In reply to Richard J:
It's an interesting article, but it's hard to take seriously as a piece of criticism, because it opens with:
"First, string theory predicts that the world has 10 space-time dimensions, in serious disagreement with all the evidence of one's senses. Matching string theory with reality requires that one postulate six unobserved spatial dimensions of very small size wrapped up in one way or another. All the predictions of the theory depend on how you do this, but there are an infinite number of possible choices, and no one has any idea how to determine which is correct."
There are many, many, many successful theories that make (correct) predictions that are in "disagreement with all the evidence of one's senses". At least until one knows how to look - the wave/particle nature of, well, everything springs to mind.
"The second concern is that even the part of string theory that is understood is internally inconsistent. This aspect of the theory relies on a series expansion, an infinite number of terms that one is supposed to sum together to get a result. Whereas each of the terms in the series is probably finite, their sum is almost certainly infinite."
The Standard Model is internally inconsistent, and so is relativity. This does not mean that they are useless theories.
I'm not trying to claim that string theory does anything it doesn't do; I was just intrigued by the use of "believed".
> Holly, sorry for temporarily hijacking your thread for something with nothing to do with the very interesting bit of mathematics you asked about.
Um... yes... sorry.