Not Even Wrong

I’d recently been wondering whether the archives of the Bourbaki group would be put on-line, and today noticed that there’s a project to do so, with results available here. One can read copies of “La Tribu”, internal reports on the activities of the group, up through 1953. There are a wide variety of interesting mathematical documents, often consisting of attempts to write up one subject or another, efforts that sometimes made it into the published books, often not.

One subject that Bourbaki struggled with over the years was that of how to set out the foundations of differential geometry. My colleague Hervé Jacquet likes to tell about how Chevalley at one point made an effort to do so, with the peculiar starting point of defining things in terms of “cubes”. I wasn’t sure whether to believe him, but here it is. According to Borel, in 1957 Grothendieck presented the group with his own take on the question of manifolds:

Grothendieck lost no time and presented to the next Congress, about three months later, two drafts:

Chap. 0: Preliminaries to the book on manifolds. Categories of manifolds, 98 pages

Chap. I: Differentiable manifolds, The differential formalism, 164 pages

and warned that much more algebra would be needed, e.g., hyperalgebras. As was often the case with Grothendieck’s papers, they were at points discouragingly general, but at others rich in ideas and insights. However, it was rather clear that if we followed that route, we would be bogged down with foundations for many years, with a very uncertain outcome.

I don’t see these documents on the list, perhaps documents from the later years are still to appear.

The documents often start out with some unvarnished comments, here’s an example, from Chevalley’s report on a text about semi-simple Lie algebras:

Au moment d’écrire ces observations, je me demande si ce ramassis des méthodes les plus éculées et les plus pisseuses, ces résultats les moins généraux possibles établis de la manière la plus incompréhensible possible, ne sont pas un canular intrabourbachique monté par le rédacteur. Même s’il en est ainsi, je me laisse prendre au canular et présente les observations suivantes.

Unlike physics, mathematics has managed to remain immune from efforts to promote pseudo-scientific agendas, financed with the goal of mixing up science and religion. I don’t see any reason to believe this is going to change, but I just noticed that the Templeton foundation is funding a program here in New York later this month on the topic of Mathematics and Religion.

The program will take place at the Philoctetes Center, which is run out of a townhouse on the Upper East Side and supports a variety of activities that you can read about here. The organization ran into serious trouble with its funding recently since its investments were managed by Bernard Madoff. A year before the scandal broke, Philoctetes sponsored a panel discussion (accessible here) on The Future of the Stock Market, which featured Madoff as a panelist. Because of these losses, the Center has had to look for funding elsewhere, and has found some from the Templeton Foundation.

One notable thing about the Mathematics and Religion panel is that it doesn’t include much at all in the way of mathematicians. Of the six participants, one is Max Tegmark, a physicist prominently involved in Templeton-funded multiverse studies, but the only mathematician is Edward Nelson. Nelson is quite far from the mainstream of mathematics, with a religion-infused recent paper entitled Warning signs of a possible collapse of contemporary mathematics, available here. Unlike the case of multiverse pseudo-science, which has drawn support from leading figures in the physics community, this sort of point of view about mathematics has attracted zero interest among mathematicians.

The Mathematics and Religion panel isn’t any threat to mathematics, and is part of a larger and much more worthy program about mathematics at Philoctetes funded by Templeon. In November there will be a panel discussion on Mathematics and Beauty that sounds interesting, I might even try and make it over there to see it (last year I did attend a talk at Philoctetes given by Barry Mazur). The Mathematics and Religion panel is associated with something more serious, a talk by Loren Graham on his book Naming Infinity. It’s a book I read earlier this year, but don’t think I ever got around to writing about here on the blog. I wasn’t completely convinced by some of the claims it makes about the relation between religious practices and the work of certain Russian mathematicians. The story it tells about the religious sect of “Name Worshipers” and the history it recounts of one part of the Russian mathematical community are quite fascinating.

