The Nash Musings

Since the news of the tragic death recently of John Nash and his wife in an automobile accident last weekend, some of those who were at Princeton during the same time I was (late 70s, early 80s) have been exchanging emails of their memories of Nash from that time. It turns out that two of them, Mark Schneider and Steven Bottone, had transcribed some of Nash’s blackboard writings in a notebook. Here’s Steve’s account of this:

Back in May 1979, just after our general examination, Mark Schneider and I decided we would write down some of the writings that Nash left on the blackboards around Jadwin. Mark sat in a wheeled desk chair with a steno notebook in hand and I wheeled him from board to board as he transcribed the musings. I believe if we had done this even six months earlier we would have had a lot more interesting samples of Nash’s writings, but I think he was already starting to tail off on his output by May 1979. As far as I know, we were the only Princetonians who thought of compiling any of this. I have made a PDF out of the musings.

Since I suspect quite a few people are curious about these blackboard writings (including me, they mostly had ended by the time I got to Princeton in late 1979), Mark and Steve have allowed me to make the pdf available, see the link above. Mark points out that they didn’t actually see Nash writing these, so his authorship is an assumption. Steve notes that the handwriting was distinctive, and that the general assumption was that Nash was the author.

Update: Princeton has now made available publicly Nash’s graduate school records, see here.

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This Week’s Hype

I’m busy with other things, so no possible way I can keep up with the claims about string theory flooding the media for some reason these days. It’s hard enough to find the time to read all of this, much less write something thoughtful about it… One obvious point to make though is that none of it acknowledges the obvious: the widely promoted idea that we can get a unified theory and explain the Standard Model by using a theory of strings has turned out to be an empty one. The result of tens of thousands of papers and more than 30 years of work is that all the evidence is that if you can get something this way that looks at all like the Standard Model, you can get anything. Normally when that happens you simply acknowledge the problem and give up, but for some reason that hasn’t happened. Instead of a description of this straightforward situation, the public gets the following:

  • Frank Close describes the situation as

    In recent years, however, many physicists have developed theories of great mathematical elegance, but which are beyond the reach of empirical falsification, even in principle. The uncomfortable question that arises is whether they can still be regarded as science. Some scientists are proposing that the definition of what is “scientific” be loosened, while others fear that to do so could open the door for pseudo-scientists or charlatans to mislead the public and claim equal space for their views…

    Is physics moving towards an era in which elegance will suffice and into the domain of theories that are beyond the reach of experimental proof? Or will empirical evidence remain the arbiter of science?

    Close correctly identifies the problematic nature of multiverse pseudo-science, but misses the basic facts about the string theory landscape. This is not a theory of “great mathematical elegance”, quite the opposite, and there is no such thing developed “in recent years”. If you go back 30 years, there were then claims of “elegant” string theory models, but those never worked out. KKLT is the opposite of “elegant”.

  • Clifford Johnson takes the Close piece as a starting point to explain his own view. He lacks interest in string unification, thinks that string theory should be thought of as a “method” for solving problems. He doesn’t really explain though why it is a “method” that deserves so much more attention than any number of other methods used in physics. He also doesn’t acknowledge that, besides the huge amount of TOE hype (which he and other string theorists often appear on TV to promote), the hype problem for the string theory “method” may be just as bad. For example, he was quite proud of his efforts to promote string theory as the method to understand heavy-ion physics (see here and here), but that’s something that really hasn’t worked out very well.
  • Over at Starts With a Bang, by Sabine Hossenfelder, there’s Will the LHC be able to test String Theory: Definitely maybe. The article actually does a very good job of explaining why the answer is “no”, so I have no idea why the misleading headline. The fact that the AdS/CFT heavy ion predictions haven’t worked out is explained, with the comment that

    The LHC, thus, has already tested string theory!

    and that this failed, which might be a more accurate headline.

