Why Paranjape Is Wrong : Can Mathematical Sciences Quote The Precise Value Of Infinity?

This article provides a scientific empirical counterpoint to Professor Makarand Paranjape’s opinion, most recently expressed in the Swarajya magazine –

A square is nothing but a rectangle with all its four sides being equal in length. Whether one language defines a square as a subset of the category of rectangles, or the other views it as an independent category of geometry with similarity to the rectangle, is a matter of convention and the definitions used by the respective language’s grammar. Neither is less right nor more wrong.

There was a time in the Bharatiya economy when fractions of a single paisa was of significant value and one cannot round it down to the closest round paisa value, let alone the closest rupee value. Now paisa value is hardly even noticed in daily transactions. Was the economy more precise then, in the past, and less precise now? In fact the traders in the markets (such as stock or commodity or derivatives exchange) who are involved in arbitration trading will still vouch for the value of a paise or even a fraction of it. Such is the precision of the economy. It is neither lost nor gained. It is the perspective of the user and the viewer that changes with the purpose, circumstance and the reference (language) used.

Precision itself is just imprecise. It is all relative, not only to the accuracy of mensuration, but to multiple factors.

How precise is our counting? If one cylindrical chalk piece is broken into two, how many pieces of chalk are left? Is it still one, two or two halves of one? Assume if it was not ever known to the observer that the chalk piece(s) were ever actually one “single” piece. The issue becomes even more complex. Clearly, such precise sounding numbers have no real precision even in mathematics, let alone philosophy. Numbers are just abstract conventions and provide a huge degree of practical convenience. Since they are relatively well defined in the language of mathematics they give us an illusion of perfection and precision. It is all relative.

Travesty of precision. In fact in the schools of empirical mathematics of the Hindu system called ganitam, this lack of perfection is supremely recognised. Ganitam itself is an empirical practical science with limitations. It was the misunderstanding of the decimal place system, Bharatiya numerals and its power (just the addition of zeros to the end of a number transformed it and made it multiple times more valuable than its initial value) that made the Church consider them evil initially, then once its practicality (in navigation, for example) was ascertained and understood, the same was ordained as divinely perfect: this has been elucidated by C K Raju, an internationally published and renowned mathematician and history of science academician.

Sadly, the axiomatic approach of the Greek philosophy was also added to this hypothesis of “divine” perfection of mathematics propounded by the Church. Axioms are largely unproven statements considered somehow fundamentally “true.”  Thus we arrive at the confusion about the precise nature of science and mathematics and the never ending hunt for physical constants. Even the velocity of light is not perfectly constant as is now acknowledged in physics. The nature of time remains unidentified, yet the velocity of light (which in itself is measured in a derivative unit of distance upon time) was once adjudged to be a universal constant.

Versatile as verses. The entire mathematical and other scientific treatises (Sastras) of Indic languages, be it Sanskrit or Tamil, were in verses. In fact, equations and numbers (such as the value of Pi, various constants, etc.) were all written in the form of verses. It is not just mathematics, but Paninian “grammar” itself was written in verses. The fact that allegorical and metaphorical poetry is also written in verses, does not make all verses prone for multiple interpretations and inaccuracies. In fact, many verses were so versatile that the solution given to the so-called Euler’s theorem by Vedanta Deskiar about 800 years or thereabouts before Euler gives meaning (in praise of Rama) if read forward, in praise of Krishna if read in the reverse word order, and many such combinations with different meanings; yet each reading provides the mathematical solutions too.

If versatility of the Indic genius and the Sanskrit language verses are considered imprecise, it is because they redefine precision itself to a degree unknown to, and arguably incapable of for, modern science or Western mathematics. The verses of ganitam stand testimony to the precision of the Indic thought, be it spiritual or be it material sciences.

Truth is a theological and / or a philosophical concept and is often mistaken for a scientific concept. Thus to translate from modern science to vedanta / sankya and vice-versa, we need to develop a translational framework for both “truth”and “standard” for the two family of languages to be able to talk to and enrich each other fruitfully. And that is where the future lies.

(Acknowledgements: Thanks to Shri Sudarshan T Nadathur for the review of the draft).

AUTHOR PROFILE: A medic and a graduate of the University of Cambridge, England, currently involved in inter-disciplinary research.


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About the Author

Murali KV
A medic and a graduate of the University of Cambridge, England, involved in inter-disciplinary research for the inculcation of a scientific rigour in the outdated fields of humanities: putting “science” into social sciences
  • Moksha

    Excellent article both in content and in style.