A chef cooks food, and people eat it. A tailor makes clothes, and people wear them. An artist has an audience, an engineer has end users, a teacher has students. Someone out there benefits directly from what you do. Make them happy, and they’ll let you know. Piss them off, and they’ll stop hiring you.
Science benefits people too…but most of its benefits are long-term. The first person to magnetize a needle couldn’t have imagined worldwide electronic communication, and the scientists who uncovered quantum mechanics couldn’t have foreseen transistors, or personal computers. The world benefits just by having more expertise in it, more people who spend their lives understanding difficult things, and train others to understand difficult things. But those benefits aren’t easy to see for each individual scientist. As a scientist, you typically don’t know who your work will help, or how much. You might not know for years, or even decades, what impact your work will have. Even then, it will be difficult to tease out your contribution from the other scientists of your time.
We can’t ask the customers of the future to pay for the scientists of today. (At least, not straightforwardly.) In practice, scientists are paid by governments and foundations, groups trying on some level to make the future a better place. Instead of feedback from customers we get feedback from each other. If our ideas get other scientists excited, maybe they’ll matter down the road.
This is a risky thing to do, of course. Governments, foundations, and scientists can’t tell the future. They can try to act in the interests of future generations, but they might just act for themselves instead. Trying to plan ahead like this makes us prey to all the cognitive biases that flesh is heir to.
But we don’t really have an alternative. If we want to have a future at all, if we want a happier and more successful world, we need science. And if we want science, we can’t ask its real customers, the future generations, to choose whether to pay for it. We need to work for the smiles on our colleagues faces and the checks from government grant agencies. And we need to do it carefully enough that at the end of the day, we still make a positive difference.
In physics, what you don’t know can absolutely hurt you. If you ignore that planets have their own gravity, or that metals conduct electricity, you’re going to calculate a lot of nonsense. At the same time, as physicists we can’t possibly know everything. Our experiments are never perfect, our math never includes all the details, and even our famous Standard Model is almost certainly not the whole story. Luckily, we have another option: instead of ignoring what we don’t know, we can parametrize it, and estimate its effect.
Estimating the unknown is something we physicists have done since Newton. You might think Newton’s big discovery was the inverse-square law for gravity, but others at the time, like Robert Hooke, had also been thinking along those lines. Newton’s big discovery was that gravity was universal: that you need to know the effect of gravity, not just from the sun, but from all the other planets as well. The trouble was, Newton didn’t know how to calculate the motion of all of the planets at once (in hindsight, we know he couldn’t have). Instead, he estimated, using what he knew to guess how big the effect of what he didn’t would be. It was the accuracy of those guesses, not just the inverse square law by itself, that convinced the world that Newton was right.
If you’ve studied electricity and magnetism, you get to the point where you can do simple calculations with a few charges in your sleep. The world doesn’t have just a few charges, though: it has many charges, protons and electrons in every atom of every object. If you had to keep all of them in your calculations you’d never pass freshman physics, but luckily you can once again parametrize what you don’t know. Often you can hide those charges away, summarizing their effects with just a fewnumbers. Other times, you can treat materials as boundaries, and summarize everything beyond in terms of what happens on the edge. The equations of the theory let you do this, but this isn’t true for every theory: for the Navier-Stokes equation, which we use to describe fluids, it still isn’t known whether you can do this kind of trick.
Parametrizing what we don’t know isn’t just a trick for college physics, it’s key to the cutting edge as well. Right now we have a picture for how all of particle physics works, called the Standard Model, but we know that picture is incomplete. There are a million different theories you could write to go beyond the Standard Model, with a million different implications. Instead of having to use all those theories, physicists can summarize them all with what we call an effective theory: one that keeps track of the effect of all that new physics on the particles we already know. By summarizing those effects with a few parameters, we can see what they would have to be to be compatible with experimental results, ruling out some possibilities and suggesting others.
In a world where we never know everything, there’s always something that can hurt us. But if we’re careful and estimate what we don’t know, if we write down numbers and parameters and keep our options open, we can keep from getting burned. By focusing on what we do know, we can still manage to understand the world.
The road to this conference was a bit of a roller-coaster. It was originally scheduled for early March. When the organizers told us they were postponing it, they seemed at the time a little overcautious…until the world proved me, and all of us, wrong. They rescheduled for October, and as more European countries got their infection rates down it looked like the conference could actually happen. We booked rooms at the DESY guest house, until it turned out they needed the space to keep the DESY staff socially distanced, and we quickly switched to booking at a nearby hotel.
