Not Even Wrong

I was out in Stony Brook for the past couple days, to attend festivities surrounding the inauguration of the new building there which will house the Simons Center for Geometry and Physics. The Center is funded by Jim Simons, whose Renaissance Technologies is one of the world’s most successful hedge funds. The plan is to ultimately have six permanent members (half in physics, half in math) and a director, as well as quite a few postdocs and visitors. The founding director of the center is John Morgan, who until recently was my colleague here in the math department at Columbia. Mike Douglas is a permanent member in physics, current and recent senior visitors include Nikita Nekrasov and Graeme Segal.

The building is quite attractive, with the two lower floors forming a public area that includes two auditoriums, an atrium and a dining area which will serve lunch and bring together the local math and physics communities. The three upper floors have offices and seminar rooms. Construction is nearly finished, but not quite, with part of the ground floor still walled off for some last-minute work. The atrium features a large mural containing a selection of historically important equations, the choice of which evidently was a major undertaking. Guests noted one typo, but luckily the current mural is a temporary printed one, with the plan to cut the equations in stone not yet implemented.

Tuesday night featured a gala opening event, with music provided by the Emerson quartet, and short speeches from various dignitaries. Simons was presented with an original edition of one of the works of Isaac Newton, with the comment that he had shown much greater success than Newton at turning things into gold. He gave a wonderful talk describing the early stages of interaction between math and physics that he was involved in as chair of the math department at Stony Brook in the early seventies. Evidently soon after his arrival he was invited to meet with Frank Yang, who had just started up an institute for theoretical physics there. Yang described his current research on gauge theory, which Simons claims to not have understood a word of. The same thing happened again a year later. However, the third time this happened, Simons all of a sudden realized that what Yang was talking about was something that geometers knew very well: a connection in a principal bundle. This led to a series of lunch-time lectures by Simons to the physicists, to visitor Is Singer getting interested and taking what he learned back to MIT and Atiyah at Oxford, and finally to the modern period of interaction between math and physics that began in the mid-seventies centered around questions related to instantons.

On Wednesday, the Simons Center hosted a day-long inaugural conference (videos and slides of talks should appear on their web-site at some point). Appropriately, the first talk was an inspirational one from Michael Atiyah, going over a wide variety of different mathematical ideas. One theme was the quaternions, with Atiyah pointing out that Hamilton had written down a square-root of the Laplacian many decades before this trick was re-discovered by Dirac in writing down the Dirac equation. After recalling the relation between the division algebras (real and complex numbers, quaternions, octonions) and the Hopf invariant one problem, Atiyah suggested that the Freudenthal magic square has a similar relationship to the Kervaire invariant one problem, with the recent complicated proof by Hopkins et al. an analog of the original Adams proof in the Hopf case, with the analog of Atiyah’s “postcard proof” still to be discovered. He ended with some comments about ideas of Alain Connes about non-commutative geometry and the Riemann hypothesis, and suggested that the conjectured self-adjoint operator that could explain the Riemann hypothesis might be the Hamiltonian of quantum gravity. I noticed that Atiyah was supposed to be giving a talk at the IAS today with the impressive title of “Quantum Gravity and the Riemann Hypothesis”, but it appears to have been canceled.

The second morning talk was a rather rambling and elementary one by Polyakov about topics related to Wick rotation, ending with the claim that in the gravitational case the usual ideas about Wick rotation fail and this has something to do with explaining the cosmological constant. The afternoon began with a talk by my colleague Andrei Okounkov using symplectic resolutions to study quantum cohomology, followed by Witten whose topic was “A New Look at Khovanov Homology”. This talk covered similar material to the ones described here, involving a really beautiful story about various 3 and 4 dimensional topological quantum field theories. As in the earlier talks though, at the end there’s a transition to 5 and 6 dimensional theories where I got just as lost as before. I had been hoping that the Simons Center talk would explain the ideas I was missing, but I fear that there’s no way around digging into the details in Witten’s recent paper about this. The last talk was by Cumrun Vafa, who gave a very nice and elementary discussion of the “wall-crossing” phenomena in certain 2d qfts, as motivation for recent work on wall-crossing in 4d gauge theories.

The talks were uniformly of very high quality, it’s wonderful to see that the Simons Center is off to a great start.