  • There’s a long interview with Sean Carroll at the Edge website. He’s quite defensive about the multiverse, claims it’s a prediction of our best theories, and gives his usual characterization of multiverse critics as zealots unable to understand the idea of an indirect test

    But certain zealous colleagues of mine are saying that because you can’t see the other universes in the multiverse or because you can’t see the little super strings moving around, these theories are not falsifiable and, therefore, should not count as science.

    He’s also defensive about string theory, there the argument is

    Either we will bring it down to earth and connect it to the world we see or people will lose interest. People cannot maintain this optimistic idea that we’re going to get the right theory of quantum gravity, the theory of everything, if it’s literally decades and decades of people writing down equations and never predicting the experimental outcome of anything. But we’re not there yet. It would be a terrible shame if we gave up on string theory when maybe next year someone will figure out how to bring it in connection to observations, or maybe ten years from now it will happen. This is how science works, and this is it at work.

    The problem here is that it is “literally decades and decades of people writing down equations and never predicting the experimental outcome of anything”, and no matter how many decades of this go on, someone can always argue that “maybe next year”. He’s avoiding the very real issue at the center of things: why hasn’t string theory been held to account for its failures the way any normal speculative scientific idea is supposed to?
    As far as his current interests go, from what he says, he seems to be losing interest in the multiverse, which soon may no longer be a hot topic, and moving into research into complexity and consciousness.

Posted in This Week's Hype | 22 Comments

John Nash 1928-2015

I was sorry to hear this morning that John Nash and his wife Alicia died yesterday in a car crash (news story here). They were in a taxi on the New Jersey Turnpike, heading home from the airport after a trip to Norway where Nash was awarded the Abel Prize.

Nash’s mathematical career was cut short by the onset of mental illness, which he then struggled with for many years. Sylvia Nasar’s A Beautiful Mind is a wonderful biography, doing a great job of accurately portraying Nash’s life, including the role of the mathematics community in its various parts. The movie version is another story, especially in the way it shows Nash’s mathematical achievements as somehow being due to his delusions, when what really happened is that the onset of delusional thinking is what made it no longer possible for him to continue doing research at the highest level.

During the years I was a graduate student in Princeton, Nash was often to be seen, especially in the mathematics/physics library, and I talked to him a few times. The first time was when he stopped me one day, told me he had seen my name on the physics department picture board, and was curious about the origin of my last name. While I had heard stories about Nash, that he was mentally ill, spent his time writing delusional things on the hallway blackboards, he seemed fine to me. This was a period (early 1980s) when he had stopped writing on the blackboards and was successfully dealing with the illness. I was very glad to see how later on he was able to lead a more normal life and enjoy the recognition he deserved.

Update: The New York Times has an excellent long obituary of Nash this morning, presumably mostly prepared before his death.

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Various News

  • First test collisions at 6.5 TeV/beam at the LHC are tentatively scheduled for Thursday morning.
  • At CERN today there’s a workshop about the Higgs Machine Learning Challenge.
  • Also on the topic of LHC data analysis news, Tommaso Dorigo announces the award of a grant for the AMVA4NewPhysics project.
  • Sabine Hossenfelder has a review, slideshow and discussion of the Dawid book on “String theory and the scientific method” (which I wrote about here and here).
    Much of the discussion is about the “No Alternatives” argument, but at this point I don’t even see how it applies here. The Landscape shows that string theory unification is a failed program, which rules it out. As for whether “gravitation is due to the spin two massless mode of a superstring” is the only alternative, these days my impression is that many prominent theorists are pursuing alternatives, that gravity is supposed to be an “emergent” phenomenon coming from something else.
  • For those sticking to the 1984 point of view though, there’s a workshop on some interesting mathematics that’s part of that story (super geometry, super moduli spaces) going on at the Simons Center.
  • Last week on Jeopardy (see here), no one got this question:

    Nima Arkani-Hamed is using this number dimension, the next one beyond time, to rock the physics world.

