DO HUMANS UNDERSTAND INFINITY?

By Nikhil Handa

Before you get all self-righteous with me, shouting you know exactly what infinity is and telling me that I’m a stupid idiot for even dreaming up this question, hear me out. Well, actually, don’t hear me out, I feel rather scared for my safety if I’m around someone who feels the need to shout at me because I doubted their knowledge of infinity, so you can actually just leave.

But for the people who didn’t yell and insult me quite as much, I ask you this: Sure, you may understand infinity, but do you understand infinity? Now don’t you dare say ye- okay you said yes. Are you sure you understand infinity though? Like super duper sure? How about if I rephrase it so that I’m not being as frustratingly vague: you may understand the concept of infinity, but can you truly imagine it? Aha, now this is where we delve into the deep stuff.

We’re all familiar with the idea of the infinite. There is no exact definition, but the infinite refers to something without any limit. Notice how I said there is no exact definition? Well that can’t be right, because discussing the infinite doesn’t take away our ability to use Google, right? Actually, for once, Google is wrong. It defines infinity as ‘a number greater than any assignable quantity or countable number’. That may seem legitimate at first glance, but if our own number system is infinite, how can it be the case that something (the thing that Google describes) is bigger than infinity? And if something infinite has no limit as we established, how can it have a quantity?

The answer to those questions is that humans are lazy. And I’m not just talking couch potato lazy, I’m talking premium cushion luxury sofa Irish baked potato lazy. We have an uncanny tendency to label anything too big for us to imagine as ‘infinite’. Here’s a little fact: the universe is not actually infinite, as some of us may have been told. Its just very, very, very, a few more very-s and ten extremely-s, big, and even those quantifiers would not be doing it justice whatsoever. And yet we just decide that it is infinite because of how inconceivably big it is. We have also done the same thing before, when we considered the amount of grains of sand it would take to fill the universe (which was considerably smaller to us then back in 400BC when we thought this). This is until Aristotle came along and spent what have must been an incredibly dull Sunday afternoon to work out how many grains of sand it would actually take (inventing some really big numbers in order to do this, given the size limitations of the number system at the time). And so, it seems reasonable to say that humans can indeed understand the infinite, but we are just too lazy to do so, preferring to use the infinite to describe things that are incredibly big.

But there is yet another twist to this tale, this one coming from the ideology of religion. It is common lore that God is omnipotent, an unlimited creator who can do anything. But using that same idea, surely it is then illogical for God to be finite. How is it that someone with infinite power can still be confined to a finite form? Therefore, we can conclude that God is therefore infinite. Perfect, glad we established that, we can now move on. Except we can’t, as I’m sure none of you are surprised about if you’ve noticed the course of this article so far.

Here is the issue: can we imagine an infinite God? In short, yes, but actually, no. We can imagine the idea of God being infinite, but we cannot envisage how a ‘thing’ can be infinite. That is perfectly reasonable. We have a finite knowledge, and we consider ‘things’ to be entities, and entities are countable, whereas infinity is not. Therefore, it seems we cannot understand the concept of God, nor things being infinite.

However, for what seems like the umpteenth time in this article, this is not the end of the story just yet. So far, we have established that we can understand very big things as long as we are bothered, but that we cannot understand infinite things. But what about things that aren’t quite so literal? This is where us humans can feel good about ourselves once more: we can understand the infinite nature of the number system rather easily. We understand that regardless of how big of a number we think of, we can always add one, we can

always double it, we can always square it. Not only that, but we can grasp the fact that some number sequences are infinite in nature and will never reach a goal.

But with that, we have finally reached the end of this story. It seems that we can actually draw a somewhat accurate conclusion from our various back and forths: Humans can understand the concept of infinity, especially in a more abstract sense, but when it comes to infinite and tangible objects, we’re not so reliable. I feel as though that is a rather neat summary of what certainly isn’t a neat topic.

Until we come across the realisation that our current idea of infinity allows us to mathematically suggest that 1=0. Oops. So close, yet so far.