Not Even Wrong

The latest issue of the Notices of the AMS contains several things very much worth reading. There’s the second part of a wonderful biographical article about Grothendieck written by Allyn Jackson (for some comments about the first part, see an earlier posting).

There’s also an excellent short expository piece by Barry Mazur that explains a bit about one of Grothendieck’s influential and still only partially understood ideas, that of a “motive”. In algebraic geometry the standard ways of defining topological invariants of topological spaces are of limited use, and one wants a much more algebraic notion of such an invariant. This is what a motive is supposed to somehow provide, but to even show that such conjectural motives have the properties one would like requires solving perhaps the biggest open problem in algebraic geometry, the Hodge Conjecture.

Finally there’s a thought-provoking piece called The Elephant in the Internet by Daniel Biss about the effect of the internet on the mathematics literature. It contains some comments about the difference between standards in physics and mathematics, including an analogy of mathematics as classical and physics as popular music. His conclusion that “our current relationship to the Internet has the undeniable effect of degrading the sacrosanct status of the mathematical text” seems to me excessive and it’s a shame that he feels “hesitant to post my papers online; it always feels a little like leaving my infant in a dumpster.” I have some sympathy for his worry that preprint archives and contact with the more journalistic physics literature may make the mathematics literature much less authoritative than it used to be (this was also the concern of a similar article by Jaffe and Quinn published in the AMS Bulletin in 1993). But the lost golden age that Biss yearns for was not so golden. Much of the math literature was written to very high standards of rigor, but often in ways that made such uncompromising demands on the reader that virtually no one who was not already an expert could hope to understand what was being said. The fact that the internet has provided venues for much sloppier, unpolished, but more expository articles also has its very positive aspects.

There’s a fascinating interview with Atiyah and Singer now on-line. It was conducted in May at the time they were awarded the Abel prize. The interview and Atiyah and Singer’s acceptance speeches are also available in video form.

The whole interview is very much worth reading and both Atiyah and Singer make extensive comments about the relation of mathematics and physics. Atiyah makes the provocative prediction that ideas from quantum theory will ultimately have a revolutionary effect on number theory, helping to understand why the Riemann hypothesis or Langlands conjectures are true. He notes that Wiles says this is nonsense. He also predicts that new progress in theoretical physics will come from a better understanding of classical four-dimensional geometry. By this I think he has in mind something like twistor methods. Singer’s comments about string theory are probably typical of the attitude of many mathematicians. He says that, because of the Landscape “you cannot expect to make predictions from string theory. Its inital promise has not been fulfilled”, but he still is an “enthusiastic supporter of superstring theory”, largely because of the interesting mathematics it leads to.

Singer also makes the following sociological comment about mathematics, but I think what he has to say is also very true in physics:

“I observe a trend towards early specialization driven by economic considerations. You must show early promise to get good letters of recommendations to get good first jobs. You can’t afford to branch out until you have established yourself and have a secure position. The realities of life force a narrowness in perspective that is not inherent to mathematics. We can counter too much specialization with new resources that would give young people more freedom than they presently have, freedom to explore mathematics more broadly, or to explore connections with other subjects, like biology these day where there is lots to be discovered.

When I was young the job market was good. It was important to be at a major university but you could still prosper at a smaller one. I am distressed by the coercive effect of today’s job market. Young mathematicians should have the freedom of choice we had when we were young.”

Over at Preposterous Universe Sean Carroll has some comments on the anthropic principle and the landscape.

He describes one extreme of the spectrum of opinion about this as people who think the whole thing is completely non-scientific, giving what he sees as being the two kinds of objections such people make, neither of which he thinks make sense. Since I’m one of these extremists, I think I should try and explain why and exactly what the nature of my objections are, since they’re not exactly the ones Sean mentions.

The first objection Sean attributes to extremists like myself is that of accusing users of the anthropic principle of “giving up” by assigning the parameters of the standard model to a selection effect instead of calculating them. This is very much David Gross’s objection, and while I would agree with it as a socio/psychological characterization of the behavior of Susskind et. al., my own version of this objection is a bit differerent. For any given supposed fundamental theory, some observables will be calculable from first principles, and others will be aspects of the particular state we are in, dependent on the history of how we got here. Given a particular observable, in some fundamental theories it may be calculable, in others environmental. But the theory is supposed to tell us which it is going to be. The standard model tells us that the earth-sun distance is environmental, and that the magnetic moment of the electron is calculable. It is silent about the origin of its 20 or so parameters, and whether they are environmental or calculable. It is one of the first jobs of any theory that purports to go beyond the standard model to give some sort of explanation of where these parameters come from, which of them are in principle calculable and which aren’t.

