From Wholeness to Wholeness : three types of mathematics

In my previous post I have given some idea about vedanta or the Upanishads which are the foundations of India philosophy and spirituality. Most of the stanzas of the Upanishads do not subject themselves to easy understanding. That is also one of the reasons why many epics were written so that the common man can also have some glimpses into the the mystic world of the ancient Rishis.

As far as the evolution of the Indian thought system is concerned, zero has been as much a mathematical concept as a mystic one.  The whole philosophy of Buddha is based on sunyata – nothingness. By using zero (Sunya), numbers have multiplied their own value. Finally a way has been found to make something out of ‘nothing’.

In eastern philosophy, existence was conceived of 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 – the existence is pervaded by Brahman.

While ‘nothingness’ was the basis of a rebellious religion and philosophy, ‘nothing’ was the starting point in the evolution of mathematics. On this background I am tempted to divide mathematics into three realms.

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. 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 and weak bird is carried along once it is a part of the formation.

Maybe, the Hindi proverb –Ek aur ek gyarah ( one plus one becomes eleven) – is based on this principle of group dynamics.  

Then, there is the mathematics of the transcendental or the mathematics of the mystical experience.  Here is the first declaration of the Ishavashya Upanishad:

Purnamadah purnamidam purnat purna mudachhate. 
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.) 

Even though it is difficult to understand this sloka with our logical mind, some indications can be given. For example  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 in either of these two different containers 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.

We can also see it in the context of transmission of knowledge. When a teacher whole heartedly  transmits knowledge, his knowledge does not get diminished. When a competent teacher transmits knowledge to a receptive student, purnat puna mudachayte is no more confined to the pages of a book as a mystic impracticable concept.

Maybe, that is that reason many educational institutes have included it as part of their logo.

PS : This is the alphabet W post of my April A to Z challenge 2020. My theme this year is ‘Mera Gaon Mera Desh’ where in I explore various facets of India and also some places and events of India I have been closely associated with.

All posts of the AtoZChallenge can be accessed here.

25 thoughts on “From Wholeness to Wholeness : three types of mathematics

  1. What a wonderful explanation of logical, dynamics, and transcendental Mathematics. All of them make perfect sense in their respective contexts.

    Liked by 1 person

  2. I remember my math teacher at college, Prof Baby Augustine, quoting this Purnamadah shloka while introducing the concept of infinity to us. Infinity – minus infinity is still infinity, he said, take away purnam from purnam and purnam will remain.

    Liked by 1 person

  3. Amazing. So much insight into the realms of mathematics. You’ve explained the three sections in very simple and understandable terms. Thank you for sharing your knowledge. 🙂

    Liked by 1 person

  4. Thanks for explaining the concept of the prayer . I used to say it without really undershot it could become a whole from a whole . I hope I’ve understood it correctly and say the prayer more meaningfully.

    Liked by 1 person

  5. Very well explained.
    I like the rose-plant example.
    May the roses of knowledge bloom.
    Our India is so rich. We gave important maths concepts to the world. High time India is recognized.

    Liked by 1 person

  6. At the end of chantings or everyday prayers or even at the end of Yoga session, I have chanted the shloka “Om Purna madam, purna midam…” thousands of times but learned its relevance with your post.
    Thanks for enlightening me.


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