One of the hardest things for us mere mortals to wrap our heads around is the universe.  It’s huge!  There aren’t the adjectives to describe how big the universe is.  Take all the adjectives you know to describe something large and then multiply them all together and maybe you’ll have an inkling about how big the universe is.

But if the universe is this big…thing…surely it must have a shape, right?  Right!  Wikipedia has a decent description of the possible shapes of the universe.  Basically, there are three theoretical shapes of the universe: flat, spherical, and hyperbolic.  It’s still pretty confusing, though.  Let me see if I can make it a little easier to understand.

We are pretty sure that the universe is flat.  Using the word “flat” doesn’t really mean anything when we use our normal definition of “flat”, though.  After all, how can a very obviously three dimensional world be considered flat.  The trick is we’re not really talking about the shape.  We’re talking about the curvature of space.

Time for a geometry lesson.  Draw three points on a sheet of paper.  Connect them to form a triangle.  If you took a protractor and measured the three angles inside the triangle, they would add up to 180 degrees.  Now, take that same principle and apply it to the universe!  First, freeze time.  Then, pick any three stars that you can see.  Connect them to form a triangle.  If you took the universe’s largest protractor and measured the three angles inside the triangle, you’d come up with 180 degrees.  Flat!  All experimentation so far points to this holding for any three points in the universe.

“Well, duh!  How else would the universe be shaped?”, you ask?  A flat universe is completely understandable to most people with a high school education.  That’s because everyone has been exposed to Euclidean geometry.  The other two theoretical shapes are non-Euclidean.

But what does non-Euclidean geometry even mean?  Going back to our triangle example, a Euclidean triangle will always have it’s internal angles add up to 180 degrees.  A non-Euclidean triangle will NOT ALWAYS add up to 180 degrees.  (Sorry, complete aside here.  Euclidean starts with a vowel but saying “an Euclidean” just sounds weird.  That is all.)

The easiest way to wrap your head around this is to think of a sphere.  Take whatever ball you have handy and pick three points.  Draw lines again to form a triangle.  You have just created a non-Euclidean triangle in curved space!

Let’s take a very specific example using the Earth.  Pretend you’re on the equator.  Start walking north until you’re at the north pole.  Turn 90 degrees to your left.  Whoa, wait a second!  You’re facing directly south now!  That can’t be right.  But it is!  Ok, fine, you’re flexible, so start walking south again.  You will soon find yourself right back at the equator.  Turn 90 degrees left again and you’ll be facing east.  Walk east some distance along the equator until you reach your starting point.  Without a doubt, you just created an equilateral  triangle.  But wait, 90 + 90 + 90 = 270 degrees!  Welcome to non-Euclidean space.  So when they say there is a spherical universe, they mean that even though it may appear that you are walking a straight line, you are really walking a slightly curved line.

Despite the fact that all signs point to a flat universe, I find the idea of a spherical universe very attractive.  Imagine being able to walk across the universe in a straight line and eventually ending up right back were you started, just like if you walked along the equator and end up back where you started!  Of course, you’d have to not only freeze time, but you’d also have to stop gravity in order to do that.  It’s also possible that I’m just talking out my ass.

Though I understand the idea of a hyperbolic universe, words fail me in trying to describe it.  Basically, a hyperbolic universe is a strange combination of a flat universe and a spherical universe.  It ends up looking somewhat like a horse’s saddle.  Space is still curved, but it’s not curved uniformly like it would be on a sphere.  So when you are traveling along one of the sides of a triangle, it is possible that you can go from bending in one direction to bending in another and the line ends up looking more line an ‘S’.

The universe is a crazy, fun place!  Hopefully, this helps you guys understand it a little better.