Tag Archives: DoingScience

Getting Started in Saclay

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I started work this week in my new position, as a permanent researcher at the Institute for Theoretical Physics of CEA Paris-Saclay. I’m still settling in, figuring out how to get access to the online system and food at the canteen and healthcare. Things are slowly getting into shape, with a lot of running around involved. Until then, I don’t have a ton of time to write (and am dedicating most of it to writing grants!) But I thought, mirroring a post I made almost a decade ago, that I’d at least give you a view of my new office.

Amplitudes 2023 Retrospective

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I’m back from CERN this week, with a bit more time to write, so I thought I’d share some thoughts about last week’s Amplitudes conference.

One thing I got wrong in last week’s post: I’ve now been told only 213 people actually showed up in person, as opposed to the 250-ish estimate I had last week. This may seem fewer than Amplitudes in Prague had, but it seems likely they had a few fewer show up than appeared on the website. Overall, the field is at least holding steady from year to year, and definitely has grown since the pandemic (when 2019’s 175 was already a very big attendance).

It was cool having a conference in CERN proper, surrounded by the history of European particle physics. The lecture hall had an abstract particle collision carved into the wood, and the visitor center would in principle have had Standard Model coffee mugs were they not sold out until next May. (There was still enough other particle physics swag, Swiss chocolate, and Swiss chocolate that was also particle physics swag.) I’d planned to stay on-site at the CERN hostel, but I ended up appreciated not doing that: the folks who did seemed to end up a bit cooped up by the end of the conference, even with the conference dinner as a chance to get out.

Past Amplitudes conferences have had associated public lectures. This time we had a not-supposed-to-be-public lecture, a discussion between Nima Arkani-Hamed and Beate Heinemann about the future of particle physics. Nima, prominent as an amplitudeologist, also has a long track record of reasoning about what might lie beyond the Standard Model. Beate Heinemann is an experimentalist, one who has risen through the ranks of a variety of different particle physics experiments, ending up well-positioned to take a broad view of all of them.

It would have been fun if the discussion erupted into an argument, but despite some attempts at provocative questions from the audience that was not going to happen, as Beate and Nima have been friends for a long time. Instead, they exchanged perspectives: on what’s coming up experimentally, and what theories could explain it. Both argued that it was best to have many different directions, a variety of experiments covering a variety of approaches. (There wasn’t any evangelism for particular experiments, besides a joking sotto voce mention of a muon collider.) Nima in particular advocated that, whether theorist or experimentalist, you have to have some belief that what you’re doing could lead to a huge breakthrough. If you think of yourself as just a “foot soldier”, covering one set of checks among many, then you’ll lose motivation. I think Nima would agree that this optimism is irrational, but necessary, sort of like how one hears (maybe inaccurately) that most new businesses fail, but someone still needs to start businesses.

Michelangelo Mangano’s talk on Thursday covered similar ground, but with different emphasis. He agrees that there are still things out there worth discovering: that our current model of the Higgs, for instance, is in some ways just a guess: a simplest-possible answer that doesn’t explain as much as we’d like. But he also emphasized that Standard Model physics can be “new physics” too. Just because we know the model doesn’t mean we can calculate its consequences, and there are a wealth of results from the LHC that improve our models of protons, nuclei, and the types of physical situations they partake in, without changing the Standard Model.

We saw an impressive example of this in Gregory Korchemsky’s talk on Wednesday. He presented an experimental mystery, an odd behavior in the correlation of energies of jets of particles at the LHC. These jets can include a very large number of particles, enough to make it very hard to understand them from first principles. Instead, Korchemsky tried out our field’s favorite toy model, where such calculations are easier. By modeling the situation in the limit of a very large number of particles, he was able to reproduce the behavior of the experiment. The result was a reminder of what particle physics was like before the Standard Model, and what it might become again: partial models to explain odd observations, a quest to use the tools of physics to understand things we can’t just a priori compute.

