Googolplex

I love infinity. It’s such a strange concept, highly intriguing, and genuinely something that I like to sink my teeth into mathematically. Thinking about it, it’s such a simple theory and one that anyone who is taught basic mathematics must quickly realise and I distinctly remember finding out about it. What’s the biggest number you can think of? Add 1 to it and boom, you have the theory of mathematical infinity.

The practicality of infinity is bullish, to say the least. If we assumed that our universe is infinite, then suddenly everything is possible. I mean everything. Anything that is probable, is true, and has happened, somewhere. If we exist, then, in theory another one of us exists in a certain place in the universe. This actual means, that using probabilities, we can work out how far we would have to travel to meet the next version of ourselves. Which is 2^10^118 m (after some fun calculations that I won’t detail) which is pretty big. It has to be the case if our universe is infinite. So there is an infinite amount of space, so an infinite amount of worlds, and as such an infinite number of me and you and everyone else. Strange? Yeah it is. Kind of freeing actually.

Also, it means that there is no side to the universe. Or centre. Of up or down. It just is there, forever, recurring forever and ever. That’s a good way to think about it.

Or is it? If you think about our world, we know it’s not infinite. We understand now it’s a globe and that’s the reason it goes on forever. Tell that to an ant. It sees the world as flat, with very few dimensions other than the ones it knows. It can’t perceive the difference in horizons, nor can it perceive the shape of the world, and as such, it is infinite and continues on forever, infinitly. But you return back to where you were without turning around. That makes sense to us because we’ve seen the Earth, and we know the shape of it. This might be the way the universe is designed: a shape that not yet we can understand in our 3 dimensions of space and 1 of time, we cannot fathom that how there can be more than these four dimensions, but there might be – it’d mean that going in once direction forever would get you back to where you started, like Earth.

It’s a strange thought that too, that it might not be infinite in real terms, but to us it is.

Numerically though, infinity makes a mockery of us even more. Imagine a list of every number. 1 2 3 4 5 6 7 8 9 10 etc. Take only the even numbers. 2 4 6 8 10 etc. Which is the bigger list? Well, that’s the problem. Because, they are both the same. You’d think that the even list would be shorter, but no because of how we count. If we were to count the even list, they’d match up like 2-1, 4-2, 6-3, 8-4 etc, all the way up. This means that a list half of infinity is still infinity. Confused? You will be.

Take the infinite hotel problem. Imainge a hotel with an infinite number of rooms that is full. There’s no way I can get a room, right? Not true – all you'd have to do is move the rooms up one. Move room 1 to room 2 and so on, meaing that there is always room at an infinite hotel, even if it is fully booked. Then imagine an infinite number of people leave, you’d think the answer would be that the hotel would be empty, right? Not true. Even if 4 people stay, an infinite number of people have left… so ∞ + 1 = ∞ BUT ∞ - ∞ = anything. Crazy!

The most common analogy for infinity is the Monkey-Typewriter thought experiment. It demonstrates an infinite universe quite well. However, its not so much the fact that the monkey has the time to do it, it’s the improbability that it will happen that infinity sorts out. The equal probability of the Monkey typewriting is a man buying a lottery ticket each week and winning each week for 29 thousand years straight. That’s improbable – highly improbable – but still, possible.

Anyway, I think the number Googol is ace: 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

A googolplex is this number as the power of 10:
10^10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

…Which is such a large number that you couldn’t even write it in the universe without running out of space – even if you wrote a zero on every single particle in the universe, you still wouldn’t have enough space. That’s a big number.