On Thursday on Capitol Hill, the House Subcommittee on Energy and Environment of the Committee on Science and Technology will hold a hearing with the title Investigating the Nature of Matter, Energy, Space and Time. Witnesses will be Hugh Montgomery of the Jefferson Lab, Lisa Randall of Harvard, Pier Oddone of Fermilab and Dennis Kovar from DOE. A webcast of the hearing should be available.

To brief the subcommittee, someone put together the hearing charter available here. It does a reasonably good job of explaining at a popular level what particle and nuclear physicists are working on and what problems they are trying to solve. Unfortunately the part of the document on particle physics is marred by some stale string theory hype, with the subcommittee told that:

Unification was Einstein’s great, unrealized dream, and recent advances in a branch of physics known as string theory give hope of achieving it. Most versions of string theory require at least seven extra dimensions of space beyond the three we are used to. The most advanced particle accelerators may find evidence for extra dimensions, requiring a completely new model for thinking about the structure of space and time…

Understanding the very early formation of the universe will require a breakthrough in physics, which string theory may provide.

Selling the US investment in machines like the Tevatron and the LHC as being about extra dimensions seems to me to be a mistake. Very few physicists believe it likely that this is what the LHC is going to find, and the failure to find promised extra dimensions at the LHC will not be helpful in a few years when the US particle physics community is trying to convince Congress to fund a next-generation accelerator.

The charter doesn’t explain what the LHC is really good for and why physicists are so excited about it: finally the energy-scale of electroweak symmetry breaking is being reached, with the promise of finding out what sort of physics is behind this phenomenon and responsible for mass. There’s no need for string theory hype to justify the interest and importance of this sort of very fundamental research, bringing in failed highly speculative ideas is likely to actually be counter-productive. The case for the current and planned US particle physics program is a very strong one, I hope the witnesses are able to make it clearly and forcefully to the subcommittee.

Update: The hearing is going on now, with a break for a vote. The webcast is here. The first question from Representative Vern Ehlers, a physicist, was for Lisa Randall, and he asked if there is any experimental proof or corroboration of string theory. Instead of answering the question with a straightforward “No”, and explaining that string theory makes no predictions, Randall did what she could to obfuscate the issue. She answered by going on about how, while string theory was speculative, it has led to ideas testable at accessible energies: supersymmetry and large extra dimensions. I suspect her answer left Ehlers and others still confused about the issue he was asking about. Avoiding public acknowledgment of the failure of string theory unification seems to extend even to Congressional testimony….

Update: There’s a press release here.

Update: The video webcast of the hearing is now available from the hearing web-page.

Nature this week has two stories about the Perimeter Institute. There’s a long one entitled The edge of physics, which emphasizes Perimeter’s wealth and success, starting off:

Working at the Perimeter Institute for Theoretical Physics comes with certain perquisites. Whenever recruits arrive at the Toronto airport, for example, they are met by a limousine and driven west along Canada’s Route 401 into the rich farmlands of Ontario. Eighty-five kilometres later, the limousine works its way through the streets of the town of Waterloo, and lets them out in front of a sleek building of black, green and glass squares that stands next to a pond in Waterloo Park. Stepping inside, the recruits find wall-to-wall blackboards, working fireplaces, a sauna, multiple dispensers of free coffee and the Black Hole Bistro, which serves free lunches on Wednesdays.

Neil Turok is the new director, and he plans to double the full-time faculty from 12 to 25. The institute already has more theory postdocs than anywhere else in the world (44) and is aiming for a research staff of 250, including visitors. For comparison, the Princeton IAS has 5 permanent faculty in physics and about 20 postdocs. Perimeter has an endowment of 200 million Canadian dollars, a figure they hope to double.

The same issue has a review by Joao Magueijo of Howard Burton’s book about his experience as first director of Perimeter (my own review is here). Magueijo’s take on Perimeter is rather scathing, seeing it as a “sad tale”, having sold out on its original anti-establishment concept:

The institute’s aim was to “make waves, big waves”, and it got off to a promising start. Burton — a youthful outsider who had only just finished his physics PhD went about his job with maverick flair, challenging the scientific establishment, attacking its tribalism and allergy to innovation. Here was an opportunity to do things differently: to promote originality, to flatten hierarchy and empower the young researchers actively driving the field. It sounded utopian, but it was worth a try.

