Not Even Wrong

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.

Various things from the past couple days related to Susskind, the Landscape, and his book The Cosmic Landscape:

The paper Computational Complexity of the Landscape I by Frederik Denef and Michael Douglas is out. They show that even in simplified models of string theory vacua the problem of finding a model with CC in the anthropically determined range is NP-hard. This strongly indicates that in practice you can’t ever do what landscapeologists have optimistically hoped might be possible: pick out those vacua with anthropically acceptable values of the CC, and somehow use them to make predictions. Denef and Douglas end by bringing up a peculiar possibility: what if direct evidence for string theory is found (they’re kind of vague on how this going to happen…), but the problem of actually identifying our vacuum state remains intractable?

This raises the possibility that we might someday convince ourselves that string theory contains candidate vacua which could describe our universe, but that we will never be able to explicitly characterize them.

Lubos has a posting about this, including an exchange of comments with Frederik. On the whole I tend to see eye to eye with Lubos about the Landscape, although not here, where he’s frantically trying to dismiss the Denef-Douglas results, which look pretty solid to me.

The Philadelphia Enquirer has an editorial entitled A scientific leap, but without the faith, by Amanda Gefter, who did the recent interview with Susskind in New Scientist. Gefter tries to argue that string theory, unlike intelligent design, is science despite not being falsifiable. I don’t have the time or energy here to do justice to her argument or the problems I have with it (for one thing, she thinks string theory is breathtakingly beautiful). Science and Theology News has an article about the Gefter editorial called Intelligent design versus string theory which kind of misses the point, claiming that string theory can be falsified.

This month’s American Scientist has a review of Susskind’s book by cosmologist John Peacock entitled A Universe Tuned for Life . The review is pretty much uncritical, and mainly happy that Susskind is anti-religion:

These obligatory small criticisms should in no way detract from Susskind’s tremendous achievement. This book is a fine piece of popular science writing, but it is particularly significant for the timeliness of its message. Susskind emphasizes that the whole structure of the universe requires an active Creator no more than does the human eye or the temperature of the Earth. At a time when more and more people seem happy with a creation that took place 6,009 years ago, this lesson needs repeating.

Peacock actually feels that Susskind doesn’t go far enough in trashing the 20th century idea that there is some simple, compelling physical theory that explains the way the world works:

But if life on Earth is a random accident in a universe where only chance yielded laws of physics suitable for life, why stop there? Perhaps string theory itself is nothing special and only part of a wider spectrum of possible prescriptions for reality. If the search for a unique and inevitable explanation of Nature has proved illusory at every step, is it really plausible that suddenly string theory can make everything right at the last? Reading Susskind’s book should make you doubt that possibility, in which case we may have reached the end of the search for underlying simplicity that has driven physics since the beginning.

Finally, last night’s new papers on the arXiv included the surprising inclusion of one on Emergent Gravity by Jack Sarfatti. Famously, supposedly Sarfatti had been banned from publishing on the arXiv, but now I guess the arXiv has changed it standards. I still haven’t heard from them about why they’re banning trackbacks to this site, but perhaps there’s an explanation as to why they have finally found a paper by Sarfatti acceptable. It includes exactly two references, one to a 1976 paper about defects in condensed matter physics, the second to, you guessed it, Susskind’s The Cosmic Landscape.

Update: Chris W. correctly points out that I mistakenly had Gefter referring to string theory as “strikingly beautiful”, when it was general relativity she was referring to in this context.

Update: As a commenter pointed out, there’s a long, uninformed discussion of string theory and intelligent design over at The Panda’s Thumb. Many of the people commenting over there seem to believe that string theory is testable, and even invoke the latest SLAC story. Please don’t bring that particular discussion over here now. If you’re in the mood, contribute over there. Unfortunately I don’t have the time or energy at the moment…

There’s a beautiful survey paper about elliptic cohomology that Jacob Lurie, an AIM 5-year fellow in the math department at Harvard, has recently put on his home page. This paper has been discussed a bit already by David Corfield and by Urs Schrieber.

I don’t have time right now to try and write up something comprehensible about those parts of the elliptic cohomology story that I kind of understand, and in any case I want to spend more time reading Lurie’s paper. It brings into the elliptic cohomology story several of my favorite pieces of mathematics (Atiyah-Segal completion, Freed-Hopkins-Teleman), in a way that I don’t yet understand. But in any case there’s a lot of very beautiful and very new mathematics in this paper, mathematics that has tantalizing relations to quantum field theory.

The SLAC web-site today has a feature article entitled SLAC Physicists Develop Test For String Theory*. The “*” refers to a footnote to the title saying “Under Certain Conditions”. This is about the 10⁵⁰⁰th news story making this kind of announcement that has appeared over the past twenty years (like this recent one), and the title is just as incorrect and misleading as all the others.

The story starts with

String theory solves many of the questions wracking the minds of physicists, but until recently it had one major flaw — it could not be tested. SLAC scientists have found a way to test this revolutionary theory, which posits that there are 10 or 11 dimensions in our universe.

and is about a paper by JoAnne Hewett, Ben Lillie and Thomas Rizzo entitled Black holes in many dimensions at the LHC: testing critical string theory. This paper is perfectly reasonable, discussing a proposal for getting information about the number of extra dimensions, assuming Tev-scale gravity (a huge assumption most people think unlikely) and thus production of black holes at the LHC. If the number of extra dimensions is bigger than 6, then 10d superstring theory is ruled out (one can make similar comments about 11d M-theory, whatever that is).

Like all news articles of this kind, this one is misleading in the extreme, since “SLAC Physicists Develop Test For String Theory” is likely to make the unwary think that string theory is now testable. In addition, it’s flat out wrong, since the writer made the critical decision to replace “critical string theory” by “string theory”. Granting the unlikely assumption that the LHC sees extra dimensions and measures their number. if this turns out to be more than 6 or 7, string theorists will likely just point out that it is only “critical” string theory which lives in 10 dimensions. In recent years there has been much talk about string theories outside the critical dimension. For some discussion of this, see the comment thread of a recent Cosmic Variance posting, where string theorists Eva Silverstein and Clifford Johnson maintain that they see reasons to believe in the existence of string theories in dimensions other than 10. For some flavor of the discussion, here’s what Clifford has to say:

…the “person on the street” all too often hears (or implicitly gathers from posts like this) the phrase “string theory requires D=10/11″, and it is simply not true and in some years we may well have to be spending a lot of time undoing yet another uncautious claim when/if after doing phenomenology better we find that we don’t need to start in higher D and then “compactify”. We’ll have to go around telling everyone (on the tv shows and radio shows and magazines) “oh…that thing we said about extra dimensions? We were just kidding”…. Just like we’re doing now with the whole “unique vacuum” and “theory of everything” phrases…

Clifford seems fond of the idea of sub-critical strings, perhaps even strings in four dimensions (another enthusiast of this idea is Warren Siegel), while Stanford string theorist Silverstein advocates the study of super-critical strings, exactly the ones that would get around the “test” promoted today by her colleagues at SLAC.

Update: SLAC has replaced this article on their website with a new, much more accurate version, entitled “SLAC Physicists Develop Framework-Dependant Test For Critical String Theory”. The original version got wide distribution, even appearing on Slashdot.