Not Even Wrong

Harvard mathematician Barry Mazur has many new things up on his web-site. These include an expository article on motives (this via David Corfield), and a foreword to a forthcoming popular book called Fearless Symmetry : Exposing the Hidden Patterns of Numbers. This book looks to be the first popular book to deal with the modern use of group representations in number theory, explaining what reciprocity laws are and a bit about the Langlands program.

The concept of a motive and that of using representations of Galois groups constructed using things like motives are two of the most important ideas in modern number theory. Some of the latest developments in this field concern extensions of the Langlands program involving p-adic modular forms. Mazur and Buzzard are teaching courses on this topic, and Mazur has put some lecture notes up on his course web-site. These courses are part of a special semester on Eigenvarieties at Harvard.

Mazur also has a revised version of his expository piece on category theory, a short piece about Serge Lang, and some very non-basic notes for a “Basic Notions” seminar.

Nature has a short article entitled Physicists told to confront those big questions about the Foundational Questions Institute call for proposals. There’s a very positive quote about this from Lee Smolin, who is on the advisory board, but also a much more skeptical one from Paul Steinhardt: “Metaphysics is running rampant through string theory and cosmology,” he says. “I would like to see things go a little bit in the other direction.”

Kimball Martin’s web-site of Exceptional MathReviews includes one by Robert Oeckl about a paper of the Bogdanovs. For more about them see here, here, here, and here. Remarkably, they seem to have some support from at least one string theorist.

Via Bitch Ph.D., perhaps the strangest math-related web-site I’ve ever seen.

The High Energy Physics Advisory Panel (HEPAP) is meeting today and tomorrow in Washington. Presentations there will include one from Bush’s science advisor, John Marburger, and should be available on-line soon.

This weekend, the Mathematical Sciences Research Institute (MSRI) will be dedicating its new building, named after Shiing-Shen Chern. As part of the festivities, Roger Penrose will be giving talks, including a public lecture Sunday on Fashion, Faith and Fantasy in modern theoretical physics.

The second LHC Olympics were recently held at CERN and the talks are available on-line. This is a rather unusual exercise designed to get string theorists and other not-so-hardcore phenomenologists involved in analyzing simulated LHC data. There seem to me to be two big problems with this. First of all, there are no backgrounds in this simulated data, and understanding these backgrounds is going to be the main problem with the LHC data for quite a while. It will be the experimenters who will have to do this, and they may need help from theorists, but help of a very different nature than what this exercise is aiming at. Secondly, once backgrounds are understood and potential signals are extracted, I doubt that the LHC experimenters will be releasing the kind of data simulated here for use by theorists. I suspect they’ll be doing the kind of analysis going on at the LHC Olympics themselves and releasing the results as papers under their own names. For more about this, see postings by Lubos here and here. The first of these drew the following comment from a European phenomenologist:

Phenomenology has been always been strong in Europe, hundreds of ppl work in this field since decades, and most consider this contest as child’s play. Guess why no European team took part in this activity, right within a truly European institution which has scores of local phenomenologists? It is a bit like if a few phenomenologists decide to learn string theory and organize a contest in Princeton about who can build the best string model….

While this exercise is unrealistic, it may at least clarify various issues about how testable certain specific scenarios really will be at the LHC.

The latest Seed Magazine has some interesting articles. One about mathematical proof discusses problems with proofs in mathematics that may be too complicated to be properly refereed, especially the recent work by Thomas Hales on the Kepler conjecture. It ends with a depressingly silly comment by Keith Devlin:

I see a parallel between the uncertainty of these proofs and developments in physics like string theory, where we’re developing mathematical theories of matter that may forever remain elusive to experimental verification.

This is the same kind of foolishness as the comment that “physicists may have to rethink what it means for a theory to explain experimental data” because of string theory (see here).

Another Seed article that has gotten a lot of attention because of it’s topic is one called Getting Physical about physicists and sex. See commentary here, here and here. This last link is to Jennifer Ouellette’s new blog Cocktail Party Physics, which is of independent interest.

Michael Douglas has written up his talk at the recent Solvay conference, with the title Understanding the Landscape. For previous postings about this conference, see here, here, and here.

