Hexadecimal metric system
Michael F.
"I've met somebody, who claimed to have worked out a hexadecimal metric
system. I've never seen it en detail, though."
I don't think that I ever met Christoph, but that's me who developed
the new hexadecimal metric system in spring 1989. Since December 1993
this proposal is now online at www.florencetime.net.
Michael
Jukka K. Korpela
> that's me who developed
> the new hexadecimal metric system in spring 1989. Since December 1993
> this proposal is now online at www.florencetime.net.
That doesn't sound just pointless; it's also a fundamental conceptual
confusion.
The metric system defines primarily a collection of units. For ease of
use, it also specifies multiples of units. Whether numbers are
expressed in decimal, or hexadecimal, or binary, or in Roman numerals,
on verbally, is orthogonal to the system of units.
Should someone want to define multiples and submultiples that
correspond to multiplication or division by 16 rather than 10,
that's of course a possible entertainment, though completely pointless.
But it would not create a "hexadecimal metric system".
We don't use a "binary metric system" when we store numeric values of
physical quantities in binary notation.
--
Yucca, http://www.cs.tut.fi/~jkorpela/
Michael F.
On verbally:
one trillion hexadecimal (Exa) = (16 ^ 5) ^ 3
one billion hexadecimal (Tera) = (16 ^ 5) ^ 2
one million hexadecimal (Mega) = (16 ^ 5) ^ 1
Example of a hexadecimal numeral in English language:
0x F,EDCBA.9 : fifteen million, forteenty-thirteen thousand,
twelve hundred, eleventy-ten units and nine sixteenth.
0x10 (sixteen) is called "onety".
0x11 = onety-one, 0x12 = onety-two etc.
Paul
This idea of a hexadecimal metric system is completely crazy.
Especially I liked the way how coming back to the ancient units like
the foot, the palm and the digit in an excellent and progressive
manner. The digit measure as the half of circumference of Earth divided
three times per 1024. That's really concrete and graspable. Also your
unambiguous hexadecimal "omni-literal" number digits (easy and
distinguishing intelligible between odd and even digits) in are much
better than the actual 0 to 9 and A to F standard.
At present I don't know if your proposal is consistent, but if this is
the case it will revolutionise metrology and the world will be changing
on. If your important works exist since 1989, we all missed some
trains. Courage, forge ahead. I think that's really conceivable that
your proposal, by taking the best of Metric & Imperial Systems, will
soon replace this "bourgeois French decimal meter", like you designate
it.
Grace to your ingenious new "omni-literal" digits, the hexadecimal
system became at long last perspicuous and manageable. In ancient times
measures often have been binary, but it lacked an unambiguous
positional hexadecimal arithmetic system. Not any more. I think your
"universal hexadecimal foot" will win recognition. One day soon, we'll
have a hexadecimal monetary system and change one "B" coin against two
"t" coins.
But the most important is that we'll better understand computer
programs. That's good.
Paul
Michael F.
established opinion of the world entire - just like my friend
Nikolaus C. from Cracow (1473-1543) - I really need such
encouragements.
(But Nikolaus by publishing his works only several months before his
death not defended his cognizances. That's why an other Italian about
90 years later was still interdicted to teach it, house arrested at
Arcetri next to Florence, constrained to retract and surely treated to
be a "crackpot" and "demagogue". This was, not even in obscure
Middle-Ages, but in verity happened in Modern Times.)
Now I perceived an erratum in my very first message. If it is true that
I worked out the hexadecimal metric system (provable) in 1989, the
Internet domain florencetime.net is online since December 2003 only
(not since 1993) and also Christoph Paeper, here, spoke about it in
2004 (not in 1994 of course). Excuse for this doubled erratum.
So long, Michael F.
Edgar del Ray
I agree that it does sound confusing but it NOT incorrect to call it a
"hexadecimal metric system" for the following reasons.
1. The word metric derives from the Greek word 'metron' meaning to
measure and does NOT imply any specific number base.
2. The front page of the website is in French and refers to "Le site
officiel de Bureau International de la métrologie hexadécimale". The
pertinent point being that in English it is "The site of the
International Bureau of hexadecimal metrology.". Thus it does not call
it a 'hexadecimal metric system" but a "hexadecimal metrology system".
3. The so called metric system does not exist but there is a system of
weights and measures called in English the "International System of
Units" from the French "Systeme International".
4. Simply because the S.I. system has the base unit of length measure
called the "metre" and is orthoganal to a base 10 number system does
not qualify it to be called "The" metric system.
Apart from the above points, I would not agree with Msr.
Florencetime's choice of 16 as as the basis for a system of weights
and measures particularly as I disagree with his main point that a
binary series of measures is of more practical use than any other.
One has only to look at the long life of the system of measures that
used 12 as as basis to refute his argument, one shared by may people
before. Secondly, although he notes that 16 digits = 1 foot, this was
not the prime division used by the Romans for fractional values.
Although the Romans used 1, 5 and 10 and their multiples for integer
values, their system of fractions were based on twelfths and further
subdivisions by 12 which is the origin of the English inch and ounce.
