouring ointment lady"? give me a break... I think I will stick
with Gardiner, Faulkner and Budge.
Vol I p 446
"The goddess Bast is usually represented in the form of a woman
with the head of a cat but she also has at times the head of a lioness
surmounted by a snake; in her right hand she holds a sistrum and in her
left an aegis with the head of a cat or lioness on top of it...
If we are to seek for the derivation of the word bast in Egyptian
we must connect it with the word for fire [bes] and regard the goddess
as a personification of the sun which made itself manifest in the form of heat"...
"Bast and Sekhet(not Sekhmet) are described as closely connected forms of a
female personification of the heat and light of the sun god and wherin they
are made to act as destroyers of the enemies of the sun god and of the deceased."
Look up Q7 in Gardiner and you will see det fire
In the form Budge uses it [bes] it has the sense of fire brand or torch
but keep in mind Bastet is a middle Egyptian word and here Budge is talking
about an ancient Egyptian etymology.
Faulkner p 78 [b3s] devour follows the name Bastet (devouring desire)
In other words "female personification of heat" refers to (lust and passion)
Bast and Sekhet are a couple of hot chicks
Bast and Sekhet are also foreign gods from desert regions
where the sun can both be a good friend and a terrible enemy.
> For BEGINNERS, I would say:
> STAY AWAY from this book until you have a very firm grasp of
> Egyptian society and culture. ... For ADVANCED USERS, I would say:
> Yes, you should probably read this, but be sure that when Budge
> makes a statement that there's some way to verify what he's saying,
> or your research could be seriously skewed.
>"""
>
>That one had a sentence for you too, Steve. But not the last one.
From the passage above you can see how Budge does provide useful information
and also how if you don't immediately understand it you can check it out
in Gardiner and Faulkner or whatever other sources you may chose to acquire.
>And here's another review:
>
>"""
>Budge's works are generally considered a bit of an Egyptological
>embarrassment; his intentions were noble but he seemed to favor
>quantity over quality when it came to research ... This book, like
>all of his others, is rife with errors, contradictions,
>mistranslations of the ancient texts and sadly void of references
>for Budge's countless "scientific" assertions. ... The amateur
>Egyptolgist may use this book with a grain of salt and opt instead
>for scholarly recent books by Meeks or Hornung.
>"""
Faulkner lists Budge under abbreviations of texts and books cited
Gardiner puts him in his list of Abbreviations.
>
>The last sentence of that one would be good advice for you, Steve.
[mph(.w) ntj nj ph=f tw]
>
>Remember, believe half of what you read, none of what you hear, and
>the opposite of what you see on the Web.
[nn-wn ph.wj=fj]
>
>>>>The Romans did the same to the Greeks as the Greeks did to the
>>>>Egyptians sky father=Jupiter=Zeus-pitar=Nu-Ptah etc;
>>>
>>>More confusion. The Latin is <Iu:piter>, the Greek, <Zeus
>>>pate:r>, from PIE */dyeu-p@ter-/; nothing to do with Egyptian.
>>
>> from
>> http://www.bartleby.com/61/25/Z0012500.html
>>
>> Zeus
>> NOUN: Greek Mythology The principal god of the Greek pantheon,
>> ruler of the heavens, and father of other gods and mortal heroes.
>> ETYMOLOGY: Greek. See dyeu- in Appendix I. WORD HISTORY: Homer's
>> Iliad calls him "Zeus who thunders on high" and Milton's Paradise
>> Lost, "the Thunderer,"
>>
>> so it is surprising to learn that the Indo-European ancestor of
>> Zeus was a god of the bright daytime *sky*.
>
>Funny, scholars who actually know something about it don't find it
>surprising. In fact it makes a great deal of sense in the
>primitive IE pantheon, as best we can reconstruct it.
While you are at it try and explain why a primitive backwoods
rustic IE linguistics with its pantheon should dominate an older
more sophisticated pantheon that had existed for millenia in the
civilized cities.
In the context above the author is pointing out that there are
two versions
1.)thunder god associated with storms
2.)sky father associated with bright sunny day
The suggestion is that an older form has been replaced with a borrowing.
>
>
>> [Egyptian nu-ptah, sky
>> father (Nu is the sky and Ptah, whose head is blue, is its
>> creator)]
>>
>> Zeus is a somewhat unusual noun in Greek,
>> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ having both a stem Zn-
>> (as in the philosopher Zeno's name) and a stem Di-(earlier Diw-).
>
>It's not rare for Greek (or any other IE language) to have
>variations where different _stems_ are built from a single _root_.
Again the suggestion is that its borrowed into Greek
>
>> In the Iliad prayers to Zeus begin with the vocative form Zeu
>> pater, "o *father* Zeus."
>
>Yes, that's the expected vocative form of "Zeus".
>
>You're quoting a lot of reasonably accurate material as if it
>supports your case, but unfortunately it doesn't have any bearing
>on your claims whatsoever.
I understand that you don't see the connection yet, but then
you have some reading to do and afterwards we will see
if you learned anything.
>
>
>> Father Zeus was the head of the Greek pantheon; another ancient
>> Indo-European society, the Romans, called the head of their
>> pantheon Ipiter or Iuppiter-Jupiter. *The -piter part of his name
>> is just a reduced form of pater, "father,"* and Iov corresponds to
>> the Zeu in Greek: Ipiter is therefore precisely equivalent to Zeu
>> pater and could be translated "father Jove." Jove itself is from
>> Latin Iov", the stem form of Ipiter, an older version of which in
>> Latin was Diov", showing that the word once had a d as in Greek
>> Diw-.
>
>None of which indicates any derivation from Egyptian...
Ask yourself what Egyptian god has a blue head
and then read some more abstracts at Amazon
till you find out why...
>
>> An exact parallel to Zeus and Jupiter is found in the Sanskrit god
>> addressed as Dyau pitar: pitar is "father," and dyau means "sky."
>> We can equate Greek Zeu pater, Latin I-piter, and Sanskrit dyau
>> pitar and reconstruct an Indo-European deity, *Dyus pter, who was
>> associated with the sky and addressed as "father."
>
>Indeedie. Are you going to claim that the speakers of Sanskrit
>also borrowed the name from the Egyptians?
Sanskrit and Greek come along how many millenia after ancient Egyptian?
>
>> Comparative philology has revealed that the "sky" word refers
>> specifically to the bright daytime sky, as it is derived from the
>> root meaning "to shine." This root also shows up in Latin dis
>> "day," borrowed into English in words like diurnal. "Closely
>> related to these words is Indo-European *deiwos "god," which shows
>> up, among other places, in the name of the Old English god Tw in
>> Modern English Tuesday, "Tiw's day." *Deiwos is also the source of
>> Latin dvus "pertaining to the gods," whence English divine and the
>> Italian operatic diva, and deus, "god," whence deity."
>
>None of which has anything to do with Egyptian...
Ask yourself what Egyptian god has a blue head
and then read some more abstracts at Amazon
till you find out why...
>
>> Next you will tell me that the Hittites had no knowledge of
>> Egyptian gods and the Egyptians and Greeks no knowledge of Hittite
>> gods
>
>Completely irrelevant to your claims. The word "Zeus" and the god
>it referred to, and their cognates in the other IE languages, come
>from the PIE language and the culture that spoke it. Do you claim
>that Egyptian cultural imperialism dominated southeast Europe and
>the Eurasian steppes in 4000 BCE?
Is that where and when you think we should look for PIE?
Apparently you haven't ever really thought this out...
Who is it you think is living in the Eurasian steppes c 4000 BC?
How do they subsist? Are they hunter gatherers or settled farmers?
What size are their populations, how far apart are they and how
often do they get together?
The horse was just beginning to be used as a beast of burden and
perhaps occasionally ridden c 1800 BC. On the other hand boats
were carrying cargos between India and Mesopotamia in the Jemdet Nasr
You have a lot of reading to do.
>Bobby Bryant
>Austin, Texas
steve
steve
>
>On Tue, 14 May 2002 16:13:12 -0600, steve wrote:
>
>> In article <abrv66$d3t$1...@geraldo.cc.utexas.edu>,
>> bdbr...@mail.utexas.edu says...
>>>
>>>On Tue, 14 May 2002 14:23:44 -0600, steve wrote:
>>>
>>>> Show me how the Greeks would use an abacus to generate the well
>>>> known architectual proportions used in the various orders of
>>>> architecture
>>>
>>>AIUI, they didn't use an abacus or Egyptian arithemetic either;
>>>they used 1:1 or foreshortened scale geometric constructions on
>>>the walls of the cella, and removed them during the finishing.
>>>These have been discovered on at least one temple that was never
>>>finished.
>>
>> I'm not talking about the layout by the tekton. I'm talking about
>> the design of the system by the arch tekton or master builder. See
>> Normands "Parallel of the Orders of Architecture"
>
>What precisely does this book say to support your claims? Give a
>short quote and a page number, please. By chance I'll be on campus
>tomorrow, and not far from the Classics Library.
You will need the Authors name; R A Cordingley
Look at Fig 4 p 12
and A-E. Method of Drawing the Renaissance orders
Plate 36 setting out of volutes
What I want you to think about is the design of the system
you can bring your abacus if you think it will help.
>
>> Drawings to scale were made by the Egyptians and used for
>> construction in the OK.
>
>And this supports your claim, how?
I was asking you to show me how the Greeks would use an abacus
to generate the well known architectual proportions used in the
various orders of architecture. The point is the proportions
are established by geometry and an abacus is useless.
As far as scale goes, the Egyptian use of a layout grid
based on a septenary system of measures and unit fractions
almost forced them into the fibonacci series.
>> Though determination of which proportions are pleasing to the eye
>> is often linked to the fibonacci series, they occur naturally out
>> of a septenary system of standards of measure that uses unit
>> fractions...
>
>Enough with the obfuscation. Got any peer-reviewed publications that
>you can cite to support your claim about the origin of the word
>"mathematics"?
You can read some of my papers on "Egyptian unit fractions in
InScription - Journal of Ancient Egypt; Vol 1 1997, Vol 2 1998
Brian M. Scott
>In article <3ce188b1....@enews.newsguy.com>, b.s...@csuohio.edu says...
>>On Tue, 14 May 2002 20:23:44 GMT, whi...@shore.net (steve) wrote:
>>>In article <3ce153de....@enews.newsguy.com>, b.s...@csuohio.edu says...
>>>>On Tue, 14 May 2002 17:35:13 GMT, whi...@shore.net (steve) wrote:
>>>>>>>Egyptian: [ma3't] true [mh] (cubit measure); [ma3't mh] (true measure)
>>>>>>>If you go by the fact that the Greeks and Romans used Egyptian unit fractions
>>>>>>>to perform their calculations
>>>>>>They didn't.
>Baloney.
You know, repetition won't make it any truer.
>"The earliest Egyptian and Greek fractions were *usually unit fractions*
Yes, we've heard that before. Half of it, the part about the
Egyptians, is irrelevant to your claim. The rest is only marginally
relevant, since it refers only to the Greeks, not the Romans, and only
to '[t]he earliest ... Greek fractions' at that.
[...]
>>>>As usual, you don't know what you're talking about.
>>>Baloney on Rye.
>>>http://www.mathpages.com/home/whyunits.htm
>>Bad site: no references, and no indication of authorship.
>Bad Site? really??? Kevin Brown?? Stanford??? means nothing to you?
If there is anything on the site to indicate that it is Kevin Brown's
or to associate it with Stanford, such information is well hidden.
And no, Kevin Brown doesn't mean much to me. He has compiled a
collection of decent short articles on mathematics, history of
mathematics, and physics, and I've seen him talk reasonably
competently (though not completely without error) about mathematics
and its history on sci.math
>no references? What do you call this?
>http://www.mathpages.com/rr/bibliog/bibliog.htm
Since it's in the subdirectory http://www.mathpages.com/rr/, on its
face it's a bibliography for the section of the site called
'Reflections on Relativity'. Close examination, however, shows that
although most of it deals with physical topics, it does include a
handful of books on mathematics and the history of mathematics. It's
impossible to say whether *they* were misplaced, or whether the
bibliography is really for the entire site; it does not appear to
contain enough purely mathematical sources for the latter hypothesis,
however.
In any case it is merely a bibliography, not a set of references for
specific claims. If you don't understand the difference, feel free to
ask for an explanation.
>perhaps you would have to be a mathematician to enjoy it.
I am. However, it would be of more use to a mathematical physicist.
>>>>For starters, you're confusing calculation with representation.
>>>Baloney.
>>>Brian you have no interest in or knowledge of the Egyptians
>>>Greeks and Romans use of unit fractions
>>>http://www.mathpages.com/home/kmath340.htm
>>>http://www.mathpages.com/home/whyunits.htm
>>>or of the modern mathematicians
>>>who are working on them.
>>Wrong on all counts. As usual.
>You just proved me right.
>>Not only do I know rather more about
>>the history of calculation and numeration systems than you do, I have
>>the advantage of actually understanding some mathematics.
>Tell us what you know about Kevin Brown and unit fractions Brian
I've already summarized what I know of Kevin Brown. Why you think
that this has anything to do with knowledge of mathematics is a
mystery, however: even if he were of any particular significance,
knowledge of mathematics certainly doesn't require knowledge of
mathematicians. As for unit fractions, I know (and have taught) far
more about them than I have time or desire to type (or to inflict on
sci.lang, where the subject is wildly off-topic).
>>>http://www.mathpages.com/home/kmath315.htm
>>>http://www.mathpages.com/mobius/mobius.htm
>>Irrelevant.
>That you don't understand the relevence doesn't make it irrelevant.
Oh, by all means feel free to explain exactly what linear fractional
transformations have to do with unit fractions; I could use a laugh.
>>>http://www.ics.uci.edu/~eppstein/numth/egypt/
My, but you are a clumsy liar! I dismissed most of the material on
David Eppstein's site for what it is: puzzles of no great mathematical
significance. You are now listing the entire main table of contents
for Brown's MathPages, a different site altogether, most of which has
nothing whatsoever to do with unit fractions
>>>>As we know from
>>>>numerous pictures (among other sources), the Greeks and Romans did
>>>>most of their *calculation* with the functional equivalent of the abacus.
>>>Baloney.
>>>Show me how the Greeks would use an abacus to generate the
>>>well known architectual proportions used in the various orders
>>>of architecture
>>You really haven't a clue about early uses of calculation, have you?
>Null response; if you can't do it why not just say so.
There's nothing to do. Your question is based on your own
misconceptions.
>>[snip unit fractions and Fibonacci numbers, a modern connection
>>unknown to the Greeks]
>!!!
>unknown to the Greek mathematicians, but known to the Egyptian architects?
Known to neither. And obviously not understood by you.
>http://www.bath.ac.uk/brlsi/egypt.htm
>http://mtcs.truman.edu/~thammond/history/Fibonacci.html
The second contains nothing that is to the point, and the first notes
that claims for an elaborate proportional system underlying Egyptian
architecture are not supported by actual measurements.
>"Technical Analysis from A to Z"
>By Steven B. Achelis
>"Leonardo Fibonacci was a mathematician who was born in Italy
>around the year 1170. It is believed that Mr. Fibonacci discovered
>the relationship of what are now referred to as Fibonacci numbers
>while studying the Great Pyramid of Gizeh in Egypt.
[...]
>http://www.equis.com/free/taaz/fibonacci.html
Mr Achelis appears not to know what he's talking about; perhaps he's
your long-lost cousin?
>>>Tell us why the Greeks would use an abacus for this. The Greeks based their
>>>mathematics on geometry rather than numerical analysis.
>>Not true.
>False. The Greeks did not use numerical analysis
You're wrong.
>> It's quite clear from the sophistication of the
>>_Arithmetica_ of Diophantus that they must have had a fairly strong
>>non-geometric tradition, albeit almost *nothing of it survives*.
That's not what I wrote. The asterisks are your dishonest addition.
>http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Diophantus.html
>"The most details we have of Diophantus's life come from the Greek Anthology,
>compiled by Metrodorus around 500 AD. This collection of puzzles contain
>one about Diophantus which says:-
His life is irrelevant. What is important is that we have six of the
probably 13 books of his 'Arithmetica' and thus a very good idea of
the level of his knowledge. What is mostly lost, as you would have
understood if you could actually read, is the earlier work by others
on which it must have been partly based.
[...]
>>But all of this is also irrelevant, since most serious computation was
>>done in connection with mercantile activities, and most non-mercantile
>>computation was astronomical, not purely mathematical.
>Baloney.
Fact. Your ignorance is showing again.
>The achievements of Greek geometry amount to nothing more than
>the ability to calculate how to double a talent in the Agora?
Are you really so stupid as to have so badly misread what I wrote?
And so ignorant as to think that most Greek geometry dealt with
numerical computation? <sigh> Yes, probably.
>>>> (Indeed, two Roman abaci about the size of a modern pocket
>>>>calculator still survive.) How they *recorded* the results of these
>>>>calculations is another matter.
>>>Baloney.
>>The abaci do indeed survive. So does knowledge of how the results of
>>computations were recorded.
>>>>As we know from
>>>>numerous pictures (among other sources), the Greeks and Romans did
>>>>most of their *calculation* with the functional equivalent of the abacus.
>Show me the abacus the Greeks used to determine how to formulate their
>classical mathematical problems. They wouldn't have allowed it was a proof
>if someone did work out how to square a circle, double a cube and trisect
>an angle with an abacus.
This is a non sequitur, and an exceptionally stupid one at that,
inasmuch as even you appear dimly to recognize that numerical
calculation, the subject of my comment, has nothing to do with these
problems.
>>>The calculation is dependant on unit fractions not decimals
>>No one said anything about decimals.
[snip irrelevance]
>>They *did* in fact use positional notation for astronomical purposes,
>>but it was sexagesimal, not decimal.
>bssst
>try sexagesimal and decimal...plus unit fractions
No. The positional notation used for astronomical purposes was
entirely sexagesimal as a positional notation. I shan't bother to
explain, as I doubt that you even know what that means or how to tell.
I'll merely say that you're confusing Greek and Roman notational
systems in general with the specific one used for astronomical
calculations (and used, I might add, well into the Middle Ages).
[...]
>>>>>Egyptian unit fractions were in common use by the Greeks and Romans
>>>>>and in Europe as late as Medieval times.
>>>>In *common* use? No.
>>>In common use yes! First in the Attic and then in the Ionian system.
>>Your claim was that unit fractions were in common use by Greeks, by
>>Romans, and in the European Middle Ages. Taken as a whole the
>>statement is false.
>No its not. You use "Egyptian unit fractions" nearly every day
>in "making change in commercial transactions". Thus, a penny = $1/100;
>a nickel = $1/20; a dime = $1/10; a quarter = $1/4; a fifty-cent piece = $1/2
Tsk, tsk, tsk. Do you really think that this weaseling won't be seen
for what it is? Especially by those of us who remember Tuxtla?
>>>>The Romans *occasionally* used unit fractions
>>>>in the Egyptian fashion, but as a rule they simply used duodecimal
>>>>fractions, either approximating if necessary (e.g., representing 5/9
>>>>as ~7 unciae, or septunx), or translating into even smaller units
>>>>(e.g., 2/3 unciae = 16 scruples).
>>>Baloney.
>>>The Romans used factor rich decimal, hexadecimal and octal systems
>>>to make the use of unit fractions easier.
>>No, child. Sixteen and eight are *not* conveniently divisible by a
>>variety of smaller integers,
[snip squink about measures]
>>>>Exactly. And this system continued in use into the Middle Ages for
>>>>astronomical work.
>>>Yes Brian the Egyptian astronomical calculations were copied by the Greeks
>>The subject is notational systems used for astronomical calculations,
>>not the calculations themselves, and the system in question is
>>Babylonian, not Egyptian.