    I wouldn’t have either…

  • For a bit of mathematics history, you might want to read Beilinson on Gelfand’s seminar.
  • Natalie Wolchover at Quanta keeps on coming up with interesting physics stories not seen anywhere else, last week covering news about ultra-high energy cosmic rays.

Update: Successful test with first collisions at 13 TeV this morning at the LHC, see here.

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Lurie and Categorifying the Fourier Transform

Before I turn to the main topic of this posting, a lecture by Jacob Lurie, I’d like to point to something else involving him, a comment and posting at Mathematics Without Apologies, a blog you should be following anyway. On the topic of the usefulness of “proof assistants”, I liked Lurie’s point that a major problem with this is:

Working in a formal system, more or less by definition, means that you can’t ignore steps which are routine and focus attention on the ones that contain the fundamental ideas.

But if you want to discuss this, it should be over there, the topic of this posting is something very different.

Last week I noticed that Lurie had given a talk at Harvard on “Categorifying Fourier Theory”, which is available here. I enjoyed watching it, ending up quite intrigued by the abstract picture he was painting, but rather discouraged by the lack of any example that would give insight into what it might be useful for. Neglecting to mention the example that explains why an abstract theorem is useful is unfortunately all-too-common practice among mathematicians. Perhaps in this case with Dick Gross, Jean-Pierre Serre and John Tate in the front row, he felt it unnecessary. Luckily though, he gave the same talk recently in Arizona, and there (in the question session) did give a fascinating motivating example.

His starting point was the Fourier transform, which one can generalize to any abelian group G, and think of as identifying complex functions on G with complex functions on the dual (or character) group G^. The standard Fourier transform is the case G=G^=R, Fourier series are the case G=U(1), G^=Z. He then went on to discuss two levels of abstraction, or categorification of this. The first identifies a representation of G on a vector space V with a function from G^ to vector spaces (the isotypic decomposition of the representation). The second identifies representations of G on categories with representations of G^ on categories.

It was this equivalence of representations on categories that was his main result, for which in Arizona he gave the example of G the group of invertible Laurent series. The idea is that this group can be identified with its dual group G^ (in some sense as algebraic groups), using the Weil symbol (for a definition and context, see here). Lurie’s claim that was new to me was that the equivalence in this case is essentially the GL(1) version of the general local geometric Langlands conjecture, which is supposed to be an equivalence of two representations on categories, for more general (non-abelian) groups G.

At least for me, understanding of some sophisticated mathematical phenomenon really starts when I understand the simplest example of the phenomenon. For the number field case of Langlands theory, my initial efforts to understand the subject didn’t lead anywhere until I realized that maybe it was best to first think about the local version, which was a statement about representation theory that I could make some sense of. I was hopeful that thinking about the simplest case of that, the abelian case, would give great insight, found though that the Abelian case is already quite non-trivial (local class field theory). For the geometric Langlands case, I found that the discussion of the local version in Edward Frenkel’s book was very helpful, but I always wondered about the abelian case. Now I’m hopeful that the abelian story is something that although I’ve never seen it, is well-understood, and that a helpful reader will point me to a reference.

Another reason for being interested in this particular topic is that it has some connection to the relationship between Langlands theory and QFT that first got me interested in all of this. Back in 1987 Witten wrote some fascinating papers giving an abstract formulation of free fermion theories on Riemann surfaces (see here and here) with tantalizing connections to what later became geometric Langlands. In this work the group of invertible Laurent series and the Weil symbol play a central role. There was also later work by Takhtajan on this, see here and here. I wonder why the most recent version of the last reference deletes the material on the multiplicative group case, which is the one Lurie mentions.

Posted in Langlands | 12 Comments

Next Week’s Hype

I know I should be coming up with material on different topics here, but the multiverse stuff sometimes is just too hard to ignore.

Next week’s Comicpalooza in Houston will feature string theorist Gerald Cleaver. His blurb tells us that:

His EUCOS team conducts long-term systematic computer-based studies of global phenomenology of parameter spaces of the string landscape of around 10,500 possible string-derived universes and its theorized multiverse realization.

