We were sitting around a table en famille when my six-year old grandson piped up: Granddad what’s infinity plus three?

The wee fellow is fond of numbers.  The bigger the better.  We talked round it a bit and got on to other things.  I knew I had an answer, it just wasn’t there yet.

I could see he had grasped ‘infinity’ as an idea and ‘three’ as another similar idea.  Logically then, it is possible to add to infinity.  His mistake was to relegate infinity to an idea the same as an idea of three, which kind of subtracts from infinity.  I could hardly tell him that. Children will readily dismiss an adult when he doesn’t know what he’s talking about.

Later I realised we chant the answer every morning at SRSG.

Om pῡrṇam adaḥ pῡrṇam idaṁ pῡrṇāt pῡrṇam udacyate|
pῡrṇasya pῡrṇam ādāya pῡrṇam evāvaśiṣyate

Om that is full/complete/perfect! This is full/complete/perfect! Perfection arises from the Perfect!
Taking the Perfect of the perfect, It remains as the Perfect alone

I found a second translation which replaces ‘complete’ with ‘infinity’.

THAT is infinite, THIS is infinite; From THAT, THIS comes. THIS added or removed from THAT, the Infinite remains as Infinite. (Swami Krishananda, Divine Life Society)

The passage is found in the Brihadaranyaka Upanishad 5.1.1.)

The prayers are very difficult to understand because they express very deep thinking. It is a delight to have my understanding prompted by one so young.

Years ago I was taught a mantra with a similar sense:

Om Pūrnaham chinmātrā’ham aham eva svāhā

Om I am full, I am the measure of consciousness, I am everything.

The ‘aham’ is not the ego sense but the oneness of the entire universe.

But let’s get back to addition and subtraction before the wee boy gets bored.

The essential problem is to find a way of describing infinity as infinite and therefore outside the categories where logic holds and confines. For infinity to be properly infinity it must include what is not; what could be or has been, thus beyond time. This is where we find shesha or residue. In Indian metaphysics and mythology shesha underlies the existent, making it possible. In Indian mathematics it is the remainder after subtraction. Shesha is also known as ananta which means infinity, literally ‘without end’.

You could think of space as infinity but space is not emptiness, not quite. The Indians regard space as an element, a thing of sorts. Einstein supports this by showing how space bends with gravity. Shesha, the remainder, lies beyond.  It is said in modern cosmology that the universe is ever expanding, so it must expand into what is not. That is a bit of a mystery. Infinity would have to include that otherwise it would not be complete. Marvellously, we are also told by the physicists that atoms display identical properties. So, there is the infinitely large and the infinitely small in the existent and the non-existent. The Indians considered this in the Nāsadīya Sūkta (Rig Veda 10.129).

It begins:

Then even non-existence was not there, nor existence,
There was no air then, nor the space beyond it.
What covered it? Where was it? In whose keeping?
Was there then cosmic fluid, in depths unfathomed?

In verse 4 we read:

The sages who have searched their hearts with wisdom
know that which is, is kin to that which is not.

It ends:

Whence all creation had its origin,
the creator, whether he fashioned it or whether he did not,
the creator, who surveys it all from highest heaven,
he knows — or maybe even he does not know.

My grandson might be interested to learn that modern physics also gives us the zero-energy universe hypothesis’ where the total amount of energy in the universe is exactly zero: the amount of positive energy in the form of matter is exactly cancelled out by its negative energy in the form of gravity. This has been called ‘a universe from nothingness’ where matter with positive energy and gravitational field with negative energy exist in balance. THIS and THAT or THAT and THIS. So, everything is also zero. Everything right beside nothing and both count to completeness. They have to according to this hypothesis or there wouldn’t be anything. In yoga we have shunya or asamprajnata, empty consciousness which is completeness. We are latently in a state of unrealised completeness where zero is the sign of everything.

So when I next see my grandson, maybe he’ll ask me again: Granddad what is infinity plus three? And I’m ready. I will answer the question with a question, the typical philosopher’s approach: Cauley, what is Cauley plus three? He’ll stop and think. Silence. See, Granddad isn’t so dumb.

Editor’s Note:

Jim teaches yoga in Scotland. He has received 500 hour certification through the Himalayan Yoga Tradition – Teacher Training Program (HYT-TTP).