>>[snip irrelevant references]
>Brian you can snip things that refute you without response if you like
>but you certainly aren't going to make your case by ignoring the facts.
When you actually manage to find a refutation of anything I've said,
I'll be sure to let you know. In the meantime recommend you to try
distinguishing relevant from irrelevant facts and facts from wishful
thinking, but I have little hope of any success on your part.
Brian M. Scott
>In article <absdop$l3c$1...@geraldo.cc.utexas.edu>, bdbr...@mail.utexas.edu says...
>>On Tue, 14 May 2002 16:52:44 -0600, steve wrote:
>>> In article <3ce16c4e....@enews.newsguy.com>,
>>> b.s...@csuohio.edu says...
[snip more evidence that Steve can't distinguish between a deity and
its name]
>>>> and is from PIE */wen-/ 'to desire, strive for'.
>>> No, not even close.
>>And you're an authority who can dispute with the experts, eh?
>Experts don't have to dispute.
Obviously Steve hasn't had much exposure to experts!
[...]
>If it is true that you have never read Budge, and have no idea
>why he was knighted for his work it might be worth your while
>to check him out.
Elton John was also knighted for his work.
>He may be of some use to people like you who are interested beginners,
Isn't he cute when he condescends? I'm convinced that he's genuinely
too stupid to realize what a spectacle he routinely makes of himself.
[...]
>Many of the Books Budge wrote Amazon gives five stars.
Which simply means that they were popular with a bunch of readers. It
says nothing about the scholarly value of the books.
[...]
>>> from
>>> http://www.bartleby.com/61/25/Z0012500.html
>>> Zeus
>>> NOUN: Greek Mythology The principal god of the Greek pantheon,
>>> ruler of the heavens, and father of other gods and mortal heroes.
>>> ETYMOLOGY: Greek. See dyeu- in Appendix I. WORD HISTORY: Homer's
>>> Iliad calls him "Zeus who thunders on high" and Milton's Paradise
>>> Lost, "the Thunderer,"
>>> so it is surprising to learn that the Indo-European ancestor of
>>> Zeus was a god of the bright daytime *sky*.
>>Funny, scholars who actually know something about it don't find it
>>surprising. In fact it makes a great deal of sense in the
>>primitive IE pantheon, as best we can reconstruct it.
>While you are at it try and explain why a primitive backwoods
>rustic IE linguistics with its pantheon should dominate an older
>more sophisticated pantheon that had existed for millenia in the
>civilized cities.
A non sequitur, if not a deliberate attempt to change the subject,
demonstrating once again Steve's inability to write English and his
confusion of language with culture. (Peter, you know everybody: who
does 'primitive backwoods rustic IE linguistics'?)
>In the context above the author is pointing out that there are
>two versions
>1.)thunder god associated with storms
>2.)sky father associated with bright sunny day
>The suggestion is that an older form has been replaced with a borrowing.
No, it isn't. That's almost as creative a reading as Steve's version
of the Tale of the Shipwrecked Sailor -- the one that he got by
unwittingly trying to read the text backwards because he didn't know
the most basic fact about Egyptian hieroglyphs.
[...]
>>> An exact parallel to Zeus and Jupiter is found in the Sanskrit god
>>> addressed as Dyau pitar: pitar is "father," and dyau means "sky."
>>> We can equate Greek Zeu pater, Latin I-piter, and Sanskrit dyau
>>> pitar and reconstruct an Indo-European deity, *Dyus pter, who was
>>> associated with the sky and addressed as "father."
>>Indeedie. Are you going to claim that the speakers of Sanskrit
>>also borrowed the name from the Egyptians?
>Sanskrit and Greek come along how many millenia after ancient Egyptian?
Steve has a little trouble with post hoc, ergo propter hoc. I suspect
that he also fails to realize that Mycenaean Greek is actually
attested only about a millennium after the start of the Old Kingdom.
[...]
BMS
Mike Cleven
> On Tue, 14 May 2002 16:10:13 GMT, whi...@shore.net (steve) wrote:
>
> [...]
>
>
>>There should be no confusion of astronomy, astrology and mathematics
>>because essentially they are all different approaches to the same thing.
>
>
> No, they're not.
Yes they WERE - before the Age of Reason. Or don't you know that Newton
and Kepler primarily viewed themselves as astrologers?
--
Mike Cleven
http://www.cayoosh.net (Bridge River Lillooet history)
http://www.hiyu.net (Chinook Jargon phrasebook/history)
Harlan Messinger
>In article <cq93eu85neom5ftc9...@4ax.com>, h.mes...@comcast.net says...
>>
>>whi...@shore.net (steve) wrote:
>>
>>>In article <3ce153de....@enews.newsguy.com>, b.s...@csuohio.edu says...
>>>>
>>>>On Tue, 14 May 2002 17:35:13 GMT, whi...@shore.net (steve) wrote:
>>>>
>>>>>>>Egyptian: [ma3't] true [mh] (cubit measure); [ma3't mh] (true measure)
>>>>
>>>>>>>If you go by the fact that the Greeks and Romans used Egyptian unit fractions
>>>>>>>to perform their calculations
>>>>
>>>>>>They didn't.
>>>>
>>>Baloney.
>>>
>>>"The earliest Egyptian and Greek fractions were usually unit fractions
>>>(having a numerator of 1), so that the fraction was shown simply by writing
>>>a numeral with a mark above or to the right indicating that the numeral
>>>was the denominator of a fraction."
>>>http://members.aol.com/jeff570/fractions.html
>>
>>Jeff 570 of prestigious AOL University? Do you know the *source* of
>>his information? You can't just point to any old page on the Internet
>>and call it "corroboration".
>
>What you should take away from this page is that what I'm trying
>to explain to Brian would be common knowledge to most reasonably
>bright high school students.
Wait a minute--you believe most reasonably bright high school students
are familiar with the details of the development of mathematical
methods and representation in the Middle East, Greece and Rome in
ancient times?
Bobby D. Bryant
> In article <absdop$l3c$1...@geraldo.cc.utexas.edu>, bdbr...@mail.utexas.edu says...
>>
>>On Tue, 14 May 2002 16:52:44 -0600, steve wrote:
>>
>>> In article <3ce16c4e....@enews.newsguy.com>,
>>> b.s...@csuohio.edu says...
>>
>>>> <Zeus> is from PIE */dyeu-/ 'to shine'.
>>>
>>> deus or deity is also proposed,
>>
>>Be aware that multiple words can be derived from the same word in a
>>proto-language. Be aware also that Greek and Latin are different
>>languages, although related.
>
> Perhaps more to the point are these links
>
> http://ccat.sas.upenn.edu/~jfarrell/courses/spring96/myth/feb12.html
> http://www.geocities.com/geenath_2000/greek1.html
Nothing there to support your claims.
>>> but as you go on to write
>>> Zeus pate:r you should admit the meaning is sky father.
>>
>>That's is indeed what it means. But it's derived from PIE morphemes
>>(and shows up _independently_ in Greek, Latin, Sanskrit, and maybe
>>some others).
>
> That is one theory.
That's the theory that all educated scholars subscribe to.
> "One of the central characteristics of both Zeus and Jupiter
> is that they are considered to be the "fathers" of many of
> the other gods, and to be the symbolic "fathers" of the
> universe as a whole. Jupiter's name actually shows this:
> the Romans also called him "Diespiter" and understood this
> name to mean "Dies pater" = "Father of the Day" or "Sky Father".
> "Pater" (="Father") is also a common epithet of the Greek Zeus,
> who is frequently addressed as "Zeus pater" (="Father Zeus").
> Now, the similarity of the names "Jupiter" and "Zeus pater"
> is noticeable, and anyone conversant with the Indo-European
> hypothesis might well wonder whether the names were related.
> If one then learns that there is a a sky god in the ancient
> Indian pantheon named "Dyaus-pitar" and that this god shows
> many of the same characteristics ascribed to Zeus and Jupiter,
> it becomes difficult not to see the same pattern at work in
> mythology that we have observed in the case of languages."
That actually contradicts what you're trying to argue.
> Another is that of the Greeks themselves.
>
> "Linguistically, these cultures were outside the Indo-European family,
> and the general shape of their religious systems too differs from that
> of the Greeks. Nevertheless, Herodotus did not shrink from tracing
> certain Greek institutions to the Egyptians in particular, and from
> identifying certain Greek gods and goddesses with Egyptian counterparts.
Yes, that was a popular sport in the ancient world. And notice the
qualification "certain", which covers the fact that the main
deities were *not* derived from Egypt.
> There is, moreover, the myth of Io and her descendants Io was the
> daughter of the King of Argos. Seduced by Zeus, she wandered to Egypt
> and gave birth to a child, Epaphus. Epaphus became the father of Libya
> -- the name of a large part of northern Africa -- and of Belus, who in
> turn became the father of Danaus and Aegyptus. Danaus returned to his
> ancestral Argos, while Aegyptus became king of Egypt.
>
> (A portion of this myth is the subject of Aeschylus' Suppliants
> or Suppliant Maidens.) Thus, acconrding to this myth, the Greeks
> and the Egyptians were actually related through their ancestors
> Danaus and Aegyptus, two brothers descended from the Argive heroine Io."
Again, a popular sport in the ancient world. The Romans claimed to
be of Trojan descent. (And for that matter, so did the English
almost two millenia later.)
>>> As for the word for father<peter<pater<pitar<ptah
>>
>>Bogus etymology detected. "pitar" is the specifically Sanskrit
>>variant, and derives from a form almost identical to the Greek
>>"pate:r", except that the 'a' was a laryngeal rather than an
>>ordinary vowel.
>
> Sanskrit and Greek came along a bit later than ancient Egyptian.
Irrelevant to your claims.
> If the Greek Herodotus is correct
He wasn't. Nor was he correct when he reported that inscriptions
on the pyramids told how many onions were used to pay the
construction workers.
> certain Greek gods and goddesses
> had Egyptian counterparts. If you accept that Lapis Lazuli and
> Carnelian came to Egypt in the predynastic Naqada II from India
> and Afghanistan by whatever routes and chains of middleman you
> might allow that by Greek times the Egyptians had a cultural
> sphere of influence that probably equaled or exceeded that of PIE.
Spheres of influence do not automatically extend along trade
routes. (And if you thought they did, how would you know which way
the influence extended?)
>>> As for the word for sky Egyptian nu
>>> http://www.abcgallery.com/C/correggio/correggio5.html
>>
>>True or not, it's completely irrelevant to the IE etymology.
>
> Not necessarily. Sure Egyptian is Afroasiatic but that wouldn't
> prevent the Greeks from borrowing the Egyptian mythology along with
> certain Greek institutions from the Egyptians in particular, and from
> identifying certain Greek gods and goddesses with Egyptian counterparts
>>
>>
>>> <Venus> is Latin, not Greek,
>>>
>>> Gee Brian, where do you think the Latin names came from?
>>>
>>> Look in any common dictionary. The Romans adopted the entire Greek
>>> pantheon
>>
>>No, the Romans already had their own pantheon, which they mapped
>>onto the Greek while preserving the original names. They _did_
>>borrow a few from the Greeks (sometimes via the Etruscans, as with
>>Herakles), and in the later period they borrowed exotic gods from
>>all over the Middle East. But the basic pantheon that you learn in
>>gradeschool is almost entirely native.
>
> Which Roman gods predated Rome? Keep in mind that everybody borrowed
> everything from everyone else and tell me which Roman gods you think
> originated with the Romans and when their mythos dates to.
Juppiter, Neptune, etc.
>>> just as the Greeks adopted the Egyptian
>>
>>Not in general. Some of their pantheon is very obviously derived
>>from the IE tradition.
>
> Some of it goes back long before any IE tradition.
Possibly, probably even, but not in the way you suggest.
> Some of it
> is derived from Mesopotamia. Try picking a specific god you think
> is IE and lets see what that gods antecedents are.
We've been talking about the Sky Father for a couple of days
already. Your antecedents are bogus.
>>Others have unknown origins, presumably adopted from the aborigines.
>
> What aboriginees? Australian aboriginees? Trace the origins back as
> far as what you are familiar with and lets see where it goes from
> there.
"Aborigine" means "the people who lived there first". For Greeks,
Romans, and Indians it means the people who lived in Greece, Italy,
and India before the IE speakers arrived. (Pedantic note: those
might not really be the "first" people to live in those regions,
but unfortunately we can't trace the prehistory back any further,
so the term is used as a term of convenience. FWIW it's a Latin
word, and the Roman authors used it as above. Livy, IIRC, uses it
in his mythical description of the prehistory of Rome.)
>>I don't think any of the gods from the
>>main pantheon can be derived from Egyptian sources, though like the
>>Romans they adopted all manner of exotica in the later period.
>
> So is Herodotus mistaken or just misinformed?
Probably both. As I said above, deriving pantheons from other
pantheons was a popular passtime in the ancient world.
BTW, if you actually look at the mythology pertaining to the
various gods, you find more reason to believe the Greek pantheon,
or at least the stories told about them, derived from Mesopotamia.
Clearly, they wouldn't waste their time on you like we are.
>>>>These are clearly not borrowings Egyptian.
>>>
>>> You are clearly not very knowledgable about pantheons. Try reading
>>> Budge "Gods of the Egyptians" 2 vol or look at any of the on line
>>> material, its no secret.
>>
>>Most on-line material is rubbish. Budge appears not to be much
>>better, as witness these reviews on Amazon:
>
> Your knowledge of Egyptology is derived from Amazon abstracts?
>
> If it is true that you have never read Budge, and have no idea
> why he was knighted for his work it might be worth your while
> to check him out.
>
> He may be of some use to people like you who are interested beginners,
> his work includes the cartouches of all the kings listed by dynasty,
> the names of gods broken down into nome gods, foreign gods, gods of
> the hours of the day and night,etc with lots of cross referencing
> plus a number of books about Egypt in general, "The Nile", "The Mummy",
> Cleopatra's Needle,...Many of the Books Budge wrote Amazon gives five stars.
>
> Later you will find he's useful when you are trying to read an inscription
> and want to see how the names of the gods were spelled and what the various
> forms of the titles and formulas were. To use him effectively you need Gardiner,
> Faulkner, Baines and Mal'ek, Loprieno and Wilkenson at a minimum.
You have made it perfectly clear that you are trying to master the
advanced material without bothering with the basics.
The archaic IE cultures didn't have much influence on Egypt or
Mesopotamia, except for one Hurrian kingdome in northern
Mesopotamia. Your argument is completely irrelevant, partly due to
erroneous assumptions, partly because it has nothing to do with
what I've been trying to explain to your.
> In the context above the author is pointing out that there are
> two versions
> 1.)thunder god associated with storms
> 2.)sky father associated with bright sunny day
You are amazed that the Sky Father wields the thunderbold?
> The suggestion is that an older form has been replaced with a borrowing.
Not at all. Ask yourself where the thunder comes from.
>>> [Egyptian nu-ptah, sky
>>> father (Nu is the sky and Ptah, whose head is blue, is its
>>> creator)]
>>>
>>> Zeus is a somewhat unusual noun in Greek,
>>> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ having both a stem Zn-
>>> (as in the philosopher Zeno's name) and a stem Di-(earlier Diw-).
>>
>>It's not rare for Greek (or any other IE language) to have
>>variations where different _stems_ are built from a single _root_.
>
> Again the suggestion is that its borrowed into Greek
The suggestion of certain parties who know nothing of historical
linguistics.
>>> In the Iliad prayers to Zeus begin with the vocative form Zeu
>>> pater, "o *father* Zeus."
>>
>>Yes, that's the expected vocative form of "Zeus".
>>
>>You're quoting a lot of reasonably accurate material as if it
>>supports your case, but unfortunately it doesn't have any bearing
>>on your claims whatsoever.
>
> I understand that you don't see the connection yet, but then
> you have some reading to do and afterwards we will see
> if you learned anything.
Actually, I have done a great deal of reading in historical
linguistics and classial civilization. That's how I know you're
peddling bunkum.
>>> Father Zeus was the head of the Greek pantheon; another ancient
>>> Indo-European society, the Romans, called the head of their
>>> pantheon Ipiter or Iuppiter-Jupiter. *The -piter part of his name
>>> is just a reduced form of pater, "father,"* and Iov corresponds to
>>> the Zeu in Greek: Ipiter is therefore precisely equivalent to Zeu
>>> pater and could be translated "father Jove." Jove itself is from
>>> Latin Iov", the stem form of Ipiter, an older version of which in
>>> Latin was Diov", showing that the word once had a d as in Greek
>>> Diw-.
>>
>>None of which indicates any derivation from Egyptian...
>
> Ask yourself what Egyptian god has a blue head
Why would that be relevant?
> and then read some more abstracts at Amazon
> till you find out why...
I certainly put more stock in skeptical Amazon reviews than I do in
your believe-anything-about-egypt claims.
>>> An exact parallel to Zeus and Jupiter is found in the Sanskrit god
>>> addressed as Dyau pitar: pitar is "father," and dyau means "sky."
>>> We can equate Greek Zeu pater, Latin I-piter, and Sanskrit dyau
>>> pitar and reconstruct an Indo-European deity, *Dyus pter, who was
>>> associated with the sky and addressed as "father."
>>
>>Indeedie. Are you going to claim that the speakers of Sanskrit
>>also borrowed the name from the Egyptians?
>
> Sanskrit and Greek come along how many millenia after ancient Egyptian?
What has that got to do with anything?
>>> Comparative philology has revealed that the "sky" word refers
>>> specifically to the bright daytime sky, as it is derived from the
>>> root meaning "to shine." This root also shows up in Latin dis
>>> "day," borrowed into English in words like diurnal. "Closely
>>> related to these words is Indo-European *deiwos "god," which shows
>>> up, among other places, in the name of the Old English god Tw in
>>> Modern English Tuesday, "Tiw's day." *Deiwos is also the source of
>>> Latin dvus "pertaining to the gods," whence English divine and the
>>> Italian operatic diva, and deus, "god," whence deity."
>>
>>None of which has anything to do with Egyptian...
>
> Ask yourself what Egyptian god has a blue head
> and then read some more abstracts at Amazon
> till you find out why...
Repeating cluelessness won't help acquire a clue.
>>> Next you will tell me that the Hittites had no knowledge of
>>> Egyptian gods and the Egyptians and Greeks no knowledge of Hittite
>>> gods
>>
>>Completely irrelevant to your claims. The word "Zeus" and the god
>>it referred to, and their cognates in the other IE languages, come
>>from the PIE language and the culture that spoke it. Do you claim
>>that Egyptian cultural imperialism dominated southeast Europe and
>>the Eurasian steppes in 4000 BCE?
>
> Is that where and when you think we should look for PIE?
Yes.
> Apparently you haven't ever really thought this out...
I'm less interested in thinking it out than in studying the
evidence.
> Who is it you think is living in the Eurasian steppes c 4000 BC?
> How do they subsist? Are they hunter gatherers or settled farmers?
> What size are their populations, how far apart are they and how
> often do they get together?
Some, at least, were pastoralists.
> The horse was just beginning to be used as a beast of burden and
> perhaps occasionally ridden c 1800 BC.
Archaeology says otherwise. IIRC, cheek pieces, burials, clay
toys, etc. show that the horse was domesticated in Eurasia as early
as the fifth millenium.
> On the other hand boats
> were carrying cargos between India and Mesopotamia in the Jemdet Nasr
Which is completely irrelevant to your claims.
> You have a lot of reading to do.
*You* need to be more critical about what sources you read and
believe.
