On a long car journey without a radio or cd. I started to create a model universe based on flatland.
The universe is pretty much newtonian. It has two really big spatial dimensions and a thrid one of just one metre. The Z axis loops around like those really small dimensions from string theory. I introduced Mr Square to this universe. Mr. Square is 50cm*50cm and 10 cm high. Looking along the X or Y axis he sees into the far distance. But looking along the Y axis he sees the back of his head.
The universe has a tree like lifeform one metre high. It`s skin is a cylinder. It grows along the Z axis. When Mr. Square looks at it it stretches to infinity along the Z axis. It has a turtle exactly one metre high. The turtle stands on it`s own back.
Then I gave the Z axis some topology. Not only is it a metre long. It has an 180 degree twist. Mr square looks at the back of his own head in mirror image. The tree must either twist to connect up proprly or have symmetrical innards. The turtle faces the opposite direction every 1 metre. (Usefull for looking out for predators)
Then I startedthinking about extra time dimensions. With an extra infinate time dimension flatland would carry on pretty much the same until the advent of flatland einstein. For low velocities Mr. Square would not percieve any difference in his day to day life. He would just progress at the same rate through both time dimesions.
BUT. What happens if the extra time dimension looped. Say it was only one second in length. What would happen then? What would happen if the time dimension were twisted like the second universes space dimension? I can`t visualise this at all. Help please.