Unfortunately, reality failed to comply with Burton’s plan. The best days of this haven of free-thinking came while it was still a ‘theoretical’ theoretical physics institute — before the scientists arrived. The anecdotes Burton narrates in the chapter ‘The Trouble with Physicists’ ring hilariously true. But there was also a fatal flaw in Perimeter’s concept — scientists tend to define ‘originality’ as what they personally do. Soon the institute’s quest for novelty became hijacked by the agendas of the field’s usual culprits, and Burton himself came under attack from them….

Burton tried to replicate the US establishment in Canada, but he was often outbid and exploited by opportunists who used Perimeter as a trampoline to boost their US careers.

By the time Perimeter matured, five years later, the divide between the quixotic first hires and the new wave was painfully evident. The openness of the early days was replaced by Princeton-style hush-hush and invitation-only meetings. The idealists openly confessed that they wished they could find another benefactor, to “start anew and this time do it right”. Something had gone wrong: the sought utopia had become a dystopia.

Scientific originality has become big business: being anti-establishment sounds great. Yet few want to take the risks necessary to achieve it. Originality is encouraged in public pronouncements only to be punished when practical decisions are made. Perhaps Perimeter’s tale proves that there is no recipe for original science: it happens anarchically and by accident, in spite of, rather than because of, scientific institutions.

Update: Sabine Hossenfelder, who recently spent three years at PI, has her take on the Nature articles here.

Tonight will be the premiere of a new TV series called Flashforward, based on a novel with a plot that involves the Alice detector at CERN. CERN has put up a web-site about this, to reassure people that CERN isn’t about to change time around. The web-site is along the same lines as the one they put up about Dan Brown’s Angels and Demons, to reassure people that CERN wasn’t producing quantities of antimatter that could be used in a bomb.

Dan Brown has a new novel out this week, entitled The Lost Symbol. The plot evidently revolves around a researcher in “Noetic Sciences”, who is quite the expert on “What the Bleep” pseudo-science, as well as string theory. Here’s where she learns that string theory was known to the ancients:

…I want to study cutting edge THEORETICAL physics. The future of science! I really doubt Krishna or Vyasa had much to say about superstring theory and multidimensional cosmological models.”

“You’re right, they didn’t.” Her brother paused, a smile crossing his face. “If you’re talking superstring theory …” He wandered over to the bookshelf yet again. “Then you’re talking about THIS book here.” He heaved out a colossal leather-bound book and dropped it with a crash onto the desk. “Thirteenth-century translation of the original medieval Aramaic.”

“Superstring theory in the thirteenth century ?!” Katherine wasn’t buying it. “Come on!”

Superstring theory was a brand new cosmological model. Based on the most recent scientific observations, it suggested the multidimensional universe was made up not of THREE … but rather of TEN dimensions, which all interacted of vibrating strings.

Katherine waited as her brother heaved open the book, ran through the ornately printed table of contents, and then flipped to a spot near the beginning of the book. “Read this.” He pointed to a faded page of text and diagrams.

Dutifully, Katherine studied the page. The translation was old-fashioned and very hard to read, but to her utter amazement, the text and drawings clearly outlined the EXACT same universe heralded by modern superstring theory – a ten-dimensional universe of resonating strings. As she continued, she suddenly gasped and recoiled. “My God, it even describes how six of the dimensions are entangled and act as one?!” She took a frightened step backwards. “What IS this book?”

Her brother grinned. … “The complete Zohar.”

(Thanks to Greg Sivco for the transcription).

Perhaps CERN-TH may want to put up another Dan Brown web-site at CERN to reassure people that the strings in 10d stuff has nothing much to do with reality and isn’t likely to lead to whatever trouble it leads to in the novel.

For more on this, Salon has a book review entitled Dan Brown swaps pseudohistory for pseudoscience.

