The latest issue of Nature has an article by Barry Mazur about recent progress on the Sato-Tate conjecture due to Mazur’s Harvard colleague Richard Taylor and collaborators. My meager understanding of this result is that it involves extending the Taniyama-Shimura-Weil conjecture from the case of the two-dimensional representation of GL(2) to symmetric powers of this representation.
Mark Trodden and Christine Dantas both have well-done reviews of Alex Vilenkin’s Many Worlds in One, which I wrote about here. Mark implicitly compares the book very favorably to Susskind’s recent one promoting similar ideas. I kind of disagree with him about the book, feeling that, no matter how well done, promoting to the general public science consisting of highly speculative ideas that seem to be untestable is not a good idea. It’s true that the multiverse cannot be simply dismissed on the grounds that one can’t directly observe it, but if the idea is to be considered part of science one has to come up with some way to test it. So far no one has been able to come up with a plausible proposal for how to do so, and there are solid arguments that this is inherently impossible.
[In the comment section Mark writes in to correct me, saying that he just contrasts Vilenkin’s attitude to that of others, and was not referring to Susskind’s book, which he hasn’t read.]
Update: A commenter points out that on his MySpace site Kaku has posted a copy of a forthcoming article by him that is supposed to appear in New Scientist. It is about the controversy over string theory, but doesn’t at all deal with the criticisms of the theory contained in my book and Smolin’s. It does contain a thoroughly dishonest paragraph about me, misrepresenting my position at Columbia (Kaku is well aware than I am a faculty member and teach graduate courses here, as well as administering the department computer system), and describing me as a “former particle physicist” (he’s well aware I have recently written a book on the subject of particle physics and continue to conduct research on the subject; then again, many people consider him to be a “former particle physicist”). He ascribes my criticism of string theory to jealousy over having been turned down for tenured positions at prestigious universities in favor of string theorists, and misquotes something I wrote about string theory:
String theory has only a “poetic relationship” to reality.
I never have said or written anything like this. He is misrepresenting a point I made in the book that string theory is a quite complex mathematical structure that only has a very distant relationship to musical notes and vibrating physical strings:
Once one starts learning the details of ten-dimensional superstring theory, anomaly cancellation, Calabi-Yau spaces, etc., one realizes that a vibrating string and its musical notes have only a poetic relationship to the real thing at issue.
The paragraph about me is dishonest and misleading, and so is much of the rest of the article. Kaku claims that string theory is being criticized because it cannot be directly tested by observing vibrating string modes. Critics of string theory are well aware that many theories can only be indirectly tested, and the arguments we are giving are about lack of any predictions at all. He describes five “indirect tests of string theory”, neglecting to mention that string theory makes no definite predictions about what the five kinds of experiments being described will actually see. In particular, his claim that “string theory makes specific, testable predictions about the physical properties of dark matter” is simply untrue.
Some of the article is devoted to criticizing “media hype”, and a “spoiled society, always demanding immediate results”. Given his own role over the last twenty years in over-hyping and over-promising results from string theory, this is kind of funny to read. In the end, his response to the critics is similar to that of Susskind: less than honest ad hominem attacks, misrepresentation of criticism, and insistence that any evaluation of the success or failure of string theory be postponed to the far distant future, at a time when he will no longer be around.
[Note: Michio Kaku has had this article removed from his web-site, explaining to me that it was a very preliminary draft, without any fact checking, which was never meant to see the light of day]
Update: From Stanley Deser, perhaps the shortest arXiv theory paper ever.