On the other hand, amplitudes does do a priori computations pretty well as well. Fabrizio Caola’s talk opened the conference by reminding us just how much our precise calculations can do. He pointed out that the LHC has only gathered 5% of its planned data, and already it is able to rule out certain types of new physics to fairly high energies (by ruling out indirect effects, that would show up in high-precision calculations). One of those precise calculations featured in the next talk, by Guilio Gambuti. (A FORM user, his diagrams were the basis for the header image of my Quanta article last winter.) Tiziano Peraro followed up with a technique meant to speed up these kinds of calculations, a trick to simplify one of the more computationally intensive steps in intersection theory.

The rest of Monday was more mathematical, with talks by Zeno Capatti, Jaroslav Trnka, Chia-Kai Kuo, Anastasia Volovich, Francis Brown, Michael Borinsky, and Anna-Laura Sattelberger. Borinksy’s talk felt the most practical, a refinement of his numerical methods complete with some actual claims about computational efficiency. Francis Brown discussed an impressively powerful result, a set of formulas that manages to unite a variety of invariants of Feynman diagrams under a shared explanation.

Tuesday began with what I might call “visitors”: people from adjacent fields with an interest in amplitudes. Alday described how the duality between string theory in AdS space and super Yang-Mills on the boundary can be used to get quite concrete information about string theory, calculating how the theory’s amplitudes are corrected by the curvature of AdS space using a kind of “bootstrap” method that felt nicely familiar. Tim Cohen talked about a kind of geometric picture of theories that extend the Standard Model, including an interesting discussion of whether it’s really “geometric”. Marko Simonovic explained how the integration techniques we develop in scattering amplitudes can also be relevant in cosmology, especially for the next generation of “sky mappers” like the Euclid telescope. This talk was especially interesting to me since this sort of cosmology has a significant presence at CEA Paris-Saclay. Along those lines an interesting paper, “Cosmology meets cohomology”, showed up during the conference. I haven’t had a chance to read it yet!

Just before lunch, we had David Broadhurst give one of his inimitable talks, complete with number theory, extremely precise numerics, and literary and historical references (apparently, Källén died flying his own plane). He also remedied a gap in our whimsically biological diagram naming conventions, renaming the pedestrian “double-box” as a (in this context, Orwellian) lobster. Karol Kampf described unusual structures in a particular Effective Field Theory, while Henriette Elvang’s talk addressed what would become a meaningful subtheme of the conference, where methods from the mathematical field of optimization help amplitudes researchers constrain the space of possible theories. Giulia Isabella covered another topic on this theme later in the day, though one of her group’s selling points is managing to avoid quite so heavy-duty computations.

The other three talks on Tuesday dealt with amplitudes techniques for gravitational wave calculations, as did the first talk on Wednesday. Several of the calculations only dealt with scattering black holes, instead of colliding ones. While some of the results can be used indirectly to understand the colliding case too, a method to directly calculate behavior of colliding black holes came up again and again as an important missing piece.

The talks on Wednesday had to start late, owing to a rather bizarre power outage (the lights in the room worked fine, but not the projector). Since Wednesday was the free afternoon (home of quickly sold-out CERN tours), this meant there were only three talks: Veneziano’s talk on gravitational scattering, Korchemsky’s talk, and Nima’s talk. Nima famously never finishes on time, and this time attempted to control his timing via the surprising method of presenting, rather than one topic, five “abstracts” on recent work that he had not yet published. Even more surprisingly, this almost worked, and he didn’t run too ridiculously over time, while still managing to hint at a variety of ways that the combinatorial lessons behind the amplituhedron are gradually yielding useful perspectives on more general realistic theories.

Thursday, Andrea Puhm began with a survey of celestial amplitudes, a topic that tries to build the same sort of powerful duality used in AdS/CFT but for flat space instead. They’re gradually tackling the weird, sort-of-theory they find on the boundary of flat space. The two next talks, by Lorenz Eberhardt and Hofie Hannesdottir, shared a collaborator in common, namely Sebastian Mizera. They also shared a common theme, taking a problem most people would have assumed was solved and showing that approaching it carefully reveals extensive structure and new insights.