But again, to bring us back to your original claim: can you show a
single peer-reviewed source for your claim that Greek
manthano:/mathe:somai is derived from an Egyptian source?
Bobby Bryant
Austin, Texas
Peter T. Daniels
> >While you are at it try and explain why a primitive backwoods
> >rustic IE linguistics with its pantheon should dominate an older
> >more sophisticated pantheon that had existed for millenia in the
> >civilized cities.
>
> A non sequitur, if not a deliberate attempt to change the subject,
> demonstrating once again Steve's inability to write English and his
> confusion of language with culture. (Peter, you know everybody: who
> does 'primitive backwoods rustic IE linguistics'?)
Gee, thanks ... I don't look at the squink any more, but your replies
always seem to present the gist. Probably you could check out the late
Georges Dumézil and Edgar Polomé. Watkins seems to deal with the more
sophisticated urban elite IE linguistics ...
--
Peter T. Daniels gram...@att.net
Bobby D. Bryant
What do the _Renaissance_ orders have to do with the origin of the
Greek word ma(n)th- ?
> What I want you to think about is the design of the system you can
> bring your abacus if you think it will help.
>>
>>> Drawings to scale were made by the Egyptians and used for
>>> construction in the OK.
>>
>>And this supports your claim, how?
>
> I was asking you to show me how the Greeks would use an abacus to
> generate the well known architectual proportions used in the
> various orders of architecture. The point is the proportions are
> established by geometry and an abacus is useless.
And my point was that the proportions were established by geometric
_construction_, so that neither the abacus nor Egyptian mathematical
procedures were needed.
> As far as scale goes, the Egyptian use of a layout grid based on a
> septenary system of measures and unit fractions almost forced them
> into the fibonacci series.
And even if true, that's *completely* irrelevant to your original
claim.
>>> Though determination of which proportions are pleasing to the
>>> eye is often linked to the fibonacci series, they occur
>>> naturally out of a septenary system of standards of measure that
>>> uses unit fractions...
>>
>>Enough with the obfuscation. Got any peer-reviewed publications
>>that you can cite to support your claim about the origin of the
>>word "mathematics"?
>
> You can read some of my papers on "Egyptian unit fractions in
> InScription - Journal of Ancient Egypt; Vol 1 1997, Vol 2 1998
Do you really expect to convince skeptics by citing _yourself_? Even
after showing how clueless you are on some very basic matters?
My university's library doesn't carry that august journal. Please
answer the following:
a) Is it a peer-reviewed journal?
b) Did you present your etymology of Greek ma(n)th- in any of your
papers published in it?
c) Did you cite a source -- other than yourself -- for your
etymology?
d) Was _that_ source in a peer-reviewed journal?
If the answer to all four questions is 'yes', than give me the souce
you cited (complete with publication info and page number, so I can
find it). Otherwise, prepare for immediate admission to my bozo
filter's database.
Bobby Bryant
Austin, Texas
Bobby D. Bryant
Truly, that's no more bizarre than some of the other claims he's
pushing.
Bobby Bryatn
Austin, Texas
steve
>>"The earliest Egyptian and Greek fractions were *usually unit fractions*
>
>[...]
>
>>>>>As usual, you don't know what you're talking about.
>
>>>>Baloney on Rye.
>
>>>>http://www.mathpages.com/home/whyunits.htm
>
>>>Bad site: no references, and no indication of authorship.
>
>>Bad Site? really??? Kevin Brown?? Stanford??? means nothing to you?
>
>If there is anything on the site to indicate that it is Kevin Brown's
>or to associate it with Stanford,
Aside from that if you were actually familiar with the topic I
would expect you to have encountered some of the players and be
familiar with their work and web sites, yes.
such information is well hidden.
No it isn't, most people know that if you see a URL like:
"http://www.mathpages.com/rr/bibliog/bibliog.htm"
You can cut to the chase or slashdot.
Try a websearch for slashdot and you will find some useful information.
slashdot. Results 1 - 10 of about 2,080,000.
>And no, Kevin Brown doesn't mean much to me. He has compiled a
>collection of decent short articles on mathematics, history of
>mathematics, and physics, and I've seen him talk reasonably
>competently (though not completely without error) about mathematics
>and its history on sci.math
>
>>no references? What do you call this?
>>http://www.mathpages.com/rr/bibliog/bibliog.htm
...
>In any case it is merely a bibliography, not a set of references for
>specific claims. If you don't understand the difference, feel free to
>ask for an explanation.
If you read some of the material you would see the references
http://www.mathpages.com/mobius/mobius.htm
"(cf. Complex Functions, p 32, Jones and Singerman, 1987)."
The bibliography is extensive because what a bibliography does
is list the books that contain the references.
>>perhaps you would have to be a mathematician to enjoy it.
>
>I am. However, it would be of more use to a mathematical physicist.
Any mathematician ought to find most of his work interesting.
(see below)
>>>>>For starters, you're confusing calculation with representation.
>
>>>>Baloney.
>
>>>>Brian you have no interest in or knowledge of the Egyptians
>>>>Greeks and Romans use of unit fractions
>
>>>>http://www.mathpages.com/home/kmath340.htm
>>>>http://www.mathpages.com/home/whyunits.htm
>
>>>>or of the modern mathematicians
>>>>who are working on them.
>
>>>Wrong on all counts. As usual.
>
>>You just proved me right.
>
>>>Not only do I know rather more about
>>>the history of calculation and numeration systems than you do, I have
>>>the advantage of actually understanding some mathematics.
>
>>Tell us what you know about Kevin Brown and unit fractions Brian
>
>I've already summarized what I know of Kevin Brown.
Yes :)
>Why you think
>that this has anything to do with knowledge of mathematics is a
>mystery, however: even if he were of any particular significance,
>knowledge of mathematics certainly doesn't require knowledge of
>mathematicians.
Actually what you have to say doesn't require any knowledge at all.
>As for unit fractions, I know (and have taught) far
>more about them than I have time or desire to type (or to inflict on
>sci.lang, where the subject is wildly off-topic).
I'm sure you have discovered all sorts of wonderful nurbs
but unfortunately the proofs won't fit in the margins.
>
>>>>http://www.mathpages.com/home/kmath315.htm
>>>>http://www.mathpages.com/mobius/mobius.htm
>
>>>Irrelevant.
>
>>That you don't understand the relevence doesn't make it irrelevant.
>
>Oh, by all means feel free to explain exactly what linear fractional
>transformations have to do with unit fractions; I could use a laugh.
Its just an example by way of introduction to the topic as you
would know if you had read more of his papers.
If you read this introductory paper you will discover that he finds
a General Periodicity Condition that allows him to build tables
that give the roots of polynomials whose coefficients are
diagonal elements of Pascal's triangle from which he derives
the Cauchy distribution in probability theory.
Because unit fractions are precise and can be expressed
in the form of tables they make excellent filters
for math functions.
The general phrase "most of this"
would to most readers include most all the cites I gave
>
>>>>>As we know from
>>>>>numerous pictures (among other sources), the Greeks and Romans did
>>>>>most of their *calculation* with the functional equivalent of the abacus.
>
>>>>Baloney.
>
>>>>Show me how the Greeks would use an abacus to generate the
>>>>well known architectual proportions used in the various orders
>>>>of architecture
>
>>>You really haven't a clue about early uses of calculation, have you?
>
>>Null response; if you can't do it why not just say so.
>
>There's nothing to do. Your question is based on your own
>misconceptions.
The Greeks did it through the use of geometry. You can't do geometry
on an abacus. Why you ask? Because of irrationals. Geometry can be
thought of as a graphical representation of analytic geometry
or numerical analysis which is largely a study of the fluxions
or transformations you just dismissed above.
>
>>>[snip unit fractions and Fibonacci numbers, a modern connection
>>>unknown to the Greeks]
>
>>!!!
>>unknown to the Greek mathematicians, but known to the Egyptian architects?
>
>Known to neither. And obviously not understood by you.
If you read a little Gillings or for that matter Kevin Brown
you will understand how the cyclic periodicity of unit fraction
sequences lends itself to tables which is one of the forms in
which the Egyptians used them
>
>>http://www.bath.ac.uk/brlsi/egypt.htm
>>http://mtcs.truman.edu/~thammond/history/Fibonacci.html
>
>The second contains nothing that is to the point, and the first notes
>that claims for an elaborate proportional system underlying Egyptian
>architecture are not supported by actual measurements.
Baloney
In fact the Egyptian layout grids use the fibonacci series
in the form of the golden section and golden rectangle
which are easily derived from the nature of their
septenary measures and use of unit fractions.
>
>>"Technical Analysis from A to Z"
>>By Steven B. Achelis
>
>>"Leonardo Fibonacci was a mathematician who was born in Italy
>>around the year 1170. It is believed that Mr. Fibonacci discovered
>>the relationship of what are now referred to as Fibonacci numbers
>>while studying the Great Pyramid of Gizeh in Egypt.
>
>[...]
>
>>http://www.equis.com/free/taaz/fibonacci.html
>
>Mr Achelis appears not to know what he's talking about; perhaps he's
>your long-lost cousin?
I guess you put anyone who disagrees with you in that catagory
so I should have a long list of relatives.
>
>>>>Tell us why the Greeks would use an abacus for this. The Greeks based their
>>>>mathematics on geometry rather than numerical analysis.
>
>>>Not true.
>
>>False. The Greeks did not use numerical analysis
>
>You're wrong.
Please provide us an example of the Greek numerical analysis you
are referring to.
>
>>> It's quite clear from the sophistication of the
>>>_Arithmetica_ of Diophantus that they must have had a fairly strong
>>>non-geometric tradition, albeit almost *nothing of it survives*.
>
>That's not what I wrote. The asterisks are your dishonest addition.
I just emphasised a hedge you might have prefered we not notice.
It shows that your speculative assumption, "they must have had..."
has no evidence to back it up
>
>>http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Diophantus.html
>
>>"The most details we have of Diophantus's life come from the Greek Anthology,
>>compiled by Metrodorus around 500 AD. This collection of puzzles contain
>>one about Diophantus which says:-
>
>His life is irrelevant.
The part you snipped was an anecdote about him written by a Greek
contemporary using unit fractions to do so.
...
>>>But all of this is also irrelevant, since most serious computation was
>>>done in connection with mercantile activities, and most non-mercantile
>>>computation was astronomical, not purely mathematical.
>
>>Baloney.
>
>Fact. Your ignorance is showing again.
>
>>The achievements of Greek geometry amount to nothing more than
>>the ability to calculate how to double a talent in the Agora?
>
>Are you really so stupid as to have so badly misread what I wrote?
>And so ignorant as to think that most Greek geometry dealt with
>numerical computation? <sigh> Yes, probably.
Hey, you are the one who wrote "most serious computation
was done in connection with mercantile activities" not me...
What's more you seem to think
"most non-mercantile computation was astronomical, not purely mathematical"
That would be news to the Greek geometers like Ptolemy who were concerned
with earth measures.
>>>>> (Indeed, two Roman abaci about the size of a modern pocket
>>>>>calculator still survive.) How they *recorded* the results of these
>>>>>calculations is another matter.
>
>>>>Baloney.
>
>>>The abaci do indeed survive. So does knowledge of how the results of
>>>computations were recorded.
>
>>>>>As we know from
>>>>>numerous pictures (among other sources), the Greeks and Romans did
>>>>>most of their *calculation* with the functional equivalent of the abacus.
>
>>Show me the abacus the Greeks used to determine how to formulate their
>>classical mathematical problems. They wouldn't have allowed it was a proof
>>if someone did work out how to square a circle, double a cube and trisect
>>an angle with an abacus.
>
>This is a non sequitur, and an exceptionally stupid one at that,
>inasmuch as even you appear dimly to recognize that numerical
>calculation, the subject of my comment, has nothing to do with these
>problems.
So if its your position that the classical mathematical problems of
the Greeks required no calculation and what you mean by calculation
was principally restricted to commerce, would you claim the Greeks
had no knowledge of trigonometry?
>
>>>>The calculation is dependant on unit fractions not decimals
>
>>>No one said anything about decimals.
...
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Greek_numbers.html
http://pespmc1.vub.ac.be/POS/Turchap9.html
Decimals are among the the number bases the Egyptians and the Greeks used.
>
>>>They *did* in fact use positional notation for astronomical purposes,
>>>but it was sexagesimal, not decimal.
>
>>bssst
>>try sexagesimal and decimal...plus unit fractions
>
>No. The positional notation used for astronomical purposes was
>entirely sexagesimal as a positional notation.
Wrong. The Greeks learned astronomy from the Egyptians whose
astronomical notation was decimal.(Decans is a word used
by the Greeks to describe the Egyptian decimal system)
http://www.clas.ufl.edu/users/rhatch/HIS-SCI-STUDY-GUIDE/0011_egyptianContrib2Astron.html
"The Egyptians listed 36 groups of stars called decans
These decans allowed them to tell time at night because
the decans will rise 40 minutes later each night.
Theoretically, there were 18 decans, however, due to dusk and twilight
only twelve were taken into account when reckoning time at night.
Since winter is longer than summer the first and last decans were
assigned longer hours. Tables to help make these computations have
been found on the inside of coffin lids. The columns in the tables
cover a year at ten day intervals.
The decans are placed in the order in which they arise
and in the next column, the second decan becomes the first and so on.
Astronomy was also used in positioning the pyramids. They are aligned
very accurately, the eastern and western sides run almost due north
and the southern and northern sides run almost due west.
The pyramids were probably originally aligned by finding north or south,
and then using the midpoint as east or west. This is because it is possible
to find north and south by watching stars rise and set.
However, the possible processes are all long and complicated. So after north
and south were found, the Egyptians could look for a star that rose either
due East or due West and then use that as a starting point rather than the
North South starting point.
This would result in the pyramids being more accurately aligned with
the East and West, which they are, and all of the errors in alignment
would run clockwise, which they do. This is because of precession of
the poles which is very difficult to view.
This theory is further substantiated by the fact that the star B Scorpii’s
rising-directions match with the alignment of the pyramids on the dates
at which they were built.
Ancient Egyptians also used astronomy in their calendars.
There life revolved the annual flooding of the Nile.
This resulted in three seasons, the flooding,
the subsistence of the river, and harvesting.
These seasons were divided into four lunar months.
However, lunar months are not long enough to allow
twelve to make a full year. This made the addition
of a fifth month necessary. This was done by requiring
the Sirius rise in the twelfth month because Sirius
reappears around the time when the waters of the Nile flood.
Whenever Sirius arose late in the twelfth month a thirteenth month was added."
Here is an example of Egyptian astronomy being continued in a Greek city
in the time of the Roman emperor Antonius Pius
The "Sothic rising" of Sirius coincided with the beginning
of the solar year only once every 1460-1456 years.
This rare event took place in AD 139 during the reign of
the Roman emperor Antonius Pius, and was commemorated by
the issue of a special coin at Alexandria. Earlier heliacal
risings would have taken place in around 1321-1317 BC and
2781-2777 BC. The period that elapsed between these risings
is known as the "Sothic Cycle".
If you need another example of the Greeks fascination with Egyptian
astronomy consider the ceiling of the temple of Dendara
> I shan't bother to
>explain, as I doubt that you even know what that means or how to tell.
>I'll merely say that you're confusing Greek and Roman notational
>systems in general with the specific one used for astronomical
>calculations (and used, I might add, well into the Middle Ages).
wrong again.
The early Greeks thought Solid geometry was necessary to study astronomy
and their solid geometry was based on unit fractions.
Ptolemy who lived 100-178 AD is known for his studies of Geography and Astronomy
*used sexagesimal fractions in his calculations*. He wrote the Almagest which used
extensive chord table of trig functions. This choresponded to our sin tables and
was the 1st modern table in mathematics.
crd(a ) = the length fo the chord corresponding to an arc of a degrees
in a circle whose radius is 60.
http://www.math.sfu.ca/histmath/math380notes/math380.html
http://216.239.51.100
"To some extent Egyptian mathematics has had some, though rather negative,
influence on later periods. Its arithmetic was widely based on the use of
unit fractions, a practice which probably influenced the Hellenistic and
Roman administrative offices and thus spread further into other regions of
the Roman empire. The influence of this practice is visible even in works
of the stature of *the Almagest, where final results are often expressed
with unit fractions in spite of the fact that the computations themselves
were carried out with sexagesimal fractions. And this old tradition doubtless
contributed much to restricting the sexagesimal place value notation to a
purely scientific use*."
http://www.cassiopaea.org/cass/biblewho6.htm
...
>>>>>>Egyptian unit fractions were in common use by the Greeks and Romans
>>>>>>and in Europe as late as Medieval times.
>
>>>>>In *common* use? No.
>
>>>>In common use yes! First in the Attic and then in the Ionian system.
>
>>>Your claim was that unit fractions were in common use by Greeks, by
>>>Romans, and in the European Middle Ages. Taken as a whole the
>>>statement is false.
>
>>No its not. You use "Egyptian unit fractions" nearly every day
>>in "making change in commercial transactions". Thus, a penny = $1/100;
>>a nickel = $1/20; a dime = $1/10; a quarter = $1/4; a fifty-cent piece = $1/2
>
>Tsk, tsk, tsk. Do you really think that this weaseling won't be seen
>for what it is? Especially by those of us who remember Tuxtla?
>
>>>>>The Romans *occasionally* used unit fractions
>>>>>in the Egyptian fashion, but as a rule they simply used duodecimal
>>>>>fractions, either approximating if necessary (e.g., representing 5/9
>>>>>as ~7 unciae, or septunx), or translating into even smaller units
>>>>>(e.g., 2/3 unciae = 16 scruples).
>
>>>>Baloney.
>
>>>>The Romans used factor rich decimal, hexadecimal and octal systems
>>>>to make the use of unit fractions easier.
>
>>>No, child. Sixteen and eight are *not* conveniently divisible by a
>>>variety of smaller integers,
>
>[snip squink about measures]
Perhaps you will enjoy reading about Egyptian unit fractions more
if you learn how expressing common units as the sum of other units
can provide a factor rich enviornment. Consider Pascal's triangle
and its relation to powers of 2 and unit fractions
Gillings, Richard J. Mathematics in the Time of the Pharaohs.
Engels, Hermann. Quadrature of the Circle in Ancient Egypt. Historia Mathematica vl 4 ( 1977),
Parker, R. A., and Neugebauer, Otto. Egyptian Astronomical Texts. 1960--1969. 3 vols.
Bruins, Evert M. Egyptian Astronomy. Janus vl 52 ( 1965),
Van der Waerden, Bartel Leendert.Science Awakening II: The Birth of Astronomy. 1974,
Neugebauer, Otto. A History of Ancient Mathematical Astronomy. Book III: Egyptian Astronomy. 1975.
Archibald, Raymond Clare. Bibliography of Egyptian Mathematics.
The Rhind Mathematical Papyrus, vl I.
Supplement, in vl II. Edited by Chace, Arnold Buffum et al.
>>>>>Exactly. And this system continued in use into the Middle Ages for
>>>>>astronomical work.
>
>>>>Yes Brian the Egyptian astronomical calculations were copied by the Greeks
>
>>>The subject is notational systems used for astronomical calculations,
>>>not the calculations themselves, and the system in question is
>>>Babylonian, not Egyptian.
Decan, a Greek word for an Egyptian decimal unit of ten degrees
'36 the circumference of a circle divided sexigesimally into 360 degrees
commonly used in Astronomy and for that matter medieval astrology.
Zodiac, a division of the sky into 12 parts of three decans each.
(see Egyptian star clocks)
>
>>>[snip irrelevant references]
>
>>Brian you can snip things that refute you without response if you like
>>but you certainly aren't going to make your case by ignoring the facts.
