The Two Facets of Geometry

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Editor: Prof. K.V. Krishna Murty

One of the most significant stages in the development of modern science is the comprehension of transcendental numbers. With the advent of these numbers the boundary between number and geometry was removed. The papers in this volume the two facets of geometry have their origin in the nascent ideas of Sri Kalyanananda Bharati Swamy expressed in his book Purnamimamsadarasanam which raised the status of a circle to that of Godhead. It is hoped that the readers would benefit by scrutiny of the ideas in these papers.

Gurajada Suryanarayana Murthy the author of this book began his career of research in theoretical physics at physical Research Laboratory Ahmedabad. In 1955 he joined Tata Institute of fundamental Research Bombay and was deputed to Royal institute of technology, Stockholm Sweden in 1959 for advanced research and obtained his Ph.D. Degree in 1961. He moved to Bhabha Atomic Research Center in 1968 and retired from service on superannuation in 1991.

After retirement he started connecting the field of mathematics and the field of metaphysics and he published two books (i) Srichakram - its Geometry & Metaphysics and (ii) Paratatva Ganita Darshanam. The present volume is a collection of four of his other papers in the same direction.

Counting and duality emerge out from a single point. A corollary of this statement is that Mathematics and duality are inseparable, since Mathematics is nothing but an extended process if counting. Counting and logic are the facets of the same coin. Logic, again, has a dual role. It can make a mind both extravert and introvert simultaneously. As an embodiment of logic, mathematics too has a dual nature of manifesting itself as a number and a line, which represent space and time independently and jointly. Of these two, the line has a stronger ability to transcend space and time.

The sages of Tantra Vidya had utilized this aspect of Mathematics of lines", i.e., Geometry and worked wonders on this subject. Unfortunately, the theory behind such Tantra Mathematics and its channels of expansion have been lost and we have inherited mere text books of Tantra, with a variety of Yantra and Mantras.

Rare Saints like Sri Kalyananda Bharati of 19m Century and genius mathematician like Dr.G.S.Mu1ty of 20th Century were gifted with the required insight to understand, explore and explain the inner depths of Tantric Mathematics and the present work" The Two Facets of Geometry" is an example of their explorations. Some of the so called modern mathematicians may not be interested in this type of mathematical analysis but that can it diminish the value of this study, since it definitely opens new horizons of mathematical logic, which can connect the finite and infinite.

The papers are really meant for research scholars of advanced mathematics and we hope that our Universities will encourage their students and scholars to study these papers, so that they can probe more deeply and bring out more and more precious gems.

It is with this vision that, I-SERVE has undertaken the publication of this book. I - SERVE, a research institute dedicated to dig out the technical details of the ancient Vedic Sciences, divided ancient mathematics, for the sake of convenience, into three parts viz., Mathematics of (i) the Vedic periods (ii) the Tantrik periods and (iii) the Vedic Mathematics of Bharati Krishna Teertha.

In the first category, I-SERVE already published a wonderful work "Presiddhantic Indian Astronomy" by late Prof. K.D. Abhyankar. In the third category volumes on Vedic Arithmatics and Vedic Algebra are prepared by I-SERVE and awaiting a suitable publisher. In the 2nd Category (The Tantra Category), the experts available are very few. We are fortunate that Dr. G.S. Murty, a frontline physicist and mathematician of international repute, has been working slowly in this line, since a few decades and some of his papers, in this field were published by I—SERVE in some of its conference volumes.

We are glad that we are able to put those and other papers of Dr. G.S. Murty, related to this subject, in a sequential order and publish them as a book. We are aware that no perfection can be claimed in this type of research, since it is almost like a pilot project. However, our efforts are fruitful, if it can trigger enthusiasm in the researchers of mathematics.

We are sure that this collection would provoke new thoughts, open new annals of study and reveal newer depths of ancient Indian Mathematics, through thoughtful and blessed readers.

We thank Dr. G.S. Murty for his ready acceptance to publish his papers in a book form. We also thank all those pious hands and hearts whose cooperation is making I-SERVE survive and succeed.