Hyperspace and the 4th Dimension
Date: 9/20/95 at 18:32:20 From: Anonymous Subject: Hyperspace May we have a general definition of hyperspace? Our setting is a tenth grade geometry class.
Date: 10/7/95 at 11:22:17 From: Doctor Andrew Subject: Re: Hyperspace Hi. In all the science fiction I've read hyperspace has seemed to be an area in the 4th dimension but not in our 3rd dimensional universe. I think authors generally conceive of our third dimensional universe as some really convoluted shape in the 4th dimension. An analogy would be to draw something looking like a small intestine on a piece of paper and declare that in normal movement a spacecraft has to stay in the boundaries of this shape. So, to get from one end to another could take a really long time. When a spacecraft "goes into hyperspace" it crosses this boundary. Since the shortest distance between two points on the piece of paper is a line, going through hyperspace can save a lot of time. This is my impression from what I've read; it's not really mathematical. There may be issues of relativity involved with how the shape of a 3 dimensional universe fits into the 4th dimension. If you are just wondering what the 4th dimension would be like, I would start by thinking of the simplest shape we know in 4 dimensions: a sphere. Imagine a set of points that is equidistant from a 4th dimensional point (w,x,y,z). Distance is just the sum of the squares of the distances like in 3 dimensions. This helped me think about it. I remember that the book Flatland was fun to read; I read it in 9th grade. It talks about the 4th dimension and how it would be perceived by three-dimensional creatures. If we come up with something more formal about hyperspace we'll be glad to send it to you. I haven't really come across anything about it in any math classes; I'm not really sure it is a useful notion in Mathematics. The 4th dimension is useful, as is any dimension, but I think hyperspace is more of a Physics/Sci Fi sort of thing. -Doctor Andrew, The Geometry Forum
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