mathematics , mysticism......

[Dominique.Thillaud]

At 20:35 +0200 21/05/97, Jacob Baltuch wrote:
>
>In any case I assume such properties should only be included if
>a culture possesses a decimal positional system, which seems to
>exclude pretty much all cultures except India and those who borrowed
>the decimal positional system from India, i.e. Muslim civilization
>and Western Europe. It seems to exclude China, Egypt, Rome and
>Greece, as well as the hypothetical speakers of PIE since presumably
>they were not using positional systems, but also Mesopotamia
>(60-based positional system) or Mesoamerica (20-based positional
>system). Of course I'd be happy to be corrected on any of this.

	There is here some confusion between numbers (mathematical and very
abstract) and their representations with digits (symbols) who are just
linguistical: one, 7, two, fourty are digits (words), 37, fourty-two are
representations of numbers with sentences. The question to know if thirteen
is a digit or a sequence of digits is approximatively the same that to know
if Vrkodara is a word or not.
	The various numeration systems have different properties, useful or
not.
The old systems such that IIIOO = 23 (I=1, O=10) are very easy to
understand, not positional (IOIOI = 23), good for ordering and addition (no
need of memorize the sum of two digits), then excellent for an economy
based on counting and without remuneration of wealth (multiplication is
hard and Romans needed abacs to do it).
	Our modern system, based on the use of 0, is better for our
civilization but introduce new properties such '9 and sums of digits'.
That's not a property of the abstract number 9! So, if 9 is a mystical
number, that's because 9 = 3*3
or 9 = 2*2*2 + 1, or &c.
	I agree with philosophical importance of the NUMBER 0 (void), and
with mathematical and economical importance of the DIGIT 0 (formerly a dot
= a place without digit). Linked, yes, but not the same thing.
	Regards,
Dominique

	P.S. 1: I don't believe human gestation has anything to do with 9:
273 (statistical duration) : 29.5 (lunar month) = 9.25 and this 0.25 is too
great (birth's moon and conception's mood are not the same!). More: I don't
know how Indians counted the durations before Indian mathematicians, but in
ancient Greece where the Olympic Games were 'pentaeterikoi' (each 'five'
years), human gestation was 10 months.
	P.S. 2: Arithmetic is a hard branch of mathematics, yes, but with
very few rapports with the very simple 'arithmetic' used to compute with
numbers. And, for me, Pythagorus is NOT a mathematician but, if an historic
person, a philosoph or a RSi ('his' theorem was named much later just
because the mystical
property 3*3 + 4*4 = 5*5, a constatation, not a theorem!).

Dominique THILLAUD
Universite' de Nice Sophia-Antipolis, France