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Dear Steve
Thanks for your helpful answer. As regards the second part of my questions, what is the mechanism of transformation from one dimension to another, could you please check if the following makes sense, and is what i am saying alternative, mainstream or just dumb

A line cannot curve before the second dimension of plane exists, and a plane cannot curve until the third dimension of cube exists. Likewise a cube will move into the fourth dimension only once it begins to curve. The curve provides the seed of the next dimension. One theory states that each dimension has an infinitely small curve within, so that it very slowly unfolds into the next dimension. A line with an infinitely small curve will eventually bend round to meet itself, thus creating a circle in the next dimension, a plane. When a plane curves it will create a tube in the third dimension.  Another possibility (my thought) is that rather than the curve existing all through a dimension, it is there in potential but only begins to manifests once a dimension is fully unfolded and stretched to its utmost capacity. Think of a rubber band stretched in a line to infinity. It will begin to curve due to underlying curved spacewtime. So that only when a plane has stretched to its full capability does it begins to bend into the next dimension of cube.

thanks

Jeremy

Answer
No, lines don't have to curve before they can exist in two dimensions.  A cube can exist in four dimensions without any curvature at all.  Your notion associated with dimensions aren't quite on.  If a line is curving, then you already have a second dimension for it to curve in.  You need to give up traditional notions of "curvature" in order to understand dimensions.

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Dr. Stephen O. Nelson

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I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.

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I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.

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Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.

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