I have been lucky. Since school, I have had the experience to study from really exceptional mathematics teachers who have made mathematics shape my worldview like no other discipline has.
It had started with Mr Osahan at school – a man who loved geometry and saw it in every aspect of life. And then Mr Manshant had deeply ingrained the twelfth class mathematics with a crystal-like clarity in me. Things were beautiful and you could see the beauty so clearly.
During undergraduate, I learnt that mathematicians are actually the most imaginative and creative sort of people. They work with things which cannot even be seen by human eye. When I was first introduced to the idea of dealing with an Rn space, I was boggled and quite terribly confused too. I clearly remember Mam Archana’s introductory Linear Algebra classes in college. Suddenly the entire world had changed as if – she talked of groups, fields, subspaces and I could never imagine a picture of the concepts in my head. I had walked up to her after class one day and told her that this was bothering me. It was making me uneasy – those lists of definitions and absence of pictures. She tried her best to persuade me to somehow extrapolate things from the tangible ones, try and imagine things in R3 and then try to assume a parallel in Rn. I was more confused and remained unconvinced for long. Why would you like to do that? It was stupid, I thought.
It was then a chance sitting with my mamu once (who is a mathematics enthusiast to the core), that I saw light. “Why can’t I see these?”, I had asked him out of deep concern.
He had replied in that calm, unruffled tone - “We can’t see a lot of things in life, but that does not mean we stop studying them.”
“But what does that mean?”
“You can’t see God, but you still study Him, right? How is that? Through His PROPERTIES! Every morning you call Him Fearless, Benevolent, Omnipresent, Omniscient, Fatherly etc – those are His properties and based on those you conjure up an image of Him.
Similarly, you can’t really see a field, subspace – so you try to study them through their properties - a field through its eight properties, a subspace through its own properties. Thus you try to form an idea of how those mathematical objects may behave.”
The argument had satiated my curiosity, suddenly all the linear algebra classes assumed a new, higher role in my undergrad life. I started to revere it like nothing else. It was something transcendental, I felt.
Fantasy worlds with such exceptional properties leading me towards a perfection of sorts, it was a beautiful new realm for me. It excites me still, even more.
And then, I have to tell you about Dr Mohan Singh, a retired mathematics professor who has been my math-smitten uncle’s inspiration. I got a chance to study from him last year – and that too one-to-one. He taught me real analysis and topology. Mathematics would soon blend with theology and leave me all awed at the beauty of it. He is a man who lives and breathes mathematics. It was hard not to get more inspired, more excited, more enamoured by the field.
Once while explaining me a basis, he remarked – “For a topologist, a square and a circle is the same. Because they generate the same topology. If you go and tell this to a man on the street, he might laugh at you. But that’s the truth -a square and a circle are the same.”
Once our topology - theology detours had begun and we were coming to a conclusion that logic is not everything afterall. He gave me examples after examples from the history of mathematics where compromises were made even in a rigorous and seemingly-perfect field like mathematics (especially after Bertrand Russel discovered gaping flaws in Cantor’s set theoretical concepts). Since logic itself was not flawless, the point was that to reach God and when dealing with the domain of spirituality to study the Ultimate Perfection in the cosmos, one must abandon all logic and proceed with submission in heart and that's it.
I expressed deep unease. But then the topologist analogy helped and clarified things perfectly. Just like the concept of ‘circle and square being same’ is illogical for a common man but perfectly logical for a topologist, similarly, what might be seen as illogical in the world of spirituality might be perfectly logical from a higher perspective. After all, it is not the 'absence of logic' but a domain where a 'higher logic' prevails! *
A couple of days ago, at a workshop on bayesian inference, the instructor made a tangential remark somewhere during his lecture. He knew of a guy who claimed to see five dimensions when meditating under a blanket with a flashlight! (Considering time as 4th dimension in the 3-d space is all normal humans can imagine.) Makes me wonder, perhaps there are creatures on other planets who can see higher dimensions beyond R4.
As I think of it, I just get even more wonder-struck!
Wow.
*Caveat: Just to prevent any misinterpretations, when I mention spirituality, I do not mean religion or any superstitions built around them. Spirituality is about recognising one spirit in all human beings and rising above prejudices. On a personal level, I am a serious believer in rationality and feel that I have acquired this trait from my belief in Sikhism.
