In case none of you are aware, there is a truth in the universe that is constant everywhere and under any circumstances. It is that the very small (microcosmic) will always mirror the very large (macrocosmic). Thus we find similarities between planets and atoms, Human society and ant colonies, etc.

The reason I mention this is because it is an important tool for understanding. If there is something which seems very complex and near impossible to easily comprehend, always try looking for something similar but more readily understandable, and then draw inferences between the two.

For example, a Human has a brain that does all the working out, a bit like a computers processor. A brain has long term memory, just like a hard drive, and short term memory just like a computers RAM. The similarities go on and on, and if you understand either of them already, it can help you to understand the other.

With that out of the way, let’s move on to infinity. Can you think of anything that is like infinity, but less complicated or easier to understand? Well, first let’s look at the rules by which infinity is defined…

Infinity;

Cannot be halved (without getting infinity still)

Cannot be divided in any way (same as above brackets)

Cannot be doubled (same)

Cannot be multiplied (and again)

Cannot have any extra digits added to it (and one more time!)

Okay, what we’re looking for subscribes to the exact same rules, excluding the last one. I’ll just tell you shall I?!

Nothing/Zero;

Cannot be halved (without getting zero still)

Cannot be divided in any way (same as above brackets)

Cannot be doubled (same)

Cannot be multiplied (and again)

Cannot have any extra digits TAKEN FROM it (and one more time!)

As you can see, the last rule is the same but reversed.

So nothingness and infinity live by virtually identical rules. Isn’t that counter to common sense?! It’s a very important detail, as it highlights another universally constant rule:

Any extreme has an opposite extreme of the same nature.

Nothingness might be considered the absence or lack of all things, right? That is, you could have no ‘money’, for example, and that would not mean nothingness because you still have other things… what I’m saying is that nothingness is the absence of *everything*, rather than the absence of just one thing.

Why is that so important? Because infinity has the same rule reversed… that is, infinity is the presence of *everything*, just like nothingness is the absence of everything. What this means is that you could never have an “infinite number of” peas, or elephants, etc. Peas are only one thing.

This is hard to grasp, but this basically means that infinity is a naturally squared value. It would better be understood as ‘infinite everything’ or ‘infinite infinity’.

Have I lost anyone, or fried any brains yet?! Any headaches, or anyone need another coffee?!

There’s some major points we just glossed over back there. For example, infinity, like nothingness, cannot be divided into component parts. That is, just like nothingness is not made up of little ‘somethings’, infinity is not either. It has no beginning or end, and no middle, just the same as nothingness.

What this means is that our universe is not infinite, without question. We can see quite clearly that we are surrounded by and indeed composed of finite things. The finite and the infinite are not compatible at all.

A concept many people confuse with infinity is something often called ‘progressive’ or ‘potential infinity’. This is where things like numbers come in. If you start from 1, you could go on counting for ever and ever and ever, and you would always be able to add one more. You could never count to infinity. No matter how high you count, the distance between your present number and actual infinity, is always the same – infinite!

(This reminds me of the light speed issue – no matter how fast you approach a light source, the light still seems to be at the same speed. But that’s another subject!)

People often talk about whether or not time had a beginning, whether it has an end, and whether it is infinite. We know that time is finite because it is full of component ‘moments’. We know it has a beginning because all things finite have beginnings.

That’s another important point: anything finite is something which physically exists and can be perceived in the physical universe in which you and I live. Anything which exists with us here has a beginning therefore, or else it would not exist yet!

Time doesn’t have an end, but that still doesn’t make it infinite. You could always add one more second. Time is finite.

Now because the finite and the infinite are incompatible, we can see a number of other truths from this. Scientists speak of ‘infinitesimals’, or of particles that are infinitely small, having no mass. This is simply not possible in the physical (finite) universe. Light has mass, and so does everything else.

Unless you’ve disagreed with me somewhere along the line, we’ve now established why spacetime is finite, had a beginning, but has no particular end.

The biggest question on most minds should be, if the universe is not infinite, what is outside of it? Is there an edge, and what is beyond it?

Insides and outsides are properties of finite things, like a ball has an inside and outside. But what if that ball was the ONLY thing that existed, and there was nothing else in existence? Well, there would be nothing outside the ball, nothingness and infinity. That ball is the universe – floating in nothingness as the only thing that exists.

This is getting deep huh?! I wonder if anyone has read this far down?!

Next question: so what if you pick a direction and just keep going? Do you hit anything? Do you come back to where you started?

No. The universe (the finite stuff floating around in nothingness) is expanding, and will always expand faster than anything can travel to reach the ‘edge’ of it. When scientists speak of the future collapse of the universe, it is not the universe that will collapse, it is the contents of it. The universe takes on whatever size it needs to in order to accommodate the contents.

This theory goes further too… why does the ‘finite’ exist? Because of another universally constant rule: all pairs of opposite extremes have a middle-ground between them. The finite is the balance between infinity and nothingness.