Vedanta and Mathematics

[Jaldhar H. Vyas]

On Sat, 21 Feb 1998, Ram Chandran wrote:

> The mathematical concept of Sample Space in Set Theory contains the two
> sub spaces:
> (1) Omega  - which includes all the elements of the space.
> (2) Null  - which contains no element.
> Omega and Null are mutually exclusive and complementary to each other.
> Identification one of them is both  necessary and sufficient.  Null
> space is actually the resultant residue after the full establishment of
> Omega.  Every abstract theory or model can be characterized by  a set
> of  axioms and a set of sample points that satisfy those axioms.  The
> elaboration of Vedanta is parallel to the concepts described in the
> sample space with specified axioms and rule.
>
> The two fundamental concepts of Vedanta -- Brahman and Maayaa are
> equivalent to Omega and Null spaces of the sample spaces. Brahman is
> everything and Maayaa is nothing!  But Maayaa is essential to comprehend
> Vedanta and the  Null space is essential to understand Set theory. This
> may explain why historians of the world are able to recognize the
> mathematical talents of our Seers and Sages.  The theory of real numbers
> represents another abstract algebra where Infinity represents Omega Zero
> represents the Null.  It is no wonder that the origin of infinity and
> zero is India and specifically Vedanta. At last, the worlds of
> mathematicians have also acknowledged the contributions of ancient
> Indians to fundamental concepts in mathematics, astronomy and religion.
>

While we do indeed have a rich mathematical heritage, it has nothing to do
with Vedanta really.  Rather the first mathematical formulas
we have (in the Shulvasutras) deal with problems involved in building
altars for Vedic yagnas.  Jyotish provided another impetus and in fact
ganit is considered a branch of jyotish.

> Mathematical theories and Vedanta are valid within the well- defined
> axioms and rules of algebra. A violation of mathematical rules can be
> detected and correctly easily.  Advaita, Dwaita and Vishistadwaita are
> developed using assumptions and axioms that are based on beliefs.  All
> of three do not violate the underlined principles of algebra.
> Mathematical assumptions and rules are accepted universally. On the
> other hand  the fundamental assumptions of Vedanta depend on the beliefs
> and consequently violations are often pointed out by nonbelievers.
>

This is equally true of mathematics.  Mathematics cannot be "proved" in
its entirety either.  (In fact no logical system can be entirely
self-consistent)  If you take a different set of postulates, you can come
up with an equally valid Mathematics.  In the case of the various schools
of Vedanta and Mimamsa, axioms are not based on beliefs but on words--The
words of the Veda.  This does leave some room for ambiguity (otherwise
there would not be multiple darshans) but no more than any other logical
system.

--
Jaldhar H. Vyas <jaldhar at braincells.com>