Last week was a birthday conference for one of the pioneers of my sub-field, Ettore Remiddi. I wasn’t there, but someone who was pointed me to some of the slides, including a talk by Stefano Laporta. For those of you who didn’t see my post a few weeks back, Laporta was one of Remiddi’s students, who developed one of the most important methods in our field and then vanished, spending ten years on an amazingly detailed calculation. Laporta’s talk covers more of the story, about what it was like to do precision calculations in that era.
“That era”, the 90’s through 2000’s, witnessed an enormous speedup in computers, and a corresponding speedup in what was possible. Laporta worked with Remiddi on the three-loop electron anomalous magnetic moment, something Remiddi had been working on since 1969. When Laporta joined in 1989, twenty-one of the seventy-two diagrams needed had still not been computed. They would polish them off over the next seven years, before Laporta dove in to four loops. Twenty years later, he had that four-loop result to over a thousand digits.
One fascinating part of the talk is seeing how the computational techniques change over time, as language replaces language and computer clusters get involved. As a student, Laporta learns a lesson we all often need: that to avoid mistakes, we need to do as little by hand as possible, even for something as simple as copying a one-line formula. Looking at his review of others’ calculations, it’s remarkable how many theoretical results had to be dramatically corrected a few years down the line, and how much still might depend on theoretical precision.
Another theme was one of Remiddi suggesting something and Laporta doing something entirely different, and often much more productive. Whether it was using the arithmetic-geometric mean for an elliptic integral instead of Gaussian quadrature, or coming up with his namesake method, Laporta spent a lot of time going his own way, and Remiddi quickly learned to trust him.
There’s a lot more in the slides that’s worth reading, including a mention of one of this year’s Physics Nobelists. The whole thing is an interesting look at what it takes to press precision to the utmost, and dedicate years to getting something right.
Ask a doctor or a psychologist if they’re sure about something, and they might say “it has p<0.05”. Ask a physicist, and they’ll say it’s a “5 sigma result”. On the surface, they sound like they’re talking about completely different things. As it turns out, they’re not quite that different.
Whether it’s a p-value or a sigma, what scientists are giving you is shorthand for a probability. The p-value is the probability itself, while sigma tells you how many standard deviations something is away from the mean on a normal distribution. For people not used to statistics this might sound very complicated, but it’s not so tricky in the end. There’s a graph, called a normal distribution, and you can look at how much of it is above a certain point, measured in units called standard deviations, or “sigmas”. That gives you your probability.
Give it a try: how much of this graph is past the line? How about ?
What are these numbers a probability of? At first, you might think they’re a probability of the scientist being right: of the medicine working, or the Higgs boson being there.
That would be reasonable, but it’s not how it works. Scientists can’t measure the chance they’re right. All they can do is compare models. When a scientist reports a p-value, what they’re doing is comparing to a kind of default model, called a “null hypothesis”. There are different null hypotheses for different experiments, depending on what the scientists want to test. For the Higgs, scientists looked at pairs of photons detected by the LHC. The null hypothesis was that these photons were created by other parts of the Standard Model, like the strong force, and not by a Higgs boson. For medicine, the null hypothesis might be that people get better on their own after a certain amount of time. That’s hard to estimate, which is why medical experiments use a control group: a similar group without the medicine, to see how much they get better on their own.
Once we have a null hypothesis, we can use it to estimate how likely it is that it produced the result of the experiment. If there was no Higgs, and all those photons just came from other particles, what’s the chance there would still be a giant pile of them at one specific energy? If the medicine didn’t do anything, what’s the chance the control group did that much worse than the treatment group?
Ideally, you want a small probability here. In medicine and psychology, you’re looking for a 5% probability, for p<0.05. In physics, you need 5 sigma to make a discovery, which corresponds to a one in 3.5 million probability. If the probability is low, then you can say that it would be quite unlikely for your result to happen if the null hypothesis was true. If you’ve got a better hypothesis (the Higgs exists, the medicine works), then you should pick that instead.
In school, you learn that the world around you is made up of chemical elements. There’s oxygen and nitrogen in the air, hydrogen and oxygen in water, sodium and chlorine in salt, and carbon in all living things. Other elements are more rare. Often, that’s because they’re unstable, due to radioactivity, like the plutonium in a bomb or americium in a smoke detector. The heaviest elements are artificial, produced in tiny amounts by massive experiments. In 2002, the heaviest element yet was found at the Joint Institute for Nuclear Research near Moscow. It was later named Oganesson, after the scientist who figured out how to make these heavy elements, Yuri Oganessian. To keep track of the different elements, we organize them in the periodic table like this:
In that same school, you probably also learn that the elements aren’t quite so elementary. Unlike the atoms imagined by the ancient Greeks, our atoms are made of smaller parts: protons and neutrons, surrounded by a cloud of electrons. They’re what give the periodic table its periodic structure, the way it repeats from row to row, with each different element having a different number of protons.