Then Europe’s second wave hit. Cases in Denmark started to rise, so Germany imposed a quarantine on entry from Copenhagen and I switched to remote participation. Most of the rest of the participants did too, even several in Germany. For the few still there in person they have a variety of measures to stop infection, from fixed seats in the conference room to gloves for the coffee machine.
The content has been interesting. It’s an eclectic mix of review talks and talks on recent research, all focused on different ways to integrate (or, as one of the organizers emphasized, antidifferentiate) functions in quantum field theory. I’ve learned about the history of the field, and gotten a better feeling for the bottlenecks in some LHC-relevant calculations.
This week was also the announcement of the Physics Nobel Prize. I’ll do my traditional post on it next week, but for now, congratulations to Penrose, Genzel, and Ghez!
You’ve probably heard of the myth of the solitary scientist. While Newton might have figured out calculus isolated on his farm, most scientists work better when they communicate. If we reach out to other scientists, we can make progress a lot faster.
Even if you understand that, you might not know what that reaching out actually looks like. I’ve seen far too many crackpots who approach scientific communication like a spammer: sending out emails to everyone in a department, commenting in every vaguely related comment section they can find. While commercial spammers hope for a few gullible people among the thousands they contact, that kind of thing doesn’t benefit crackpots. As far as I can tell, they communicate that way because they genuinely don’t know any better.
So in this post, I want to give a road map for how we scientists reach out to other scientists. Keep these steps in mind, and if you ever need to reach out to a scientist you’ll know what to do.
First, decide what you want to know. This may sound obvious, but sometimes people skip this step. We aren’t communicating just to communicate, but because we want to learn something from the other person. Maybe it’s a new method or idea, maybe we just want confirmation we’re on the right track. We don’t reach out just to “show our theory”, but because we hope to learn something from the response.
Then, figure out who might know it. To do this, we first need to decide how specialized our question is. We often have questions about specific papers: a statement we don’t understand, a formula that seems wrong, or a method that isn’t working. For those, we contact an author from that paper. Other times, the question hasn’t been addressed in a paper, but does fall under a specific well-defined topic: a particular type of calculation, for example. For those we seek out a specialist on that specific topic. Finally, sometimes the question is more general, something anyone in our field might in principle know but we happen not to. For that kind of question, we look for someone we trust, someone we have a prior friendship with and feel comfortable asking “dumb questions”. These days, we can supplement that with platforms like PhysicsOverflow that let us post technical questions and invite anyone to respond.
Note that, for all of these, there’s some work to do first. We need to read the relevant papers, bone up on a topic, even check Wikipedia sometimes. We need to put in enough work to at least try to answer our question, so that we know exactly what we need the other person for.
Finally, contact them appropriately. Papers will usually give contact information for one, or all, of the authors. University websites will give university emails. We’d reach out with something like that first, and switch to personal email (or something even more casual, like Skype or social media) only for people we already have a track record of communicating with in that way.
By posing and directing our questions well, scientists can reach out and get help when we struggle. Science is a team effort, we’re stronger when we work together.
After Amplitudes was held online this year, a few of us at the Niels Bohr Institute were inspired. We thought this would be the perfect time to hold a small online conference, focused on the Calabi-Yaus that have been poppinguplately in Feynman diagrams. Then we heard from the organizers of Elliptics 2020. They had been planning to hold a conference in Mainz about elliptic integrals in Feynman diagrams, but had to postpone it due to the pandemic. We decided to team up and hold a joint conference on both topics: the elliptic integrals that are just starting to be understood, and the mysterious integrals that lie beyond. Hence, Elliptics and Beyond.
The conference has been fun thus far. There’s been a mix of review material bringing people up to speed on elliptic integrals and exciting new developments. Some are taking methods that have been successful in other areas and generalizing them to elliptic integrals, others have been honing techniques for elliptics to make them “production-ready”. A few are looking ahead even further, to higher-genus amplitudes in string theory and Calabi-Yaus in Feynman diagrams.
We organized the conference along similar lines to Zoomplitudes, but with a few experiments of our own. Like Zoomplitudes, we made a Slack space for the conference, so people could chat physics outside the talks. Ours was less active, though. I suspect that kind of space needs a critical mass of people, and with a smaller conference we may just not have gotten there. Having fewer people did allow us a more relaxed schedule, which in turn meant we could mostly keep things on-time. We had discussion sessions in the morning (European time), with talks in the afternoon, so almost everyone could make the talks at least. We also had a “conference dinner”, which went much better than I would have expected. We put people randomly into Zoom Breakout Rooms of five or six, to emulate the tables of an in-person conference, and folks chatted while eating their (self-brought of course) dinner. People seemed to really enjoy the chance to just chat casually with the other folks at the conference. If you’re organizing an online conference soon, I’d recommend trying it!