>
>When you actually manage to find a refutation of anything I've said,
>I'll be sure to let you know. In the meantime recommend you to try
>distinguishing relevant from irrelevant facts and facts from wishful
>thinking, but I have little hope of any success on your part.
Do you deny the Greeks borrowed their astronomical unit of the decan
from the Egyptians, or that Ptolomy was still being influenced by and
using Egyptian mathematics two centuries into the CE and that the
units derived by the Egyptians were still in use in medieval times?
Because the influence of unit fractions were visible in works of the
stature of Ptolomy's Almagest, where final results are often expressed
with unit fractions you might want to ask yourself why they persisted
so long and why they still intrigue modern mathematicians.
The tradition of using unit fractions contributed to restricting the
sexagesimal place value notation to a purely scientific use well into
medieval times.
Greek arithmetic was widely based on the use of unit fractions. This
practice influenced the Hellenistic and Roman administrative offices
and thus spread further into other regions of the Roman empire from
where it has come down to us in things like our systems of weights,
measures and coinage.
Consider how the system works by doubling and then consider how for
practical commercial considerations it can be used to solve the
classical problems of Greek antiquity such as doubling the cube.
(Each row corresponds to a row of Pascals triangle with its
quadratic coefficients and to an Egyptian Horus Eye fraction.)
1 yx^3= 1 1
~1.26 yx^3= 2 1 1
~1.59 yx^3= 4 1 2 1
2 yx^3= 8 1 3 3 1
~2.5 yx^3= 16 1 4 6 4 1
~3.17 yx^3= 32 1 5 10 10 5 1
4 yx^3= 64 etc;
~5 yx^3= 128
~6.34 yx^3= 256
8 yx^3= 512
steve
Richard R. Hershberger
>
> Gee Brian, where do you think the Latin names came from?
>
> Look in any common dictionary. The Romans adopted the
> entire Greek pantheon just as the Greeks adopted the
> Egyptian and the Egyptians adopted gods and goddesses
> from Mesopotamia and points beyond.
>
> http://www.seds.org/nineplanets/nineplanets/venus.html
> "Venus (Greek: Aphrodite; Babylonian: Ishtar)
> is the goddess of love and beauty."
>
> If you want to you can trace her origins all the way back to India.
>
> > and is from PIE */wen-/ 'to desire, strive for'.
>
> No, not even close.
>
by a humble layman such as myself. 4th edition American Heritage
Dictionary derives <Venus> from the Latin common noun <venus>, meaning
"love", and ultimately from the PIE *wen. This is, mirabile dictu,
exactly what Brian said.
I do admire, however, your citation of the Students for the
Exploration and Development of Space website. It take real chutzpah,
or at least cluelessness, to use that in support of a linguistic
argument.
I like you, Steve. You make me laugh.
steve
>>>>> <Zeus> is from PIE */dyeu-/ 'to shine'.
>>>>
>>>> deus or deity is also proposed,
>>>
>>>Be aware that multiple words can be derived from the same word in a
>>>proto-language. Be aware also that Greek and Latin are different
>>>languages, although related.
>>
>> Perhaps more to the point are these links
>>
>> http://ccat.sas.upenn.edu/~jfarrell/courses/spring96/myth/feb12.html
>> http://www.geocities.com/geenath_2000/greek1.html
>
>Nothing there to support your claims.
It points out that the Greeks attributed their borrowings to Egypt.
"Linguistically, these cultures were outside the Indo-European family,
and the general shape of their religious systems too differs from that
of the Greeks. Nevertheless, Herodotus did not shrink from tracing certain
Greek institutions to the Egyptians in particular, and from identifying
certain Greek gods and goddesses with Egyptian counterparts. There is,
moreover, the myth of Io and her descendants Io was the daughter of the
King of Argos. Seduced by Zeus, she wandered to Egypt and gave birth to
a child, Epaphus. Epaphus became the father of Libya -- the name of a
large part of northern Africa -- and of Belus, who in turn became the
father of Danaus and Aegyptus. Danaus returned to his ancestral Argos,
while Aegyptus became king of Egypt. (A portion of this myth is the
subject of Aeschylus' Suppliants or Suppliant Maidens.) Thus, acconrding
to this myth, the Greeks and the Egyptians were actually related through
their ancestors Danaus and Aegyptus, two brothers descended from the
Argive heroine Io."
>>>> but as you go on to write
>>>> Zeus pate:r you should admit the meaning is sky father.
>>>
>>>That's is indeed what it means. But it's derived from PIE morphemes
>>>(and shows up _independently_ in Greek, Latin, Sanskrit, and maybe
>>>some others).
>>
>> That is one theory.
>
>That's the theory that all educated scholars subscribe to.
That's a foolish and remarkably ethnocentric incorrect generalization.
>
>> "One of the central characteristics of both Zeus and Jupiter
>> is that they are considered to be the "fathers" of many of
>> the other gods, and to be the symbolic "fathers" of the
>> universe as a whole. Jupiter's name actually shows this:
>> the Romans also called him "Diespiter" and understood this
>> name to mean "Dies pater" = "Father of the Day" or "Sky Father".
>> "Pater" (="Father") is also a common epithet of the Greek Zeus,
>> who is frequently addressed as "Zeus pater" (="Father Zeus").
>> Now, the similarity of the names "Jupiter" and "Zeus pater"
>> is noticeable, and anyone conversant with the Indo-European
>> hypothesis might well wonder whether the names were related.
>> If one then learns that there is a a sky god in the ancient
>> Indian pantheon named "Dyaus-pitar" and that this god shows
>> many of the same characteristics ascribed to Zeus and Jupiter,
>> it becomes difficult not to see the same pattern at work in
>> mythology that we have observed in the case of languages."
>
>That actually contradicts what you're trying to argue.
This summary of the theory that you think "all educated scholars
subscribe to" is one theory. Having stated it so as to show his
familiarity with it the author continues with a different theory.
>
>> Another is that of the Greeks themselves.
>>
>> "Linguistically, these cultures were outside the Indo-European family,
>> and the general shape of their religious systems too differs from that
>> of the Greeks. Nevertheless, Herodotus did not shrink from tracing
>> certain Greek institutions to the Egyptians in particular, and from
>> identifying certain Greek gods and goddesses with Egyptian counterparts.
>
>Yes, that was a popular sport in the ancient world. And notice the
>qualification "certain", which covers the fact that the main
>deities were *not* derived from Egypt.
Actually it was the main deity. Egypt has a variety of roles for its deity
or neter, but they are all aspects of the same Being. Essentially its a
system of paired opposites resolved in a synthesis which Greeks like Plato
found useful in dialectic.
>
>> There is, moreover, the myth of Io and her descendants Io was the
>> daughter of the King of Argos. Seduced by Zeus, she wandered to Egypt
>> and gave birth to a child, Epaphus. Epaphus became the father of Libya
>> -- the name of a large part of northern Africa -- and of Belus, who in
>> turn became the father of Danaus and Aegyptus. Danaus returned to his
>> ancestral Argos, while Aegyptus became king of Egypt.
>>
>> (A portion of this myth is the subject of Aeschylus' Suppliants
>> or Suppliant Maidens.) Thus, acconrding to this myth, the Greeks
>> and the Egyptians were actually related through their ancestors
>> Danaus and Aegyptus, two brothers descended from the Argive heroine Io."
>
>Again, a popular sport in the ancient world. The Romans claimed to
>be of Trojan descent. (And for that matter, so did the English
>almost two millenia later.)
The Romans acknowledged that the Etruscans were connected to Troy
just as the English acknowledge the most ancient written ancestor
of their language traces back to Anatolia and the Greeks showed
the same recognition of their antecedents.
>>>> As for the word for father<peter<pater<pitar<ptah
>>>
>>>Bogus etymology detected. "pitar" is the specifically Sanskrit
>>>variant, and derives from a form almost identical to the Greek
>>>"pate:r", except that the 'a' was a laryngeal rather than an
>>>ordinary vowel.
>>
>> Sanskrit and Greek came along a bit later than ancient Egyptian.
>
>Irrelevant to your claims.
Usually in trying to trace words back in time, an etymology acknowledges
the earlier existence of similar words that may be borrowed from other
cultures. I doubt that you have studied much of ancient Egypts language
and literature but if you ever should you might learn something.
>
>> If the Greek Herodotus is correct
>
>He wasn't. Nor was he correct when he reported that inscriptions
>on the pyramids told how many onions were used to pay the
>construction workers.
You would of course realise that you are changing the subject
to get away from dealing with what he said about
>
>> certain Greek gods and goddesses
>> had Egyptian counterparts. If you accept that Lapis Lazuli and
>> Carnelian came to Egypt in the predynastic Naqada II from India
>> and Afghanistan by whatever routes and chains of middleman you
>> might allow that by Greek times the Egyptians had a cultural
>> sphere of influence that probably equaled or exceeded that of PIE.
>
>Spheres of influence do not automatically extend along trade
>routes. (And if you thought they did, how would you know which way
>the influence extended?)
Spheres of influence do extend along trade routes. That's why people
study trade routes. The influence generally extends in both directions
Both cultures have things the other wants and that is why there is trade.
>
>>>> As for the word for sky Egyptian nu
>>>> http://www.abcgallery.com/C/correggio/correggio5.html
>>>
>>>True or not, it's completely irrelevant to the IE etymology.
>>
>> Not necessarily. Sure Egyptian is Afroasiatic but that wouldn't
>> prevent the Greeks from borrowing the Egyptian mythology along with
>> certain Greek institutions from the Egyptians in particular, and from
>> identifying certain Greek gods and goddesses with Egyptian counterparts
>>>
>>>> <Venus> is Latin, not Greek,
>>>>
>>>> Gee Brian, where do you think the Latin names came from?
>>>>
>>>> Look in any common dictionary. The Romans adopted the entire Greek
>>>> pantheon
>>>
>>>No, the Romans already had their own pantheon, which they mapped
>>>onto the Greek while preserving the original names. They _did_
>>>borrow a few from the Greeks (sometimes via the Etruscans, as with
>>>Herakles), and in the later period they borrowed exotic gods from
>>>all over the Middle East. But the basic pantheon that you learn in
>>>gradeschool is almost entirely native.
>>
>> Which Roman gods predated Rome? Keep in mind that everybody borrowed
>> everything from everyone else and tell me which Roman gods you think
>> originated with the Romans and when their mythos dates to.
>
>Juppiter, Neptune, etc.
Jupiter is transparently a copy of Zeus and Neptune a copy of Poseidon.
>>>> just as the Greeks adopted the Egyptian
>>>
>>>Not in general. Some of their pantheon is very obviously derived
>>>from the IE tradition.
>>
>> Some of it goes back long before any IE tradition.
>
>Possibly, probably even, but not in the way you suggest.
In the way I suggest and in other ways as well. Try picking out
the references to Egypt in the Epic of Gilgamesh and the references
to Hittite gods on Egyptian cartouches.
>
>> Some of it
>> is derived from Mesopotamia. Try picking a specific god you think
>> is IE and lets see what that gods antecedents are.
>
>We've been talking about the Sky Father for a couple of days
>already. Your antecedents are bogus.
After you have spent a bit more time studying Egypt come back and
tell me that again.
>
>>>Others have unknown origins, presumably adopted from the aborigines.
>>
>> What aboriginees? Australian aboriginees? Trace the origins back as
>> far as what you are familiar with and lets see where it goes from
>> there.
>
>"Aborigine" means "the people who lived there first".
Lived where first?
>For Greeks, Romans, and Indians it means the people who lived
>in Greece, Italy, and India before the IE speakers arrived.
So if the IE speakers first arrived in Greece c 1650 BC
everyone who lived there before then was an aborigine?
(Pedantic note: those
>might not really be the "first" people to live in those regions,
>but unfortunately we can't trace the prehistory back any further,
Of course we can, what do you think Archaeologists and Anthropologists do?
>so the term is used as a term of convenience. FWIW it's a Latin
>word, and the Roman authors used it as above. Livy, IIRC, uses it
>in his mythical description of the prehistory of Rome.)
Are you using the word in the sense of before we lived here savages
and barbarians who did't speak our language occupied our land?
>
>>>I don't think any of the gods from the
>>>main pantheon can be derived from Egyptian sources, though like the
>>>Romans they adopted all manner of exotica in the later period.
>>
>> So is Herodotus mistaken or just misinformed?
>
>Probably both. As I said above, deriving pantheons from other
>pantheons was a popular passtime in the ancient world.
Are you aware of a number of other classical sources other than
Herodotus who shared the same mistaken misinformation?
>
>BTW, if you actually look at the mythology pertaining to the
>various gods, you find more reason to believe the Greek pantheon,
>or at least the stories told about them, derived from Mesopotamia.
>
So did the Egyptian pantheon. It was by the way, an ongoing and
continuing process rather than a one shot deal.
Lots of experts seem to like to waste their time on me,
often quite politely.
>
>>>>>These are clearly not borrowings Egyptian.
>>>>
>>>> You are clearly not very knowledgable about pantheons. Try reading
>>>> Budge "Gods of the Egyptians" 2 vol or look at any of the on line
>>>> material, its no secret.
>>>
>>>Most on-line material is rubbish. Budge appears not to be much
>>>better, as witness these reviews on Amazon:
>>
>> Your knowledge of Egyptology is derived from Amazon abstracts?
>>
>> If it is true that you have never read Budge, and have no idea
>> why he was knighted for his work it might be worth your while
>> to check him out.
>>
>> He may be of some use to people like you who are interested beginners,
>> his work includes the cartouches of all the kings listed by dynasty,
>> the names of gods broken down into nome gods, foreign gods, gods of
>> the hours of the day and night,etc with lots of cross referencing
>> plus a number of books about Egypt in general, "The Nile", "The Mummy",
>> Cleopatra's Needle,...Many of the Books Budge wrote Amazon gives five stars.
>>
>> Later you will find he's useful when you are trying to read an inscription
>> and want to see how the names of the gods were spelled and what the various
>> forms of the titles and formulas were. To use him effectively you need Gardiner,
>> Faulkner, Baines and Mal'ek, Loprieno and Wilkenson at a minimum.
>
>You have made it perfectly clear that you are trying to master the
>advanced material without bothering with the basics.
You mean the Amazon abstracts?
Which one would that be? Subuartu? Do you have a good idea of
how to define the extent of the Hurrians in northern Mesopotamia
and when the best time to do so might be?
> Your argument is completely irrelevant, partly due to
>erroneous assumptions, partly because it has nothing to do with
>what I've been trying to explain to your.
Try and define where IE populations were when the Hurrians of
Northern Mesopotamia first came into contact with southern Mesopotamia.
>
>> In the context above the author is pointing out that there are
>> two versions
>> 1.)thunder god associated with storms
>> 2.)sky father associated with bright sunny day
>
>You are amazed that the Sky Father wields the thunderbold?
No, I'm pointing out that its two different attributes being emphasised
as the essence of the god, suggesting two different perspectives because
of two different points of origin.
>
>> The suggestion is that an older form has been replaced with a borrowing.
>
>Not at all. Ask yourself where the thunder comes from.
The Hittite weather god An who if you desire to do so can be traced
back to a nice mixture of Yam, Baal,and Yah and who has a direct line
of descent to Poseidon and Neptune only after being joined with Yam.
>
>>>> [Egyptian nu-ptah, sky
>>>> father (Nu is the sky and Ptah, whose head is blue, is its
>>>> creator)]
>>>>
>>>> Zeus is a somewhat unusual noun in Greek,
>>>> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ having both a stem Zn-
>>>> (as in the philosopher Zeno's name) and a stem Di-(earlier Diw-).
>>>
>>>It's not rare for Greek (or any other IE language) to have
>>>variations where different _stems_ are built from a single _root_.
>>
>> Again the suggestion is that its borrowed into Greek
>
>The suggestion of certain parties who know nothing of historical
>linguistics.
You do realise that the attributes of gods were being traded back and forth
before historical linguistics existed?
>
>>>> In the Iliad prayers to Zeus begin with the vocative form Zeu
>>>> pater, "o *father* Zeus."
>>>
>>>Yes, that's the expected vocative form of "Zeus".
>>>
>>>You're quoting a lot of reasonably accurate material as if it
>>>supports your case, but unfortunately it doesn't have any bearing
>>>on your claims whatsoever.
>>
>> I understand that you don't see the connection yet, but then
>> you have some reading to do and afterwards we will see
>> if you learned anything.
>
>Actually, I have done a great deal of reading in historical
>linguistics and classial civilization. That's how I know you're
>peddling bunkum.
So do you equate "a great deal of reading in historical linguistics
and classical civilization" with a knowlede of the mythology of the ANE?
Have you done a great deal of reading in Sumerian, Akkadian and ancient Egyptian?
>
>>>> Father Zeus was the head of the Greek pantheon; another ancient
>>>> Indo-European society, the Romans, called the head of their
>>>> pantheon Ipiter or Iuppiter-Jupiter. *The -piter part of his name
>>>> is just a reduced form of pater, "father,"* and Iov corresponds to
>>>> the Zeu in Greek: Ipiter is therefore precisely equivalent to Zeu
>>>> pater and could be translated "father Jove." Jove itself is from
>>>> Latin Iov", the stem form of Ipiter, an older version of which in
>>>> Latin was Diov", showing that the word once had a d as in Greek
>>>> Diw-.
>>>
>>>None of which indicates any derivation from Egyptian...
>>
>> Ask yourself what Egyptian god has a blue head
>
>Why would that be relevant?
That you can even ask the question speaks volumes.
What color would you expect a sky fathers head to be?
>
>> and then read some more abstracts at Amazon
>> till you find out why...
>
>I certainly put more stock in skeptical Amazon reviews than I do in
>your believe-anything-about-egypt claims.
Personally I am not a believer.
If you are no offense, but that explains your position.
>
>>>> An exact parallel to Zeus and Jupiter is found in the Sanskrit god
>>>> addressed as Dyau pitar: pitar is "father," and dyau means "sky."
>>>> We can equate Greek Zeu pater, Latin I-piter, and Sanskrit dyau
>>>> pitar and reconstruct an Indo-European deity, *Dyus pter, who was
>>>> associated with the sky and addressed as "father."
>>>
>>>Indeedie. Are you going to claim that the speakers of Sanskrit
>>>also borrowed the name from the Egyptians?
>>
>> Sanskrit and Greek come along how many millenia after ancient Egyptian?
>
>What has that got to do with anything?
Think about it.
>>>> Comparative philology has revealed that the "sky" word refers
>>>> specifically to the bright daytime sky, as it is derived from the
>>>> root meaning "to shine." This root also shows up in Latin dis
>>>> "day," borrowed into English in words like diurnal. "Closely
>>>> related to these words is Indo-European *deiwos "god," which shows
>>>> up, among other places, in the name of the Old English god Tw in
>>>> Modern English Tuesday, "Tiw's day." *Deiwos is also the source of
>>>> Latin dvus "pertaining to the gods," whence English divine and the
>>>> Italian operatic diva, and deus, "god," whence deity."
>>>
>>>None of which has anything to do with Egyptian...
>>
>> Ask yourself what Egyptian god has a blue head
>> and then read some more abstracts at Amazon
>> till you find out why...
>
>Repeating cluelessness won't help acquire a clue.
Consider it a homework assignment. I have given you a clue
go check out your leads.
>
>>>> Next you will tell me that the Hittites had no knowledge of
>>>> Egyptian gods and the Egyptians and Greeks no knowledge of Hittite
>>>> gods
>>>
>>>Completely irrelevant to your claims. The word "Zeus" and the god
>>>it referred to, and their cognates in the other IE languages, come
>>>from the PIE language and the culture that spoke it. Do you claim
>>>that Egyptian cultural imperialism dominated southeast Europe and
>>>the Eurasian steppes in 4000 BCE?
