mathematics , mysticism......

[jacob.baltuch at euronet.be]

Patricia M. Greer wrote:

>> If there is one number that can be called the mystical number
>> supreme in India, it is SUnya = 0.  Whole philosophies
>> in Buddhism, Tantric Hinduism, Jainism, etc. are constructed
>> around this number and concept.  At the recent Seminar on SUnya
>> (Feb. 97) held by INSA and IGNCA in New Delhi,  the topic was
>> explored in depth and many interesting papers were presented.
>>
>It seems to me that the 9 is closely related to the 0,
>since it in effect acts as a zero when added to any other
>number -- eg.  7 + 9= 16 = 1+6 = 7.

This is again a consequence the same property of decimal
numeration we were talking about in a previous thread,
namely that the remainder of any number by 9 is equal to
the remainder of the sum of its decimal digits by 9
(btw, I guess you could call 16 = 1+6, impressionistic
mathematics :), which implies that not only 9 but any of its
multiples "acts as a zero"...

Look: 123 + 36 = 159, and 1+2+3=6 while 1+5+9=15 and 1+5=6.

(Wow!)

This is not a property of 9 but of the decimal system;
multiples of 5 would have it in a 6-based numeration system,
multiples of 7 in a 8-based numeration system, multiples of 11
in a duodecimal system, multiples of 59 in a sexagesimal system
of course "multiples of 1", that is, any number (!) does in a binary
system: multiples of N-1 will always exhibit such "magic" properties
in an N-based positional numeration system.

How old is the decimal numeration system in India? If one includes
properties of the decimal representation among what supposedly
made 9 remarkable to ancient India, shouldn't one first make sure
that those properties were apparent?

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.