Update: I just did take another look at Witten’s recent paper, and realized that the part involving 5 and 6 dimensional theories is not there, but in a paper in progress on “Five-branes and Knots”. So, that story will just have to wait for now…

SLAC’s SPIRES database has a link you can use to search for articles heavily cited during 2009 and 2010. Just looking at the hep-th papers, three are review articles of older work on applying AdS/CFT to condensed matter physics, three are about Erik Verlinde’s claims that gravity is an “entropic force”, and the rest are about Petr Horava’s non-relativistic theory of quantum gravity.

The story of hep-th in 2009/10 seems to be that the only new ideas getting attention are ones coming from prominent string theorists who have become apostates advocating non-string theory approaches to quantum gravity. The idea of getting gravity out of simple thermodynamics didn’t get much attention back in 1995 when Ted Jacobson was discussing it, partly because it didn’t seem to go anywhere, partly because the conventional wisdom was that the spin-two massless mode of a string was the reason for gravity. Now that, fifteen years later, a prominent string theorist is promoting the idea (see his recent Harvard colloquium on the topic here), it is getting a lot of attention.

Those abandoning string theory as an explanation for quantum gravity do need to be careful in how they describe what they are doing; see for example the first part of the most heavily cited hep-th paper of 2009 (Horava’s), which begins as follows:

In recent decades, string theory has become the dominant paradigm for addressing questions of quantum gravity. There are many indications suggesting that string theory is sufficiently rich to contain the answers to many puzzles, such as the information paradox or the statistical interpretation of black hole entropy. Yet, string theory is also a rather large theory, possibly with a huge landscape of vacua, each of which leads to a scenario for the history of the universe which may or may not resemble ours. Given this richness of string theory, it might even be logical to adopt the perspective in which string theory is not a candidate for a unique theory of the universe, but represents instead a natural extension and logical completion of quantum field theory. In this picture, string theory would be viewed—just as quantum field theory—as a powerful technological framework, and not as a single theory.

If string theory is such an apparently vast structure, it seems natural to ask whether quantum gravitational phenomena in 3 +1 spacetime dimensions can be studied in a self-contained manner in a ‘‘smaller’’ framework. A useful example of such a phenomenon is given by Yang-Mills gauge theories in 3 + 1 dimensions. While string theory is clearly a powerful technique for studying properties of Yang-Mills theories, their embedding into string theory is not required for their completeness: In 3 + 1 dimensions, they are UV complete in the framework of quantum field theory.

In analogy with Yang-Mills, we are motivated to look for a ‘‘small’’ theory of quantum gravity in 3 + 1 dimensions, decoupled from strings.

Update: A commenter points out that Verlinde has just received a 2 million euro grant to support this kind of research, more info available here.

Earlier this year the Bogdanov brothers published Le Visage de Dieu, yet another book dealing with their ideas about the big-bang and pre-big-bang physics. This follows their earlier Avant le Big Bang, and L’équation Bogdanov : Le secret de l’origine de l’Univers? a book that they somehow got Lubos Motl to take credit for. I haven’t seen the new book, but it seems that it takes off from George Smoot’s comment that looking at the CMB was like “seeing the face of God.” Somehow the brothers have managed to get well-known cosmologists Robert Wilson, Jim Peebles and John Mather to contribute pieces to the book.

In other Bogdanov news, I hear from a Paris correspondent that an interesting document has recently come to light, a report commissioned by the CNRS after the Bogdanov Affair made headlines back in 2002. For press coverage of this, see here, here, here. The CNRS critique, from November 2003 is detailed, harsh and devastating. For instance, about Igor Bogdanov’s thesis (which ended up being published in multiple copies in several respectable journals, including the highly thought of Classical and Quantum Gravity), the conclusion is “la valeur de ce travail est nulle”, this work is of no value.

Update: For another informative article about the Bogdanovs, from this summer, see here.

Back in 2005 an illustrious group was organized to produce a report addressing the state of science and technology in the United States, resulting in what became known as the “Gathering Storm” report since it was entitled Rising Above the Gathering Storm. This report recommended that various steps should be taken to increase the number of science Ph.D.s produced in the US and going into the US labor market (while noting that there was no evidence of a shortage of such Ph.D.s).