Cristian Vergu, in turn, delved deep into the literature to build up a novel and unusual integration method. We’ve chatted quite a bit about it at the Niels Bohr Institute, so it was nice to see it get some attention on the big stage. We then had an afternoon of trips beyond polylogarithms, with talks by Anne Spiering, Christoph Nega, and Martijn Hidding, each pushing the boundaries of what we can do with our hardest-to-understand integrals. Einan Gardi and Ruth Britto finished the day, with a deeper understanding of the behavior of high-energy particles and a new more mathematically compatible way of thinking about “cut” diagrams, respectively.

On Friday, João Penedones gave us an update on a technique with some links to the effective field theory-optimization ideas that came up earlier, one that “bootstraps” whole non-perturbative amplitudes. Shota Komatsu talked about an intriguing variant of the “planar” limit, one involving large numbers of particles and a slick re-writing of infinite sums of Feynman diagrams. Grant Remmen and Cliff Cheung gave a two-parter on a bewildering variety of things that are both surprisingly like, and surprisingly unlike, string theory: important progress towards answering the question “is string theory unique?”

Friday afternoon brought the last three talks of the conference. James Drummond had more progress trying to understand the symbol letters of supersymmetric Yang-Mills, while Callum Jones showed how Feynman diagrams can apply to yet another unfamiliar field, the study of vortices and their dynamics. Lance Dixon closed the conference without any Greta Thunberg references, but with a result that explains last year’s mystery of antipodal duality. The explanation involves an even more mysterious property called antipodal self-duality, so we’re not out of work yet!

At Amplitudes 2023 at CERN

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I’m at the big yearly conference of my sub-field this week, called Amplitudes. This year, surprisingly for the first time, it’s at the very appropriate location of CERN.

Somewhat overshadowed by the very picturesque Alps

Amplitudes keeps on growing. In 2019, we had 175 participants. We were on Zoom in 2020 and 2021, with many more participants, but that probably shouldn’t count. In Prague last year we had 222. This year, I’ve been told we have even more, something like 250 participants (the list online is bigger, but includes people joining on Zoom). We’ve grown due to new students, but also new collaborations: people from adjacent fields who find the work interesting enough to join along. This year we have mathematicians talking about D-modules, bootstrappers finding new ways to get at amplitudes in string theory, beyond-the-standard-model theorists talking about effective field theories, and cosmologists talking about the large-scale structure of the universe.

The talks have been great, from clear discussions of earlier results to fresh-off-the-presses developments, plenty of work in progress, and even one talk where the speaker’s opinion changed during the coffee break. As we’re at CERN, there’s also a through-line about the future of particle physics, with a chat between Nima Arkani-Hamed and the experimentalist Beate Heinemann on Tuesday and a talk by Michelangelo Mangano about the meaning of “new physics” on Thursday.

I haven’t had a ton of time to write, I keep getting distracted by good discussions! As such, I’ll do my usual thing, and say a bit more about specific talks in next week’s post.

Cabinet of Curiosities: The Deluxe Train Set

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I’ve got a new paper out this week with Andrew McLeod. I’m thinking of it as another entry in this year’s “cabinet of curiosities”, interesting Feynman diagrams with unusual properties. Although this one might be hard to fit into a cabinet.

Over the past few years, I’ve been finding Feynman diagrams with interesting connections to Calabi-Yau manifolds, the spaces originally studied by string theorists to roll up their extra dimensions. With Andrew and other collaborators, I found an interesting family of these diagrams called traintracks, which involve higher-and-higher dimensional manifolds as they get longer and longer.

This time, we started hooking up our traintracks together.

We call diagrams like these traintrack network diagrams, or traintrack networks for short. The original traintracks just went “one way”: one family, going higher in Calabi-Yau dimension the longer they got. These networks branch out, one traintrack leading to another and another.

