# mathematics , mysticism......

jacob.baltuch at euronet.be jacob.baltuch at euronet.be
Fri May 23 02:15:35 UTC 1997

```Dominique Thillaud 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.

No, representations with digits is just as mathematical an object
as the numbers themselves. It is a mapping of the natural numbers
(say) in the set of finite sequences of a finite set of symbols
(the digits).

Yes, at the linguistic level, there is also a kind of numeration
system, if you consider "one", "two", "three", "four", ..., "a hundred",
"a thousand", ..., "a million", to be its digits, and "one million
two thousand three hundred twenty [= two tens] (and) three" to be
a sequence of "digits", but that was *not* the numeration system
that I was talking about. In that sense the Indian system (that is
that of the, say, Sanskrit language) is no more positional than that
of Latin or Chinese.

The linguistic numeration systems are never positional, that I know,
so it should have been pretty clear that I did not have that one
in mind.

123 and "one hundred twenty three" are belong to two distinct numeration
systems as sequence of symbols.

You should distinguish the digit 3 and the digit "three". One is a
graphical-symbolic object, the other is a linguistic object.

It should be obvious that the two do not coincide, and neither is
a representation of the other. You don't read "13" as "one three"
but as "thirteen".

```