On Sunday 03 July 2005 14:06, Timothy C. Cahill wrote:

> > Not if you put a zero to the right of another number.
>
> Dear Stephen & all,
>
> Yes, well you could be right about the direct influence of
> a concept like su~n~na on mathematicians of the 2nd century. I
> guess I was fixating on the earliest contributions --a bad
> orientalist habit! In the 600 or so years between Panini and
> Nagarjuna grammar had become India's premier "science". It's
> *very* likely that Nagarjuna was trained to some degree in
> 'VyaakaraNa' (and in Andhra, no less!) and so it would be hard
> to test whether his ideas on su~n~na were unconnected to
> grammatical usages of 'zero' suffixes.

The zero suffix is a more advanced concept than the zero
quantity, in the same way that the empty set is more advanced
than zero or even negative numbers.

> My point is that what
> ancient Indians did with the analysis of language was far more
> sophisticated in the centuries BCE than what they did with
> math. This is what I mean about 'lopa' being a 'basis' for
> zero.
>
> Gunnar's recent point about zero's value as a place holder
> provides a good parallel. In derivational procedures a 'zero'
> affix is often required to hold its place so that conditions
> are met for subsequent grammatical operations. It can
> disappear without a trace, or by leaving a change in accent,
> or by changing a vowel (guNa or vrddhi). So in one sense or
> another it is 'empty'.
>
> For a possible modern parallel it might be useful to think
> of how guys good in math took to computer science /
> programming like ducks to water. So too (maybe!) ancient
> intellectuals trained in grammar took to math in due time.
> Nagarjuna, I'd guess, was more like Nietschze (who eschewed
> philology) in that he disregarded these mere technical
> accomplishments in favor of expanding intellectual horizons.
> Lesser minds could work out the details!

Among the parallels in modern math and computer science, one
could consider

IEEE Floating Point Arithmetic: NaN, Not a Number

Conway numbers and games: (,)=0, the number consisting of two
sets of no numbers. As a game, this means that the next player
loses, i.e. there are no moves left for either player; (0,0)=*,
the game in which the next player to move wins.

Constructive Set Theory, in which one begins with the empty set,
then the set containing the empty set, then sets containing
either or both of them, and so on to multiple infinities,
everything being constructed out of the one original empty set,
with no actual objects.

Goedel's undecidable sentences

LISP: NIL=(), the empty list

APL or J: '', the empty character vector; i. 0, numeric vector of
length 0; <i. 0, an atom containing an empty vector; 0 5$1, a
table of five columns but no rows, to which rows can be added
later.

> best,
> Tim Cahill
>
>
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