In principle, these are much more complicated diagrams. But we find we can work with them in almost the same way. We can find the same “starting point” we had for the original traintracks, the set of integrals used to find the Calabi-Yau manifold. We’ve even got more reliable tricks, a method recently honed by some friends of ours that consistently find a Calabi-Yau manifold inside the original traintracks.

Surprisingly, though, this isn’t enough.

It works for one type of traintrack network, a so-called “cross diagram” like this:

But for other diagrams, if the network branches any more, the trick stops working. We still get an answer, but that answer is some more general space, not just a Calabi-Yau manifold.

That doesn’t mean that these general traintrack networks don’t involve Calabi-Yaus at all, mind you: it just means this method doesn’t tell us one way or the other. It’s also possible that simpler versions of these diagrams, involving fewer particles, will once again involve Calabi-Yaus. This is the case for some similar diagrams in two dimensions. But it’s starting to raise a question: how special are the Calabi-Yau related diagrams? How general do we expect them to be?

Another fun thing we noticed has to do with differential equations. There are equations that relate one diagram to another simpler one. We’ve used them in the past to build up “ladders” of diagrams, relating each picture to one with one of its boxes “deleted”. We noticed, playing with these traintrack networks, that these equations do a bit more than we thought. “Deleting” a box can make a traintrack short, but it can also chop a traintrack in half, leaving two “dangling” pieces, one on either side.

This reminded me of an important point, one we occasionally lose track of. The best-studied diagrams related to Calabi-Yaus are called “sunrise” diagrams. If you squish together a loop in one of those diagrams, the whole diagram squishes together, becoming much simpler. Because of that, we’re used to thinking of these as diagrams with a single “geometry”, one that shows up when you don’t “squish” anything.

Traintracks, and traintrack networks, are different. “Squishing” the diagram, or “deleting” a box, gives you a simpler diagram, but not much simpler. In particular, the new diagram will still contain traintracks, and traintrack networks. That means that we really should think of each traintrack network not just as one “top geometry”, but of a collection of geometries, different Calabi-Yaus that break into different combinations of Calabi-Yaus in different ways. It’s something we probably should have anticipated, but the form these networks take is a good reminder, one that points out that we still have a lot to do if we want to understand these diagrams.

Learning for a Living

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It’s a question I’ve now heard several times, in different forms. People hear that I’ll be hired as a researcher at an institute of theoretical physics, and they ask, “what, exactly, are they paying you to research?”

The answer, with some caveats: “Whatever I want.”

When a company hires a researcher, they want to accomplish specific things: to improve their products, to make new ones, to cut down on fraud or out-think the competition. Some government labs are the same: if you work for NIST, for example, your work should contribute in some way to achieving more precise measurements and better standards for technology.

Other government labs, and universities, are different. They pursue basic research, research not on any specific application but on the general principles that govern the world. Researchers doing basic research are given a lot of freedom, and that freedom increases as their careers go on.

As a PhD student, a researcher is a kind of apprentice, working for their advisor. Even then, they have some independence: an advisor may suggest projects, but PhD students usually need to decide how to execute them on their own. In some fields, there can be even more freedom: in theoretical physics, it’s not unusual for the more independent students to collaborate with other people than just their advisor.

Postdocs, in turn, have even more freedom. In some fields they get hired to work on a specific project, but they tend to have more freedom as to how to execute it than a PhD student would. Other fields give them more or less free rein: in theoretical physics, a postdoc will have some guidance, but often will be free to work on whatever they find interesting.

Professors, and other long-term researchers, have the most freedom of all. Over the climb from PhD to postdoc to professor, researchers build judgement, demonstrating a track record for tackling worthwhile scientific problems. Universities, and institutes of basic research, trust that judgement. They hire for that judgement. They give their long-term researchers free reign to investigate whatever questions they think are valuable.