A local paper has a news story: Physicist to discuss multiverse theory at comic convention. According to the article:

Cleaver is a physicist and early universe cosmologist at Baylor University whose area of expertise is string theories, or the concept that there are not one but multiple universes in existence…

Cleaver said when the multiverse theory was first investigated scientifically in the 1980s, the formulas made it look like a string, hence the name, but was later revised to be more spherical or bubble-like. Some call the universes “bubbleverses” as a result….

Cleaver said there are four levels of universes with ours being in the first and most simple level. The second level has its forces and can contain that of the first. The third has its own and can contain the first two and likewise with the fourth level.

String theory remains just that – a theory. Cleaver, however, feels scientists are close to proving the theory. It could be a matter of a few days or a few years but he and others like him press on with the belief that reality is bigger and much stranger than fiction.

According to his website, besides the string landscape,

Cleaver is also interested in the general concept of multiverse, not just the string/M-derived class. In his spare time he is writing a book on philosophical and theological implications of a multiverse and has contributed related chapters in associated books…

Cleaver is also a member of the XP4 division of Icarus Interstellar, a non-profit organization created by his Ph.D. graduate Dr. Richard Obousy. Members of XP4 are exploring advanced propulsion systems and energy generation concepts for interstellar spacecraft, including possible string/M-theory realization of the Alcubierre effect.

For Cleaver’s views on theology and the multiverse, see his articles here. Last fall he gave a talk to students at Baylor explaining that

a multiverse is the likely natural mechanism through which the God of infinitudes grants inherent freedom to a spatially and/or temporally infinite creation. In other words, the multiverse is God’s means of indeterminacy in action.

Update: Keeping up with the hype is getting to be beyond my powers. Just this morning there’s:

  • The idea that “string theory allows time travel at the LHC” has been revived, reported on here, and Morgan Freeman has it on Through the Wormhole. This first appeared back in 2011, discussed here then.
    By the way, the same site has convincing evidence for time travel, reporting earlier this year that Large Hadron Collider Predecessor May Be Four Times Larger, Much More Powerful.
  • Nova has something about yet another paper describing how we’re going to observe the multiverse through bubble collisions. The paper at least admits the obvious, that if such things were observable, almost surely we would have already seen them:

    a certain amount of tuning must be applied in order to construct models that produce signatures that are possibly observable but not yet ruled out by data.

Posted in This Week's Hype | 28 Comments

Contested Boundaries

Apologies for too much recent posting here about the tired topic of the string wars. I hope to soon make amends by writing about something new I learned about geometric Langlands.

The summer 2015 issue of Perspectives in Science has an excellent article about the debate over string theory entitled Contested Boundaries: The String Theory Debates and Ideologies of Science (also available here), by Sophie Ritson and Kristian Camilleri. It deals with the debate from a point of view bringing together aspects of history, philosophy and sociology, while staying away from the technical aspects of the controversy.

The article has an interesting take on the debate, not taking sides as to who is right or wrong, but examining what the central issues have been and the ways people involved have chosen to make their case. One point made that I’d never thought of is that while this debate concerns an issue that comes up often, that of the boundary of what is science and what isn’t, here the usual roles are reversed:

In most scientific controversies in which we find scientists engaging in boundary work, the boundary dispute is generally over whether an unorthodox or minority view or approach should be regarded as science, pseudoscience, or pathological science. UFOology, parapsychology, intelligent design, and cold fusion all represent cases of this sort. The “ideological attempts to define science,” as Gieryn explains, are largely motivated by the desire “to justify and protect the authority of science by offering principled demarcations from poachers or impostors” (Gieryn 1999, p. 26). However, in the case of string theory, it is the dominant research program in a well-established field of science that has been forced to defend its credentials as “scientific” (Taylor 1996, pp. 177–9).