The problem with the whole Landscape idea is that it is so ill-defined that it can’t even tell you what things are calculable and what things are environmental. You don’t know what the fundamental M-theory is that is supposed to be producing the Landscape and governing the dynamics of how the universe evolves in it. String theorists would probably claim that while they don’t know exactly what the fundamental theory is, they may know enough about it to make conjectures about what the Landscape should look like, at least in certain limiting cases. The problem is that their conjectures not only don’t allow them to calculate anything, they don’t even allow them to determine what is going to be calculable. The problem with string theory is not that it can’t calculate the vacuum energy, it is that it can’t calculate anything. Some string theorists are now using the Landscape picture purely as an excuse to get them out of this embarassing situation. “Not our fault we can’t calculate anything beyond the Standard Model, because maybe nothing beyond the Standard Model is calculable”. If they had a well-defined fundamental theory which exhibited this behavior, one might take them seriously, but until they do, the whole picture is nothing more than an elaborate excuse for failure. A question that should be asked of anyone promoting this stuff: show us using string theory which of the Standard Model parameters are calculable and which are environmental. If they can’t do this they shouldn’t be taken seriously.

The second objection Sean attributes to the likes of me is that we object to the explanatory use of entities that are unobservable in principle, like multiple universes. This isn’t really my objection to the Landscape. If a compelling fundamental theory existed that made lots of correct testable predictions, and such a theory predicted lots of unobservable universes, I’d happily believe in their existence. But, absent such a compelling theory, people who go on about unobservable multiple universes are not behaving very differently from those theologians who supposedly took an interest in angels and pins. Science is about coming up with explanations for the way the world works, explanations that can in principle be tested by making more observations of the world. If you’ve been working on a theory for twenty years and it has totally failed to make any testable predictions, you should admit failure and move on, not engage in elaborate apologetics for why your theory can’t predict anything.

Witten is giving a colloquium talk next week at Princeton on the topic of “Supersymmetry Pro or Con”. His talk is a last-minute replacement for one about “Recent Results from WMAP” by Lyman Page. WMAP was supposed to report the results from the analysis of the second year’s worth of satellite data early this year, but this has been delayed quite a bit already, and evidently is being delayed even more. Does anyone know why?

This weblog thing is getting out of control. It seems that Frank Wilczek’s wife has one, as well as his daughter. What about you, Frank?

Witten’s talk this morning at the KITP on “The Future of String Theory” is now available. He only talked for about fifteen minutes and then took some questions. I thought it was a rather weird performance. Not only did Witten not really have anything to say about the future of string theory, he didn’t even discuss the present state of the theory. The most recent thing about string theory he mentioned is the now seven year-old AdS/CFT correspondence. He drew the standard picture of Feynman diagram vs. string world-sheet, claiming it indicates that space-time is an “emergent phenomenon”. He even noted that he has been drawing the same picture for nearly twenty years now and he still doesn’t know in what sense this “emergent space-time” idea is true, although AdS/CFT is the closest thing to the kind of thing he is looking for. Now not only space-time is supposed to be “emergent”, but so is the string itself, although he admits he doesn’t know what this means.

Instead of looking optimistically to the future, Witten’s talk was extremely defensive. He started off trying to defend why string theorists work on string theory (basically because it is a non-trivial extension of QFT, contains gravity and has lead to important mathematical results). Much of his very short talk was taken up by mentioning criticisms of string theory and giving unconvincing responses to them. He didn’t say anything in the bulk of his talk about the Landscape or twistor string theory, or anything else going on these days in the field.

There were several questions from the audience. Someone asked him if he would still believe as strongly in string theory if the LHC didn’t find supersymmetry. He somewhat evaded the question, saying he would be less optimistic about how well we can ever understand the world, but implying that he wouldn’t consider this as evidence against string theory itself, repeating the same defense of why he did string theory that his talk started with.

The last question was about the anthropic principle and the Landscape. He began his answer with something like “Well…..(nervous laughter)… uh…..” then finally said more or less “I’d be happy if it is not right, but there are serious arguments for it, and I don’t have any serious arguments against it.” So I guess he comes down on the Weinberg side (“I don’t like it, but maybe we have to accept that our fundamental theory can’t explain any of the things it is supposed to”) vs. the Gross side (“people who think this way have given up doing physics”).