Science News is running a long interview with Murray Gell-Mann, who will be celebrating his 80th birthday tomorrow. Gell-Mann was arguably (Feynman is one who would argue..) the most influential figure in theoretical particle physics throughout the 1950s and 1960s. In the interview, he gives the standard story about the cosmological constant/supersymmetry/hierarchy problem, expecting superpartners to be accessible at the LHC design energy, although perhaps not at its initial energy of 3.5 TeV/beam. If superpartners don’t show up at 7 TeV/beam, he says:

Well, we’d have to see exactly how bad it is. I mean how high up you go and still don’t find anything and so on. But yes, one might have to discard this whole line of reasoning.

Gell-Mann describes himself as not a string theorist, but someone who thought it was promising and continues to do so, claiming:

I was a sort of patron of string theory — as a conservationist I set up a nature reserve for endangered superstring theorists at Caltech, and from 1972 to 1984 a lot of the work in string theory was done there.

He speculates about what is missing in string theory as follows:

I am puzzled by what seems to me the paucity of effort to find the underlying principle of superstring theory-based unified theory. Einstein didn’t just cobble together his general relativistic theory of gravitation. Instead he found the principle, which was general relativity, general invariance under change of coordinate system. Very deep result. And all that was necessary then to write down the equation was to contact Einstein’s classmate Marcel Grossmann, who knew about Riemannian geometry and ask him what was the equation, and he gave Einstein the formula. Once you find the principle, the theory is not that far behind. And that principle is in some sense a symmetry principle always.

Well, why isn’t there more effort on the part of theorists in this field to uncover that principle? Also, back in the days when the superstring theory was thought to be connected with hadrons rather than all the particles and all the forces, back in that day the underlying theory for hadrons was thought to be capable of being formulated as a bootstrap theory, where all the hadrons were made up of one another in a self-consistent bootstrap scheme. And that’s where superstring theory originated, in that bootstrap situation. Well, why not investigate that further? Why not look further into the notion of the bootstrap and see if there is some sort of modern symmetry principle that would underlie the superstring-based theory of all the forces and all the particles. Some modern equivalent of the bootstrap idea, perhaps related to something that they call modular invariance. Whenever I talk with wonderful brilliant people who work on this stuff, I ask what don’t you look more at the bootstrap and why don’t you look more at the underlying principle. . . .

Lubos Motl seems to have calmed down a bit recently, and his latest posting is about the Gell-Mann interview. He describes Gell-Mann as not just a patron of string theory, but a holy patron of string theory, with the comments quoted above “the holy word”. They inspire him as he continues to work a few hours a day towards finding the holy grail of string theory: some fundamental principle that defines the theory non-perturbatively.

Searches for such a principle go back at least 25 years, to 1984 and the explosion of interest in string theory as a unified theory. After the first efforts to base unification on a Calabi-Yau, it soon became clear that more was needed than string perturbation theory. Just one of many such attempts that I remember was that of Friedan/Shenker in 1986, who hoped that in some sense the moduli space of all Riemann surfaces would somehow carry a unique vector bundle with flat connection. There were many others.

Lubos entered the field ten years later, after discoveries about dualities had led to Witten’s conjecture of the existence of an “M-theory” that would reduce in various limits to the known string theories. At the time, the hot candidate for such a theory was something called Matrix theory, and Lubos made his reputation with work on this. His thinking these days grows out of the “M-theory” conjecture that he first started working on as an undergraduate 13 years ago, and probably reflects well the kind of speculative hopes that drove this area of research from the beginning:

It also seems extremely likely that some UV/IR links – modeled by the modular invariance in the context of perturbative closed strings – will be important for the formulation of the ultimate principle. Non-perturbatively, it seems obvious that such a link will have to constrain the black hole microstates, i.e. the generic high-mass particle species in any theory of quantum gravity. The spectrum and detailed structure of the black hole microstates must be linked to low-energy fields and all of their higher-order interactions. These conditions will admit a limited number of solutions that will coincide with the allowed configurations of string/M-theory.