This presents an intriguing departure from most studied episodes of boundary work. String theory currently enjoys a privileged status by virtue of being the dominant paradigm within theoretical physics. Yet string theorists have found themselves forced to defend the scientific legitimacy of their research against charges that it has degenerated into a form of “metaphysics,” “non-science,” or “bad science.” In doing so, string theorists have attempted to “loosen” the methodological definition of science, while critics try to impose a stricter definition.

The emphasis of the article is on the string theory debate, not the multiverse, and I’m (accurately) quoted as defending string theory as “scientific”. When I wrote about this in my book back in 2002-3, I had no idea that multiverse pseudo-science would take hold among prominent theorists, a situation that raises issues I never thought would come up (the sort of thing Steinhardt is hoping for help with from the philosophers, see the last posting). The parts of the book about the “is it science?” question are ones I would write differently today, based on both recent history and new things I’ve learned about the philosophy of science.

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About That Smoking Gun…

Aeon magazine has just published a long piece on the current state of cosmology by Ross Andersen. One focus is on Paul Steinhardt and his claims that the popular multiverse/eternal inflation scenario doesn’t explain what it is supposed to, and is compatible with almost any experimental result. The BICEP2 fiasco, where multiverse proponents first claimed a “smoking gun” vindication from B-modes, then went on to claim that no B-modes was just as good for their theory once they disappeared, is the main topic of the article (for a previous posting about this, see here).

That’s why Steinhardt was surprised to see inflationary theorists clinking glasses when BICEP2 announced a high swirls figure. ‘They declared victory,’ he told me. ‘They said it was smoking-gun proof! Just what they expected!’

But then a few months passed and BICEP2’s interpretation started to look wobbly. In June, Linde told New Scientist that he didn’t like the way BICEP2’s swirls were being treated as a smoking gun for inflation. In July, Guth made similar statements to the Washington Post. Steinhardt was furious. He thought it was flip-flopping. He began to wonder if any data would disturb the serene certainty of inflationary theorists. ‘It was Andre Linde who used the “smoking gun” language in the first place,’ he told me. ‘Now he says it doesn’t make a difference what BICEP2 says. How can it be that not seeing gravitational waves is fine, and then seeing them is a smoking gun, and then not seeing them is fine again?’

Steinhardt explains that the underlying problem is that the underlying problem is an inherently untestable paradigm, compatible with anything:

The theory’s weaknesses can be explained away with the same glib shrug that accompanies the retort: ‘God just made it that way.’

A dominant, infinitely flexible multiverse theory could make it easy not to strain for the next leap forward. It could lead to a chilling effect on new ideas in cosmology, or worse, a creative crisis. Steinhardt thinks we’re already there. ‘Andre Linde has become associated with eternal inflation because he thinks the multiverse is a good idea,’ he told me. ‘But I invented it, too, and I think it’s a horrible idea. It’s an emperor’s new clothes story. Except in that story, it’s a child who points out that the Emperor has no clothes. In this case, it’s the tailors themselves telling us that the theory is not testable. It’s Guth and Linde.’

His hope for how the subject will get saved from itself is with help from philosophers:

‘The outside community isn’t recognising the problem,’ he said. ‘This whole BICEP2 thing has made some people more aware of it. It’s been nice to have that aired out. But most people give us too much respect. They think we know what we’re doing. They take too seriously these voices that say inflation is established theory.’

I asked him who might help. What cavalry was he calling for?

‘I wish the philosophers would get involved,’ he said.