The KITP in Santa Barbara is having a conference in honor of its 25th anniversary on the topic of “The Future of Physics”. Some of yesterday’s talks are already online. I’ve been watching Weinberg’s talk on “Where do we Stand?” this morning (a commenter also wrote in a little while ago while I was watching to recommend it). Weinberg gives a good summary of the present state of conventional wisdom about particle theory. He goes over the standard arguments that the standard model should be thought of as an effective low energy theory, and that doing so explains many of its features, with the two big exceptions of the scale of the vacuum energy and the electroweak symmetry breaking scale.

He promotes his “prediction” of the cosmological constant, and recalls that supersymmetry is the standard way of dealing with the low electroweak scale or hierarchy problem. But he then explains the problems with all known ways of breaking supersymmety, concluding that “no satisfactory theory of supersymmetry exists, where supersymmetry breaking is accounted for in the framework of particle physics.”

As for the “Landscape”, he notes that Gross hates it, says that “I don’t love it”, that it’s a disappointment, but one that we may have to get over. He makes some extensive comments about string theory, saying that it has had a history of advances leading to momentary optimism, but ultimately disappointment, with the bottom line that after 20 years we understand string theory much better but are no closer to contact with physics. He ends his comments about string theory with a rather weird remark that maybe it is wrong to look for a “guiding principle” behind string theory, that all there is to it is that it is the only way of extending the standard model to include gravity in 4d. I guess he is implying that string theory is not a fundamental beautiful theory, but, like S-matrix theory just a general framework imposed by consistency.

In general, Weinberg sounded to me old, tired and discouraged. Like just about all the leaders in the field, he refuses to publicly acknowledge the obvious possibility that the explanation for why string theory doesn’t predict anything or have any known fundamental principles is that it is just a wrong idea. He’s so discouraged about string theory that he has stopped working on it himself for the last fifteen years, but doesn’t have the energy or optimism to envisage any alternatives. He ends his talk with some real downers, one of which he calls the “LHC nightmare”, that the LHC will just see a single new scalar particle and nothing else. The second nightmare is that observations of the CMB will never see anything that tells us more about the early universe, just a 1/f spectrum, no evidence of the effects of gravitational waves.

All in all Weinberg ended up not giving a very optimistic view of the “Future of Physics”, but something closer to John Horgan’s argument about the “End of Physics”.

Tomorrow there will be a panel on “Field Theory and Mathematics” which should be interesting. Also, Witten will be talking on the “Future of String Theory”. It will be interesting to see if he is any more optimistic than Weinberg, and more specifically if he’ll come down on the Gross (“I hate it”) or Weinberg (“I don’t love it, but maybe it’s right”) side of the Landscape issue.

Well, my prediction of who would win this year’s Nobel prize in physics turned out to be correct. No, I didn’t have any inside information about this at all. I suppose I should mention that many of my friends will not be so impressed by this feat since they have heard me make this same prediction incorrectly every one of the last 15 years or so. Sooner or later I had to be right, and it was dumb luck that it happened the first year I had a public forum in which to make this prediction.

Congratulations to Gross, Politzer and Wilczek!

Last week I was in a bookstore and ran across a new book by Emanuel Derman called My Life as a Quant: Reflections on Physics and Finance. Derman got a particle theory Ph. D. here at Columbia in 1973 when he was one of Norman Christ’s first students. He then went on to post-docs at Penn, Oxford and Rockefeller and a tenure track job at Boulder. By 1980 he had decided he didn’t want to stay in Boulder, partly because his wife couldn’t get a job there, so he left academia for a job at Bell Labs.

In 1985 he went to work in the financial industry at Goldman Sachs, staying there until 2002, interrupted by a one-year stint at Salomon. He’s now back at Columbia, teaching in the Financial Engineering program run by the IEOR (Industrial Engineering and Operations Research) department of the Engineering school. This kind of master’s program is extremely popular; besides IEOR, the math and stat departments collaborate on a separate MA program in the Mathematics of Finance which has been wildly successful. Each year we get more and better applicants, and they seem to do very well on the job market when they get out.

The first half of Derman’s book gives a good view of what it was like to be a theorist of the phenomenological variety during the seventies and early eighties. The second half has a nice description of the mathematical problems involved in pricing options and mortgage-backed securities, as well as many comments on what it is like to work in the financial industry. He was one of the earliest particle theorists to do this, but many others have followed him there in recent years, some of whom are regular commenters here.