Douglas’s article is mainly a series of excuses for why string theory can’t predict anything. He begins with an historical analogy, comparing the present state of string theory to that of quantum mechanics in the period 1913-1926, and the Bohr model of the hydrogen atom to N=4 supersymmetric YM and AdS/CFT. This kind of analogy has some rather obvious problems: it took 13 years to get from the Bohr model to the complete theory of QM, whereas the idea of string unification has been around for about 30 years, with not the slightest sign of success. More importantly, the Bohr model of the hydrogen atom gave a fairly accurate prediction of the spectrum of the hydrogen atom, so it was clear that there was something very right about it. On the other hand, N=4 supersymmetry YM doesn’t predict anything that corresponds to the real world. In a footnote, Douglas writes:

A similar analogy was made by David Gross in talks given around 2000. However, to judge from his talk here, he now has serious reservations about it.

but I’m not sure what reservations of Gross this refers to.

Douglas’s second analogy is a “chemical” analogy, basically pointing to the fact that deriving bulk properties of solids from the underlying many-particle Schrodinger equation is difficult if not impossible. Again, this isn’t a very good analogy. The problem isn’t that you have a simple theory whose ground state is hard to identify because of the numbers of degrees of freedom, like in condensed matter physics. The problem instead is that the ground state of the superstring doesn’t look like the real world. Douglas describes the current situation as:

Perhaps all this is a nightmare from which we will awake, the history of Kekule’s dream being repeated as farce.

He goes on to give the standard argument for the landscape, referring to it by the novel name of the Weinberg-Banks-Abbott-Brown-Teitelboim-Bousso-Polchinski et. al. solution to the cosmological constant problem, but notes that:

On further developing these analogies, one realizes that we do not know even the most basic organizing principles of the stringy landscape.

and proceeds to discuss a little bit two topics that he hopes might be related to this problem, but I don’t see any evidence for this. One topic is an abstract proposal for a metric on the “space of all CFTs”, the other is the classification of D-branes on a Calabi-Yau in terms of a derived category.

He goes on to discuss his recent work with Denef on computational complexity, which indicates that even if our universe corresponds to some local minimum in the landscape, there is no hope of ever identifying which one it is and actually computing anything about the real world. In his concluding section, he admits that there is no evidence of any simple structure in the landscape, and argues that maybe this is just the way the world is:

Still, our role as physicists is not to hope that one or the other picture turns out to be more correct, but to find the evidence from experiment and theory which will show us which if any of our present ideas are correct.

The problem with his invocation of the role of experimental evidence is that he has just finished making an excellent case that there is no hope at all of ever getting any such evidence for string theory. He seems to have completely abandoned without comment his project of the last few years of counting vacua in hopes of making statistical predictions, and is left with not a single idea about how one can ever hope to get a prediction of any kind out of this framework. In this kind of circumstance, standard scientific practice is to acknowledge that this is a failed project and go on to something else. Douglas not only refuses to acknowledge the failure of string theory, he doesn’t anywhere even mention the possibililty that the underlying idea might be wrong.

Yesterday’s hep-th preprints included another landscape one, Probabilities in the Landscape by Alexander Vilenkin. Vilenkin shows no more evidence of having a viable way of ever making a physical prediction than does Douglas, but like Douglas invokes experimental confirmation at the end of his paper, then closes with one prediction that is sure to be accurate:

It seems safe to predict that we will hear more on this subject in the future.

For some more entertaining reading, take a look at A Comment on Emergent Gravity by Waldyr A. Rodrigues Jr. Rodrigues says that he gave as an exercise to his students to find the errors in Jack Sarfatti’s recent arXiv posting Emergent Gravity. Sarfatti had been blocked for many years from posting on the arXiv, but the arXiv moderators recently relented, perhaps because this paper includes a section at the end about the landscape. Susskind’s recent book is one of only two references in the paper. Sarfatti’s paper has gone through six drafts, three of which are on the arXiv, and the latest of which incorporates some of the objections from Rodrigues. Rodrigues however concludes his paper thus:

Sarfatti’s paper we regret to say, is unfortunately a potpourri of nonsense Mathematics. The fact that he found endorsers which permitted him to put his article in the arXiv is a preoccupying fact. Indeed, the incident shows that endorsers did not pay attention to what they read, or worse, that there are a lot of people with almost null mathematical knowledge publishing Physics papers replete of nonsense Mathematics…

A careful reading of [Sarfatti’s paper] shows that his hypotheses are completely ad hoc assumptions, since in our view no arguments from Physics or Mathematics are given for them. Summing up, we must say that Sarfatti’s claim to have deduced Einstein’s equations as an emergent phenomena is a typical example of self delusion and wishful thinking.

