bilglik 6

Bilgilik 331
Consider trying to draw two parallel lines on a sphere. You might start off well, but would
quicky 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 kinds 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 little 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 try to travel
infinitely, but ultimately, you would
only end up arriving back to 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 just because
you’d 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 disk until it becomes
something like this: Or warp what you are seeing like this: All of the objects in this
image are squares. However, they are squares that are obeying our rule that all their lines
must be diverging