Some (meanuing much) confusion

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Some (meanuing much) confusion

Postby NRS » Wed Feb 03, 2010 7:55 pm

I've been reading some of the material from an old page trying to describe the 4th dimmension in relation to the 3rd by describing the 3rd in relation to the second. Why is it that the description of 4d space seems to be almost the same as a 3d space without gravity? It seemed to be a median point between 3d spaces, sort of like being able to reach into a picture on the wall, you being in a 3d space, with access to another 3d space. What exactly amI missing? :\
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Re: Some (meanuing much) confusion

Postby PWrong » Thu Feb 04, 2010 4:50 am

Which page were you reading?

Why is it that the description of 4d space seems to be almost the same as a 3d space without gravity?

It's not like that at all, but in some contexts it can be similar, if you're stuck on the ground and don't care about up or down. On Earth, you're mostly limited to two dimensions: East-West and North-South. You can also jump up and down, but you don't have much freedom in that direction. You're limited in how high you can jump, and how deep you can dig. If you lived on a 4D planet, you'd have the same problems with going up and down, but you now have three other dimensions you can move freely in. So if you ignore the up-down dimension, it's similar to being a spacecraft in 3D because you have the same degrees of freedom.

Does that help?
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Re: Some (meanuing much) confusion

Postby wendy » Thu Feb 04, 2010 7:16 am

Hyperspace, is simply "space over solid-space". The idea of relating 4d to 3d as 3d to 2d is that we can see 2d's hyperspace as real space, and that by analogy, we might reason 4d space as 3d space.

You should be wary of space-time diagrams, and other "4d" stuff from physics.

Space-time, either newtonian or einstein, is merely a matter of overlaying pictures, rather like the flip-cartoons kids might do in books.

The diagrams where you see curvature, like deep holes around stars, is not space-time. It is intended to be a billiard ball table, where the ball is pulled into deep holes by (real) gravity. In practice, all space is curved, but it's not curved in anything. Instead, the length of arc varies with angle at every point, and that in the presence of large masses, the lengths of arc is longer. Since space is in tension, the "straight path" across any point divides the length equally, which means there could be fewer degrees on one side than the other. Straight lines, then bend in towards masses, because the arc-length is greater there.

In four dimension, there is indeed time and gravity. Where we use 4d space-time or 4d space-curvature, the four-dimensionals use 5-d space-time or 5d space-curvature diagrams. The pictures we draw for books show space-time or space-curvature for two-dimensional worlds.
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the dream we dream together is reality.

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