“Delightfully anthropocentric,” Prof. Snik’wah says of today’s xkcd. (When last heard from, the good Professor was apologizing for dead blackbirds in Arkansas. The problem, of course, is funding; if zi’i could afford to hire better transport contractors, such things wouldn’t happen. There really are universal principles of social interaction.)

String theory has a curious place in modern physics. On the one hand you have the string theorists themselves, who are ready, willing, and able to explain everything from the Big Bang to Jerard Loughner by reference to their work; on the other you find the majority of physicists and their allies, who point out that not only is there no way to set up an experiment to test it, the theory itself says there’s no such experiment. The cartoonist at xkcd is clearly allied with the latter group, which ridicules (or worse) string theory on the ground that if there is no experiment to prove it there are no physical effects of it, so it doesn’t matter if it’s true or not.

This is a somewhat shortsighted attitude. String theory produces some mind-blowingly abstruse mathematics, and mathematics need not have use — mathematicians themselves will tell you that the amazing thing about math is that it sometimes appears to reflect things that are going on in the observable Universe and is therefore useful. There is no apparent reason why this would be so, and really good mathematicians do it because it occupies their minds with enjoyable puzzles. It’s as if you could build space probes based on the principles of solitaire (which is partly true, come to think). It’s not at all uncommon for a branch of mathematics to be fully developed, complete with professional journals and meetings at conferences, years or decades before anybody discovers a useful application. String theorists find that immensely hopeful. Someday we will be vindicated, and all will bow before us!

Meanwhile mainstream physics occupies itself with a different puzzle, involving black holes. It is a principle of physics that entropy is conserved and is always increasing — never mind what entropy is; it’s a quality of the Universe and the things within it. It is also, perhaps somewhat less forcefully, a principle of physics that nothing can pass the event horizon of a black hole. It follows that all the entropy of everything which has fallen into the interior of the black hole must be visible on the surface, and since the things that fall into the black hole are three-dimensional and the surface of the black hole is only two-dimensional, a fundamental quality of the Universe needs only two dimensions to exist. This leads to the unsettling possibility that there really are only two dimensions, and the third is an illusion. Of course, since there are no black holes nearby for physicists to play with (which is, on the whole, a good thing) no experiment can be set up to test the notion, but unlike with string theory it is possible in principle to imagine one.

One of the major features of string theory is the existence of multiple dimensions. The number varies according to the whim and/or mathematical formulations of the specific theorist, but is always greater than the familiar three. We don’t experience the others — volume can be calculated in proportion to the third power of the “size” of the object, and it comes out right — because the additional dimensions are tightly curled, with all their energy (and entropy) confined to what we see as less than the Planck dimension, which is the smallest possible measurement that can exist in the Universe.

Professor Snik’wah chortles. Zi’i is not a physicist, of course; “he” is an allopodologist with a minor in exobiology, but he does have an intelligent layman’s knowledge of other scientific disciplines, and is more familiar with physics than most scientists in his discipline simply from riding around in starships and having contact with their crews and engineers. According to his understanding, there are an infinite number of dimensions — apparently this is contested — any two of which, if they are spacelike, form a Universe and create the necessary third, allowing particles (and us) to exist. Each such Universe has, theoretically, zero extent in any of the other dimensions. Imagining that the other dimensions must exist within a Universe such as the one we experience is hubristic self-aggrandizement, and leads to errors in thinking and mathematical formulations.

I dunno. They lost me at differential equations, so seeing humility as a mathematical quantity is ‘way over my pay grade.

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