Holding a conference online means that a lot of people can attend who otherwise couldn’t. We had over a hundred people register, and while not all of them showed up there were typically fifty or sixty people on the Zoom session. Some of these were specialists in elliptics or Calabi-Yaus who wouldn’t ordinarily make it to a conference like this. Others were people from the rest of the amplitudes field who joined for parts of the conference that caught their eye. But surprisingly many weren’t even amplitudeologists, but students and young researchers in a variety of topics from all over the world. Some seemed curious and eager to learn, others I suspect just needed to say they had been to a conference. Both are responding to a situation where suddenly conference after conference is available online, free to join. It will be interesting to see if, and how, the world adapts.
I’m a baby academic. Two years ago I got my first real grant, a Marie Curie Individual Fellowship from the European Union. Applying for it was a complicated process, full of Word templates and mismatched expectations. Two years later the grant is over, and I get another new experience: grant reporting.
Writing a report after a grant is sort of like applying for a grant. Instead of summarizing and justifying what you intend to do, you summarize and justify what you actually did. There are also Word templates. Grant reports are probably easier than grant applications: you don’t have to “hook” your audience or show off. But they are harder in one aspect: they highlight the different ways different fields handle uncertainty.
If you do experiments, having a clear plan makes sense. You buy special equipment and hire postdocs and even technicians to do specific jobs. Your experiments may or may not find what you hope for, but at least you can try to do them on schedule, and describe the setbacks when you can’t.
As a theorist, you’re more nimble. Your equipment are computers, your postdocs have their own research. Overall, it’s easy to pick up new projects as new ideas come in. As a result, your plans change more. New papers might inspire you to try new things. They might also discourage you, if you learn the idea you had won’t actually work. The field can move fast, and you want to keep up with it.
Writing my first grant report will be interesting. I’ll need to thread the gap between expectations and reality, to look back on my progress and talk about why. And of course, I have to do it in Microsoft Word.
This is already pretty unreasonable for many undergrads. But think about PhD students.
Suppose you’re a foreign PhD student at a US university. Maybe your school is already planning to have classes online this fall, like Harvard is. Maybe your school is planning to have classes in person, but will change its mind a few weeks in, when so many students and professors are infected that it’s clearly unreasonable to continue. Maybe your school never changes its mind, but your state does, and the school has to lock down anyway.
As a PhD student, you likely don’t live in the dorms. More likely you live in a shared house, or an apartment. You’re an independent adult. Your parents aren’t paying for you to go to school. Your school is itself a full-time job, one that pays (as little as the university thinks it can get away with).
What happens when your school goes online? If you need to leave the country?
You’d have to find some way out of your lease, or keep paying for it. You’d have to find a flight on short notice. You’d have to pack up all your belongings, ship or sell anything you can’t store, or find friends to hold on to it.
You’d have to find somewhere to stay in your “home country”. Some could move in with their parents temporarily, many can’t. Some of those who could in other circumstances, shouldn’t if they’re fleeing from an outbreak: their parents are likely older, and vulnerable to the virus. So you have to find a hotel, eventually perhaps a new apartment, far from what was until recently your home.
Reminder: you’re doing all of this on a shoestring budget, because the university pays you peanuts.
Can you transfer instead? In a word, no.
PhD students are specialists. They’re learning very specific things from very specific people. Academics aren’t the sort of omnidisciplinary scientists you see in movies. Bruce Banner or Tony Stark could pick up a new line of research on a whim, real people can’t. This is why, while international students may be good at the undergraduate level, they’re absolutely necessary for PhDs. When only three people in the world study the thing you want to study, you don’t have the luxury of staying in your birth country. And you can’t just transfer schools when yours goes online.
I hope that this policy gets reversed, or halted, or schools find some way around it. At the moment, anyone starting school in the US this fall is in a very tricky position. And anyone already there is in a worse one.
As usual, I’m going to ask that the comments don’t get too directly political. As a partial measure to tone things down, I’d like to ask you to please avoid mentioning any specific politicians, political parties, or political ideologies. Feel free to talk instead about your own experiences: how this policy is likely to affect you, or your loved ones. Please also feel free to talk more technically on the policy/legal side. I’d like to know what universities can do to work around this, and whether there are plausible paths to change or halt the policy. Please be civil, and be kind to your fellow commenters.