In practice, there are some restrictions. Usually, you’re supposed to research in a particular field: at an institute for theoretical physics, I should probably research theoretical physics. (But that can mean many things: one of my future colleagues studies the science of cities.) Further pressure comes from grant funding, money you need to hire other researchers or buy equipment that can come with restrictions attached. When you apply for a grant, you have to describe what you plan to do. (In practice, grant agencies are more flexible about this than you might expect, allowing all sorts of changes if you have a good reason…but you still can’t completely reinvent yourself.) Your colleagues themselves also have an impact: it’s much easier to work on something when you can walk down the hall and ask an expert when you get stuck. It’s why we seek out colleagues who care about the same big questions as we do.

Overall, though, research is one of the free-est professions there is. If you can get a job learning for a living, and do it well enough, then people will trust your judgement. They’ll set you free to ask your own questions, and seek your own answers.

Enfin, Permanent

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My blog began, almost eleven years ago, with the title “Four Gravitons and a Grad Student”. Since then, I finished my PhD. The “Grad Student” dropped from the title, and the mysterious word “postdoc” showed up on a few pages. For three years I worked as a postdoc at the Perimeter Institute in Canada, before hopping the pond and starting another three-year postdoc job in Denmark. With a grant from the EU, three years became four. More funding got me to five (with a fancier title), and now nearing on six. Each step, my contract has been temporary: at first three years at a time, then one-year extensions. Each year I applied, all over the world, looking for a permanent job: for a chance to settle down somewhere, to build my own research group without worrying about having to move the next year.

This year, things have finally worked out. In the Fall I will be moving to France, starting a junior permanent position with L’Institut de Physique Théorique (or IPhT) at CEA Paris-Saclay.

A photo of the entryway to the Institute, taken when I interviewed

It’s been a long journey to get here, with a lot of soul-searching. This year in particular has been a year of reassessment: of digging deep and figuring out what matters to me, what I hope to accomplish and what clues I have to guide the way. Sometimes I feel like I’ve matured more as a physicist in the last year than in the last three put together.

The CEA (originally Commissariat à l’énergie atomique, now Commissariat à l’énergie atomique et aux énergies alternatives, or Alternative Energies and Atomic Energy Commission, and yes that means they’re using the “A” for two things at the same time), is roughly a parallel organization to the USA’s Department of Energy. Both organizations began as a way to manage their nation’s nuclear program, but both branched out, both into other forms of energy and into scientific research. Both run a nationwide network of laboratories, lightly linked but independent from their nations’ universities, both with notable facilities for particle physics. The CEA’s flagship site is in Saclay, on the outskirts of Paris, and it’s their Institute for Theoretical Physics where I’ll be working.

My new position is genuinely permanent: unlike a tenure-track position in the US, I don’t go up for review after a fixed span of time, with the expectation that if I don’t get promoted I lose the job altogether. It’s also not a university, which in particular means I’m not required to teach. I’ll have the option of teaching, working with nearby universities. In the long run, I think I’ll pursue that option. I’ve found teaching helpful the past couple years: it’s helped me think about physics, and think about how to communicate physics. But it’s good not to have to rush into preparing a new course when I arrive, as new professors often do.

It’s also a really great group, with a lot of people who work on things I care about. IPhT has a long track record of research in scattering amplitudes, with many leading figures. They’ve played a key role in topics that frequent readers will have seen show up on this blog: on applying techniques from particle physics to gravitational waves, to the way Calabi-Yau manifolds show up in Feynman diagrams, and even recently to the relationship of machine learning to inference in particle physics.

Working temporary positions year after year, not knowing where I’ll be the next year, has been stressful. Others have had it worse, though. Some of you might have seen a recent post by Bret Deveraux, a military historian with a much more popular blog who has been in a series of adjunct positions. Deveraux describes the job market for the humanities in the US quite well. I’m in theoretical physics in Europe, so while my situation hasn’t been easy, it has been substantially better.

First, there’s the physics component. Physics has “adjunctified” much less than other fields. I don’t think I know a single physicist who has taken an adjunct teaching position, the kind of thing where you’re paid per course and only to teach. I know many who have left physics for other kinds of work, for Wall Street or Silicon Valley or to do data science for a bank or to teach high school. On the other side, I know people in other fields who do work as adjuncts, particularly in mathematics.