>>
>> Is that where and when you think we should look for PIE?
>
>Yes.
What do you find when you look?
>
>> Apparently you haven't ever really thought this out...
>
>I'm less interested in thinking it out than in studying the
>evidence.
>
I see, you would like to skip the formulating questions part
and just flip to the back of the book for the answers.
>
>> Who is it you think is living in the Eurasian steppes c 4000 BC?
>> How do they subsist? Are they hunter gatherers or settled farmers?
>> What size are their populations, how far apart are they and how
>> often do they get together?
>
>Some, at least, were pastoralists.
Settled pastorialists in the Eurasian steppes c 4000 BC?
or do you mean nomadic pastorialists? What animals have they
domesticated that they are pasturing? Do they farm to provide
food for their animals or are they hunters and gatherers?
Can they make pottery?
>> The horse was just beginning to be used as a beast of burden and
>> perhaps occasionally ridden c 1800 BC.
>
>Archaeology says otherwise.
Cite me your archaeological evidence for people riding horses c 4000 BC.
>IIRC, cheek pieces,
What cheek pieces, from where, dated when?
(put Mallory back in the circular file where he belongs)
> burials,
what do horse bones in a trash midden tell you about horseriding
>clay toys,
what clay toys, from where, dated when?
On the basis of the calibrated age (ranging from 2331 to 1989 b.c.)
of two charcoal samples from rooms 1 and 9, adjoining the courtyard
room 8, and an assessment of other pottery vessels, the one-handled,
flat-based, jars from Sweyhat may be dated within the late Early
Bronze Age period, ca. 2300-2100 b.c.
http://www.oi.uchicago.edu/OI/AR/92-93/92-93_Sweyhat.html (Israel)
http://www.oi.uchicago.edu/OI/MUS/PA/IRAN/PAAI/IMAGES/PER/SCU/6G2_4.html
> etc. show that the horse was domesticated in Eurasia as early
>as the fifth millenium.
bssst
Try and be specific. Pick a site and cite the evidence
(If you want you can go back and check out the archives
for the last time this was discussed here for references)
>
>> On the other hand boats
>> were carrying cargos between India and Mesopotamia in the Jemdet Nasr
>
>Which is completely irrelevant to your claims.
You really don't have any idea of how it would be relevant do you?
Here is your next clue: Indo-European
>
>> You have a lot of reading to do.
>
>*You* need to be more critical about what sources you read and believe.
I'm happy to stick to the archaeologists field reports available online
How about you?
>
>But again, to bring us back to your original claim: can you show a
>single peer-reviewed source for your claim that Greek
>manthano:/mathe:somai is derived from an Egyptian source?
I gave you the phrase [m3at mh] look it up in Gardiner and or Faulkner.
and see if you can figure out why the etymology for mathematics as the
Greek word for learned would want to consider where the Greeks learned
the true measure of their mathematics and how what they learned applies.
steve
I guess it depends on your definition of reasonably bright.
I'm willing to stipulate that your average high school student
isn't much smarter or more knowledgable than the people
still posting to usenet.
steve
>...
>>>> I'm not talking about the layout by the tekton. I'm talking
>>>> about the design of the system by the arch tekton or master
>>>> builder. See Normands "Parallel of the Orders of Architecture"
>>>
>>>What precisely does this book say to support your claims? Give a
>>>short quote and a page number, please. By chance I'll be on
>>>campus tomorrow, and not far from the Classics Library.
>>
>> You will need the Authors name; R A Cordingley
>>
>> Look at Fig 4 p 12
>> and A-E. Method of Drawing the Renaissance orders Plate 36 setting
>> out of volutes
>
>What do the _Renaissance_ orders have to do with the origin of the
>Greek word ma(n)th- ?
The renaissance orders came about as a result of studies of the Greeks
standards of measure and proportion. Comparions of measured drawings
of the surviving components of their architecture revealed that the
Greeks were using standards of measure and mathematics borrowed
from Egypt and the Romans had similarly borrowed from the Greeks.
In other words the Greeks ma(n)th- (learned) their mathematics
from the [ma3t mh] (true measure) of the Egyptians.
>> What I want you to think about is the design of the system you can
>> bring your abacus if you think it will help.
>>>
>>>> Drawings to scale were made by the Egyptians and used for
>>>> construction in the OK.
>>>
>>>And this supports your claim, how?
>>
>> I was asking you to show me how the Greeks would use an abacus to
>> generate the well known architectual proportions used in the
>> various orders of architecture. The point is the proportions are
>> established by geometry and an abacus is useless.
>
>And my point was that the proportions were established by geometric
>_construction_, so that neither the abacus nor Egyptian mathematical
>procedures were needed.
Geometric construction is an Egyptian mathematical procedure
based on proportions derived from a grid constructed with the
use of a table of unit fractions.
"Ancient Egyptian Construction and Architecture"
Somers Clarke and Engelbach, fig 53 and 54 p 52 and 53
>
>> As far as scale goes, the Egyptian use of a layout grid based on a
>> septenary system of measures and unit fractions almost forced them
>> into the fibonacci series.
>
>And even if true, that's *completely* irrelevant to your original claim.
>
Hardly. Where do you think the Greeks learned their geometry?
>
>>>> Though determination of which proportions are pleasing to the
>>>> eye is often linked to the fibonacci series, they occur
>>>> naturally out of a septenary system of standards of measure that
>>>> uses unit fractions...
>>>
>>>Enough with the obfuscation.
Go read enough of what I have cited to you that
you understand the connections and save us both
some time.
Osophos
bill...@my-deja.com (Bill) writes:
>What is the origin of the word "Mathematics" ?
>I guess it comes from greek ?
And
In article <3ce0b24e$0$4696$afc3...@news.optusnet.com.au>, "Sebastian Hew"
<rada...@hotmail.com> writes:
>Yes, it does indeed come from the Greek μαθηματικός, probably via Latin
>and/or French.
And
In article <307E8.6008$Ok3.3...@news1.news.adelphia.net>, whi...@shore.net
(steve) writes:
>Dictionaries give mathematics < L mathemalicus < Gk mathema (learning)
>but surely that raises the question who did the Greeks and Romans learn
>their mathematics from?
>
>Egyptian: [ma3't] true [mh] (cubit measure); [ma3't mh] (true measure)
>
>If you go by the fact that the Greeks and Romans used Egyptian unit fractions
>to perform their calculations you might want to consider the Egyptian words
>[mh] (cubit measure); [ma3't mh] (true measure) as the Gk etymology of
>mathema
>[ma3't] (accurate, correct, straight, plumb, level, upright)
>[gm ma3't] (you have found the answer correctly)
And
In article <3CE11159...@mew.uni-erlangen.de>, Uwe Hercksen
<Herc...@mew.uni-erlangen.de> writes:
>you should not confuse astronomy, astrology and mathematics.
Etc. One doesn't need to be a student of arcane history (or language, or
"mathematics" ) to understand the main-line etiology of the word, on the one
hand, and of its modern referent, on the other. Mathematics (the orthographic
form mathematikos will do nicely here) is ancient Greek-- probably
pre-Doric---in origin, and was their interlingual synonym for our education:
It was the Greeks' generic term for the passing on of accumulated cultural
lore. The mythos was the "textbook" for this process, for, without mathematics
in *our* understanding of the word, and all the literal vocabulary we gradually
accumulated from our multicultural past, precivilized and early post-civilized
man used metaphor to pass on abstract ("invisible") concepts. The myth was
actually a factual description of what humans had gathered about the world in
astronomy, archeology, psychology, . . .(to use our "discipline" terms), but
expressed in metaphor. Mathematikos had nothing to do with what *we* mean by
mathematics.
That latter meaning began from a retrospective (probably European) look at
ancient Greece from the time of Pythagoras. In Pythagoras' day, the Greeks had
taken to the practice of forming secret cults organized for the purpose of
studying and discussing aspects of the world not culturally available through
mathematikos and mythos. Each cult had its "thing," and Pythagoras formed one
around counting and number. Mostly he was interested in what we call
arithmetic (arithmos and techne) and numerology; he held that mathematikos
(education) via arithmos (number) was very beneficial to the human mind (he
was right). Euclid, who came later, was personally interested in ways by which
to measure surface areas. The later Occidentals put Euclid's plane geometry
into its then accumulating bag of mathematics, according to our understanding
of the word, which then included (in addition to locally accumulated counting
and measuring devices) Mesopotamian, Egyptian, Roman, Arabic, and other ancient
culture's means of counting and measuring.
Counting and measuring, however, go way back to paleolithic times. Man has
always been interested in "getting at" the ambiguous mysteries of the world
around him. Perceptually discerning this from that (which is what the word
intelligence means), man needed more definition, a higher resolution, to what
he perceived. This thing, that thing, and the other thing came to have number
words, later single ciphers, such as '3." There was adding this thing to that
thing and more things, and taking away this thing and that thing from a pile of
things---which ultimately became our "addition" and "subtraction." But many
phenomena in the environment were not neatly *things*---physically bounded
objects that man could perceptually grasp all-at-once. And some things, and
some of these other phenomena, were "somehow like" others and "somehow not
like" yet others. In order to more finitely grasp these differences, man
invented unitizing---imposing artificial segments on them; these *could* be
counted. He used for his unitizing standards some object taken from his natural
world, even his own body---the biblical "stone" and "rod," e.g.; the "inch"
(thumb phalange), "foot," "hand," and so on---until the relatively recent
metric system, which is pure artifice (with water being mostly the only
remaining natural standard). This unitizing is what we now know as
measurement.
By or sometime during the Sumerian culture, some clever fellows had developed a
scheme by which addition and subtraction of large numbers could be
streamlined---multiplication and division, respectively. These could be used
for counting real objects, and for counting artificial units of measurement.
Modern mathemeticians distinguish between "quantity" as how much and "number"
as how many, but it is a silly distinction; they both boil down to counting
either actual objects or imaginary units, for how much is inevitably converted
into countable units.
Very handy as TOOLS, but not integral with cosmoterrestrial reality. The
universe is not "mathematical" in the modern sense, though very mathematical in
the old Greek educational sense. Unfortunately, civilized man has been wont to
make the universe in his own image; if not his own physical likeness (as in
"God"), then in the image and likeness of his own invented tools. Consider as
just one relatively modern example Newton's mechanistic universe, which is
modeled directly on the technological achievements of the medieval period with
gears and wheels; hence "clocks" (bells), that signal man's notions of time.
And there is that modern physicist (forget his name) who claimed the universe
is a computer, and another who claimed it is a holograph. Lately, man's
prowess with "higher math" (repeat: his own invention) has prompted him to
assume that the universe itself is mathematical.
This makes the universe very unlearnable-from. The tools cleverly designed to
aid in understanding the universe have become the obstacles which prevent
understanding of it.
Brian M. Scott
wrote:
>Brian M. Scott wrote:
>> On Tue, 14 May 2002 16:10:13 GMT, whi...@shore.net (steve) wrote:
>> [...]
>>>There should be no confusion of astronomy, astrology and mathematics
>>>because essentially they are all different approaches to the same thing.
>> No, they're not.
>Yes they WERE - before the Age of Reason.
No, they weren't, even assuming that you're ignoring the world outside
Europe. In the early Middle Ages, the main non-mercantile use of
mathematics and astronomy in Europe was the computus, or calculation
of the ecclesiastical calendar, which had nothing to do with
astrology. Fibonacci's _Liber Abaci_ (1202) had, so far as I know,
nothing to do with astrology *or* astronomy. Nicole Oresme's brillian
mathematical work in the 14th c., which foreshadows the integral
calculus, was applied to mechanics, not (primarily) astronomy or
astrology, and he wrote several books against astrology (though to be
sure he accepted the almost universal view that the heavens exert some
influence on large-scale events).
> Or don't you know that Newton
>and Kepler primarily viewed themselves as astrologers?
I know that Newton did not. Kepler certainly worked as a professional
astrologer; Newton, however, appears to have had little if any
interest in it (though he did have some odd notions about alchemy and
religion). See <http://www.phys.uu.nl/~vgent/astrology/newton.htm>
for a summary of the evidence. And even if you were right, this would
hardly show that mathematics, astronomy, and astrology were considered
different approaches to the same thing, but merely (as is rather
obvious) that they are closely related.
Brian
Brian M. Scott
<bdbr...@mail.utexas.edu> wrote:
>On Wed, 15 May 2002 00:13:31 -0600, steve wrote:
>> In article <abse8p$lfa$1...@geraldo.cc.utexas.edu>,
>> bdbr...@mail.utexas.edu says...
[...]
>>>Enough with the obfuscation. Got any peer-reviewed publications
>>>that you can cite to support your claim about the origin of the
>>>word "mathematics"?
>> You can read some of my papers on "Egyptian unit fractions in
>> InScription - Journal of Ancient Egypt; Vol 1 1997, Vol 2 1998
These should be Issue 1 and Issue 2, respectively.
>Do you really expect to convince skeptics by citing _yourself_? Even
>after showing how clueless you are on some very basic matters?
>My university's library doesn't carry that august journal. Please
>answer the following:
>a) Is it a peer-reviewed journal?
It appears to be a publication by and for enthusiasts. The fact that
it has published several articles by Steve and by Clyde A. Winters
strongly suggests that it is not peer-reviewed. (If you've never run
into Clyde, take a look at <http://homepages.luc.edu/~cwinter/>.)
>b) Did you present your etymology of Greek ma(n)th- in any of your
>papers published in it?
According to the table of contents, he wrote two articles (or possibly
one article in two parts) on his pet subject, 'Egyptian standards of
measure'. There is no mention of anything on Egyptian unit fractions.
<http://ourworld.compuserve.com/homepages/PaulBadham/inscript.htm>
[...]
Brian
Herman Rubin
Mike Cleven <iro...@bigfoot.com> wrote:
>Uwe Hercksen wrote:
>> Gary Vellenzer schrieb:
>>>In late antiquity and the Middle Ages, "mathematicus" meant astrologer.
>>>What we call mathematics was considered a subfield of astrology.
>> Hello,
>> you should not confuse astronomy, astrology and mathematics.
>In ancient times "people did"; actually they just didn't make the
>separation, as people post-1700 or so tend to.....
>My own bit on this: what's the possibility of a Babylonian/Chaldean root
>behind Gr. mathema; the Egyptian suggestion is OK, but mathematics (and
>astronomy/astrology) came to Greece from Babylon, not from Egypt.
This is by no means clear. It seems that the Greek
philosophers, such as Plato, considered Egypt to be worth
emulating, but not Babylonia and Persia.
The idea of using the same characters in different
places in an expansion, base 60 for the Babylonians,
does not seem to have been considered by the Greeks.
Also, the Babylonians used sexagesimal fractions to many
places, and the Greeks seem to have stuck with the
clumsy "Egyptian" fractions, and did not develop decimal
fractions.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
steve
>
>On Wed, 15 May 2002 09:19:39 GMT, Mike Cleven <iro...@bigfoot.com>
>wrote:
>
>>Brian M. Scott wrote:
>>> On Tue, 14 May 2002 16:10:13 GMT, whi...@shore.net (steve) wrote:
>
>>> [...]
>
>>>>There should be no confusion of astronomy, astrology and mathematics
>>>>because essentially they are all different approaches to the same thing.
>
>>> No, they're not.
>
>>Yes they WERE - before the Age of Reason.
>
>No, they weren't, even assuming that you're ignoring the world outside
>Europe. In the early Middle Ages, the main non-mercantile use of
>mathematics and astronomy in Europe was the computus, or calculation
>of the ecclesiastical calendar, which had nothing to do with
>astrology.
Just out of curiosity, what other than astrology, do you think
was the main mercantile use of astronomy in the early middle ages?
Where do you think the calendars used in Medieval Europe originated?
How do you think people checked the passing of days, weeks, months
seasons and years?
What do you think the passing of time had to do with astronomical
observations and the signs of the zodiac?
How do you think an ecclesiatical date such as Easter was computed?
>Fibonacci's _Liber Abaci_ (1202) had, so far as I know,
>nothing to do with astrology *or* astronomy.
That's what we have been telling you. The abacus was fine
for commercial transactions and might be of utility in
the arithmetic necessities of geometry, but just as music
is a code word for order and harmonic sequence, astronomy
is a code word for analytic geometry and calculus; ie
fluxions or the study of transformational change.
>Nicole Oresme's brillian
>mathematical work in the 14th c., which foreshadows the integral
>calculus, was applied to mechanics, not (primarily) astronomy or
>astrology, and he wrote several books against astrology (though to be
>sure he accepted the almost universal view that the heavens exert some
>influence on large-scale events).
Astronomy and astrology can find the fibonacci series useful.
Astronomy takes the standard of motion, measures, weighs and
judges it, puts it in sequence and determines from that
what the expected consequence might be. When you start
talking about consequences thats where
the astrology kicks in.
"Whereas at the outset geometry is reported to have concerned
itself with the measurement of muddy land, she now handles
celestial as well as terrestrial problems. She has extended
her domain to the furthest bounds of space." -- (
Hodder and Stoughton, The Story of Euclid, 1901)
>
>>Or don't you know that Newton
>>and Kepler primarily viewed themselves as astrologers?
Actually Newton viewed himself as more of an alchemist,
but in the same way Keppler was an astrologer.
>
>I know that Newton did not.
Newon wrote considerably more about alchemy and astrology
than he did about science and he was more interested in
the transformation of elements mathematically as with
fluxions than he was with what we call science.
> Kepler certainly worked as a professional
>astrologer; Newton, however, appears to have had little if any
>interest in it (though he did have some odd notions about alchemy and
>religion). See <http://www.phys.uu.nl/~vgent/astrology/newton.htm>
Is this news to you Brian? Why do you think Newton was so interested in Egypt?
If you eventually get to where you can think of an
/alchemist/christian fundamentalist/astrologer/pyramidiot
like Newton as having a valid methodology despite its not quite
being scientific, that might be useful.
Bottom line those things are just labels and what goes
up still comes down in accordance with his theories.
>for a summary of the evidence. And even if you were right, this would
>hardly show that mathematics, astronomy, and astrology were considered
>different approaches to the same thing, but merely (as is rather
>obvious) that they are closely related.
They are different approaches to the same thing.
Their methodology is a part of what we call the Socratic method,
which is also the reason they are related in their natural philosophy
and as standards of the dialectic.
>Brian
steve
Brian M. Scott
>>>"The earliest Egyptian and Greek fractions were *usually unit fractions*
>>Yes, ...
>>[...]
I figured that the really blatant dishonesty was about due. The
comment that you're misrepresenting reads in full:
Yes, we've heard that before. Half of it, the part about
the Egyptians, is irrelevant to your claim. The rest is
only marginally relevant, since it refers only to the Greeks,
not the Romans, and only to '[t]he earliest ... Greek fractions'
at that.
I'd have thought that by now even you would have realized how
pointless this sort of lie is, when the evidence is at Google (and in
this case probably even still on most news servers).
>>>>>>As usual, you don't know what you're talking about.
>>>>>Baloney on Rye.
>>>>>http://www.mathpages.com/home/whyunits.htm
>>>>Bad site: no references, and no indication of authorship.
>>>Bad Site? really??? Kevin Brown?? Stanford??? means nothing to you?
>>If there is anything on the site to indicate that it is Kevin Brown's
>>or to associate it with Stanford,
>Aside from that if you were actually familiar with the topic I
>would expect you to have encountered some of the players and be
>familiar with their work and web sites, yes.
<shrug> Kevin Brown isn't a major player in anything.
>>such information is well hidden.
