In Hyperbolicland, there is a lot of space.  Land is cheap.  Everybody has a big yard.  Yet you don't have to walk very far to get to all your friends.

When you're in a room, everything looks pretty much the same.  You might notice that the four corners of the room aren't quite 90 degree angles, but rather 89 degree angles.  Big deal.

When you take the train, things look different.  Looking out the window, it is not the case that far-away things appear to pass slowly.  They whiz by almost as fast as the near things.  In fact, you can measure the speed of the train by seeing how fast the far-away things appear to be whizzing.

So, after just a couple of minutes on the train, you are in a totally different place.  Completely different.  Everything you saw out of either window when you started, no matter how far away (even the moon or sun or distant galaxies), is now just a tiny dot directly behind you.  Everything you see out the windows now, no matter how far away, is completely new.

Which brings us to the point that trains were never invented, as there is no real need for them.  If you need coal, and only one in a billion square miles contains a coal mine, then there will be a coal mine just a couple of miles from your home.  Old fashioned transportation, even walking, is quite sufficient for almost any purpose.

There are no cities, and no countryside.  An even mix can be maintained, and everybody in the world still lives near each other, in one large "city" (if you insist on using that term).

Population explosions are no big deal.  Every time the population doubles, the "city" just gets a few streets wider, and it can easily accomodate all the new people.  So there is a huge population.  Nobody really knows how many people there are, but you can be sure it's a number that would take a while to write down..

The big danger is getting lost.  If you walk a few miles, and don't keep very careful track of where you went, then there's no hope you'll find your way home -- pretty much any direction you go, you will soon just be walking farther away from home.  The flip side is that it's easy to run away.  If you escape from prison, you don't have to go far before there's no chance they'll find you.  There's so much space within such a short distance that they'd have no hope of combing very far.

If you walk 20 miles, leaving everything you knew as a little speck behind you, and then turn say 90 degrees and walk 20 miles again, then how should you head straight back home?  The straightest route home will take you very close to where you turned.  In general, if you take some zig-zag route, the straight line route is never very far from you, and you usually can't do much better than retracing your steps exactly..

If you're on a spaceship, then you will feel a force pulling you away from the center-line (direction of motion) of the spaceship.  This is like the familiar centrifugal force you feel on a rotating object.  So artificial gravity can be maintained by the motion of the ship alone, with no need for rotation.  If all the struts holding the ship together were to be suddenly give way, the ship's pieces would start falling away from each other (as if the ship were slowly exploding).  They would separate faster and faster until after a rather short time, each piece would be in its own part of the universe, all the other pieces appearing as distant specks.

Here is a java game that, if you're good at games, will let you experience what it's like to fly around in hyperbolic space.