Deveraux blames the culture of his field, but I think funding also must have an important role. Physicists, and scientists in many other areas, rarely get professor positions right after their PhDs, but that doesn’t mean they leave the field entirely because most can find postdoc positions. Those postdocs are focused on research, and are often paid for by government grants: in my field in the US, that usually means the Department of Energy. People can go through two or sometimes even three such positions before finding something permanent, if they don’t leave the field before that. Without something like the Department of Energy or National Institutes of Health providing funding, I don’t know if the humanities could imitate that structure even if they wanted to.

Europe, in turn, has a different situation than the US. Most European countries don’t have a tenure-track: just permanent positions and fixed-term positions. Funding also works quite differently. Department of Energy funding in the US is spread widely and lightly: grants are shared by groups of theorists at a given university, each getting funding for a few postdocs and PhDs across the group. In Europe, a lot of the funding is much more concentrated: big grants from the European Research Council going to individual professors, with various national and private grants supplementing or mirroring that structure. That kind of funding, and the rarity of tenure, in turn leads to a different kind of temporary position: one not hired to teach a course but hired for research as long as the funding lasts. The Danish word for my current title is Adjunkt, but that’s as one says in France a faux ami: the official English translation is Assistant Professor, and it’s nothing like a US adjunct. I know people in a variety of forms of that kind of position in a variety of countries, people who landed a five-year grant where they could act like a professor, hire people and so on, but who in the end were expected to move when the grant was over. It’s a stressful situation, but at least it lets us further our research and make progress, unlike a US adjunct in the humanities or math who needs to spend much of their time on teaching.

I do hope Deveraux finds a permanent position, he’s got a great blog. And to return to the theme of the post, I am extremely grateful and happy that I have managed to find a permanent position. I’m looking forward to joining the group at Saclay: to learning more about physics from them, but also, to having a place where I can start to build something, and make a lasting impact on the world around me.

Extrapolated Knowledge

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Scientists have famously bad work-life balance. You’ve probably heard stories of scientists working long into the night, taking work with them on weekends or vacation, or falling behind during maternity or paternity leave.

Some of this is culture. Certain fields have a very cutthroat attitude, with many groups competing to get ahead and careers on the line if they fail. Not every field is like that though: there are sub-fields that are more collaborative than competitive, that understand work-life balance and try to work together to a shared goal. I’m in a sub-field like that, so I know they exist.

Put aside the culture, and you’ve still got passion. Science is fun, it’s puzzle after puzzle, topics chosen because we find them fascinating. Even in the healthiest workplace you’d still have scientists pondering in the shower and scribbling notes on the plane, mixing business with pleasure because the work is genuinely both.

But there’s one more reason scientists are workaholics. I suspect, ultimately, it’s the most powerful reason. It’s that every scientist is, in some sense, irreplaceable.

In most jobs, if you go on vacation, someone can fill in when you’re gone. The replacement may not be perfect (think about how many times you watched movies in school with a substitute teacher), but they can cover for you, making some progress on your tasks until you get back. That works because you and they have a shared training, a common core that means they can step in and get what needs to be done done.

Scientists have shared training too, of course. Some of our tasks work the same way, the kind of thing that any appropriate expert can do, that just need someone to spend the time to do them.

But our training has a capstone, the PhD thesis. And the thing about a PhD thesis is that it is, always and without exception, original research. Each PhD thesis is an entirely new result, something no-one else had known before, discovered by the PhD candidate. Each PhD thesis is unique.

That, in turn, means that each scientist is unique. Each of us has our own knowledge, our own background, our own training, built up not just during the PhD but through our whole career. And sometimes, the work we do requires that unique background. It’s why we collaborate, why we reach out to different people around the world, looking for the unique few people who know how to do what we need.

