OK, after talking about Horizon’s program on infinity, here’s a simple (sort of) explanation of how the universe is finite and unbounded. By finite and unbounded, I’m saying the universe is a fixed (unknown) size, and yet there is no “edge”. No boundary. You can go as far as you like, and just keep going forever, without the need for the universe to be infinite in size.
To begin with, you have to accept what Albert Einsteins theory of relativity tells us. The universe is not a three dimensional object (like the Earth) but a four dimensional object (the fourth dimension being time). There are theoretical physicysts who tell us there are in fact even more than four dimensions, but that’s not important here. The problem with a four dimensional universe is that it’s not something you can visualize in your head – your (and my) understanding of the world we live is is that it is three dimensional. The Earth is a big sphere. It’s finite and unbounded because we know how big it is, but we also know we can walk around it in a straight line and never get to the end (unbounded).
To make this even simpler to think about, we can go down to just two dimensions – a clock face. As the minute hand travels around we can start at 12 o-clock, and move through each of the twelve hours on the face until we get back to twelve o-clock again. But there is nothing stopping us at that point – the hand can continue to go around and we can start to see that the twelve o-clock position is not only twelve, it is also zero at the same time. Not only that, we can start the clock from any position we like, and that position will become the zero position after a complete revolution. the twelve o-clock position has no real significance per se.
My universe is the same as the clock face. You can start from anywhere you like, travel away from that point and eventually you’ll simply come back to where you were. You’ll never come against and edge or boundary, you’ll just end up back where you started. What with the universe being a four dimensional object, you’ll also not even be aware that you have come “full circle” because you won’t in fact have travelled in a circle – you’ll have followed a “straight line” through space and time to all intents and purposes.
So there you go – just because it doesn’t have and edge, this is not a reason to believe the universe to be infinte. By the same token, just because we don’t know what it is, it is not reasonable to assume there is no “biggest number”. Just like the clock face, the biggest number exists, and in a rather neat way to describe it, it also just happens to be zero (think back to 12 o-clock – it’s the Alpha, and the Omega all at the same time). I like this idea – it has beautiful symmetry.
