Not Even Wrong

A few items of various kinds:

• A little while ago I did another podcast, this time with Hrvoje Kukina. The result is now available here.
• There’s a new French documentary out, available here, about the story of the campaign by a committee of mathematicians in the 1970s to get the Ukrainian mathematician Leonid Pliouchtch out of hands of the KGB. It’s directed by Mathieu Schwartz, whose great-uncle was Laurent Schwartz, one of the main figures in this story (see here). Another member of the committee, Michel Broué, also appears in the film.

  One of the issues discussed in the film is how mathematicians could have pulled this off, and whether the devotion of mathematicians to rigorous truth makes them more likely to take a stand on principle on an issue like this (Cédric Villani is interviewed, and takes the position that mathematicians aren’t much different than others). Another aspect of this story is that it may have been influential by making more people on the French left aware of the true nature of the Soviet system, making cooperation between different leftist parties more possible. For more about this aspect of the film, there’s a debate here.

• Source Code is a new book just out, an autobiography of Bill Gates, dealing with his early years, up to the time Microsoft moved to Seattle in early 1979. An important theme of the book is the importance to Gates of mathematics during those early years:
  

  Realizing early on that I had a head for math was a critical step in my story. In his terrific book How Not to Be Wrong, mathematician Jordan Ellenberg observes that “knowing mathematics is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world.” Those X-ray specs helped me identify the order underlying the chaos, and reinforced my sense that the correct answer was always out there–I just needed to find it. That insight came at one of the most formative times of a kid’s life, when the brain is transforming into a more specialized and efficient tool. Facility with numbers gave me confidence, and even a sense of security.

  There’s quite a lot about his years as a student at Harvard, especially about the freshman-year Math 55 class he took, which was taught by John Mather. This brought back a lot of memories for me of my experiences there a couple years later. Gates arrived as a freshman in the fall of 1973, which was two years before me. Something we had in common was not being the best students in Math 55, but somewhere in the middle. Our reactions to that however were very different, since Gates was extremely competitive:

  In our Math 55 study sessions, even as we were helping each other, we were also subtly keeping score. That was true in our broader circle of math nerds as well. Everyone knew how everyone else was doing, for instance, that Lloyd in Wigg B aced a Math 21a test or that Peter–or was it someone else?–found an error in Mather’s notes. We all grasped who among us was quicker that day, sharper, the person who “got it” first and then could lead the rest of us to the answer. Every day you strived to be on top. By the end of the first semester, I realized that my ranking in the hierarchy wasn’t what I had hoped…

  By most measures I was doing well. I earned a B+ in the first semester which was an achievement in that class. In my stark view however it was less of a measure of what I knew than how much I didn’t. The gap between B+ and A was the difference between being the top person in the class and being a fake…

  I was recognizing that while I had an excellent math brain, I didn’t have the gift of insight that sets apart the best mathematicians. I had talent but not the ability to make fundamental discoveries.

  In the book, Gates then explains how he ended up concentrating most of his effort on computer-related projects and describes those in detail. Other sources say he took the graduate course Math 250a from John Tate the spring semester of his sophomore year, but he doesn’t mention that. By that time he mostly wasn’t attending classes, getting by on cramming for finals, while spending all his time writing a BASIC compiler with Paul Allen, then heading out to Albuquerque to start Microsoft. The semester I arrived at Harvard (fall 1975) he was technically a student, but spending most of his time working for Microsoft, finally leaving Harvard halfway through his junior year.

• The KITP in Santa Barbara is now running a “What is Particle Theory?” program, talks here. Among the talks, one I can recommend is Simon Catterall’s Sneaking up on lattice chiral fermions, especially for its focus on what are called Kahler-Dirac fermions.

Update: The Math 55 textbook used during those years is available here.

Update: Looking through some old files, I see that I got a Math 55 grade of B in the fall, B+ in the spring. So, competitive with the likes of Bill Gates, but not with the best students in the class. My memory of the class and the significance of my grade is very different than his. I don’t remember being very aware of how other students in the class were doing, other than that there were a few of them sitting in the front row who had won Math Olympiads and the like, were clearly understanding things faster and better than I was. I also wasn’t that interested in how I was doing, being an average student in the class was fine with me. The main thing was to be learning as much math as fast as possible, and for that Math 55 was the perfect course.

