A physicist-turned-mathematician discusses the intersection of those disciplines, string theory’s “intellectual standstill,” and his frustration with badly written scientific papers.
Peter Woit is a Senior Lecturer in the Mathematics Department at Columbia University, where he’s worked since 1989. Prior to that, he obtained a PhD in particle physics from Princeton and did some postdoctoral work at the State University of New York at Stony Brook. Though physics and mathematics are closely related disciplines, there are often barriers in the language used by each community; Woit’s unique background affords him a sort of bilingualism.
From his vantage point in the mathematics world, Woit became an outspoken critic of string theory, even writing a book in 2006 called Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law. Alongside Lee Smolin’s The Trouble with Physics, also released in 2006, it sparked much debate that ultimately led, in Woit’s view, to a tribalism that distracted from the intellectual conversation he’d hoped for. For more than 20 years, he has maintained a blog that seeks to generate those intellectual conversations. (Like his book, the blog borrows its name, Not Even Wrong, from Wolfgang Pauli’s famous slight for ideas that are so flawed they can’t even be tested or falsified.)
Woit recently spoke with FirstPrinciples about the arc of his interesting career, his thoughts on the state of string theory nearly two decades after his book was released, and his latest work concerning unification in physics.
The interview has been condensed and edited for clarity.
FirstPrinciples: How do you think your career path has influenced your views on the state of physics today?
Peter Woit: After I got my PhD at Princeton, I started a postdoc at Stony Brook in theoretical physics in the fall of 1984, right when the so-called first superstring revolution was happening. It was in the same building as the math department and my own interests very much involved using mathematics. I actually spent more time talking to mathematicians than to physicists.
At the end of my four years at Stony Brook, it became clear that there wasn’t much of a career path for me in theoretical physics. At that point, there were very few jobs for anybody with a mathematical focus that wasn’t interested in doing string theory. I thought I might do better in a math department and ended up getting a postdoc at MSRI in Berkeley. [Editor’s note: The Simons Laufer Mathematical Sciences Institute, formerly the Mathematical Sciences Research Institute, is an independent institute on the campus of the University of California, Berkeley.]
That was the beginning of my move into the math community. Then, I came to Columbia and spent several years in a non-tenure-track faculty position. When I was trying to figure out what to do next, they were looking for somebody to take over this strange position that involved teaching a course and making sure the department computer system kept running. I said, “Okay, I guess I can do that.” And I learned a lot about Unix very quickly and I’ve been doing that under various titles since. I’m officially a Senior Lecturer, which is a non-tenured faculty position.
FP: Was the computing side of things an interest for you or a pragmatic means of continuing to support your research?
PW: It was more pragmatic. In my dissertation and some of my research work, I was trying to figure out how you properly define topological quantities in the lattice gauge theory, but I was also doing some quite serious Monte Carlo computer calculations. I did have some background in computing, but it was more about how much I was enjoying living in New York and how much I liked my experience in the math department at Columbia. Staying here was very attractive.
While there is a lot of connection between math and physics, they really are very, very different communities. They have a completely different language, completely different culture, completely different history, and they’re interested in completely different problems. It’s been a very different career than I would’ve had if I had somehow managed to stay in the physics community.
FP: Presumably, having experienced both gives you a more unique lens on how each one functions?
PW: Yeah, I can understand both points of view. For a lot of people on both sides, there’s a huge language barrier in terms of their training and the language each community uses to talk about very similar things. I’m pretty bilingual.
FP: You mentioned that the start of your career coincided with the first superstring revolution. You’ve been critical of string theory, even writing a book about it in 2006. Have you noticed any change in the conversation around string theory in the last couple decades?
PW: I think that book has held up very well. There’s just more and more evidence for the arguments I was making.
If you look at the popular perception of string theory, I think it has changed. At the time I started writing, there was little understanding outside of experts in the field what the problems with string theory were, and how significant they were. I think those have become very well publicized.
Back then, you would hear a lot of dumb things about how great string theory was. Now, you hear a lot of stupid things about how terrible string theory is. The uninformed discussion of the subject has moved in my direction; I don’t know if that’s a great achievement.
Within the subject itself, a lot of people have moved away from studying string theory. Even many of the people who are most vocal about how great string theory is or are most influential in the community are no longer actually working on it. Ed Witten rarely publishes papers on string theory anymore.
There were a lot of very vigorous arguments about this when my book and Lee Smolin’s came out. It was an eye-opener for me about the extent to which even very smart people behave in a very tribal way. Either you’re for this or you’re against this and it’s very important which side you’re on. It’s becoming more and more of a waste of time to try to have any kind of discussion about this. The people pushing string theory have made it very clear that there’s nothing that’s going to change their mind, and maybe I’m the same. It’s somewhat of an intellectual standstill.