Why did this system last so long? Because of its practical use in
everyday commerce. As further evidence, one only needs to note the
words of the Bavarians in 1842 "that the twelve part organization was
the more commonly used in civil commerce as opposed to
a 10 part organization as they were of more use in general commerce
than base 10 measures" (my translation of a section from
http://home.fonline.de/fo0126//geschichte/groessen/mas1.htm).
Not only that, but the Bavarians extended the 12 based system of
measures to 5 coherent levels as shown in the following table.
Rod Foot Inch Line Scruple
1° Ddz =12' Ddz=144'' Ddz=1728''' Ddz=20736'''' Ddz
1' Ddz= 12'' Ddz= 144''' Ddz= 1728''''Ddz
1'' Ddz= 12''' Ddz= 144'''' Ddz
1''' Ddz= 12''''Ddz
Yes 12 feet were 1 Ruthe or rod in Bavaria, thus going 1 level further
than the English who had the following measures.
12 douziéme = 1 line
12 lines = 1 inch
12 inches = 1 foot
I have not worked my way through the entirety of Msr. Florencetime's
site as my French is minimal, but may return with more comments at a
later date.
Paul
>
> I agree that it does sound confusing but it NOT incorrect to call it a
> "hexadecimal metric system" for the following reasons.
>
> 1. The word metric derives from the Greek word 'metron' meaning to
> measure and does NOT imply any specific number base.
There, I agree with you. Beyond, the term "hexadecimal metric system"
in my ears does not sound "confusing", but rather "unaccustomed".
> 2. The front page of the website is in French and refers to "Le site
> officiel de Bureau International de la métrologie hexadécimale". The
> pertinent point being that in English it is "The site of the
> International Bureau of hexadecimal metrology.". Thus it does not call
> it a 'hexadecimal metric system" but a "hexadecimal metrology system".
As I understand the French language you have to translate: "The site of
the International Bureau 'for' hexadecimal metrology." As like the BIPM
administrates the "decimal metric system", the BIMH cares for the
hexadecimal metric system (SMH). On your 3rd and 4th topo, I agree with
you entirely.
> Apart from the above points, I would not agree with Msr.
> Florencetime's choice of 16 as as the basis for a system of weights
> and measures particularly as I disagree with his main point that a
> binary series of measures is of more practical use than any other.
> One has only to look at the long life of the system of measures that
> used 12 as as basis to refute his argument, one shared by may people
> before. Secondly, although he notes that 16 digits = 1 foot, this was
> not the prime division used by the Romans for fractional values.
> Although the Romans used 1, 5 and 10 and their multiples for integer
> values, their system of fractions were based on twelfths and further
> subdivisions by 12 which is the origin of the English inch and ounce.
Like I understood M. Florencetime, he simply says that decimal system
has never been privileged in men's history "in spite of our ten
fingers; divisions per two dominated, sometimes divisions per three."
2x2x3=12. Surely a very interesting base, preferred in European
Middle-Ages. But old systems of weights and measures has been "mixed
systems", neither using one single base nor noted in a modern
positional arithmetic system like the decimal S.I. So, this one
replaced the old systems since two centuries.
The duodecimal base has been proposed very often as new, better base.
Indeed, outside the problem of the two missing digits for this
numbering system, this would be possible. But history showed that men
passed over this system, like a pure and coherent and one single base
system, for all the multitudinous advocates.
The hexadecimal system in contrary never has been proposed, excepting
the precursor John W. Nystrom (1825-1885). After him never anyone
seriously proposed a base sixteen system for weights and measures. One
of the main hindrances was the inexistence of coherent digits for this
numbering system. Because the hexadecimal system is however essential
in modern informatics, hitherto, the 0-9 & A-F digits were used, but
not before the 1950th. This composite, alpha-numeric system is IMHO not
very elegant, furthermore ambiguous needing prefix, suffix or at least
a clearing index number. The proposed sixteen omni-literal digits, 0-F:
Q,B,P,V,F,Z,S,D,T,J,C,G,K,Y,X,W, by distinguishing odd and even digits,
is really very easy to apprehend, thus easy to assimilate; unambiguous
all above.
M. Florencetime doesn't say that 16 was the "prime division used by
the Romans for fractional values". They don't have one. Dividing by 2
and 3 existed among other factors; whereas, since the beginning of
civilisation and also in Rome, the foot was invariably divided into 16
digits. Thus SMH is a "modern digital measuring system". Besides,
dividing the foot into 12 thumbs (inches) was not really used before
the beginning of the Middle-Ages. Sure in other measures other
divisions existed, but in Dry Measures for example the Roman peck (lat.
"modius" = 1/3 Roman bushel = 1/3 cubic foot) was divided into 128
Roman drawing-spoons (lat. acetabulum), like the British Measure of
Capacity "quarter" is divided into 2048 gills or the French "velte" was
divided into 256 roquilles.
But without sixteen coherent, unambiguous digits, a hexadecimal (i.e. a
pure binary) measurement system was not practicable. Not in a modern
positional arithmetic system! In Europe, we used - quasi exclusively -
the Roman number system till the middle of 15th century. Seven not
positional digits. So decimal S.I. was a progress. But it scarified all
the great old cultural measures like the "digit", the "palm", the
"foot" and the "aune" of four feet. The last one is attested since
Antiquity too.
So long Paul.