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Why does string theory have ten or eleven dimensions?
Why not, say, 44 dimensions? I won't call this short article an explanation, but I did learn something fundamental from it. Thanks to www.politicaltheory.info for the pointer.
Posted by Tyler Cowen on February 4, 2006 at 07:29 AM in Science | Permalink
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Comments
"but I did learn something fundamental from it."
What did you learn?
Posted by: Brian at Feb 4, 2006 10:27:57 AM
Quite a good explanation, actually. The constraints the number of dimensions are a little like the constraints on the number of different knots with a given number of self-intersections.
However, these theories are highly speculative, to put it mildly, and have little experimental support (don't throw that microwave background at me, I'll pass it back!)
Posted by: A Tykhyy at Feb 4, 2006 10:54:25 AM
I found Brian Greene's book the Elegant Universe to be quite
helpful in this regard.
Posted by: Dave at Feb 4, 2006 11:07:10 AM
One of the beauties of string theory, besides the main feature that it seems to be a sensible theory of quantum gravity, is that it's highly restrictive in what can and cannot happen; the constraint on the number of dimensions is a good example. Unfortunately, when you curl up the extra 6 or 7 dimensions to get down to our real world, there turn out to be zillions of different ways of compactifying, and much of that uniqueness is lost. That's why it's so far been hard to connect string theory with experiment.
Posted by: Sean at Feb 4, 2006 1:33:58 PM
Ah, but the joke was lost is translation... If the number is 42 instead of 44 then it will have great meaning to fans of Douglas Adams. :-)
Posted by: Macneil at Feb 4, 2006 2:31:17 PM
Not only, Sean. There aren't any experimental data to begin with, except for the microwave background and a few odd items. Not enough to test a theory thoroughly.
Posted by: A Tykhyy at Feb 4, 2006 4:29:09 PM
This is quite similar to the effect of dimensionality in computer algorithms. Most of the really hard problems (i.e. NP-complete and other exponential time algorithms) involve a low number of dimensions, like 3 or 4. If you have to solve a 1,000-dimensional problem, you can use simpler and faster algorithms and have a much better chance of getting a good answer![1] An intuitive explanation for this is that in a high dimensional space, you have so many choices that no matter how bad you next move is, you are unlikely to reach a dead end.
[1] Neil Gershenfeld, The Nature of Mathematical Modeling, "The Blessing of Dimensionality"
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