FP: Do you think that tribalism is readily apparent to people on both sides? Or does your home in a math department allow you to see it more clearly?
PW: One reason I wrote the book was because there were, and still are, a lot of people who agree with my point of view, but don’t feel it’s something they can express publicly. That involves confronting some influential people and there are fears about the impact on getting grant proposals approved or your students getting jobs.
FP: Why would the influential people in string theory hold more power than in, for example, loop quantum gravity or another area of research?
PW: It’s not that there are these terrible, evil string theorists keeping everyone else down. The tribalism goes both ways. Proponents of string theory don’t want to get into a fight with the influential people that are not happy with string theory.
It’s unfortunate. I think both Lee Smolin and I wrote our books hoping to open up a serious intellectual conversation and it mostly didn’t happen. Instead, it just led to a lot of weird behavior with people defending indefensible positions.
FP: Do you know Ed Witten or any of the other string theory proponents on a personal level?
PW: I do know a lot of these people personally. Witten was a postdoc at Harvard when I was an undergraduate there and I was looking for somebody to supervise a reading course. For one semester, I would go see him each week and he helped me learn some things about gauge theory. Edward Witten is a complete genius. He’s incredibly hard-working and has done absolutely amazing things.
And a lot of the more senior people in string theory now were graduate students with me. We have reasonable relations.
FP: You’ve been writing your blog for more than 20 years, attracting a significant audience and generating some interesting discussions. Have they ever influenced the direction you take with your own research?
PW: A little bit. My own research is very specialized. With string theory, it’s a very technical subject and really understanding it is quite difficult. I joke that one way I can test my understanding is by writing a blog. If I’m right, I won’t hear anything. If I’m wrong, a well-informed string theorist will immediately tell me exactly why I’m wrong.
FP: What motivates you to spend time on science communication?
PW: I think I’m trying to do something different than most science communicators, in that I’m not actually trying to speak to a large audience. I’m trying to reach a narrow group who have similar interests to myself and to provide something that’s of interest.
I’m guessing most people that visit my blog say, “What is this guy going on about?” And that’s fine. I’m well aware of how hard it is to take some of these issues that I’m interested in and convey what’s going on to as many people as possible. I have great respect for people that try to do that. But I rarely ever want to take the time to do it myself.
FP: Do you feel more scientists should be trying to communicate their work to the public?
PW: I’ve talked with various podcasters recently and there are people trying to do this in a very serious way, which is great. What I’m more concerned with is seeing academics improve the way they write technical papers. It has to do with what we reward in science, which is not good exposition. Most papers in math and physics are only designed to be readable by a small number of people working on the same thing as they are. Basically, I want people to explain their work in ways I can understand without having to read their badly written papers.
FP: Can you give us a sneak peek of what you’re working on these days?
PW: My direction really changed several years ago during COVID. When I was a graduate student in the 1980s, I started doing these calculations involving the geometry of lattice gauge fields. That part of the Standard Model was, at least conceptually, pretty clear. But when you start talking about matter particles and spinor fields, some things are very unclear.
In quantum field theory, if you want to do calculations, you need to be able to go back and forth between the standard notion of time and the geometry of spacetime that we’ve known about since Einstein. There’s the normal four-dimensional geometry in which all the directions behave the same and there’s a notion of distance that is always positive—that’s called Euclidean four-dimensional geometry. It turns out that a lot of the calculations you want to write down in quantum field theory don’t actually make sense in the Minkowski geometry, but they make sense in the Euclidean geometry.
People long ago realized that you want to be able to go back and forth between these notions of time. If you multiply time by the square root of minus-1, you make it behave like the other directions. To most people, it looks like a weird mathematical technicality. But with the geometry of spinors, when you insert this square root of minus-1, it does something fairly minor to your calculations in terms of space and time, but it completely changes the behavior of the spinors.
There’s never been a clear understanding of exactly what’s going on with this spinor geometry. I’d had an idea that would provide a new way of relating so-called internal symmetries of the theory to spacetime symmetries, but I’d convinced myself that it wouldn’t work. Then, a few years ago (during COVID lockdowns), I started thinking about it again.
About a year ago, I wrote a short paper trying to point out that there is a different way of thinking about spinor geometry, and I tried as much as possible to write in a language that physicists would understand. I think the people who I would like to get interested in this idea looked at it and said, “This guy is just giving a vague idea and he’s expressing it imprecisely,” so I’ve been trying to write something much longer and more precise.
The more I look at this, the more I’m certain that there is something very interesting going on, but it’s taking a lot of time and effort because it really requires reworking some of the basics.
