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Name: murphy
Status: N/a
Age: N/A
Location: N/A
Country: N/A
Date: Around 1993


Question:
If string theories require us to have more than 4D space time, and these other dimensions are "folded" over each other somehow, how can they meet the criterion of being literally perpendicular to all previous dimensions and still be topographically curved? And how does the number of dimensions affect the number of proposed electron types (muon taon etc)?



Replies:
Imagining strange higher-dimensional objects is one of the big joys and frustrations of many mathematicians and physicists who do this sort of thing. But it is usually a little difficult to put what they have imagined into ordinary language, since these objects usually just cannot exist in our space - and nothing like them really can, at least at the level of our normal perceptions. One of the simplest analogies that does not really work is simply the circle. What mathematicians and physicists discovered is that you can separate out the "closed-in-on-itself" property of the circle from the "curved" property - you kind of imagine a straight line segment with ends labeled A and B, and then declare that "A = B"! Such a circle of course cannot exist in the ordinary space we know, but as a mathematical object there is nothing wrong with it. Anyway, those extra dimensions you talked about all look sort of like this circle - they are straight line segments closed in on themselves without curving at all. You can also imagine a cylinder as an example - the axis of the cylinder is one dimension that extends to infinity both ways, while the circumference of the cylinder is a circle that is perpendicular to this axis. However, That is embedding the 2-dimensional cylinder into 3- dimensional space, and it turns out you do not actually need to even imagine embedding these higher dimensional spaces to work with them, although usually it is possible.

Arthur Smith



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