Nothingness is being and being nothingness… Our limited mind cannot grasp or fathom this, for it joins infinity. – Azrael of Gerona
Connections, connections, connections.
There are many things in life that have inconsequential beginnings: things that are only discovered by chance (and on curious whim). When nonchalantly sweeping past the library bookshelf and fingering the delicate spines of pristinely-kept books, I barely grasped the tremendous significance of the little stacks of paper. Together they formed an irreplaceable trove of knowledge- keys to new doors, new connections, and new worlds.
It was, therefore, pure chance that I should have picked up this little paperback from the little-visited mathematics section of our school library. Zero. It wasn’t the title that intrigued me, nor was it the unassuming cover. I wasn’t even looking for a book (we all know I have a backlog of books waiting to be read), but in my languorous sweep through the aisles, something compelled me to take it.
Of the dozens of books, I somehow picked out just the right one.
This is a mathematics book, yes. But it is a mathematics book so broadly based, so simply written, and so accessible, that little mathematical knowledge is needed to understand and enjoy it.
I know what must be crossing your mind – a mathematics book. Doesn’t pique much curiosity, or inspire any sort of intrigue in the typical person. But the concept of zero and infinity is inextricably linked with virtually every single aspect of life, be it religion, literature – even art.
The concept of zero (and infinity) has a seemingly inexorable influence on anyone who chances across it – uncannily, the book notes that almost every child has spent hours lying in bed, sinking further and further into confusion and (just a touch) of fear and awe as he/she thinks of the never-ending universe. It’s perturbing simply because I’ve forgotten – truly, my biggest fear at the age of 10 was possibly the fear of never being able to understand the universe. My mind simply couldn’t comprehend how it could go on for eternity, towards infinity – in the same way it could not wrap around the idea of a void beyond a finite universe – a place comprised of nothingness. But these are concepts that barely register any confusion when chanced upon now – I’ve accepted that I will perhaps never truly know the nature of the universe, and moved on to more pressing and local issues. I got used to them, just as I got used to the number 0. As with ∞. As anyone who has attempted to teach a child the concept of 0 or infinity will know, the two concepts are incredibly difficult to wrap around – it takes time.
Thought. A lot of thought, to the point of exasperation and rejection.
It seems that the Greeks had a similar fear (though more like a colossal fear, mixed with more diminutive notes of respect and awe). They completely rejected the notion of zero or infinity – and although it seems rather inconsequential to us as a modern day civilization that the Greeks should repel these concepts, it had serious repercussions and immense implications on basically everything that governs life today. Not only in maths, physics, science – but in philosophy, religion, art – zero plays a critical role in everything that means anything.
For centuries, actually, zero was a taboo, and avoided (or completely unheard of). For those that did grasp that vague notion of nothingness and developed an understanding of zero, it wasn’t to their benefit. Numerous mathematicians were slaughtered for threatening existing philosophies with their investigations into the number zero. As a result, it wasn’t until several hundred years ago that zero emerged.
Turns out, Western philosophy and religion viewed zero as an abomination – and yet Eastern philosophy embraced it. And there’s where the little strands, the intertwining arms of connection reached out into various aspects of my life and tied a big, fat knot. With all the talk about Extended Essays going on, I’ve mostly settled on one of my favorite books, Island, by Aldous Huxley, and started a bit of research into Mahayana Buddhism as well as Hinduism and the role of these religions in creating the mindset and philosophy for Huxley’s utopian society. A strange twist of fate made me pick up this book – it’s peculiar to note that zero and infinity had a large influence on Eastern religions – specifically Hinduism and the symbolism of duality. Creation and destruction is intermingled in Hinduism. Shiva, the god of nothingess, the lifelessness incarnate; and yet, the creator of the infinite universe. This duality is explored quite a bit in Huxley’s work.
It doesn’t end there. Just when I thought this book couldn’t get more oddly relevant and wonderful, probability theory pops up. And lo-and-behold, that happens to be pretty central to game theory, which happens to be what we’re studying in Economics now (theory of the firm and oligopolies!). Okay, so this talked about Pascal’s analysis of the value of accepting Christ as a savior- through mathematics of zero and infinity. I suppose I am getting a bit unduly excited – after all the acceptance of God is hardly related to oligopolies, but the reliance on probability theory was there – it was simply applied to a different concept.
Well, you’re thinking, that’s interesting. But nothing too astounding. But oh-ho-ho, then another little thing popped up during TOK class. We were talking about how different cultures and societies in different time periods were (and are) steeped in different paradigms, limited by their mindsets and perceptions of the world at that point in time. And that’s why people could accept that the date of creation of the world was 4004 BCE – they had no cause to question it. But then of course, as you know by now, the notion of creation is entangled with zero, and the void. You can imagine as I fidgeted and squirmed in my seat, barely restraining my excitement – I was quite literally an inch away from throwing my hands up into the air and blurting out weird and wonderful workings of zero. Not to mention string theory – Mr. Scheelbeek mentioned it in the passing and I couldn’t help but remember reading that string theory is arguably a philosophy and not a science (due to the impossibility of its testability and refutability), and its connections with zero and singularities; blackholes and wormholes; the universe and the cosmos. Layers upon layers of meaning (and even, a wisp of irony – the little joke Mr. Scheelbeek played was during an introduction lesson on Science as a area of knowledge. Haha.) Zero certainly plays a large part in our lives.
Not to mention its role in calculus. Or in various self-evident aspects of maths.
And then there’s art. What does zero have to do with something that arguably lies at the other end of the spectrum? Well, everything. Realistic, three-dimensional art wiggled its way into our world when zero was discovered, because the vanishing point, the science and maths of perspective, became critical in fine arts. Leonardo da Vinci once said: ‘Let Let no man who is not a Mathematician read the elements of my work.’
And so at the end of this book (ominously ending with ‘The universe begins and ends with zero‘, and evidently for dramatic effect), you’re left with a sense of achievement. Achievement, yes. A sense of achievement that arises from the exhilaration of drawing links, connections – fastening one idea to another in a never-ending loop of enthralling knowledge, thought, and discovery. And that’s what it all boils down to sometimes. Significance born from relationships and linkages. The wonderment that besieges the mind when a little connection registers – and the reverberating sense of certitude, of conviction that commits every single little thing to memory.
Invisible threads, are the strongest ties.