Indian Philosophy and Mathematics

Antreas P. Hatzipolakis xpolakis at HOL.GR
Fri Mar 13 11:36:29 EST 1998


Hello,

Following is a message I received from Prof. B. Ravindra.
I am fwd-ing it to the Indology list (with his permission), since one paragraph
(marked with ********) is related to Indian Philosophy.

I have some questions on the Subject: Indian Philosophy and Mathematics

1. Which was the role of the Indian Philosophy (Brahmanism)
in great S. Ramanujan's Mathematics?

2. Are there influences of Indian Philosophies on Modern Mathematical Theories/
inventions?

Thanks, and apologies for this long message and my bad English.


Greetings from Athens

Antreas


FWD Message -------------------------------------------------------------------

From: Ravindra  <ravindra at ag2.mechanik.tu-darmstadt.de>
Subject: Re: Request
To: xpolakis at hol.gr (Antreas P. Hatzipolakis)
Date: Fri, 13 Mar 1998 15:42:49 +0100 (MET)


Dear Antreas,

[...]

Some reflections on the recent debate in Math-history list concerning
Dieudonne's 'mathematics as the Music of Reason', Whiggism in Math-history
and the role of external factors in the development of pure mathematics:

In history and philosophy of science there is a distinction between
'context of discovery' and 'context of justification'. For some,
context (and process) of discovery is not a meaningful category.
(Poincare and Hadamard are exceptions)
It is probable that one's prejudices, psychological and cultural influences
might play a role in the process of discovery.
Kepler is one good example in this case. But perhaps, Riemann is a  better
example. Felix Klein speculated that Riemann might have used Electrostatic
analogies to obtain his results in complex function theory.

******** Whatever may be the case with Riemann's inspiration in complex
function theory, his investigation of Geometry was influenced also by the
teachings of the psychologist Johann Friedrich Herbart (1776-1841).
Can somebody tell me to what extent Grassmann's preoccupation with
his translation of 'Rig veda' might have influenced his 'Ausdehnungslehre'?
(Or is this a meaningful question for a historian of mathematics!)
Is it true that Brouwer acknowledges 'Gita'? (I run the risk of being
branded as ethnocentric here)
        Discussing the origins of mathematical ideas, like duality is
another example. A nice paper in a recent Isis on ''infinity'' and influence of
Cathars in thirteenth century might provide interesting reading.
The role of ergodic theory and statistical mechanics in pure mathematics
such as measure theory, inspiration for Girard's linear logic, etc one can
go on. Gibbs lectures in Bull AMS give ample number of such examples  and
remind us that the distinction between 'pure' and 'applied' is somewhat
spurious.
        The structuralist controversy in Humanities and social sciences
and Bourbaki's program have similarities. There is enough room
for speculation in Weil and Levi-strauss. (One can see its impact on
Philosophy of Stegmueller).

        The topic of this discussion is deep and one needs to
discuss 'poverty of historicism'  and how
it was countered by various philosophers and historians.
Mathematics poses several problems for Kuhnian framework.
I tend to believe that the emergence of set theory and 'modern math'
is a decisive break.
For some, paradigm is a dirty word and for Kuhn
'deconstruction' is not acceptable. One need to judge their relevance to
math-history.

Scientific process always involves in breaking with tradition and again
seeking a reunion with it.
Mathematicians (and scientists) take comfort in (whiggish?)
historical reflections (exception: Van der waerden). It is necessary for their
sustenance in their profession and inspiration for further work.
Tracing their lineage as far back in time as possible.. Was it
Schrodinger who wrote '2400 years of quantum mechanics'?

History is an ongoing dialogue between the past and the present.
                                                        (Carr!)
Another (whiggish?) example:
In the prehistory of integral calculus, an important place is occupied
by the remarkable work of Kepler ''Stereometry of Wine Barrels'' (see Vol. 9
of his Gesammelte Werke). Integrals that give the volume of solids of
revolution used in commerce were calculated in this work at a time
when the general definition of an integral had not yet appeared. The
mathematical theory of Feynman's magnificient integrals, which physicists
write in vast numbers, is not really far removed from the stereometry of
wine barrels. - Y. Manin, Mathematics and Physics, P93, Birkhaeuser.

(btw, is there an account of history of volume computations of wine barrels?
reminds me of Heidelberg schloss wine barrels!)

Recently, we learnt that volume computation is difficult!
(Computing the Volume is difficult: Proc. of the 18th Annual Symp.on
Theory of computing, pp 442-447, 1986, by  I. Barany, Z. Furedi.)

Juxtaposing these facts in such a  manner might look silly
 for a historian, but it
is exciting for those who pursue scientific activity!

As Borges said ''Every genius creates its own ancestors''.

History is not static and just a dead pile of facts.

Of course one needs to remember:

Alisdair MacIntyre in After Virtue (1984, p91):

'Charles II once invited the members of the Royal Society to explain
to him why a dead fish weighs more than the same fish alive; a number of
subtle explanations were offered to him. He then pointed out
that it does not'.

On mathematicians as the vanguards of reason and rationality:

Chance and Chaos, D. Ruelle, Chapter 2 (page 8):

''Mathematical talent often develops at an early age. This is a common
observation, to which the great Russian Mathematician Andrei N. Kolmogorov
added a curious suggestion. He claimed that the normal psychological
development of a person is halted at precisely the time when mathematical
talent sets in. In this manner, Kolmogorov attributed to himself a mental
age of twelve. He gave only an age of eight to his compatriot
 Ivan M. Vinogradov, who was for a long time a powerful and
 very much feared member of the Soviet Academy of sciences. The eight years
of Academician Vinogradov corresponded, according to Kolmogorov, to
the age when little boys tear off the wings of butterflies and attach
old cans to the tails of cats.

        Probably it would not be too hard to find counterexamples to
Kolmogorov' theory, but it does seem to be right remarkably often.''

I do not know where does one put Dieudonne in this scale
but  do believe, it is not a good idea to insist that only
eminent Mathematicians (or Field medallists alone) should tell us
what the music of reason is all about! The controversy of 'elitism'
will disappear if we shift the analogy from music to atheleticism in sports.
Indeed Hardy does compare Mathematics to doing sport, as it is difficult
to prove big theorems, as one gets older. Probably the same thing
is not true for music.

Best regards,
Ravindra
-------------------------------------------------------------------------------
Dr B. Ravindra                                  Residence:
Care Professor P. Hagedorn                      wohnung 3,
Institut fur mechanik II                        Dieburger strasse, 241
Hochschul str. 1                                Lichtenberg house
TU, Darmstadt, 64289                            Darmstadt-64287
Darmstadt, Germany
E-mail: ravindra at ag2.mechanik.tu-darmstadt.de   Phone:
Phone (off): 49-(0)-6151-162285                 (Res) 49-(0)-6151-700823
Fax: 49-(0)-6151-164125
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