Over time, we become a kind of embodiment of our accumulated knowledge. We build a perspective shaped by our experience, goals for the field and curiosity just a bit different from everyone else’s. We act as agents of that perspective, each the one person who can further our particular vision of where science is going. When we enter a collaboration, when we walk into the room at a conference, we are carrying with us all we picked up along the way, each a story just different enough to matter. We extrapolate from what we know, and try to do everything that knowledge can do.

So we can, and should, take vacations, yes, and we can, and should, try to maintain a work-life balance. We need to to survive, to stay sane. But we do have to accept that when we do, certain things won’t get done as fast. Our own personal vision, our extrapolated knowledge…will just have to wait.

Bottlenecks, Known and Unknown

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Scientists want to know everything, and we’ve been trying to get there since the dawn of science. So why aren’t we there yet? Why are there things we still don’t know?

Sometimes, the reason is obvious: we can’t do the experiments yet. Victorian London had neither the technology nor the wealth to build a machine like Fermilab, so they couldn’t discover the top quark. Even if Newton had the idea for General Relativity, the telescopes of the era wouldn’t have let astronomers see its effect on the motion of Mercury. As we grow (in technology, in resources, in knowledge, in raw number of human beings), we can test more things and learn more about the world.

But I’m a theoretical physicist, not an experimental physicist. I still want to understand the world, but what I contribute aren’t new experiments, but new ideas and new calculations. This brings back the question in a new form: why are there calculations we haven’t done yet? Why are there ideas we haven’t had yet?

Sometimes, we can track the reason down to bottlenecks. A bottleneck is a step in a calculation that, for some reason, is harder than the rest. As you try to push a calculation to new heights, the bottleneck is the first thing that slows you down, like the way liquid bubbles through the neck of a literal bottle. If you can clear the bottleneck, you can speed up your calculation and accomplish more.

In the clearest cases, we can see how these bottlenecks could be solved with more technology. As computers get faster and more powerful, calculations become possible that weren’t possible before, in the same way new experiments become possible with new equipment. This is essentially what has happened recently with machine learning, where relatively old ideas are finally feasible to apply on a massive scale.

In physics, a subtlety is that we rarely have access to the most powerful computers available. Some types of physics are done on genuine supercomputers, but for more speculative or lower-priority research we have to use small computer clusters, or even our laptops. Something can be a bottleneck not because it can’t be done on any computer, but because it can’t be done on the computers we can afford.

Most of the time, bottlenecks aren’t quite so obvious. That’s because in theoretical physics, often, we don’t know what we want to calculate. If we want to know why something happens, and not merely that it happens, then we need a calculation that we can interpret, that “makes sense” and that thus, hopefully, we can generalize. We might have some ideas for how that calculation could work: some property a mathematical theory might have that we already know how to understand. Some of those ideas are easy to check, so we check, and make progress. Others are harder, and we have to decide: is the calculation worth it, if we don’t know if it will give us the explanation we need?

Those decisions provide new bottlenecks, often hidden ones. As we get better at calculation, the threshold for an “easy” check gets easier and easier to meet. We put aside fewer possibilities, so we notice more things, which inspire yet more ideas. We make more progress, not because the old calculations were impossible, but because they weren’t easy enough, and now they are. Progress fuels progress, a virtuous cycle that gets us closer and closer to understanding everything we want to understand (which is everything).

Why Are Universities So International?

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Worldwide, only about one in thirty people live in a different country from where they were born. Wander onto a university campus, though, and you may get a different impression. The bigger the university and the stronger its research, the more international its employees become. You’ll see international PhD students, international professors, and especially international temporary researchers like postdocs.

I’ve met quite a few people who are surprised by this. I hear the same question again and again, from curious Danes at outreach events to a tired border guard in the pre-clearance area of the Toronto airport: why are you, an American, working here?