Last month the group was back, now claiming that the gathering storm has become a hurricane of nearly category 5 intensity, with a new report entitled Rising Above the Gathering Storm, Revisited: Rapidly Approaching Category 5. Yesterday they appeared before the House Science and Technology Committee. In an analysis of what happened to their recommendations, they noted that the call for more Ph.D.s had been effective, with the NSF spending $475 million on graduate student funding during FY 2009-2010. As for the effect of this on their goal of more well-paid jobs for Americans, here’s what they had to say:

A paradox exists in the debate over whether there is a shortage of scientists and engineers or whether there are too many scientists and engineers for the jobs that are available. Most business leaders maintain the former; however, with regard to the more “conventional” functions of these fields it may well be that de facto there can no longer be domestic shortages of scientists and engineers. Firms facing this proposition are simply moving work elsewhere. Similarly, the observation that many scientists and engineers elect to pursue careers in other fields is in many instances simply reflective of the value placed on education in these disciplines by business, law, and medical schools and related employers and should not necessarily be decried. However, if the sole purpose of a PhD in science is considered to be to prepare future educators in science, then a surplus of scientists (often evidenced as a surplus of Post-Doctorate researchers) seems inevitable. The Gathering Storm recommendations are based upon the premise that federal investment in research must be doubled (the report’s second highest priority recommendation)—in which case there will be commensurate increases in demand for researchers . . . and not solely for the purpose of providing educators.

It seems that the idea is that while there’s no Ph.D. shortage at the moment, the Congress will double funding for scientific research over the next few years, so just maybe there could be a shortage in the future and this must be addressed right now.

As for the “paradox” that business leaders see a shortage of the kind of trained scientists and engineers they would like to hire at the wages they would like to pay, it appears to be the same paradoxical shortage I regularly encounter of first-class plane tickets to Paris available at the price I would like to pay for them.

In the real world, the latest Notices of the AMS has data showing the number of mathematics graduate students increasing from 10,883 in fall 2008 to 11,268 last fall. The situation graduating students face is described as:

The job market for doctoral mathematicians took a decided turn for the worse during the 2008-2009 hiring season. For all mathematics departments combined, the number of full-time positions under recruitment during 2008-2009 for employment beginning in fall 2009 decreased 27%, dropping to 1,464 from 2,012 reported last year. This is smallest number of such positions reported since 1997 when it was 1,246. The number of tenured/tenure-track positions under recruitment during this period was 930, down 23% from the previous year’s figure of 1,213. The number of full-time positions filled was 1,274, with 710 of these tenured/tenure-track positions. These figures are down 30% and 27%, respectively, from the figures reported for the 2007-2008 hiring season.

For all mathematics departments combined, the number of new doctoral recipients hired for positions beginning in fall 2009 was down 13% from the previous year’s number, to 656. Likewise, there was a decrease in the number of new doctoral recipients obtaining tenure-track positions for fall 2009 with 301 such hirings reported compared to 378 reported for fall 2008.

Yet another random collection of topics of possible interest:

Commenter Shantanu points to this video of a recent colloquium by Andy Strominger at Harvard, which includes some extensive comments on the current state of string theory. Strominger is one of the most prominent string theorists in the business, and has been working in the field for more than a quarter-century since the first “Superstring Revolution” of 1984. In the talk (at about the 52 minute point), Strominger gives a “report card” for string theory, where he assigns it 3 As, 2 Bs, 3 Ds and 2 Fs, for an average grade of about C. It gets an F for making no unambiguous testable predictions, a D for prospects of saying anything about LHC, an F for the CC (Strominger isn’t sold on the anthropic landscape) and a D for cosmology. Some of the high grades are debatable, with an audience member pointing out to him that there was a tension between his A for “Not being ruled out as theory of nature” and F for no testable predictions. Strominger repeatedly claimed that most string theorists would agree with him on these grades (except maybe the F for the CC).

As an overall evaluation, he said that it was debatable whether this was a passing or failing report card, then arguing:

But this is the only student in class, so if you flunk her you have to shut the school down.

Along the same lines, a bit earlier in the talk one of his slides characterizes all that theorists can do as “go home and watch TV” if they believe in the landscape (“String theory is everything”) or if they think string theory is a failure (“String theory is nothing”). The positive argument he was trying to make is that there still is something for string theorists to do even after they are forced to give up on particle physics: they can try applying AdS/CFT and black holes to other areas of physics (nuclear physics, solid state physics, fluid mechanics).

