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Hey bizerl,We each had 106 posts. Now I'm one ahead. Your turn to catch up.What do you think is a good definition of a dimension, and how could space have four of them (not counting time?)
I like the degrees of freedom idea. I've always thought that an extra dimension would be in a direction 90 degrees to the current three. This idea only makes sense if I rattle it off glibly and don't think about it too much.
A lot of popular science authors have described extra dimensions using analogies of lower dimensions. I like the one about an ant travelling along a string. It can go forwards and backwards and therefore is travelling in one dimension. If you zoomed in really closely though, you can see that it could go left and right around the string. It wouldn't have to go far to be back where it started and this is the idea that a dimension could be curled up.
Right.Still, "degrees of freedom" must have meaning other than just a cool sounding phrase. Width is perpendicular (90 degrees) to length and height is perpendicular (90 degrees) to the plane of length and width. So what further direction/axis is there. None, I think.
Still... a virtual line is one dimensional, but a string is a three dimensional, having volume, approximating a cylinder, and an ant can crawl back and forth along the string and all around its surface.If you curl up a flat piece of paper (a 2-D plane) you will make a 3-D tube. Still no extra dimension beyond 3-D volume. Bend a tube balloon and connect it into a wheel and it's still a 3-D object in 3-D space.What say you?
A particle can be in front or behind of another, above or below, left or right. Perhaps a fourth spacial dimension would be charmward and strangeward, and would describe a different way in which particles could be adjacent that wasn't just a combination of the previous three.