2010-11-15, 06:13 PM
My dad was reading a book about this on a plane ride.
For one thing, the 4th dimension is potentially "folded up" inside of the three we have now - we're just too big to experience it. The analogy the book uses is a bug in a garden hose. If the bug is small enough, it can go on any surface and up and down, a 3 dimensional space. Eventually it would get too big to move up and down and could only move on the surfaces, and eventually it gets so big that it can only move forwards and backwards.
As for what a hypercube would look like, it's pretty easy to imagine. A line is connecting two points; a square is connecting two parallel lines equally long together at the end points. A cube is connecting those 4 corners on a cube together. So, a hyper cube is taking those 8 corners on a cube and connecting all of them to the corresponding corners on another cube; that's impossible to do in our dimension, but in the 4th dimension it works.
It's also possible to imagine what a 4-dimensional shape passing through our 3 dimensional world would look like. A hypersphere would look like a sphere getting larger and then smaller.
I hope none of this was in the videos I didn't watch.
For one thing, the 4th dimension is potentially "folded up" inside of the three we have now - we're just too big to experience it. The analogy the book uses is a bug in a garden hose. If the bug is small enough, it can go on any surface and up and down, a 3 dimensional space. Eventually it would get too big to move up and down and could only move on the surfaces, and eventually it gets so big that it can only move forwards and backwards.
As for what a hypercube would look like, it's pretty easy to imagine. A line is connecting two points; a square is connecting two parallel lines equally long together at the end points. A cube is connecting those 4 corners on a cube together. So, a hyper cube is taking those 8 corners on a cube and connecting all of them to the corresponding corners on another cube; that's impossible to do in our dimension, but in the 4th dimension it works.
It's also possible to imagine what a 4-dimensional shape passing through our 3 dimensional world would look like. A hypersphere would look like a sphere getting larger and then smaller.
I hope none of this was in the videos I didn't watch.