Citations are the bread and butter of academia, or maybe its prison cigarettes. They link us together, somewhere between a map to show us the way and an informal currency. They’re part of how the world grades us, a measure more objective than letters from our peers but that’s not saying much. It’s clear why we we want to be cited, but why do we cite others?
For more reasons than you’d expect.
First, we cite to respect priority. Since the dawn of science, we’ve kept track not only of what we know, but of who figured it out first. If we use an idea in our paper, we cite its origin: the paper that discovered or invented it. We don’t do this for the oldest and most foundational ideas: nobody cites Einstein for relativity. But if the idea is at all unusual, we make sure to give credit where credit is due.
Second, we cite to substantiate our claims. Academic papers don’t stand on their own: they depend on older proofs and prior discoveries. If we make a claim that was demonstrated in older work, we don’t need to prove it again. By citing the older work, we let the reader know where to look. If they doubt our claim, they can look at the older paper and see what went wrong.
Those two are the most obvious uses of citations, but there are more. Another important use is to provide context. Academic work doesn’t stand alone: we choose what we work on in part based on how it relates to other work. As such, it’s important to cite that other work, to help readers understand our motivation. When we’re advancing the state of the art, we need to tell the reader what that state of the art is. When we’re answering a question or solving a problem, we can cite the paper that asked the question or posed the problem. When we’re introducing a new method or idea, we need to clearly say what’s new about it: how it improves on older, similar ideas.
Scientists are social creatures. While we often have a scientific purpose in mind, citations also follow social conventions. These vary from place to place, field to field, and sub-field to sub-field. Mention someone’s research program, and you might be expected to cite every paper in that program. Cite one of a pair of rivals, and you should probably cite the other one too. Some of these conventions are formalized in the form of “citeware“, software licenses that require citations, rather than payments, to use. Others come from unspoken cultural rules. Citations are a way to support each other, something that can slightly improve another’s job prospects at no real cost to your own. It’s not surprising that they ended up part of our culture, well beyond their pure academic use.
The conference opened with a talk by Gavin Salam, there as an ambassador for LHC physics. Salam pointed out that, while a decent proportion of speakers at Amplitudes mention the LHC in their papers, that fraction has fallen over the years. (Another speaker jokingly wondered which of those mentions were just in the paper’s introduction.) He argued that there is still useful work for us, LHC measurements that will require serious amplitudes calculations to understand. He also brought up what seems like the most credible argument for a new, higher-energy collider: that there are important properties of the Higgs, in particular its interactions, that we still have not observed.
The next few talks hopefully warmed Salam’s heart, as they featured calculations for real-world particle physics. Nathaniel Craig and Yael Shadmi in particular covered the link between amplitudes and Standard Model Effective Field Theory (SMEFT), a method to systematically characterize corrections beyond the Standard Model. Shadmi’s talk struck me because the kind of work she described (building the SMEFT “amplitudes-style”, directly from observable information rather than more complicated proxies) is something I’d seen people speculate about for a while, but which hadn’t been done until quite recently. Now, several groups have managed it, and look like they’ve gotten essentially “all the way there”, rather than just partial results that only manage to replicate part of the SMEFT. Overall it’s much faster progress than I would have expected.
After Shadmi’s talk was a brace of talks on N=4 super Yang-Mills, featuring cosmic Galois theory and an impressively groan-worthy “origin story” joke. The final talk of the day, by Hofie Hannesdottir, covered work with some of my colleagues at the NBI. Due to coronavirus I hadn’t gotten to hear about this in person, so it was good to hear a talk on it, a blend of old methods and new priorities to better understand some old discoveries.
The next day focused on a topic that has grown in importance in our community, calculations for gravitational wave telescopes like LIGO. Several speakers focused on new methods for collisions of spinning objects, where a few different approaches are making good progress (Radu Roiban’s proposal to use higher-spin field theory was particularly interesting) but things still aren’t quite “production-ready”. The older, post-Newtonian method is still very much production-ready, as evidenced by Michele Levi’s talk that covered, among other topics, our recentcollaboration. Julio Parra-Martinez discussed some interesting behavior shared by both supersymmetric and non-supersymmetric gravity theories. Thibault Damour had previously expressed doubts about use of amplitudes methods to answer this kind of question, and part of Parra-Martinez’s aim was to confirm the calculation with methods Damour would consider more reliable. Damour (who was actually in the audience, which I suspect would not have happened at an in-person conference) had already recanted some related doubts, but it’s not clear to me whether that extended to the results Parra-Martinez discussed (or whether Damour has stated the problem with his old analysis).