Sarfatti will be giving the closing talk at the 22nd Pacific Coast Gravity Meeting, to be held this coming weekend at the KITP in Santa Barbara.

Mathematical Reviews is a publication of the American Mathematics Society that provides capsule reviews of essentially every mathematics research paper that is published. It has been in operation since 1940, and in recent years the entire database has been on-line, with the name MathSciNet. Some of the reviews are rather entertaining in one way or another, and the availability of this database has led to a new form of diversion among mathematicians: searching on promising words (e.g. “plagiarism”) to see what turns up. My colleague Kimball Martin has put together a new web-page entitled Exceptional MathReviews with links to the best reviews he has heard about.

One of the most famous such reviews turns out to be apocryphal. In the days before the searchable database, I had heard it claimed that one Math Review contained the following devastating evaluation: “This paper fills a much-needed gap in the literature.” It turns out that this isn’t actually true. For the real story and more about Math Reviews, see an article from the 1997 Notices of the AMS.

After more than three months of effort to try and get an answer about this, I’ve finally heard officially from the arXiv that trackbacks to my weblog are currently not being allowed by the moderators. I’m sending the following message protesting this to members of the arXiv advisory board.

To the arXiv advisory board:

Peter Woit
Department of Mathematics
Columbia University
212-854-2642

Update: Sean Carroll’s posting about this has finally shaken loose some indication of what argument was used to disallow links to my blog at the arXiv. For details, see the comment section of his posting.

Update: Lubos Motl has really outdone himself with his latest lunatic ranting about this blog. Note that, besides the blogs run by arXiv moderator Jacques Distler, Lubos’s is one of only a couple particle theory related blogs that the arXiv moderators allow trackbacks to. That trackbacks to this blog are censored, but allowed to Lubos’s (and almost no others not belonging to an arXiv moderator) should be more evidence than anyone needs that there is a serious problem with the arXiv moderation system, and it is due to the string fanaticism of the moderators.

The new Center for the Topology and Quantization of Moduli Spaces (CTQM) at Aarhus University wins my award for the most specialized pure mathematics institute. It will be hosting an opening symposium in a couple weeks featuring several talks that look interesting. If one is going to choose a specialized subject, this is an excellent one. Over the last couple decades the study of the moduli space of curves and of the moduli space of flat connections on a bundle over a surface has led to the discovery of many previously unsuspected relations between different parts of mathematics and between mathematics and physics. The fact that this subject is so fruitful remains somewhat of a mystery, and there is undoubtedly much more to be learned.

The National Academy of Sciences EPP 2010 committee should soon be producing a report with a 15 year plan for the future of high energy physics in the U.S. At the last meeting of the group last month Fermilab director Pier Oddone gave a presentation, focusing on opportunities in neutrino physics, strategy concerning the ILC, and the future of Fermilab.

Last week there was a conference on Particle Physics at the Verge of Discovery at Aspen. Lot of interesting talks on experimental particle physics. For an overview, see the summary talk by Paul Grannis.

The Templeton funded Foundational Questions Institute (FQXi) has announced that it will be publishing its inaugural request for proposals on Monday. This organization is led by Max Tegmark, who will be here at Columbia that day giving a physics department colloquium on From Derision Cosmology to Precision Cosmology. Unfortunately I have to be away that day and will miss the talk although I would have liked to attend it.

Steve Hsu, a physicist with a serious interest in economics, writes:

You might think science is a weighing machine, with experiments determining which theories survive and which ones perish. Healthy sciences certainly are weighing machines, and the imminence of weighing forces honesty in the voting. However, in particle physics the timescale over which voting is superseded by weighing has become decades — the length of a person’s entire scientific career. We will very likely (barring something amazing at the LHC, like the discovery of mini-black holes) have the first generation of string theorists retiring soon with absolutely no experimental tests of their *lifetime* of work. Nevertheless, some have been lavishly rewarded by the academic market for their contributions.