It’s not, on the face of it, an unreasonable question. Moving internationally is hard and expensive. You may have to take your possessions across the ocean, learn new languages and customs, and navigate an unfamiliar bureaucracy. You begin as a temporary resident, not a citizen, with all the risks and uncertainty that involves. Given a choice, most people choose to stay close to home. Countries sometimes back up this choice with additional incentives. There are laws in many places that demand that, given a choice, companies hire a local instead of a foreigner. In some places these laws apply to universities as well. With all that weight, why do so many researchers move abroad?

Two different forces stir the pot, making universities international: specialization, and diversification.

Researchers may find it easier to live close to people who grew up with us, but we work better near people who share our research interests. Science, and scholarship more generally, are often collaborative: we need to discuss with and learn from others to make progress. That’s still very hard to do remotely: it requires serendipity, chance encounters in the corridor and chats at the lunch table. As researchers in general have become more specialized, we’ve gotten to the point where not just any university will do: the people who do our kind of work are few enough that we often have to go to other countries to find them.

Specialization alone would tend to lead to extreme clustering, with researchers in each area gathering in only a few places. Universities push back against this, though. A university wants to maximize the chance that one of their researchers makes a major breakthrough, so they don’t want to hire someone whose work will just be a copy of someone they already have. They want to encourage interdisciplinary collaboration, to try to get people in different areas to talk to each other. Finally, they want to offer a wide range of possible courses, to give the students (many of whom are still local), a chance to succeed at many different things. As a result, universities try to diversify their faculty, to hire people from areas that, while not too far for meaningful collaboration, are distinct from what their current employees are doing.

The result is a constant international churn. We search for jobs in a particular sweet spot: with people close enough to spur good discussion, but far enough to not overspecialize. That search takes us all over the world, and all but guarantees we won’t find a job where we were trained, let alone where we were born. It makes universities quite international places, with a core of local people augmented by opportune choices from around the world. It makes us, and the way we lead our lives, quite unusual on a global scale. But it keeps the science fresh, and the ideas moving.

Building the Railroad to Rigor

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As a kid who watched far too much educational television, I dimly remember learning about the USA’s first transcontinental railroad. Somehow, parts of the story stuck with me. Two companies built the railroad from different directions, one from California and the other from the middle of the country, aiming for a mountain in between. Despite the US Civil War happening around this time, the two companies built through, in the end racing to where the final tracks were laid with a golden spike.

I’m a theoretical physicist, so of course I don’t build railroads. Instead, I build new mathematical methods, ways to check our theories of particle physics faster and more efficiently. Still, something of that picture resonates with me.

You might think someone who develops new mathematical methods would be a mathematician, not a physicist. But while there are mathematicians who work on the problems I work on, their goals are a bit different. They care about rigor, about stating only things they can carefully prove. As such, they often need to work with simplified examples, “toy models” well-suited to the kinds of theorems they can build.

Physicists can be a bit messier. We don’t always insist on the same rigor the mathematicians do. This makes our results less reliable, but it makes our “toy models” a fair amount less “toy”. Our goal is to try to tackle questions closer to the actual real world.

What happens when physicists and mathematicians work on the same problem?

If the physicists worked alone, they might build and build, and end up with an answer that isn’t actually true. The mathematicians, keeping rigor in mind, would be safe in the truth of what they built, but might not end up anywhere near the physicists’ real-world goals.

Together, though, physicists and mathematicians can build towards each other. The physicists can keep their eyes on the mathematicians, correcting when they notice something might go wrong and building more and more rigor into their approach. The mathematicians can keep their eyes on the physicists, building more and more complex applications of their rigorous approaches to get closer and closer to the real world. Eventually, like the transcontinental railroad, the two groups meet: the mathematicians prove a rigorous version of the physicists’ approach, or the physicists adopt the mathematicians’ ideas and apply them to their own theories.

A sort of conference photo

In practice, it isn’t just two teams, physicists and mathematicians, building towards each other. Different physicists themselves work with different levels of rigor, aiming to understand different problems in different theories, and the mathematicians do the same. Each of us is building our own track, watching the other tracks build towards us on the horizon. Eventually, we’ll meet, and science will chug along over what we’ve built.