Originally posted by philogean
since chess is the chosen game for intellects, what better place to pose a question and invoke an interesting conversation. one is familiar with the concept of dimensions. the 1st dim. is length and the 2nd dim. is length + bredth. the 3rd dim. is length+bredth+height. you notice that every new dimension has all the previous elements in addition to the new ...[text shortened]... refore would it not be safe to say that we do in fact live in the 4th and not the 3rd dimension.
Well, you should make a difference in time-dimensions and space-dimensions. When you describe the world we live in, you talk about space-dimensions. Time, is a first dimension. We can only move forward or backward in time (backward as in history lessons). We cannot move sideways in time.
What i like to see as a fourth dimension as a universal coordinate. Say we live in one universe, and that there are infinitely many parrallel universes. The coordinate indicating in wich universe we are in would be the fourth. Just a thought though.
I often find myself trying to imagine a hypercube (4D cube).
You can more or less draw one the following way.
0D, a point
1D, make a second point, and connect the two, you get a line.
2D, make a second line, and connect the similar ends (you can use a mirror to create a second line, and then you connect each end with it's reflection). You get a square.
3D, In the same way, make a second square, and connect each corner with it's refelction, you get a cube.
4D, Make a second cube, and connect each of the corners with their "reflections". You now have a hypercube.
There are more ways to do something alike. One is to calculate how many lower dimensional objects you have in a object. (eg 6 squares in a cube, 4 lines in a square, two points in a line. Reasoning that way, you'd get 8 cubes in a hypercube...
I gave two ways for a hypercube to be drawn, i am curious to see what others think about it...