>No it isn't, most people know that if you see a URL like:
>"http://www.mathpages.com/rr/bibliog/bibliog.htm"
>You can cut to the chase or slashdot.
>Try a websearch for slashdot and you will find some useful information.
>slashdot. Results 1 - 10 of about 2,080,000.
I know what slashdot.org is, thank you. You're babbling.
>>And no, Kevin Brown doesn't mean much to me. He has compiled a
>>collection of decent short articles on mathematics, history of
>>mathematics, and physics, and I've seen him talk reasonably
>>competently (though not completely without error) about mathematics
>>and its history on sci.math
>>>no references? What do you call this?
>>>http://www.mathpages.com/rr/bibliog/bibliog.htm
>...
>>In any case it is merely a bibliography, not a set of references for
>>specific claims. If you don't understand the difference, feel free to
>>ask for an explanation.
>If you read some of the material you would see the references
Not, however, in any of the articles relevant to unit fractions.
[...]
>The bibliography is extensive because what a bibliography does
>is list the books that contain the references.
What a pity, then, that most of the references required to make these
articles citable were omitted.
[...]
>>>>>http://www.mathpages.com/home/kmath315.htm
>>>>>http://www.mathpages.com/mobius/mobius.htm
>>>>Irrelevant.
>>>That you don't understand the relevence doesn't make it irrelevant.
>>Oh, by all means feel free to explain exactly what linear fractional
>>transformations have to do with unit fractions; I could use a laugh.
>Its just an example by way of introduction to the topic as you
>would know if you had read more of his papers.
>If you read this introductory paper you will discover that he finds
>a General Periodicity Condition that allows him to build tables
>that give the roots of polynomials whose coefficients are
>diagonal elements of Pascal's triangle from which he derives
>the Cauchy distribution in probability theory.
No, I won't, because I know enough to be able to understand what I'm
reading. First, it's not an introduction to anything else in this
collection of largely independent articles. Secondly, he doesn't
'find' a general periodicity condition: he merely states such a
condition and asserts that it can be shown to hold. Thirdly, the
table in question is merely Pascal's triangle, whose construction most
certainly does not require fractional linear transformations at all.
Finally, none of this leads to a derivation of the Cauchy
distribution: in a section independent of the discussion of
periodicity he shows that the asymptotic density of iterates of a real
sequence defined by a linear fractional recurrence follows the Cauchy
distribution.
>Because unit fractions are precise and can be expressed
>in the form of tables they make excellent filters
>for math functions.
And colorless green ideas sleep furiously.
>>>>>http://www.ics.uci.edu/~eppstein/numth/egypt/
Not at all: most folks here in sci.lang have an excellent command of
English.
[...]
> Geometry can be
>thought of as a graphical representation of analytic geometry
>or numerical analysis which is largely a study of the fluxions
>or transformations you just dismissed above.
>>>>[snip unit fractions and Fibonacci numbers, a modern connection
>>>>unknown to the Greeks]
>>>!!!
>>>unknown to the Greek mathematicians, but known to the Egyptian architects?
>>Known to neither. And obviously not understood by you.
>If you read a little Gillings or for that matter Kevin Brown
>you will understand how the cyclic periodicity of unit fraction
>sequences lends itself to tables which is one of the forms in
>which the Egyptians used them
Ah, yes; and to Steve, all tables are the same.
>>>http://www.bath.ac.uk/brlsi/egypt.htm
>>>http://mtcs.truman.edu/~thammond/history/Fibonacci.html
>>The second contains nothing that is to the point, and the first notes
>>that claims for an elaborate proportional system underlying Egyptian
>>architecture are not supported by actual measurements.
>Baloney
<shrug> Anyone who cares to do so can verify my assertion.
[...]
>>>>>Tell us why the Greeks would use an abacus for this. The Greeks based their
>>>>>mathematics on geometry rather than numerical analysis.
>>>>Not true.
>>>False. The Greeks did not use numerical analysis
>>You're wrong.
>Please provide us an example of the Greek numerical analysis you
>are referring to.
I did.
>>>> It's quite clear from the sophistication of the
>>>>_Arithmetica_ of Diophantus that they must have had a fairly strong
>>>>non-geometric tradition, albeit almost *nothing of it survives*.
>>That's not what I wrote. The asterisks are your dishonest addition.
>I just emphasised a hedge you might have prefered we not notice.
No, you emphasized a qualification that you didn't even understand
correctly: it is obvious from your initial response that you thought
that it applied to Diophantus's work. What's more, you dishonestly
failed to mention that you had tampered with the quotation.
[...]
>>>>But all of this is also irrelevant, since most serious computation was
>>>>done in connection with mercantile activities, and most non-mercantile
>>>>computation was astronomical, not purely mathematical.
>>>Baloney.
>>Fact. Your ignorance is showing again.
>>>The achievements of Greek geometry amount to nothing more than
>>>the ability to calculate how to double a talent in the Agora?
>>Are you really so stupid as to have so badly misread what I wrote?
>>And so ignorant as to think that most Greek geometry dealt with
>>numerical computation? <sigh> Yes, probably.
>Hey, you are the one who wrote "most serious computation
>was done in connection with mercantile activities" not me...
Yes, I did. Apparently you don't realize that the achievements of
Greek geometry have very little to do with numerical computation.
>What's more you seem to think
>"most non-mercantile computation was astronomical, not purely mathematical"
>That would be news to the Greek geometers like Ptolemy who were concerned
>with earth measures.
Ptolemy primary significance is as an astronomer and geographer, and
his computations, embodied in his tables, primarily served
astronomers.
[...]
>>>>>>As we know from
>>>>>>numerous pictures (among other sources), the Greeks and Romans did
>>>>>>most of their *calculation* with the functional equivalent of the abacus.
>>>Show me the abacus the Greeks used to determine how to formulate their
>>>classical mathematical problems. They wouldn't have allowed it was a proof
>>>if someone did work out how to square a circle, double a cube and trisect
>>>an angle with an abacus.
>>This is a non sequitur, and an exceptionally stupid one at that,
>>inasmuch as even you appear dimly to recognize that numerical
>>calculation, the subject of my comment, has nothing to do with these
>>problems.
>So if its your position that the classical mathematical problems of
>the Greeks required no calculation and what you mean by calculation
>was principally restricted to commerce, would you claim the Greeks
>had no knowledge of trigonometry?
[...]
>>>>[The Greeks] *did* in fact use positional notation for astronomical
>>>>purposes, but it was sexagesimal, not decimal.
>>>bssst
>>>try sexagesimal and decimal...plus unit fractions
>>No. The positional notation used for astronomical purposes was
>>entirely sexagesimal as a positional notation.
>Wrong.
Do you have any idea how stupid you look denying the obvious? I
didn't think so. I suggest that you take a break from posting to
learn what positional notation is and to read some introductory
material on Hellenistic and medieval astronomy and numeration; until
you can show at least a minimal understanding of the basics, you're a
complete waste of time (apart from providing a certain amount of
unintended humor, of course).
> The Greeks learned astronomy from the Egyptians whose
>astronomical notation was decimal.(Decans is a word used
>by the Greeks to describe the Egyptian decimal system)
Hellenistic astronomy actually owes far more to the Babylonians than
to the Egyptians.
[...]
>Here is an example of Egyptian astronomy being continued in a Greek city
>in the time of the Roman emperor Antonius Pius
Did you really think that no one would check? That URL simply brings
up the Google search page. (And the emperor's name is <Antoninus>,
not <Antonius>.)
[...]
>Ptolemy who lived 100-178 AD is known for his studies of Geography and Astronomy
>*used sexagesimal fractions in his calculations*.
Exactly. That's what I've been telling you, you dummy.
[...]
Mike Cleven
> In article <3CE136EA...@bigfoot.com>,
> Mike Cleven <iro...@bigfoot.com> wrote:
>
>>Uwe Hercksen wrote:
>>
>>>Gary Vellenzer schrieb:
>>
>
>>>>In late antiquity and the Middle Ages, "mathematicus" meant astrologer.
>>>>What we call mathematics was considered a subfield of astrology.
>>>
>
>
>>>Hello,
>>
>
>>>you should not confuse astronomy, astrology and mathematics.
>>
>
>>In ancient times "people did"; actually they just didn't make the
>>separation, as people post-1700 or so tend to.....
>
>
>>My own bit on this: what's the possibility of a Babylonian/Chaldean root
>>behind Gr. mathema; the Egyptian suggestion is OK, but mathematics (and
>>astronomy/astrology) came to Greece from Babylon, not from Egypt.
>
>
> This is by no means clear. It seems that the Greek
> philosophers, such as Plato, considered Egypt to be worth
> emulating, but not Babylonia and Persia.
Agreed; but it was _philosophy_ - religious and moral philosophy in
particular - that the Greeks found worthy in Egypt. It was commonly
conceded throughout classical times that the birthplace of mathematics
and astronomy was Chaldea, and it was from there that teachers of
mathematics and "astronomy" (astrology) came.
>
> The idea of using the same characters in different
> places in an expansion, base 60 for the Babylonians,
> does not seem to have been considered by the Greeks.
> Also, the Babylonians used sexagesimal fractions to many
> places, and the Greeks seem to have stuck with the
> clumsy "Egyptian" fractions, and did not develop decimal
> fractions.
--
Mike Cleven
> On Wed, 15 May 2002 09:19:39 GMT, Mike Cleven <iro...@bigfoot.com>
> wrote:
>
>
>>Brian M. Scott wrote:
>>
>>>On Tue, 14 May 2002 16:10:13 GMT, whi...@shore.net (steve) wrote:
>>
>
>>>[...]
>>
>
>>>>There should be no confusion of astronomy, astrology and mathematics
>>>>because essentially they are all different approaches to the same thing.
>>>
>
>>>No, they're not.
>>
>
>>Yes they WERE - before the Age of Reason.
>
>
> No, they weren't, even assuming that you're ignoring the world outside
> Europe. In the early Middle Ages, the main non-mercantile use of
> mathematics and astronomy in Europe was the computus, or calculation
> of the ecclesiastical calendar, which had nothing to do with
> astrology.
Which is quite funny, considering that most churchmen were
closet-astrologers and dabblers in the Black Arts. The ecclesiastical
calendar and the magical calendar were inseparable; the Church liked to
pretend that it purged itself of sorcerous influences, BUT.....
Fibonacci's _Liber Abaci_ (1202) had, so far as I know,
> nothing to do with astrology *or* astronomy. Nicole Oresme's brillian
> mathematical work in the 14th c., which foreshadows the integral
> calculus, was applied to mechanics, not (primarily) astronomy or
> astrology, and he wrote several books against astrology (though to be
> sure he accepted the almost universal view that the heavens exert some
> influence on large-scale events).
>
>
>> Or don't you know that Newton
>>and Kepler primarily viewed themselves as astrologers?
>
>
> I know that Newton did not. Kepler certainly worked as a professional
> astrologer; Newton, however, appears to have had little if any
> interest in it (though he did have some odd notions about alchemy and
> religion). See <http://www.phys.uu.nl/~vgent/astrology/newton.htm>
> for a summary of the evidence. And even if you were right, this would
> hardly show that mathematics, astronomy, and astrology were considered
> different approaches to the same thing, but merely (as is rather
> obvious) that they are closely related.
Well, I'll have to look up Newton's demonological works - they must be
on the net somewhere. From what I was told, his main concern in
calculating the planetary orbits was so as to more accurately predict
the behaviour of the angels who controlled their orbits.
Brian M. Scott
wrote:
>Brian M. Scott wrote:
>> On Wed, 15 May 2002 09:19:39 GMT, Mike Cleven <iro...@bigfoot.com>
>> wrote:
>>>Brian M. Scott wrote:
>>>>On Tue, 14 May 2002 16:10:13 GMT, whi...@shore.net (steve) wrote:
>>>>[...]
>>>>>There should be no confusion of astronomy, astrology and mathematics
>>>>>because essentially they are all different approaches to the same thing.
>>>>No, they're not.
>>>Yes they WERE - before the Age of Reason.
>> No, they weren't, even assuming that you're ignoring the world outside
>> Europe. In the early Middle Ages, the main non-mercantile use of
>> mathematics and astronomy in Europe was the computus, or calculation
>> of the ecclesiastical calendar, which had nothing to do with
>> astrology.
>Which is quite funny, considering that most churchmen were
>closet-astrologers and dabblers in the Black Arts. The ecclesiastical
>calendar and the magical calendar were inseparable; the Church liked to
>pretend that it purged itself of sorcerous influences, BUT.....
I've learned that it's a waste of time to argue this sort of point
with people who have already bought into caricatures of the Middle
Ages, so I'll not bother, beyond suggesting that you read a decent
introduction like David C. Lindberg's _The Beginnings of Western
Science: the European Scientific Tradition in Philosophical,
Religious, and Institutional Context, 600 B.C. to A. D. 1450_.
[...]
Brian
Mike Cleven
Must I remind you that a-spiritual views of the natural sciences were a
heresy punishable by death in those days? It may be that latter-day
scientists have made an effort to purge superstition from histories of
natural and occult sciences in those times; from my own readings (and I
do read, despite your comment "[those] who have already bought into
caricatures of the Middle Ages") there was no easy distinction between
the studies of the metaphysical and the physical until after the time of
Galileo, and not even then. What else is Giordano Bruno's work but an
effort to reconcile the mythical view of reality with the emerging
"hard" sciences; similarly Giambattista Vico? There may have been rare
individuals who made an effort to divorce themselves from the
intellectual-mystical traditions that lay around the study of the stars
(astrology) and nature (alchemy and medicine) but any attempt in those
times to publicly divorce the divine from science was likely to get one
tied up and tortured, at best. Or stupefyingly rich from dazzling
gullible nobles (e.g. Rudolf II).
I'll look up your Lindberg book and hope that it's not too dry, which
given the puacity of poetic inspiration among the academically-motivated
I should probably expect.
Brian M. Scott
>In article <3ce285e8....@enews.newsguy.com>, b.s...@csuohio.edu says...
>>On Wed, 15 May 2002 09:19:39 GMT, Mike Cleven <iro...@bigfoot.com>
>>wrote:
>>>Brian M. Scott wrote:
>>>> On Tue, 14 May 2002 16:10:13 GMT, whi...@shore.net (steve) wrote:
>>>> [...]
>>>>>There should be no confusion of astronomy, astrology and mathematics
>>>>>because essentially they are all different approaches to the same thing.
>>>> No, they're not.
>>>Yes they WERE - before the Age of Reason.
>>No, they weren't, even assuming that you're ignoring the world outside
>>Europe. In the early Middle Ages, the main non-mercantile use of
>>mathematics and astronomy in Europe was the computus, or calculation
>>of the ecclesiastical calendar, which had nothing to do with
>>astrology.
>Just out of curiosity, what other than astrology, do you think
>was the main mercantile use of astronomy in the early middle ages?
Oddly enough, I know better than to imagine that astronomy had any
mercantile use in the early Middle Ages. I expect a reader of normal
intelligence or better to recognize that 'non-mercantile' applies
principally to mathematics.
>Where do you think the calendars used in Medieval Europe originated?
>How do you think people checked the passing of days, weeks, months
>seasons and years?
>What do you think the passing of time had to do with astronomical
>observations and the signs of the zodiac?
>How do you think an ecclesiatical date such as Easter was computed?
>>Fibonacci's _Liber Abaci_ (1202) had, so far as I know,
>>nothing to do with astrology *or* astronomy.
>That's what we have been telling you.
No, it isn't, since you haven't mentioned it. It's also quite clear
that you think that it has something to do with the abacus. It
hasn't, and the title might best be translated 'The Book of
Calculations'. In it Leonardo introduced, showed how to use, and
recommended the use of Hindu-Arabic numerals and decimal positional
notation; introduced the fraction bar; studied systems of simultaneous
linear equations; stated and solved a large collection of problems
aimed at merchants, including calculation of profit on transactions
and conversion of Mediterranean currencies; stated and solved a wide
variety of other problems, some practical, some more in the nature of
puzzles, and some of genuine mathematical value; introduced the
sequence of numbers that bears his name; and studied both rational
approximations to and geometric constructions of such irrational
numbers as sqrt(10).
> The abacus was fine
>for commercial transactions and might be of utility in
>the arithmetic necessities of geometry, but just as music
>is a code word for order and harmonic sequence,
It isn't.
>astronomy
>is a code word for analytic geometry and calculus; ie
>fluxions or the study of transformational change.
My, what impressive ignorance. No, it isn't.
>>Nicole Oresme's brillian[t]
>>mathematical work in the 14th c., which foreshadows the integral
>>calculus, was applied to mechanics, not (primarily) astronomy or
>>astrology, and he wrote several books against astrology (though to be
>>sure he accepted the almost universal view that the heavens exert some
>>influence on large-scale events).
>Astronomy and astrology can find the fibonacci series useful.
A typically Whittetian non sequitur. In any case, whether Fibonacci
numbers are useful to astrologers is a matter of no interest to me;
anyone who is an astrologer today is either deluded or a fraud
interested in separating fools from their money. I know of no
important uses of the Fibonacci sequence (*not* series) in astronomy,
though it might enter by the back door in one or more of its
mathematical applications.
>Astronomy takes the standard of motion, measures, weighs and
>judges it, puts it in sequence and determines from that
>what the expected consequence might be.
A statement nicely confirming that you're as ignorant of astronomy as
you are of mathematics and linguistics.
[...]
>>>Or don't you know that Newton
>>>and Kepler primarily viewed themselves as astrologers?
>Actually Newton viewed himself as more of an alchemist,
>but in the same way Keppler was an astrologer.
>>I know that Newton did not.
>Newon wrote considerably more about alchemy and astrology
>than he did about science and he was more interested in
>the transformation of elements mathematically as with
>fluxions than he was with what we call science.
Newton wrote about alchemy but appears to have written little or
nothing about astrology. I do not know how the quantity of his
alchemical writings compares with the quantity of his scientific
writings, but his *published* scientific and mathematical work is far
more extensive than his *published* alchemical work.
[...]
Brian M. Scott
with it.
On Wed, 15 May 2002 18:50:11 GMT, whi...@shore.net (steve) wrote:
>In article <3ce285e8....@enews.newsguy.com>, b.s...@csuohio.edu says...
>>On Wed, 15 May 2002 09:19:39 GMT, Mike Cleven <iro...@bigfoot.com>
>>wrote:
>>>Brian M. Scott wrote:
>>>> On Tue, 14 May 2002 16:10:13 GMT, whi...@shore.net (steve) wrote:
>>>> [...]
>>>>>There should be no confusion of astronomy, astrology and mathematics
>>>>>because essentially they are all different approaches to the same thing.
>>>> No, they're not.
>>>Yes they WERE - before the Age of Reason.
>>No, they weren't, even assuming that you're ignoring the world outside
>>Europe. In the early Middle Ages, the main non-mercantile use of
>>mathematics and astronomy in Europe was the computus, or calculation
>>of the ecclesiastical calendar, which had nothing to do with
>>astrology.
>Just out of curiosity, what other than astrology, do you think
>was the main mercantile use of astronomy in the early middle ages?
Oddly enough, I know better than to imagine that astronomy had any
mercantile use in the early Middle Ages. I expect a reader of normal
intelligence or better to recognize that 'non-mercantile' applies
principally to mathematics.
[...]
>How do you think an ecclesiatical date such as Easter was computed?
Having actually read quite a bit on the subject, I don't think, I
know. It was actually a fairly hard problem in, say, the 8th century,
when Bede wrote a rather nice little treatise called 'De temporum
ratione'.
>>Fibonacci's _Liber Abaci_ (1202) had, so far as I know,
>>nothing to do with astrology *or* astronomy.
