From: L' Ermit (lhermit@hotmail.com)
Date: Fri Jan 18 2002 - 10:28:15 MST
And after having already disestablished the alleged claim to Tirthaji having
"discovered" Yash's precious "Vedic PI", let's trash the idea some more. And
before claiming further bias, please note the source... can you say Q.E.D.
Mermaid, If you ever get into an argument again, I suggest that you spend
more time picking the right side...
Hermit
Unscientific maths?
By S.G. Dani
Important words, like other important things, are often vulnerable to misuse
by elements inclined to derive undeserved benefits from their glory.
Practitioners of many a trade have found it advantageous to use the
adjective `scientific', even when their basic tenets and methods are quite
inconsistent with the scientific method. `Vedic' is one such word, the use
of which promises dividends, especially in the context of the peculiar
weakness of the popular mind in India. Also, the users seldom seem to be
called upon to justify themselves on account of the pious way such claims
tend to be approached.
The so called `Vedic Mathematics' (VM for short) is a case in point. It is
well-acknowledged that, as being practised, it is based on a book of Swami
Sri Bharati Krishna Tirthaji, who was the Shankaracharya at Puri from 1925
until his passing away in 1960.
As commonly understood and implicitly assumed, the adjective `Vedic' means
being from the `Vedas' or the civilisation around their time. While there
are variations on the estimates of the period involved, by any reckoning
they are at least 2500 years old. In what sense do the contents of the book
belong there? Neither has Tirthaji nor have the proteges provided any
evidence or clue in this respect that a rational mind can appreciate.
The book has a preface grandiosely titled `A Descriptive Prefatory Note on
the Astounding Wonders of Ancient Indian Mathematics'. All one finds there
is a lot of raving and ranting, followed by a vague statement to the effect
that `exceedingly tough mathematical problems' can be easily solved with the
help of some `sutras' in the Parishishta (Appendix) of the Atharvaveda.
There is no substantiation or elaboration concerning their being genuinely
from the Vedas.
It cannot be that it did not occur to Tirthaji to include such details in
the preface or elsewhere in the book.
He was, in fact, confronted by Professor K.S. Shukla, a doyen in the studies
on ancient Indian mathematics, to show the sutras, to which Tirthaji is said
to have replied that they are not in any standard Parishishta, but only in
his `own Parishishta to the Atharvaveda'!
The book also contains a short biographical sketch and an account of the
genesis of the work written by Ms. Manjula Trivedi, a disciple of Tirthaji.
She mentions that the `Revered Guruji used to say that he reconstructed the
16 mathematical formulae from the Atharvaveda after assiduous Tapas for
about eight years in the forests surrounding Sringeri'. They were not found
in any version of the Vedas. They were `reconstructed'.
Contrary to what is made out, `Vedic Mathematics' is no `system' of solving
problems in mathematics or even just arithmetic. It is only an assortment of
tricks, based on simple algebraic principles. It is thoroughly lacking in
coherence or harmony.
As one goes along the text of the book, one is introduced to various tricks
to solve certain special problems, and while doing so Tirthaji gives names
to some of the operations. `Ekadhikena Purvena', which means `by one more
than the previous one', is an operation which involves something or the
other to be done with something or the other that happens to be `previous'
in one or the other sense. Lo and behold: you have a sutra for the problem.
Mind you, the string of words does not by itself enable you to solve the
problem and in most instances even the operation it connotes needs to be
supplemented by several others. These one has to learn. It only enables you
remember something of the operation.
In the style of how matters proceed in the book, `hold the bucket' can be
said to be a sutra for milking a cow! From a mathematical point of view, the
sutras of VM are of little value. To some extent, they serve as memory aids
to the practitioners. Other than that, their sole role has been as props to
the false pretense of antiquity.
The main positive contribution of Tirthaji's book lies in highlighting some
tricks with which certain specific calculations can be done faster. In this
sense, it is comparable to Trachtenberg's methods of `high speed'
computation.
The main drawback of such methods is that they are very problem- specific
and depend heavily on identifying special features which may be exploited to
attack the problems.
Secondly, speed in computing mentally, which is the sole feature to which
they contribute to some extent, has become largely redundant in the computer
age.
(The writer is a Senior Professor at the Tata Institute of Fundamental
Research, Mumbai.)
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