Scott Aaronson describes his field of computational complexity theory as “quantitative theology”, and goes on to note:

Incidentally, it’s ironic that some people derisively refer to string theory as “recreational mathematical theology.” String theory has to earn the status of mathematical theology — right now it’s merely physics! A good place for string theorists to start their theological training is this recent paper by Denef and Douglas.

Lee Smolin is giving a course on background independent quantum theories of gravity at the Perimeter Institute, with the lectures available online.

David Corfield has an interesting posting on research programs in mathematics. It includes links to various things from Ronald Brown including a new paper on Ehresmann’s work on groupoids, and his web-page on “Higher Dimensional Group Theory”. Among other things worth reading at Brown’s site is his account of the origins of Grothendieck’s “Pursuing Stacks”.

Corfield also points to an excellent list of problems in homotopy theory from Mark Hovey. Hovey starts off with the comment

The biggest problem, in my opinion, is to come up with a specific vision of where homotopy theory should go, analogous to the Weil conjectures in algebraic geometry or the Ravenel conjectures in our field in the late 70s. You can’t win the Fields Medal without a Fields Medal-winning problem; Deligne would not be DELIGNE without the Weil conjectures and Mike Hopkins would not be MIKE HOPKINS without the Ravenel conjectures.

I first met Mike Hopkins at a conference in Guanajuato around 1990, and he made a big impression on me. One thing that most impressed me (besides his joking comment that he went into topology because it was a field full of hard-drinking and living guys who got into gun-fights (this last part was a reference to Dennis Sullivan)), was the mathematical ambition he demonstrated. He said that he had up till then made his reputation proving other people’s conjectures, but now wanted to start making his own. Mike definitely followed through on this, since a sizable number of Hovey’s problems are inspired by him. His talk on elliptic cohomology in Guanajuato was a revelation, and he has over the years continued to work in that area, coming up with dramatic new ways of thinking about the subject.

Update: There is an extensive discussion of the Smolin lectures at Christine Dantas’s website.

There’s a remarkable new paper out from Shing-Tung Yau, entitled Perspectives on Geometric Analysis. Yau is probably the dominant figure in the field of Geometric Analysis in recent years, and in this paper he gives his personal perspective on the field, including many comments on its recent history, where it is now, and where he thinks it is going.

The paper begins with a dedication to Chern, and some personal history of Yau’s interactions with him. It includes an outline of the distant and recent history of geometric analysis, mainly by giving names of the mathematicians involved. There are 755 references in the reference section, listing pretty much all the papers that Yau sees as important for one reason or another. This has to be some kind of record for number of references in a paper, especially a paper whose main text is only about 50 pages long.

Yau covers an immense amount of ground, commenting on a very wide variety of topics. This is a paper aimed at those who already know quite a bit about the subject, or who are beginning to learn it and would appreciate recommendations of what they should be reading. It includes very little in the way of expository material aimed at the beginner. There is a long section on “Ricci flow” techniques, which are the topic of a lot of current research and that Yau considers to be “the most spectacular development in the last thirty years.” He also has quite a bit to say about “Calabi-Yau” manifolds and their use in physics, commenting that they provide “a good testing ground for analysis, geometry, physics, algebraic geometry, automorphic forms and number theory.”

Another expository paper also appeared on the arXiv last night, but one of a very different nature. It’s by Ravi Vakil, a young algebraic geometer at Stanford, and it is aimed at explaining how Gromov-Witten theory has been used in recent years to study the moduli space of curves. It includes a lot of expository material about the moduli space of curves, and is designed to be understandable by the non-expert.

Lubos Motl has a posting announcing that Terence Tao will be one of the 2006 Fields Medalists. The announcement of the Fields medals is officially made at the time of the International Congress of Mathematicians, which this year will be in Madrid in August. A few months before the Congress generally there are solid rumors circulating in the math community about who the winners will be. If Lubos is right (and while I don’t know his source, this agrees with earlier speculation), the blogosphere will be responsible for a much earlier spread of rumors about this than usual.

Update: Lubos’s posting just disappeared. So, maybe this rumor is not right, or maybe it is, but whoever he got it from didn’t want it spread so publicly. His posting has been replaced with the comment “I removed information about a certain medal that was far too preliminary.”