Moreover, it’s conceivable that we won’t be able to work “fully on the worldsheet” or “fully in the spacetime”. I feel that the ultimate set of consistency rules for quantum gravity will work “simultaneously” for the generalized worldvolumes as well as spacetime. So I am spending a lot of time by attempts to import some lessons – and methods to derive or generate new degrees of freedom – from spacetimes to the worldvolumes, and vice versa.

Modular invariance, mutual locality of operators, Dirac quantization rules, similar conditions, and their generalizations play an important role. But it remains to be seen whether there is a concise, ultimate principle or set of principles, why it generalizes the conformal symmetry (and modular invariance) in the perturbative limit, and why it admits old perturbative solutions as well as new, non-perturbative solutions such as the 11-dimensional vacuum of M-theory.

Of course, one of the most obvious testing grounds for such new sets of ideas is the exceptional U-duality group of M-theory on tori – i.e. the maximally supersymmetric supergravity. The exceptional groups are pretty and they must have a pretty cool explanation in terms of a structure we still don’t fully know.

Like Gell-Mann, Lubos expects the right theory to emerge not from choice of a specific set of dynamical degrees of freedom, but by a “bootstrap”: discovery of some sort of consistency conditions that uniquely pick out the right theory. The idea is that you don’t have to get to fundamental variables at the bottom of things to rest your theory on, but can by some other means “pick yourself up by your bootstraps”. Since this doesn’t work in real life, I’ve always wondered why its advocates didn’t pick a more convincing name…

Lubos ends his posting with:

I think that some kind of bootstrap is needed to determine what “M” and its structure of symmetries really is. Is there a third person in the world who cares about this possibly most important question of science? These core topics of string theory are currently understudied at least by two orders of magnitude.

The question of why so few string theorists work on this question is an interesting one. The M-theory conjecture drove string theory research for many years. My own suspicion is that the fact of the matter is that most string theorists have just given up on it. The AdS/CFT correspondence appears to give a non-perturbative definition of string theory in a particular background (in terms of a QFT), and string theorists are more interested in investigating that than in continuing the so-far futile search for “M-theory”. In addition, arguments of landscapeologists indicate that if you did find the conjectured “M-theory”, it might be a useless untestable “theory” that could explain just about anything.

Physicists with a sense of history also have another good reason to be suspicious of calls for a new “bootstrap” program. This idea was all the rage during the sixties, but ended up a dismal failure. The conjecture that some known powerful principles (analyticity, crossing, etc..) would have a unique solution satisfying them just turned out to be wrong as a way of understanding the strong interactions. There are lots of possible solutions, and finding the right theory requires identifying the correct one: an SU(3) gauge theory with a specific, very beautiful set of geometrical degrees of freedom. This theory remains poorly understood, and the project of better understanding it recently has revived some of the bootstrap ideas, but in the context of trying out a new choice of geometrical degrees of freedom (twistors). This is now the hot idea of the subject, but it’s no longer one that promises unification via string theory. I suspect Lubos will be increasingly lonely in the pursuit of the dream of his youth, as his colleagues mostly give up on it and move on.

There’s a new Bloggingheads Diavlog up today, where philosopher of science Craig Callender and I discuss the topic of Philosophy and the String Wars. Regular readers of the blog will just get to see me make the same points as usual in video format, more interesting might be to hear Craig’s point of view on some of this. We agree about the anthropic principle.

Those who follow science-blogging controversies will have heard that certain science bloggers have announced a boycott of Bloggingheads, based on the fact that two creationist/ID types had recently been allowed to participate. I heard about this after agreeing to do this latest one, and initially the idea of such a boycott sounded to me completely bizarre. Why would anyone boycott a media outlet that produces a lot of serious and interesting content on the grounds that two out of its hundreds of participants were cranks (I can’t think of ANY completely crank-free media outlet)? So, I recently read much of the on-line discussion, including that of the original boycotters, some non-boycotters (here and here), and the discussion here with Bloggingheads founder Robert Wright, who put up a clarification of the organization’s policy here. After wading through all this, I concluded that, yes, the boycott thing is completely bizarre. For one take on the question that I pretty much fully agree with, see this one by John Horgan.