>That's what we have been telling you.
It obviously isn't, since you haven't mentioned it. It's also quite
clear that you think that it has something to do with the abacus. It
hasn't, and the title might best be translated 'The Book of
Calculations'. In it Leonardo introduced, showed how to use, and
recommended the use of Hindu-Arabic numerals and decimal positional
notation; introduced the fraction bar; studied systems of simultaneous
linear equations; stated and solved a large collection of problems
aimed at merchants, including calculation of profit on transactions
and conversion of Mediterranean currencies; stated and solved a wide
variety of other problems, some practical, some more in the nature of
puzzles, and some of genuine mathematical value; introduced the
sequence of numbers that bears his name; and studied both rational
approximations to and geometric constructions of such irrational
numbers as sqrt(10).
> The abacus was fine
>for commercial transactions and might be of utility in
>the arithmetic necessities of geometry, but just as music
>is a code word for order and harmonic sequence,
It isn't.
>astronomy
>is a code word for analytic geometry and calculus; ie
>fluxions or the study of transformational change.
My, what impressive ignorance. No, it isn't.
>>Nicole Oresme's brillian[t]
>>mathematical work in the 14th c., which foreshadows the integral
>>calculus, was applied to mechanics, not (primarily) astronomy or
>>astrology, and he wrote several books against astrology (though to be
>>sure he accepted the almost universal view that the heavens exert some
>>influence on large-scale events).
>Astronomy and astrology can find the fibonacci series useful.
A typically Whittetian non sequitur. In any case, whether Fibonacci
numbers are useful to astrologers is a matter of no interest to me;
anyone who is an astrologer today is either deluded or a fraud
interested in separating fools from their money. I know of no
important uses of the Fibonacci sequence (*not* series) in astronomy,
though it might enter by the back door in one or more of its
mathematical applications.
>Astronomy takes the standard of motion, measures, weighs and
>judges it, puts it in sequence and determines from that
>what the expected consequence might be.
A statement nicely confirming that you're as ignorant of astronomy as
you are of mathematics and linguistics.
[...]
>>>Or don't you know that Newton
>>>and Kepler primarily viewed themselves as astrologers?
>Actually Newton viewed himself as more of an alchemist,
>but in the same way Keppler was an astrologer.
>>I know that Newton did not.
>Newon wrote considerably more about alchemy and astrology
>than he did about science and he was more interested in
>the transformation of elements mathematically as with
>fluxions than he was with what we call science.
Newton wrote about alchemy but appears to have written little or
Brian M. Scott
wrote:
[...]
>Must I remind you that a-spiritual views of the natural sciences were a
>heresy punishable by death in those days?
Take a look at the variety of scientific views actually expressed by
medieval scholars, many of whom were quite happy to learn from the
Greeks and Muslims. Take a look at how very, very few were executed
for heresy, even after the Reformation, when the church actually did
get a bit more defensive.
[...]
Mikael Thompson
"Brian M. Scott" wrote:
> Newton wrote about alchemy but appears to have written little or
> nothing about astrology. I do not know how the quantity of his
> alchemical writings compares with the quantity of his scientific
> writings, but his *published* scientific and mathematical work is far
> more extensive than his *published* alchemical work.
According to Martin Gardner, his alchemical manuscripts far exceed in bulk his
writings on physics. Of course, most of it remains unpublished; John Maynard
Keynes, who bought up a lot of it when it went up for auction, said what he bought
was essentially worthless wastes of Newton's time and energy.
Mikael Thompson
Bobby D. Bryant
> In article <abtj6q$c0q$1...@geraldo.cc.utexas.edu>, bdbr...@mail.utexas.edu says...
>>>>Enough with the obfuscation.
>
> Go read enough of what I have cited to you that
> you understand the connections and save us both
> some time.
I notice that you snipped the most important part of my post, which
I repeat below for the benefit of any lurkers coming late to this
thread. (I notice also that you failed to answer *any* of these
questions.)
"""
Do you really expect to convince skeptics by citing _yourself_? Even
after showing how clueless you are on some very basic matters?
My university's library doesn't carry that august journal. Please
answer the following:
a) Is it a peer-reviewed journal?
b) Did you present your etymology of Greek ma(n)th- in any of your
papers published in it?
c) Did you cite a source -- other than yourself -- for your
etymology?
d) Was _that_ source in a peer-reviewed journal?
If the answer to all four questions is 'yes', than give me the souce
you cited (complete with publication info and page number, so I can
find it). Otherwise, prepare for immediate admission to my bozo
filter's database.
"""
Bobby Bryant
Austin, Texas
p.s. - 'plonk!'
Brian M. Scott
>>>>>> <Zeus> is from PIE */dyeu-/ 'to shine'.
>>>>> deus or deity is also proposed,
>>>>Be aware that multiple words can be derived from the same word in a
>>>>proto-language. Be aware also that Greek and Latin are different
>>>>languages, although related.
>>> Perhaps more to the point are these links
>>> http://ccat.sas.upenn.edu/~jfarrell/courses/spring96/myth/feb12.html
>>> http://www.geocities.com/geenath_2000/greek1.html
>>Nothing there to support your claims.
That's a kind assessment, considering the bungled 'father' cognates at
the geenath_2000 site.
>It points out that the Greeks attributed their borrowings to Egypt.
More accurately, the UPenn site does so. It also points out the
difficulties with this notion.
[...]
>>>>> but as you go on to write
>>>>> Zeus pate:r you should admit the meaning is sky father.
>>>>That's is indeed what it means. But it's derived from PIE morphemes
>>>>(and shows up _independently_ in Greek, Latin, Sanskrit, and maybe
>>>>some others).
>>> That is one theory.
>>That's the theory that all educated scholars subscribe to.
>That's a foolish and remarkably ethnocentric incorrect generalization.
Steve has demonstrated on many occasions that he cares more for (his
notion of) political correctness than for the facts. (His misuse of
'ethnocentric' is of course entirely unremarkable.)
[...]
> Egypt has a variety of roles for its deity
>or neter, but they are all aspects of the same Being.
It's an article of faith with Steve that his beloved Egyptians
couldn't possibly have been so unsophisticated as actually to have
believed in a multiplicity of gods.
>Essentially its a
>system of paired opposites resolved in a synthesis which Greeks like Plato
>found useful in dialectic.
One of Steve's favorite mantras!
[...]
>>Again, a popular sport in the ancient world. The Romans claimed to
>>be of Trojan descent. (And for that matter, so did the English
>>almost two millenia later.)
>The Romans acknowledged that the Etruscans were connected to Troy
>just as the English acknowledge the most ancient written ancestor
>of their language traces back to Anatolia and the Greeks showed
>the same recognition of their antecedents.
The English in question claimed to be of Trojan descent; specifically,
descended from Brutus, a legendary great-grandson of Aeneas. The most
ancient written *ancestor* of English is not to be found in Anatolia,
though the most ancient extant written *relative* of English is.
>>>>> As for the word for father<peter<pater<pitar<ptah
>>>>Bogus etymology detected. "pitar" is the specifically Sanskrit
>>>>variant, and derives from a form almost identical to the Greek
>>>>"pate:r", except that the 'a' was a laryngeal rather than an
>>>>ordinary vowel.
>>> Sanskrit and Greek came along a bit later than ancient Egyptian.
>>Irrelevant to your claims.
>Usually in trying to trace words back in time, an etymology acknowledges
>the earlier existence of similar words that may be borrowed from other
>cultures.
Confirming yet again that Steve doesn't know what an etymology is.
[...]
>>"Aborigine" means "the people who lived there first".
>Lived where first?
Anywhere.
>>For Greeks, Romans, and Indians it means the people who lived
>>in Greece, Italy, and India before the IE speakers arrived.
>So if the IE speakers first arrived in Greece c 1650 BC
>everyone who lived there before then was an aborigine?
>>(Pedantic note: those
>>might not really be the "first" people to live in those regions,
>>but unfortunately we can't trace the prehistory back any further,
>Of course we can, what do you think Archaeologists and Anthropologists do?
At present we can't. We don't even know for sure which archaeological
traces are associated with the arrival of the people who spoke the
immediate precursor of Greek.
>>so the term is used as a term of convenience. FWIW it's a Latin
>>word, and the Roman authors used it as above. Livy, IIRC, uses it
>>in his mythical description of the prehistory of Rome.)
>Are you using the word in the sense of before we lived here savages
>and barbarians who did't speak our language occupied our land?
No. (You can always tell when Steve begins dimly to sense that he's
in trouble: his creative readings become malicious as well as stupid.)
>>>>I don't think any of the gods from the
>>>>main pantheon can be derived from Egyptian sources, though like the
>>>>Romans they adopted all manner of exotica in the later period.
>>> So is Herodotus mistaken or just misinformed?
>>Probably both. As I said above, deriving pantheons from other
>>pantheons was a popular passtime in the ancient world.
>Are you aware of a number of other classical sources other than
>Herodotus who shared the same mistaken misinformation?
So what? There's a small boatload of medieval sources reporting the
most amazing rubbish. In both cases many of the sources are *not*
independent of one another.
[...]
>>>>>> and is from PIE */wen-/ 'to desire, strive for'.
>>>>> No, not even close.
>>>>And you're an authority who can dispute with the experts, eh?
>>> Experts don't have to dispute.
>>Clearly, they wouldn't waste their time on you like we are.
>Lots of experts seem to like to waste their time on me,
>often quite politely.
Until they realize just what a waste it is. Even the remarkably
patient Piotr Michalowski gave up, though not before writing this:
This whole debate is ludicrous, as once again SW refuses
to actually learn the basic principles of linguistics, history
or archaology and refuses to look at the data that people
have used as the basis for a debate. On top of that, he
refuses to analyze the standard works on a given subject,
but is ready to refute them. What else is new.
[...]
>>> Again the suggestion is that its borrowed into Greek
>>The suggestion of certain parties who know nothing of historical
>>linguistics.
>You do realise that the attributes of gods were being traded back and forth
>before historical linguistics existed?
Oh, yes. We also understand the utter irrelevance of the observation.
You do realise that the planets were following their orbits long
before Homo sapiens evolved, let alone developed the physical
sciences?
[...]
>>I certainly put more stock in skeptical Amazon reviews than I do in
>>your believe-anything-about-egypt claims.
>Personally I am not a believer.
Of course he is: he has a set of beliefs that he doesn't allow himself
to question and that he defends without regard to logic or even
honesty. The fact that they aren't (in the usual sense of the word)
religious beliefs is beside the point; I've known Christian
fundamentalists who were less credulous than Steve. (Come to think of
it, some of Steve's odd notions do have a religious component: he's a
superannuated flower-child who's bought into a fair bit of New Age
crap, though he often gives it his own peculiar twist.)
[...]
>>But again, to bring us back to your original claim: can you show a
>>single peer-reviewed source for your claim that Greek
>>manthano:/mathe:somai is derived from an Egyptian source?
>I gave you the phrase [m3at mh] look it up in Gardiner and or Faulkner.
In other words, he can't.
[...]
steve
>>...the Greeks attributed their borrowings to Egypt.
...
>>>>>>... Zeus pate:r ...sky father.
>
>>>>>...derived from PIE morphemes
>>>>>...shows up...in Greek, Latin, Sanskrit...
>>>> ....is one theory.
>
>>>That's the theory that all educated scholars subscribe to.
>
>>That's a foolish and remarkably ethnocentric incorrect generalization.
>
>Steve has demonstrated on many occasions that he cares more for (his
>notion of) political correctness than for the facts. (His misuse of
>'ethnocentric' is of course entirely unremarkable.)
Its actually described as ethnocentric by many educated scholars from india
who have a very different theory, and feel the theory you mention ought not
to dominate the discussion or characterise their dissent as representative
of an uneducated view.
>
>[...]
>
>>...Egypt has a variety of roles for its deity
>>or neter, but they are all aspects of the same Being.
>
>It's an article of faith with Steve that his beloved Egyptians
>couldn't possibly have been so unsophisticated as actually to have
>believed in a multiplicity of gods.
Most Egyptologists will allow that all the gods are included in the neter.
Its not really a question of sophistication, just a better understanding
of what "god" meant in Egyptian usage. Most Egyptian gods turn out to be
very close to what the Greeks called Ideals and aspects of a state of Being.
The amimism is symbolic, the personification Greek.
I would be interested to see any factual information in support of a different view.
If you have it please feel free to present it?
>
>>Essentially its a system of paired opposites resolved in a synthesis
>>which Greeks like Plato found useful in dialectic.
>
>One of Steve's favorite mantras!
Becuae the essence of working a dialectic
is to communicate rather than argue.
steve
Brian M. Scott
>>>...the Greeks attributed their borrowings to Egypt.
>...
>>>>>>>... Zeus pate:r ...sky father.
>>>>>>...derived from PIE morphemes
>>>>>>...shows up...in Greek, Latin, Sanskrit...
>>>>> ....is one theory.
>>>>That's the theory that all educated scholars subscribe to.
>>>That's a foolish and remarkably ethnocentric incorrect generalization.
>>Steve has demonstrated on many occasions that he cares more for (his
>>notion of) political correctness than for the facts. (His misuse of
>>'ethnocentric' is of course entirely unremarkable.)
>Its actually described as ethnocentric by many educated scholars from india
>who have a very different theory, and feel the theory you mention ought not
>to dominate the discussion or characterise their dissent as representative
>of an uneducated view.
No, it's described as ethnocentric by some Indians with a political
axe to grind, much like Clyde Winters with his fantasies of a
'(Proto-)Manding' origin for half the world's languages. Few of them,
so far as I can tell, have any knowledge of historical linguistics,
and their view therefore *is* uneducated.
[...]
steve
You probably don't see where your views are ethnocentric at all.
1.) You are lumping together all members of an ethnic group who disagree
with the theory you subscribe to and who would consider as disparaging
a remark such as "That's the theory that all educated scholars subscribe to"
just because they happen to hold a different perspecive
2.) You are characterising all who would consider disparaging a remark such as
"That's the theory that all educated scholars subscribe to" as
"having a political axe to grind" as without presenting
a single fact to support such a prejudicial speculation
3.) You are comparing them as a group to someone else who has
nothing in common with them except your disdain
4.) You are characterising their ideas as "much like...his fantasies"
when in fact there is again nothing in common but your disdain
5.) You are asserting as fact a total non-sequitor
a subjective speculation with no facts or
evidence of research to back it up and again
applying it to the group
6.) to state
"few of them so far as I can tell"
"have any knowledge of historical linguistics"
is a totally meaningless and subjective speculation
7.) You are drawing a conclusion that "their view therefore *is* uneducated".
based on nothing more than your own prejudice.
I'm not too suprised, but perhaps you can see where they
might wish to protest their credentials are being disparaged
and their scholarship slandered by an individual whose prejudice
is apparent.
steve
Bobby D. Bryant
Yes, accusations of ethnocentricity are a popular way of handwaving
away a theory that you don't like but can't refute with _evidence_.
Bobby Bryant
Austin, Texas
steve
>>>Its actually described as ethnocentric by many educated scholars from india
>>>who have a very different theory, and feel the theory you mention ought not
>>>to dominate the discussion or characterise their dissent as representative
>>>of an uneducated view.
>Yes, accusations of ethnocentricity are a popular way of handwaving
>away a theory that you don't like but can't refute with _evidence_.
One alternative theory
http://www.hinduwebsite.com/general/hittite.htm
A competely different question
"Post: What raises the characteristically skeptical or at least philosophical problem
of translation are certain Indo-European philosophies--those that argue, rightly or,
I think, quite wrongly--that there are deep problems in principle about translation.
"The argument on which these philosophies typically depend is one in which we are
to assume that on some deep, philosophical level--whether categorical, conceptual,
linguistic, infrastructural--no further argumentation or interpretation can be given,
on pain of circularity or else infinite regress. When you puzzle through what is
driving this assumption, you find--peering up at you from the bottom of the mug,
to steal a phrase from J. L. Austin--the transitivity presupposition."
http://www.vanderbilt.edu/AnS/philosophy/Faculty/Interviews/Post.html
yet another, this time focused on Basque
"Most European languages belong, together with numerous languages of southern Asia,
to one language family that goes under the name of Indo-European.
Proto-Indo-European (Proto-IE or PIE in linguists’ jargon) is a theoretical construct
representing the ‘reconstructed’, hypothetical language from which the various know
Indo-European languages are imagined to have descended. As a matter of fact, we don’t
know a great deal about this proto-language, if it ever existed at all as such, and
there is no proof that it did."
Brian M. Scott
>>>>Its actually described as ethnocentric by many educated scholars from india
>>>>who have a very different theory, and feel the theory you mention ought not
>>>>to dominate the discussion or characterise their dissent as representative
>>>>of an uneducated view.
Let's re-insert what Steve snipped here, since Bobby's response makes
much better sense that way:
No, it's described as ethnocentric by some Indians with a
political axe to grind, much like Clyde Winters with his
fantasies of a '(Proto-)Manding' origin for half the world's
languages. Few of them, so far as I can tell, have any
knowledge of historical linguistics, and their view therefore
*is* uneducated.
>>Yes, accusations of ethnocentricity are a popular way of handwaving
>>away a theory that you don't like but can't refute with _evidence_.
>One alternative theory
>http://www.hinduwebsite.com/general/hittite.htm
I've seen Mr Kumar's comments before. For the most part they're
pretty harmless. The idea IE and Anatolian may be sisters is hardly
new, however, and 'the oldest Indo-European language' is a meaningless
notion without further explanation.
>A competely different question
>"Post: What raises the characteristically skeptical or at least philosophical problem
>of translation are certain Indo-European philosophies--those that argue, rightly or,
>I think, quite wrongly--that there are deep problems in principle about translation.
>"The argument on which these philosophies typically depend is one in which we are
>to assume that on some deep, philosophical level--whether categorical, conceptual,
>linguistic, infrastructural--no further argumentation or interpretation can be given,
>on pain of circularity or else infinite regress. When you puzzle through what is
>driving this assumption, you find--peering up at you from the bottom of the mug,
>to steal a phrase from J. L. Austin--the transitivity presupposition."
>http://www.vanderbilt.edu/AnS/philosophy/Faculty/Interviews/Post.html
Philosophical mud, and a bit out of context to boot. Nothing to do
with the history of the IE languages.
>yet another, this time focused on Basque
>"Most European languages belong, together with numerous languages of southern Asia,
>to one language family that goes under the name of Indo-European.
>Proto-Indo-European (Proto-IE or PIE in linguists’ jargon) is a theoretical construct
>representing the ‘reconstructed’, hypothetical language from which the various know
>Indo-European languages are imagined to have descended. As a matter of fact, we don’t
>know a great deal about this proto-language, if it ever existed at all as such, and
>there is no proof that it did."
This is the second time in the last few days that you've provided a
URL that resolves to the Google search page. As the man says, he's
not a historical linguist. If his comments were written with the
typical reader of his page in mind, then he's simply wrong. If he was
writing for a more sophisticated reader and intended simply to point
out that any such reconstruction is necessarily incomplete and
imperfect, then he's right but misleading.
Bobby D. Bryant
> Let's re-insert what Steve snipped here, since Bobby's response makes
> much better sense that way:
The funny thing is, even after all his snipping, the Web sites he
cites don't support his claim that the PIE derivation of Greek
pate:r is an ethnocentric belief (let alone his earlier claim that
it is derived from Egyptian).
As I said earlier, it's very popular to tar your opponents with
accusations of ethnocentricity whenever you don't have any
_evidence_ to refute them with. Steve very clearly doesn't have
any evidence to present, so it's no surprise that he wants to
discuss ethnocentricity instead of evidence.
