Posting Freak
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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.
Posting Freak
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I've been thinking of how to approach this topic for a while because this is a topic of huge interest for me. I've always liked the idea that every possible choice creates an infinite branch of new dimensions, where a different choice was made. That way I can imagine us being more like a film strip than anything else, and inter-dimensional travel would just require you to know which frame you wanted to enter. This would also enable "time travel" except that you wouldn't ever be able to change anything that you know, but rather change an entirely different branch which you could observe as if it were your own.
This is highly unrealistic, I'm aware, because the amount of space needed to hold all of this information is not only infinite but unimaginable. I think it would also require for our universe to be somewhat of a living being that calculates each and every decision before it's made.
Maybe I'm not even talking about what the rest of you are. I don't know. But to me 4D space is just a multiverse of reactions.