Jesper Grimstrup and Jarl Sidelmann have an interesting new paper up on the arXiv, entitled Competition and survival in modern academia: A bibliometric case study of theoretical high-energy physics. It uses bibliometric data to study career paths in hep-th, especially how many people who start out in the field are still in it at various later times.

If you think that things are going fine in hep-th, this kind of study is of limited interest. If you think the field is in trouble, it’s of interest as pointing to one source of the trouble. The problem with this kind of thing though is that on the whole the people making decisions about what to do are the “survivors”, for whom the current system has worked out just fine. They’re the least likely people to think there’s a crisis or to see any reason to do anything about it. As for the job situation (which has been terrible since 1970), I can report that when one doesn’t have a permanent job this seems to be an important and serious problem, but once one does have a permanent job all of a sudden it seems much less important.

What has struck me most in recent decades about hep-th is not the bad job environment, but the monotone-decreasing number of interesting new ideas, now so small that I don’t think “intellectual collapse” is an unfair characterization of what’s happened. I started carefully following the latest preprints in the field more than 40 years ago, pre-arXiv, when they were collected physically at a “preprint library” in one’s institution. Most preprints in hep-th have always been minor advances, not of much interest unless you’re working on much the same problem, but in the past there were always a significant number with something really new and significant to report. The arrival in the preprint library of something new from Witten or any number of other well-known figures in the field was an event, and there also was a steady stream of new ideas coming from people not so well-known. In recent years the situation has been very different, with something worth reading appearing in the arXiv hep-th section less and less often, to the point where it’s a rare occurrence.

This slow death of the field I believe is a very real phenomenon, although I’m not sure how one could quantify it. There are multiple reasons for why it has happened, some of which are just facts of life (the SM is too good, no unexpected experimental results). I do think though that one reason is the one the authors here are trying to get at: decades and decades of a difficult job situation where the only viable way to win the game of survivor is to publish lots of papers in a dwindling number of accepted research programs. This is one problem that the field actually could do something about, but chances of that happening seem remote.

I just noticed something new showing up in Google searches, summaries of the state of scientific research areas such as this one about String Theory And Quantum Gravity. They’re produced by Nature Research Intelligence, which has been around for a couple years, trading on the Nature journal brand: “We’ve been the most trusted name in research for over 150 years.” The business model is you pay them to give you information about the state of scientific research that you can then use to make funding decisions.

Each of their pages has a prominent button in the upper right-hand corner allowing you to “Talk to an expert”. The problem with all this though is that no experts are involved. The page summarizing String Theory and Quantum Gravity is just one of tens of thousands of such pages produced by some AI algorithm. If you click on the button, you’ll be put in touch with someone expert in getting people to pay for the output of AI algorithms, not someone who knows anything about string theory or quantum gravity.

It’s very hard to guess what the impact of AI on scientific research in areas like theoretical physics will be, but this sort of thing indicates one very real possibility. Part of Nature’s previous business model was to sell high-quality summaries of scientific research content produced by the best scientific experts and journalists who consulted with such experts. This kind of content is difficult and expensive to produce. AI generated versions of this may not be very good, but they’re very cheap to produce, so you can make money as long as you can find anyone willing to pay something for them.

The relatively good quality of recent AI generated content has been based on having high-quality content to train on, such as that produced by Nature over the last 150 years. If AI starts getting trained not on old-style Nature, but on new-style Nature Research Intelligence, the danger is “model collapse” (for a Nature article about this, see here). Trained on their own output, large language models start producing worse and worse results.