BTW, would any lurkers care to step forward and declare that they
have found _anything_ that Steve has said here to be convincing?
Bobby Bryant
Austin, Texas
Richard Herring
<bdbr...@mail.utexas.edu> writes
>
>BTW, would any lurkers care to step forward and declare that they
>have found _anything_ that Steve has said here to be convincing?
Certainly. In addition to linguistics and mathematics, he has convinced
me that he also knows nothing about physics.
--
Richard Herring
Dr. Des Small
> BTW, would any lurkers care to step forward and declare that they
> have found _anything_ that Steve has said here to be convincing?
Change that "that" to an "if" and I can offer you a "no".
HTH,
Des.
--
Des Small, Scientific Programmer,
School of Mathematics, University of Bristol,
F Cameron Sipston
> In article <3ce3d95a....@enews.newsguy.com>, b.s...@csuohio.edu says...
> >
> >On Thu, 16 May 2002 12:54:07 GMT, whi...@shore.net (steve) wrote:
> >
> >>>>...the Greeks attributed their borrowings to Egypt.
> ...
> >>>>>>>>... Zeus pate:r ...sky father.
>
> >>>>>>>...derived from PIE morphemes
> >>>>>>>...shows up...in Greek, Latin, Sanskrit...
>
> >>>>>> ....is one theory.
>
> >>>>>That's the theory that all educated scholars subscribe to.
those, you mean, that you've read.
>
> >>>>That's a foolish and remarkably ethnocentric incorrect generalization.
>
> >>>Steve has demonstrated on many occasions that he cares more for (his
> >>>notion of) political correctness than for the facts. (His misuse of
> >>>'ethnocentric' is of course entirely unremarkable.)
>
> >>Its actually described as ethnocentric by many educated scholars from india
> >>who have a very different theory, and feel the theory you mention ought not
> >>to dominate the discussion or characterise their dissent as representative
> >>of an uneducated view.
> >
> >No, it's described as ethnocentric by some Indians with a political
> >axe to grind, much like Clyde Winters with his fantasies of a
> >'(Proto-)Manding' origin for half the world's languages. Few of them,
> >so far as I can tell, have any knowledge of historical linguistics,
> >and their view therefore *is* uneducated.
>
> You probably don't see where your views are ethnocentric at all.
>
> 1.) You are lumping together all members of an ethnic group who disagree
> with the theory you subscribe to and who would consider as disparaging
> a remark such as "That's the theory that all educated scholars subscribe to"
> just because they happen to hold a different perspecive
on the defensive here a moment...I would love to speak to anyone in
their native dialect. And don't believe it's anything but life but to
be able to.
However, the UK market really could do with a few, more illuminating,
texts, on where hindi meets gujerati meets urdu, and where grammar
carries vocabulary and where vocabulary carries grammar. I speak after
looking in every bookshop in a town whose population would call itself
a prosperous and egalitarian; and, finding nothing to buy my
adolescent cousin, or my cousins' adolescent kids, that will furnish
them with either.
I mean, are we receptive in creative ways in adolescence or are we
not? And do we really need to be strictly anything to understand each
others' orthographies?
Is language sound-patterns or whbta?
H.M. Hubey
> On Wed, 15 May 2002 15:39:05 GMT, whi...@shore.net (steve) wrote:
>
> >>>>>> <Zeus> is from PIE */dyeu-/ 'to shine'.
>
> >>>>> deus or deity is also proposed,
>
> >>>>Be aware that multiple words can be derived from the same word in a
> >>>>proto-language. Be aware also that Greek and Latin are different
> >>>>languages, although related.
>
> >>> Perhaps more to the point are these links
>
> >>> http://ccat.sas.upenn.edu/~jfarrell/courses/spring96/myth/feb12.html
> >>> http://www.geocities.com/geenath_2000/greek1.html
I read these once every few months, but I thought this was interesting.
let's see
Akkadian nurum (light), Arabic nur, etc
Hittite laluki (light, etc)
Turkic ya- (from which we get yulduz (star), yaltIra (shine), yan (burn), yak
(set on fire) etc)
Other related Turkic words: yarug (light), carIk (light), ciltin (spark).
Chuvash Turkic s'altar (star), a lot like star, stella
These are all via regular sound changes.
[ASIDE: ProtoTurkic had initial-n but it disappeared. Some of the words are
preserved in Hungarian. It seems to have been *ny. That would have meant
ny>y thus nyurum> *yurum. Modern Turkic I<u thus creating *yIrIm. Many old
Turkic nouns have -Vn, -Vr suffixes, and a handful of -Vm. Somewhere along
the line the -Vm/n/r became -Vk. And since there is the Turkic {s/sh,z}={l,r}
we can see *yIrIm= IshIk (Turkish for light). Other changes can also shown
to follow similar paths between Turkic and Hittite etc. END-ASIDE]
Then there is Hurrian leli (nobody seems to know exactly what it is).
But Circassian has yeli (lightning), connected with Elijah (connected with
lightning)
But Turkic yak also means "to apply ointment, as in oil, fat".
So the word seems to mean "glisten, shine, etc" and got applied to light,
shining,
star, spark, lightning, etc.
Turkic initial c/y (as in yarug/carIk) is supposed to come from*d.
But Turkic yarug can also be connected easily with IshIk.
[ASIDE: So there was some connection d=n=y. END-ASIDE}
So the root for shining/glistening/oil etc was *da-.
We can find the word for "butter, oil, fat" preserved in Circassian as "dage".
But IA/YA can be found in Sumerian (fat, butter, oil).
So we may hypothesize temporarily:
1. So it looks like *PIE *dyeu goes back apparently to a lot further than
Sumerian.
2. Everything is IE.
[Turkish still has ya: (butter, fat, oil). No change in 5,000 years or so]
How do we resolve this?
A language is not thought to possess /bdg/ before /ptk/. A language that does
not possess /ptk/ and /bdg/ would not possess *dy, or dh. How long would it
take for these changes to take place?
There are languages which do not even seem to possess /bdg/. So how old
are these languages? There are many languages that don't have anything
resembling dy, dh. How long do we have to wait until they develop them?
Where on earth can a language exist for thousands of years completely
isolated from all other languages so that it can develop changes like
t>d, and then t>th, or d>dy, or d>dy, and all these sounds which do not
seem to exist in probably a majority of the world's languages?
In the Middle of Three Continents (Mideast?)
H.M. Hubey
Osophos wrote:
> >Dictionaries give mathematics < L mathemalicus < Gk mathema (learning)
> >but surely that raises the question who did the Greeks and Romans learn
> >their mathematics from?
Turkic k is cognate often with m in IE and Semitic. There are many examples
of this in Tuna's book. I have found even more. These come from
the changes p>t>k in one branch, and p>b>m in another.
Turkic kat = to add, katIl (to join, i.e. self-add), also as koshul.
katla = to fold over, e.g. multiply
kere = times, as in 2 times 2
And it also shows up in t, e.g. terge (to calculate).
It seems to me that it has very specific meanings in one branch, not
merely "learning". Maybe learning at one time consisted of addition
and multiplication, just like today.
Yusuf B Gursey
: Osophos wrote:
:> >Dictionaries give mathematics < L mathemalicus < Gk mathema (learning)
:> >but surely that raises the question who did the Greeks and Romans learn
:> >their mathematics from?
: Turkic k is cognate often with m in IE and Semitic. There are many examples
: of this in Tuna's book. I have found even more. These come from
: the changes p>t>k in one branch, and p>b>m in another.
: Turkic kat = to add, katIl (to join, i.e. self-add), also as koshul.
ko*sh*ul is just a neologism
: katla = to fold over, e.g. multiply
: kere = times, as in 2 times 2
kere is from arabic, karra(t)
: And it also shows up in t, e.g. terge (to calculate).
Yusuf B Gursey
: [Turkish still has ya: (butter, fat, oil). No change in 5,000 years or so]
ya: is just a modern "fast" pronounciation, slurring the g~
Yusuf B Gursey
: So the root for shining/glistening/oil etc was *da-.
: We can find the word for "butter, oil, fat" preserved in Circassian as "dage".
d`a- for burning is a frequently cited nostratic word for burning. the
circassian word may very well be from archaic turkic (old bulghar), since
a couple of other archaic turkci *d`- words are known in the region
Brian M. Scott
wrote:
[...]
>Turkic k is cognate often with m in IE and Semitic.
He still doesn't know what 'cognate' means.
[...]
H.M. Hubey
Yusuf B Gursey wrote:
which ones?
H.M. Hubey
Yusuf B Gursey wrote:
> H.M. Hubey <hhu...@nj.rr.com> wrote:
>
> : Osophos wrote:
>
> :> >Dictionaries give mathematics < L mathemalicus < Gk mathema (learning)
> :> >but surely that raises the question who did the Greeks and Romans learn
> :> >their mathematics from?
>
> : Turkic k is cognate often with m in IE and Semitic. There are many examples
> : of this in Tuna's book. I have found even more. These come from
> : the changes p>t>k in one branch, and p>b>m in another.
>
> : Turkic kat = to add, katIl (to join, i.e. self-add), also as koshul.
>
> ko*sh*ul is just a neologism
Really? What are you talking about?
Tenishev and Siunchev:
qoshaq (-??) I 1) additive, increase additional; 2) added piece, extension; 3)
impurity; ~ alt?n gold with an impurity 4) print. appendix i.e. appendix to a
magazine
qoshaq (-??) II coquetry, affectedness
qoshaqlan to flirt (with); to behave affectedly, be affected
qosh in diff. senses to add; suw ~ to add water; 2) to increase; to extend; to
add on; c?c?m?a ~ lengthen a cord; 3) to cross (plants, animals),animal
husbandry; 4) to attach, to involve; to include; ishge ~ to attach to work; 5)
to unite; eki kolxoznu bir birine ~ to unite two collective farms; 6) figurative
to entangle; meni ol ishge qoshma do not entangle me in that business 7)
figurative to exaggerate
>
>
> : katla = to fold over, e.g. multiply
> : kere = times, as in 2 times 2
>
> kere is from arabic, karra(t)
Maybe in your dictionary.
Name another people who were pagan in the 17th century, stuck between high
mountain peaks, away from
Arabs who are chock full of words from Arabic.
Not to mention the obvious connections: kat, kere, kosh. You don't have to know
much
about linguistics to see these connections.
H.M. Hubey
"Brian M. Scott" wrote:
Check a dictionary.
While you are at it, check also the meaning of "extensionality".
H.M. Hubey
Actually this business of where what we today study seems
like it is ideally suited for linguists especially historical
linguists. If long time ago what was "scholarship" and
"what is to be learned" consisted of the "Quadrivium and
the Trivium, then all of today's knowledge can be traced
back to those.
If looked at on very coarse scales, what we now have
has to come from these:
-------------------------------------------------------------------
The Trivium consisted of:
Grammar
Rhetoric
Logic
The Quadrivium consisted of:
Arithmetic -- Number in itself
Geometry -- Number in space
Music, Harmonics, or Tuning Theory -- Number in time
Astronomy or Cosmology -- Number in space and time
------------------------------------------------------------------------
Many university graduates do not know much more than
this about the universe. On a coarse scale, and on some fuzzy
level, this is essentially correct.
Otherwise think of all the historical linguists who abhor
math.
Yusuf B Gursey
: Yusuf B Gursey wrote:
:> H.M. Hubey <hhu...@nj.rr.com> wrote:
:>
:> : Osophos wrote:
:>
:> :> >Dictionaries give mathematics < L mathemalicus < Gk mathema (learning)
:> :> >but surely that raises the question who did the Greeks and Romans learn
:> :> >their mathematics from?
:>
:> : Turkic k is cognate often with m in IE and Semitic. There are many examples
:> : of this in Tuna's book. I have found even more. These come from
:> : the changes p>t>k in one branch, and p>b>m in another.
:>
:> : Turkic kat = to add, katIl (to join, i.e. self-add), also as koshul.
:>
:> ko*sh*ul is just a neologism
: Really? What are you talking about?
so? it is derived from a turkic root, but it is still a neologism.
: Tenishev and Siunchev:
: qoshaq (-??) I 1) additive, increase additional; 2) added piece, extension; 3)
: impurity; ~ alt?n gold with an impurity 4) print. appendix i.e. appendix to a
: magazine
: qoshaq (-??) II coquetry, affectedness
: qoshaqlan to flirt (with); to behave affectedly, be affected
: qosh in diff. senses to add; suw ~ to add water; 2) to increase; to extend; to
: add on; c?c?m?a ~ lengthen a cord; 3) to cross (plants, animals),animal
: husbandry; 4) to attach, to involve; to include; ishge ~ to attach to work; 5)
: to unite; eki kolxoznu bir birine ~ to unite two collective farms; 6) figurative
: to entangle; meni ol ishge qoshma do not entangle me in that business 7)
: figurative to exaggerate
:>
:>
:> : katla = to fold over, e.g. multiply
:> : kere = times, as in 2 times 2
:>
:> kere is from arabic, karra(t)
: Maybe in your dictionary.
well, there are some "details" like it being present in arabic before the
turks.
: Name another people who were pagan in the 17th century, stuck between high
: mountain peaks, away from
: Arabs who are chock full of words from Arabic.
contact with arabs is not neccessary. these are literary borrowings.
in the time and palce you are refering the local rulers were at least
nominally muslim and under ottoman (muslim) rule. all that is needed.
: Not to mention the obvious connections: kat, kere, kosh. You don't have
: to know
: much
: about linguistics to see these connections.
well, against such evidence ...
:>
:>
:> : And it also shows up in t, e.g. terge (to calculate).
Yusuf B Gursey
Yusuf B Gursey
: Yusuf B Gursey wrote:
: which ones?
a word for "funeral feast", which incidentally is also mentioned in
connection with the turks in an early byzantine report.
Mike Cleven
> Actually this business of where what we today study seems
> like it is ideally suited for linguists especially historical
> linguists. If long time ago what was "scholarship" and
> "what is to be learned" consisted of the "Quadrivium and
> the Trivium, then all of today's knowledge can be traced
> back to those.
>
> If looked at on very coarse scales, what we now have
> has to come from these:
> -------------------------------------------------------------------
> The Trivium consisted of:
>
> Grammar
> Rhetoric
> Logic
>
> The Quadrivium consisted of:
>
> Arithmetic -- Number in itself
> Geometry -- Number in space
> Music, Harmonics, or Tuning Theory -- Number in time
> Astronomy or Cosmology -- Number in space and time
Worth noting here that "number" in all these senses continued to have a
mystical frame of reference a la Pythagoras or the Babylonians rather
than raw, plain numbers in the manner of modern math/physics.
> ------------------------------------------------------------------------
> Many university graduates do not know much more than
> this about the universe. On a coarse scale, and on some fuzzy
> level, this is essentially correct.
More's the pity.
>
> Otherwise think of all the historical linguists who abhor
> math.
Or Ph.D's in economics or engineering who don't know any music,
philosophy, or history before Maynard Keynes....
>
> http://www.cosmopolis.com/villa/liberal-arts.html
>
>
>
--
Mike Cleven
http://www.cayoosh.net (Bridge River Lillooet history)
http://www.hiyu.net (Chinook Jargon phrasebook/history)
Brian M. Scott
wrote:
>"Brian M. Scott" wrote:
>> On Sat, 18 May 2002 16:34:59 GMT, "H.M. Hubey" <hhu...@nj.rr.com>
>> wrote:
>> [...]
>> >Turkic k is cognate often with m in IE and Semitic.
>> He still doesn't know what 'cognate' means.
>Check a dictionary.
Why? I *do* know.
>While you are at it, check also the meaning of "extensionality".
Why? I *do* know. This one is even part of my professional bread and
butter.
Brian M. Scott
wrote:
>Actually this business of where what we today study seems
>like it is ideally suited for linguists especially historical
>linguists. If long time ago what was "scholarship" and
>"what is to be learned" consisted of the "Quadrivium and
>the Trivium, then all of today's knowledge can be traced
>back to those.
Wrong save in the most superficial sense.
>If looked at on very coarse scales, what we now have
>has to come from these:
>-------------------------------------------------------------------
>The Trivium consisted of:
> Grammar
> Rhetoric
> Logic
>The Quadrivium consisted of:
> Arithmetic -- Number in itself
> Geometry -- Number in space
> Music, Harmonics, or Tuning Theory -- Number in time
> Astronomy or Cosmology -- Number in space and time
>------------------------------------------------------------------------
>Many university graduates do not know much more than
>this about the universe.
Wrong. Many university graduates know a great deal about the universe
that is *not* part of this list and fail to know much that is.
[...]
steve
.
>The Quadrivium consisted of:
>
> Arithmetic -- Number in itself
> Geometry -- Number in space
> Music, Harmonics, or Tuning Theory -- Number in time
> Astronomy or Cosmology -- Number in space and time
A very nice dialectic,
its a pleasure to watch the transformation
of elements into their quintessence.
regards,
steve
steve
>
>H.M. Hubey <hhu...@nj.rr.com> wrote:
>
>
>: Yusuf B Gursey wrote:
>
>:> H.M. Hubey <hhu...@nj.rr.com> wrote:
>:>
>:> : So the root for shining/glistening/oil etc was *da-.
>:>
>:> : We can find the word for "butter, oil, fat" preserved in Circassian as "dage".
>:>
>:> d`a- for burning is a frequently cited nostratic word for burning.
How about Hittite dai (to put; to annoint, to dab), dais (he-took[on], became)
to annoint with oil a sacrifice before offering it to a holocaust?
to die and become a god in death
>
>:> thecircassian word may very well be from archaic turkic (old bulghar), since
>:> a couple of other archaic turkci *d`- words are known in the region
>
>: which ones?
>look up menges.
LU L IM
[(man Hantillis= a $U.G) I kisa (t n=as DINGIR ) -s (kikkissuwan dais)
When Hantillas too became old and he was about to become a god (become -SUP-ITAR)
p 43 of "Old Hittite Sentence Structure" Silvia Luraghi
regards,
steve
steve
>> -------------------------------------------------------------------
>> The Trivium consisted of:
>>
>> Grammar
>> Rhetoric
>> Logic
>>
>> The Quadrivium consisted of:
>>
>> Arithmetic -- Number in itself
>> Geometry -- Number in space
>> Music, Harmonics, or Tuning Theory -- Number in time
>> Astronomy or Cosmology -- Number in space and time
>
>Worth noting here that "number" in all these senses continued to have a
>mystical frame of reference a la Pythagoras or the Babylonians rather
>than raw, plain numbers in the manner of modern math/physics.
Arithmetic as quantitative accounting becomes positional in Geometry.
The assignment of coordinates introduces a sense of comparative
qualitative analysis as in to measure, weigh and judge rather
than simply to count or account quantitatively.
Music introduces vector analysis and makes it possible to deal
with irrationals through Analytic Geometry and Calculus
Atronomy and the ability to predict an orbit introduces probability theory
which gets into what the ancients thought of as divination,
the realm of the divine, symbolized by runes and dice.
Understanding the Quintessence of the Quadrium takes you into
the alchemical transformation of elements where mathematics
as the Philosophers Stone is both hard as a rock and malleable
as wax.
Brian will tell you these are all modern inventions
Mike is entirely correct that you can trace these as a secret
initiated wisdom passed on to Greeks like Pythagoras by the
Egyptians and Babylonians.
Modern mathematicians like Newton rediscovered them by
reading the works of the ancients and not being afraid
to explore the Trivium of their writings in process terms.
...
>Mike Cleven
regards,
steve
Uwe Hercksen
"Brian M. Scott" schrieb:
>
> Don't forget Leonardo Pisano (Fibonacci) ca.1200.
Hello,
okay, but still centuries later.
Bye