That might help, but I think other ideas are needed…

Posted in Multiverse Mania | 33 Comments

The Admiral of the String Theory Wars

The science magazine Nautilus this month has a profile of me, under the title The Admiral of the String Theory Wars. The writer, Bob Henderson, spent a lot of time talking to me and other people around here, including attending my class. I think he did a very good job of handling the complex topic of the debate over string theory, not so easily done in the context of this kind of personal story. Then again, I guess I would think that since he was mainly hearing my point of view, others may see this very differently…

Talking to Henderson brought back memories of a lot of the very odd things that happened during this period, now nearly ten years ago. I also recently realized that this week is the 10th anniversary of the date on which I sent off the final version of “Not Even Wrong” to the publisher (it then went to copy editing, was published a year later). Looking back at it now, I don’t see much that I’d change. The earliest version of the manuscript written around 2003 didn’t discuss the landscape and multiverse business, which only really got going in 2004. By 2005 I did add a chapter on this, but at the time thought doing this might be a bit unfair to string theorists. Surely they were all aware this was obvious nonsense and would quickly themselves put a stop to it. I was very wrong about that and, oddly, it’s over this argument (where I would have thought my point of view was uncontroversial) that I’ve gotten the most grief from certain prominent string theorists (e.g. Polchinski).

For the latest in the string wars, you can watch last night’s Perimeter Institute public lecture by Amanda Peet. It was a promotional effort that reminded me a lot of the kind of thing you see on late night TV, with an inspirational speaker selling a product to a rapt studio audience. The main selling points for string theory were that it “would blow your mind”, that branes explain black hole entropy (the Strominger/Vafa calculations of 20 years ago), and that the world is a hologram (Maldacena from nearly 20 years ago).

After the talk the first question read to her was the obvious one about testing these ideas experimentally. Remarkably, she claimed that string theory was testable, that published work of 10 years ago showed that it could be tested at accelerators, and so far it had passed the tests. What she was referring to was one of the weirder stories of the string wars. At the time Jacques Distler and collaborators wrote a paper entitled Falsifying String Theory Through WW Scattering, which I discussed here. They also wrote to the Wall Street Journal about this (see here). A few months later their paper was accepted by Physical Review Letters, with their claims about string theory removed, I assume at the insistence of a referee (see here). In a spectacular display of chutzpah, when the PRL paper appeared, the authors had their institutions put out press releases claiming that “Physicists Develop Test for String Theory” (see here), exactly the claim that PRL would not let them make in print. It’s this claim that Peet is now using to mislead the public at Perimeter. I think it’s their responsibility to look into this and issue a public correction. Or do they really feel that it is all right for their public lecture series to be used to mislead the public about science?

Update: I see that the Nautilus piece is part of an issue on “Error”, which also includes interesting articles about the OPERA superluminal neutrino story and about Vladimir Voevodsky.

: I probably should have included the relevant question and answer exchange with Peet, here it is:

Q: Any predictions or comments on how and when string theory might be able to be proven experimentally?

A:… there are experiments that can be done, this is published work that has been around for almost ten years now, that you can do experiments in nature in the lab without having to invent equipment that you haven’t invented yet that would test whether or not the assumptions of string theory are true or false. So far none of those experiments has shown a red flag that says string theory is wrong.

: Ethan Siegel has a blog entry and live-blogging about the Peet talk. He was hoping that Peet would discuss some sort of connection between string theory and observable physics, didn’t hear any (he seems to have missed the bogus claim about the LHC). Siegel gives an argument that string theory is in principle falsifiable, since it predicts space-time supersymmetry superpartners, although with no prediction for the mass scale. I’ve never heard this before, and I don’t know of any argument that such superpartners must appear in the spectrum of a string theory.

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First Collisions of Run 2

This morning in Geneva saw the first collisions in the revamped LHC, there’s an event display from ATLAS here, CMS here.

These collisions are just at the injection energy of 450 GeV/beam, but over the past few weeks beams have been successfully ramped up (without intentional collisions, although see page 23 here) to the planned 6.5 TeV/beam. 6.5 TeV beams have been accelerated not just with probe intensity, but with nominal bunch intensity and squeeze. They are roughly halfway through a planned 8 week beam commissioning process and on schedule, with stable beams for physics collisions still planned for around June 1. For quite a while now, 6.5 TeV/beam collisions have been possible, but no word yet on when this is planned for, I assume there will be some sort of media event at that time.

Update: Something about this from CERN here.

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