Transcendental Mathematics

As far as the evolution of the Indian thought system is concerned, zero has been as much a mathematical concept as a spiritual one.  The whole philosophy of Buddha is based on sunyata, nothingness. By the way the Sanskrit word for zero is sunya. When the philosophy, spirituality and mathematical use of zero was at its zenith in India, their western counterparts wondered how can nothing be something.

In India of the vedic age, there was no distinction  between religion and science. A highly developed form of mathematics was used to place various temples in the geography of India and to construct individual temples. The Garbhagriha – sanctum sanctorum  –  was the sunya griha where for a moment the mind of the pilgrim went blank.

In eastern philosophy, existence was conceived as the paradox of being and nothingness. Buddha’s view was that the whole existence is a great void, it is all empty and nothingness. Then came Shankara who said there is fullness in everything.

While ‘nothingness’ was the basis of a rebellious religion and philosophy, ‘nothing’ was the starting point in the evolution of mathematics.

To make things simple, and from a mathematical point of view, let me divide all mathematics into three categories.

First of all, is the logical sequential common sense mathematics where two plus two is four. It has tremendous use in our day to day affairs. All scientific progress and commercial transactions are based on this. This is the mathematics that we learn as a part of curriculum in our educational institutions. Let us call it the logical mathematics.

Secondly, there is this mathematics of the group dynamics or for simplicity let us call it the dynamic mathematics. There is a proverb in Hindi –Ek aur ek gyarah – one plus one becomes eleven. According to the logical mathematics if one person does x amount of work in a day and another does y amount of work in a day, then both will do x+y amount of work. However according to dynamic mathematics both will do much more than x+y amount of work. Whenever two people work together they create a third force in the form of group dynamics or synergy that adds something to the total output. Of course if this third force is negative, then the total output will be less than the sum of individual outputs. If two people are able to lift a stone to a height of one meter it does not mean that one person will be able to lift it to a height of half a meter. One person may not be able to lift it at all.  When a bird flies with its flock in a formation it uses less energy than it would do for the same distance if it flew individually. The synergy among the birds is such that even a sick bird that can hardly fly is carried along once it is a part of the formation.

Then, there is the mathematics of the transcendental or the mathematics of the mystical experience. Most of us are familiar with the first declaration of the Ishavasya Upanishad – Purnamadah purnamidam purnat purna mudachyate. Purnashya purnamadaya purnamevavashishyate. That is whole, and this also is whole. For only the whole is born out of the whole; And when the whole is taken from the whole, the remainder is whole.

This sloka attempts to describe the mystical experience of the ultimate reality. It is beyond logic. One has to transcend logic to get a glimpse of such mystical experience. Along with the illogical concept of zero,  when some western logicians came across such declarations, they thought that the eastern seers who composed the Upanishads were lunatics.

Even though it is difficult to understand this sloka with our logical mind some indications can be given. Now water can be divided but not liquidity. When a jug of water is taken out from a bucket full of water the quality of liquidity is neither improved nor downgraded.

Or let us take another example. There is a rose plant. We cut a branch and plant it at another place where it grows into a plant again. When we cut a live plant what we are actually taking out is the tree-ness or the essence of the tree. However the tree-ness or the essence of the first tree remains whole at the same time the new branch also grows into a whole tree. We cannot say that by cutting the earlier tree the wholeness in either has been affected.

To make things simpler (or, more confusing),  substitute the ‘purna’ in the above sloka with zero. Now you have something to argue with the logician, who has at least accepted the concept of zero i.e something is possible out of nothing.

To make things the simplest, meditate with Buddha or listen to  Shankar’s Bhajagovindam. You will realise the nothingness of everything either way.

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A Brief Note on Stephen Hawking

stephen hawking

Here is a brief introduction to Stephen Hawking from his official website: 

Stephen Hawking is the former Lucasian Professor of Mathematics at the University of Cambridge and author of A Brief History of Time which was an international bestseller. Now the Dennis Stanton Avery and Sally Tsui Wong-Avery Director of Research at the Department of Applied Mathematics and Theoretical Physics and Founder of the Centre for Theoretical Cosmology at Cambridge, his other books for the general reader include A Briefer History of Time, the essay collection Black Holes and Baby Universe and The Universe in a Nutshell.

In 1963, Hawking contracted motor neurone disease and was given two years to live. Yet he went on to Cambridge to become a brilliant researcher and Professorial Fellow at Gonville and Caius College. From 1979 to 2009 he held the post of Lucasian Professor at Cambridge, the chair held by Isaac Newton in 1663. Professor Hawking has over a dozen honorary degrees and was awarded the CBE in 1982. He is a fellow of the Royal Society and a Member of the US National Academy of Science. Stephen Hawking is regarded as one of the most brilliant theoretical physicists since Einstein.’

What does not find mention in his official website is his love life. Sometimes events of his personal life gets so much media coverage that some people develop an aversion to him and ignore his contribution to science. As a person, Stephen Hawking may seem to have crossed certain boundaries of morality, particularly the ‘Indian Standard of Morality’ with multiple affairs and marriages. However, on a lighter note- considering the fact that most of his voluntary organs are not working, even the Superman should be jealous of his female fan following.

Jokes apart – his contribution to science should not be undermined whatever ‘moral’ flaws he may have. Many of the geniuses of past and present are known for their eccentricity and bizarre behavior. Stephen Hawking comes from a culture and society where his personal life is normal acceptable behaviour. Moreover, he is not a hypocrite. His whole life is in public domain. Contrast this with the life of many of our Indian leaders and famous persons. They live/ lived a double life and are/were hypocrites.An honest biographical film about Nehru was stalled time and again. What we read as history in our text books are nothing short of fiction. The stories of Stephens and Clintons would be overshadowed by the real life events of many of our adored leaders, provided these things are available in open domain.

It is surprising that a hardcore scientist like Stephen Hawking recognises the power of love.

“I’ve been privileged to gain some understanding of the way the universe operates through my work,” he writes. “But it would be an empty universe indeed without the people that I love.”

He is a great inspiration for all of us. In spite of his physical limitations, he keeps on exploring the limitless.. and he has never lost the jest for life.

“Although I’m severely disabled, I have been successful in my scientific work,” Hawking writes. “I travel widely and have been to Antarctica and Easter Island, down in a submarine and up on a zero-gravity flight. One day, I hope to go into space.”

Stephen Hawkins is a genius. His die hard attitude is an inspiration for all. I recommend my friends to read his works, at least the bestseller – THE BRIEF HISTORY OF TIME.