I think Strominger is right that his grades and point of view about string theory are now conventional wisdom among leading theorists. What I find striking about this is the argument that if you are forced to give up on string theory, you have to “shut the school down” or “go home and watch TV”. More than 25 years of working on string theory has left Strominger and others somehow believing that there is no conceivable alternative. The failure of string theory as a theory of particle physics leads them to the conclusion that they must not abandon string theory, but instead must abandon particle physics and try and apply string theory to other fields. The obvious conclusion that string theory is just one speculative idea, and that its failure just means you have to try others, is one that they still do not seem willing to face up to.

One thing I’ve learned in life is that human beings are creatures very much obsessed with social hierarchy, and academics are even more obsessed with this than most people. So, any public rankings that involve oneself and the institutions one is part of tend to have a lot of influence. In the US, US News and World Report each year ranks the “Best Colleges”, see the rankings for National Universities here. My university’s administration tended in the past to express skepticism about the value of this ranking, which typically put us tied for 8/9 or 8/9/10. This year however, everyone here agrees that there has been a dramatic improvement in methodology, since we’re at number 4.

For most academics though, the real ranking that matters is not that of how good a job one’s institution does in training undergraduates, but the ranking of the quality of research in one’s academic field. Where one’s department fits in this hierarchy is crucial, affecting one’s ability to get grants, how good one’s students are and whether they can get jobs, even one’s salary. The gold standard has been the National Research Council rankings, which were supposed to be revised about every ten years. It turns out though that the task of making these ranking has somehow become far more complex and difficult, with more than fifteen years elapsing since the last rankings in 1995. Since 2005 there has been a large and well-funded project to generate new rankings, with release date that keeps getting pushed back. Finally, last year a 200 page book was released entitled A Guide to the Methodology of the National Research Council Assessment of Doctorate Programs, but still no rankings.

Recently the announcement was made that all will be revealed tomorrow at a press conference to be held in Washington at 1pm EDT. I hear rumors that university administrations have been privately given some of the numbers in advance, to allow the preparation of appropriate press releases (see here for an example of a university web-site devoted to this issue).

The data being used was gathered back in 2005-2006, and the five intervening years of processing mean that it is rather stale, since many departments have gained or lost academic stars and changed a lot during these years. So, no matter what happens, a good excuse for ignoring the results will be at hand.

Update: University administrations have now had the data for a week or so and are providing it to people at their institutions. For an example of this, see the web-site Berkeley set up here. All you need is a login and password….

Update: (Via Dave Bacon) Based on the confidential data provided to them last week, the University of Washington Computer Science and Engineering department has released a statement characterizing this data as having “significant flaws”, and noting that:

The University of Washington reported these issues to NRC when the pre-release data was made available, and asked NRC to make corrections prior to public release. NRC declined to do so. We and others have detected and reported many other anomalies and inaccuracies in the data during the pre-release week.

The widespread availability of the badly flawed pre-release data within the academic community, and NRC’s apparent resolve to move forward with the public release of this badly flawed data, have caused us and others to urge caution – hence this statement. Garbage In, Garbage Out – this assessment is based on clearly erroneous data. For our program – and surely for many others – the results are meaningless.

The UW Dean of the College of Engineering has a statement here where he claims that, despite 5 years of massaging, the NRC data contained obvious nonsense, such as the statistic that 0% of their graduating CS Ph.D. students had plans for academic employment during 2001-5.

Update: Boston University has broken the embargo with this press release. They give a chart showing that almost all their graduate programs have dramatically improved their ranking since the 1995 rankings, while noting that the two rankings are based on different criteria, the NRC says you can’t compare them, and the 2010 rankings in the chart are not NRC numbers, but are based on their massaging of the data. I suspect that the NRC data will be used to show that, like the kids in Lake Wobegon, all programs are above average.

For more on this story, see coverage by Steinn Sigurdsson at Dynamics of Cats.

Update: The NRC data is out, and available from its web-site. But, no one really cares about that, all they care about are the rankings, and the NRC is not directly putting those out. Instead, they’ve subcontracted the dirty work to phds.org, where you can get rankings here, using either the “regression-based” or “survey-based” score. In mathematics and physics, the lists you get are about what one would expect, with perhaps somewhat of a tilt towards large state schools compared to the 1995 rankings (most dramatically, Penn State was number 36 in 1995, number 8 or 9 this year).