There were a few talks that day that didn’t relate to gravitational waves, though this might have been an accident, since both speakers also work on that topic. Zvi Bern’s talk linked to the previous day’s SMEFT discussion, with a calculation using amplitudes methods of direct relevance to SMEFT researchers. Clifford Cheung’s talk proposed a rather strange/fun idea, conformal symmetry in negative dimensions!
Wednesday was “amplituhedron day”, with a variety of talks on positive geometries and cluster algebras. Featured in several talks was “tropicalization“, a mathematical procedure that can simplify complicated geometries while still preserving essential features. Here, it was used to trim down infinite “alphabets” conjectured for some calculations into a finite set, and in doing so understand the origin of “square root letters”. The day ended with a talk by Nima Arkani-Hamed, who despite offering to bet that he could finish his talk within the half-hour slot took almost twice that. The organizers seemed to have planned for this, since there was one fewer talk that day, and as such the day ended at roughly the usual time regardless.
For lack of a better name, I’ll call Thursday’s theme “celestial”. The day included talks by cosmologists (including approaches using amplitudes-ish methods from Daniel Baumann and Charlotte Sleight, and a curiously un-amplitudes-related talk from Daniel Green), talks on “celestial amplitudes” (amplitudes viewed from the surface of an infinitely distant sphere), and various talks with some link to string theory. I’m including in that last category intersection theory, which has really become its own thing. This included a talk by Simon Caron-Huot about using intersection theory more directly in understanding Feynman integrals, and a talk by Sebastian Mizera using intersection theory to investigate how gravity is Yang-Mills squared. Both gave me a much better idea of the speakers’ goals. In Mizera’s case he’s aiming for something very ambitious. He wants to use intersection theory to figure out when and how one can “double-copy” theories, and might figure out why the procedure “got stuck” at five loops. The day ended with a talk by Pedro Vieira, who gave an extremely lucid and well-presented “blackboard-style” talk on bootstrapping amplitudes.
Friday was a grab-bag of topics. Samuel Abreu discussed an interesting calculation using the numerical unitarity method. It was notable in part because renormalization played a bigger role than it does in most amplitudes work, and in part because they now have a cool logo for their group’s software, Caravel. Claude Duhr and Ruth Britto gave a two-part talk on their work on a Feynman integral coaction. I’d had doubts about the diagrammatic coaction they had worked on in the past because it felt a bit ad-hoc. Now, they’re using intersection theory, and have a clean story that seems to tie everything together. Andrew McLeod talked about our work on a Feynman diagram Calabi-Yau “bestiary”, while Cristian Vergu had a more rigorous understanding of our “traintrack” integrals.
There are two key elements of a conference that are tricky to do on Zoom. You can’t do a conference dinner, so you can’t do the traditional joke-filled conference dinner speech. The end of the conference is also tricky: traditionally, this is when everyone applauds the organizers and the secretaries are given flowers. As chair for the last session, Lance Dixon stepped up to fill both gaps, with a closing speech that was both a touching tribute to the hard work of organizing the conference and a hilarious pile of in-jokes, including a participation award to Arkani-Hamed for his (unprecedented, as far as I’m aware) perfect attendance.
One implication of this was that, in principle, we now knew the answer for each individual Omega diagram, far past what had been computed before. However, writing down these answers was easier said than done. After some wrangling, we got the answer for each diagram in terms of an infinite sum. But despite tinkering with it for a while, even our resident infinite sum expert Georgios Papathanasiou couldn’t quite sum them up.
Naturally, this made me think the sums would make a great Master’s project.
When Henrik Munch showed up looking for a project, Andrew McLeod and I gave him several options, but he settled on the infinite sums. Impressively, he ended up solving the problem in two different ways!
First, he found an old paper none of us had seen before, that gave a general method for solving that kind of infinite sum. When he realized that method was really annoying to program, he took the principle behind it, called telescoping, and came up with his own, simpler method, for our particular case.
Picture an old-timey folding telescope. It might be long when fully extended, but when you fold it up each piece fits inside the previous one, resulting in a much smaller object. Telescoping a sum has the same spirit. If each pair of terms in a sum “fit together” (if their difference is simple), you can rearrange them so that most of the difficulty “cancels out” and you’re left with a much simpler sum.
Henrik’s telescoping idea worked even better than expected. We found that we could do, not just the Omega sums, but other sums in particle physics as well. Infinite sums are a very well-studied field, so it was interesting to find something genuinely new.
The rest of us worked to generalize the result, to check the examples and to put it in context. But the core of the work was Henrik’s. I’m really proud of what he accomplished. If you’re looking for a PhD student, he’s on the market!