The last couple days have seen a new phenomenon, which may or may not be some sort of sign of the times. Two different papers appearing on the arXiv contain references to blog postings:

1. In last night’s Cosmological Constant Seesaw in Quantum Cosmology by Michael McGuigan, the first two references are to blog postings by Lubos Motl and Sean Carroll.

2. A revised version of a paper by Alicki et. al. appeared over the weekend. The comment section of the arXiv posting notes that the paper has been revised and expanded in response to comments about it made here and here at Dave Bacon’s blog The Quantum Pontiff (where he has a posting about this entitled Arxiv Links to Pontiff, Science at an End?).

Not clear to me what this means. Will it mean the end of science? Will SPIRES add blog entries that are referenced in papers to its database? Will they start counting blog references as well as standard citations, allowing you to search for not just “Topcite” papers, but “Topblog” ones too? Will authors of new papers start regularly getting testy e-mails from blog authors complaining that they haven’t referenced their blog postings?

This is about the sixth week in a row that the Sunday New York Times Book Review has had something about string theory or the Landscape controversy. It has become the main place in the popular press to follow this. Tomorrow’s issue contains a letter from Susskind responding to the recent review of his book by Corey Powell.

Susskind has two complaints about the review:

1. That he was not engaging in “braggadocio” by writing “as much as I would very much like to balance things by explaining the opposing side, I simply can’t find that other side” since “The comment merely reflects a fact that all parties, on both sides of the controversy, agree upon: as things stand now, there is no explanation of the fine tunings of nature other than the one discussed in my book.”

This isn’t really accurate. For fine tunings other than the CC, there are other widely accepted explanations (e.g. supersymmetry). For the CC, many people don’t believe that the anthropic string theory landscape is really an explanation, at least not a scientific one.

2. He justifiably complains that Powell accuses him of believing that we are about to discover a “final answer” to the problems of fundamental physics. He is quite right that he doesn’t actually make any such claim, and that his point of view and Powell’s don’t differ here.

Update: The Moonie-owned right-wing newspaper The Washington Times has a review of Susskind’s book. It describes the argument of the book and ends:
To religious believers, the idea that the universe is designed by a Creator to allow the existence of human life is fundamental. To Mr. Susskind and those who think like him, that idea is so unacceptable that they are willing to abandon the idea that nature follows one set of laws, the principle upon which modern science was founded.

The reviewer at least has noticed that Susskind is giving up on modern science, although he attributes this to Susskind’s unwillingness to face up to evidence for intelligent design, instead of unwillingness to face up to the failure of his pet theory.

Stephen Hawking and Thomas Hertog have a new paper out, called Populating the Landscape: A Top Down Approach. It contains his version of the anthropic landscape idea, based on his “no-boundary” idea of quantum cosmology (sometimes also referred to as the “Hartle-Hawking wavefunction”), and he refers to it as “top-down cosmology”.

Here’s part of the summary:

In a top down approach one computes amplitudes for alternative histories of the universe with final boundary conditions only. The boundary conditions act as late time constraints on the alternatives and select the subclass of histories that contribute to the amplitude of interest. This enables one to test the proposal, by searching among the conditional probabilities for predictions of future observations with probabilities near one. In top down cosmology the histories of the universe thus depend on the precise question asked, i.e. on the set of constraints that one imposes…

The top down approach we have described leads to a profoundly different view of cosmology, and the relation between cause and effect. Top down cosmology is a framework in which one essentially traces the histories backwards, from a spacelike surface at the present time. The no boundary histories of the universe thus depend on what is being observed, contrary to the usual idea that the universe has a unique, observer independent history. In some sense no boundary initial conditions represent a sum over all possible initial states. This is in sharp contrast with the bottom-up approach, where one assumes there is a single history with a well defined starting point and evolution.

and

We have also discussed the anthropic principle. This can be implemented in top down cosmology, through the specification of final boundary conditions that select histories where life emerges. Anthropic reasoning within the top down approach is reasonably well-defined, and useful to the extent that it provides a qualitative understanding for the origin of certain late time conditions that one finds are needed in top down cosmology.

I haven’t completely understood this yet, especially the author’s claims that they can use these ideas to say something about the shape of primordial fluctuation spectra, but the whole thing doesn’t sound obviously any more promising than other approaches to the anthropic landscape. Here, as usual, I agree with Lubos’s comments on this. But despite this, he seems to have removed me from his blogroll. My feelings are hurt.