I’m no expert, you should probably consult an AI about this instead, but it seems to me that one possibility is that instead of superintelligence producing ever more impressive content, we may have already hit the peak and it’s all downhill from here. A thought that occurred to me recently is that back in the 80s when people were talking about string theory as science that anomalously happened to fall out of the 21st century into the 20th, they may have been very right, but not realizing what was going to happen to science in the 21st century…

I recently realized that this would be the 2000th posting on this blog and was hoping to have something interesting to post for the occasion. Things though have been very quiet and I’m about to go off on vacation, so this will have to do. There’s been some progress on better understanding the Euclidean twistor unification ideas I’ve been working on the past few years. In particular the relation between the twistor geometry and the “spacetime is right-handed” point of view on spinors is now much clearer to me. I’ve also made progress on understand how to think of Wick rotation in terms of hyperfunctions, something I’d given up on a while back, but now see how it can work. In the coming weeks/months I hope to get some of this written up, both as some blog posts and as a new paper.

Every so often I’ve been running a “Print My Blog” gadget that turns the entire blog and comments into a single pdf, which is available here. As of late November, this was up to nearly 9000 pages.

Best wishes to all for the New Year, may my often pessimistic thoughts about the future be completely wrong.

Recently Curt Jaimungal offered to host a debate over string theory between me and a willing string theorist. Joe Conlon took him up on the offer and our discussion is now available. I think it turned out quite well, and gives a good idea of where Conlon and I agree or disagree, and some explanation of why we disagree when we do.

These days there’s a wide variety of different points of view about the topics we discuss among string theorists and theoretical physicists in general. A discussion with someone else would have covered some different topics. As here, I think most string theorists and I agree on quite a bit more than people expect. I’m happy this video provides a place to hear a discussion that goes beyond both the common sloganeering on the internet, and the extensive but one-sided content I’ve been providing over the years.

Update: For comments by John Baez on the “Great Stagnation” in fundamental physics, see here.

This past summer Nordita ran a program on quantum gravity, featuring lectures and panel discussions on various approaches to the subject. Lecture notes from the six mini-courses are now available here. There’s also a long, 39 author document called Visions in Quantum Gravity, which summarizes the panel discussions and includes further thoughts from the participants.

Reading through these contributions, what strikes me is how much “quantum gravity” has simultaneously become the dominant topic in fundamental physics research, while at the same time narrowing its vision to a short list of approaches that are disconnected from the rest of science and have gone nowhere for many decades. Besides some aspects of the asymptotically safe QG program, the only other approach that connects at all to the rest of fundamental physics (the Standard Model) is the string theory landscape program. That program is based on making “conjectures” about what a string theory/quantum gravity theory would imply if one had one, and then rebranding these “conjectures” as “predictions”, in order to be able to go to battle on Twitter and elsewhere claiming that string theory really is predictive, no matter what the critics say. Whatever this is, it’s not any sort of conventional science.

With quantum gravity cut off from the rest of fundamental physical theory, one can only connect it to experiment by coming up with a proposal for an observable purely quantum gravitational effect. There was some discussion of such proposals at Nordita, but I don’t see anything plausible there (tabletop measurements discussed seem to me to be relevant to quantum measurement theory, not to what the quantum gravitational degrees of freedom are).

Cut off from connection to experiment, there remain the deep connections to mathematics that have characterized fundamental physics, especially modern physics, with GR and the Standard Model theories very much of a geometrical nature. The Nordita program however was completely cut off from mathematics, with no mathematicians among the 39 authors, and minimal representation among them of the field of mathematical physics.

Most seriously, while GR is a very geometrical theory, the approach to geometry used here is very narrow and naive. In particular, modern differential geometry makes clear that one should think not just about the tangent bundle, but also about spinor bundles, which give a more fundamental and powerful structure. That spinors are important is very clear from observational physics: all matter fields are spinor fields. And yet, the word “spinor” doesn’t occur even once in Visions in Quantum Geometry (it occurs in the mini-courses mainly in the technical discussion of the construction of the superstring). As for the fascinating extension of spinor geometry known as twistor geometry, that is mentioned not even once by anyone. The Penrose school of trying to understand quantum gravity using spinors and twistors is completely ignored.

Given the impossibility of getting experiment to tell one how to think about the quantum nature of the gravitational degrees of freedom, putting on blinders and refusing to look at mathematics outside of a naive and narrow conception of geometry seems to me a recipe for continuing a now long tradition of failure.