Alex McColgan

But what if we were to come up with a rule?

All the lines must instead curve towards each other.

There is only one way such a universe could be drawn, and that is in a sphere.

Consider trying to draw two parallel lines on a sphere.

You might start off well, but will quickly realise that your task is impossible.

All lines would converge towards each other, intersecting at least twice as they return back to where they started.

What would a universe that was based on these kind of lines look like?

Essentially, rather than going in the straight line you thought you were going in, you actually would be travelling in a massive curve.

It's a bit like those computer games where you travel off one end of the screen only to reappear from the other side.

In a spherical universe, you could travel infinitely, but ultimately you would only end up arriving back where you started.

With a powerful enough telescope, and if light were to travel a whole lot faster all of a sudden, it would be possible to look at the back of your own head.

This kind of universe contains a finite amount of things, but it appears infinite because you just keep bumping into the same things infinite times.

Thanks to objects like black holes and powerful stars, we do indeed have evidence that our reality sometimes is a curved, spherical one, at least near large bodies of mass.

The inside of a black hole's event horizon is this kind of infinite space.

No matter what path you take, you can never get out of it.

However, let's consider our last example, the hyperbolic universe.

This one is the hardest to visualise, but the idea is simple.

Instead of having all lines remain parallel or move towards each other, every line must move away from everything.

Drawing this is inherently tricky, because everything keeps getting wider exponentially.

The only way you can do that is to either buckle your nice flat disc until it becomes something like this, or warp what you are seeing like this.