If your school is a bit more daring, you also learn that protons and neutrons themselves aren’t elementary. Each one is made of smaller particles called quarks: a proton of two “up quarks” and one “down quark”, and a neutron of two “down” and one “up”. Up quarks, down quarks, and electrons are all what physicists call fundamental particles, and they make up everything you see around you. Just like the chemical elements, some fundamental particles are more obscure than others, and the heaviest ones are all very unstable, produced temporarily by particle collider experiments. The most recent particle to be discovered was in 2012, when the Large Hadron Collider near Geneva found the Higgs boson. The Higgs boson is named after Peter Higgs, one of those who predicted it back in the 60’s. All the fundamental particles we know are part of something called the Standard Model, which we sometimes organize in a table like this:
So far, these stories probably sound similar. The experiments might not even sound that different: the Moscow experiment shoots a beam of high-energy calcium atoms at a target of heavy radioactive elements, while the Geneva one shoots a beam of high-energy protons at another beam of high-energy protons. With all those high-energy beams, what’s the difference really?
In fact there is a big different between chemical elements and fundamental particles, and between the periodic table and the Standard Model. The latter are fundamental, the former are not.
When they made new chemical elements, scientists needed to start with a lot of protons and neutrons. That’s why they used calcium atoms in their beam, and even heavier elements as their target. We know that heavy elements are heavy because they contain more protons and neutrons, and we can use the arrangement of those protons and neutrons to try to predict their properties. That’s why, even though only five or six oganesson atoms have been detected, scientists have some idea what kind of material it would make. Oganesson is a noble gas, like helium, neon, and radon. But calculations predict it is actually a solid at room temperature. What’s more, it’s expected to be able to react with other elements, something the other noble gases are very reluctant to do.
The Standard Model has patterns, just like the chemical elements. Each matter particle is one of three “generations”, each heavier and more unstable: for example, electrons have heavier relatives called muons, and still heavier ones called tauons. But unlike with the elements, we don’t know where these patterns come from. We can’t explain them with smaller particles, like we could explain the elements with protons and neutrons. We think the Standard Model particles might actually be fundamental, not made of anything smaller.
That’s why when we make them, we don’t need a lot of other particles: just two protons, each made of three quarks, is enough. With that, we can make not just new arrangements of quarks, but new particles altogether. Some are even heavier than the protons we started with: the Higgs boson is more than a hundred times as heavy as a proton! We can do this because, in particle physics, mass isn’t conserved: mass is just another type of energy, and you can turn one type of energy into another.
Discovering new elements is hard work, but discovering new particles is on another level. It’s hard to calculate which elements are stable or unstable, and what their properties might be. But we know the rules, and with enough skill and time we could figure it out. In particle physics, we don’t know the rules. We have some good guesses, simple models to solve specific problems, and sometimes, like with the Higgs, we’re right. But despite making many more than five or six Higgs bosons, we still aren’t sure it has the properties we expect. We don’t know the rules. Even with skill and time, we can’t just calculate what to expect. We have to discover it.
On Monday, Quanta magazine released an article on a man who transformed the way we do particle physics: Stefano Laporta. I’d tipped them off that Laporta would make a good story: someone who came up with the bread-and-butter algorithm that fuels all of our computations, then vanished from the field for ten years, returning at the end with an 1,100 digit masterpiece. There’s a resemblance to Searching for Sugar Man, fans and supporters baffled that their hero is living in obscurity.
If anything, I worry I under-sold the story. When Quanta interviewed me, it was clear they were looking for ties to well-known particle physics results: was Laporta’s work necessary for the Higgs boson discovery, or linked to the controversy over the magnetic moment of the muon? I was careful, perhaps too careful, in answering. The Higgs, to my understanding, didn’t require so much precision for its discovery. As for the muon, the controversial part is a kind of calculation that wouldn’t use Laporta’s methods, while the un-controversial part was found numerically by a group that doesn’t use his algorithm either.
With more time now, I can make a stronger case. I can trace Laporta’s impact, show who uses his work and for what.
In particle physics, we have a lovely database called INSPIRE that lists all our papers. Here is Laporta’s page, his work sorted by number of citations. When I look today, I find his most cited paper, the one that first presented his algorithm, at the top, with a delightfully apt 1,001 citations. Let’s listen to a few of those 1,001 tales, and see what they tell us.
Once again, we’ll sort by citations. The top paper, “Higgs boson production at hadron colliders in NNLO QCD“, is from 2002. It computes the chance that a particle collider like the LHC could produce a Higgs boson. It in turn has over a thousand citations, headlined by two from the ATLAS and CMS collaborations: “Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC” and “Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC“. Those are the papers that announced the discovery of the Higgs, each with more than twelve thousand citations. Later in the list, there are design reports: discussions of why the collider experiments are built a certain way. So while it’s true that the Higgs boson could be seen clearly from the data, Laporta’s work still had a crucial role: with his algorithm, we could reassure experimenters that they really found the Higgs (not something else), and even more importantly, help them design the experiment so that they could detect it.
The next paper tells a similar story. A different calculation, with almost as many citations, feeding again into planning and prediction for collider physics.
After that, more applications: fundamental quantities for collider physics, pieces of math that are used again and again. In particular, they are referenced again and again by the Particle Data Group, who collect everything we know about particle physics.
Further down still, and we get to specific code: FIRE and Reduze, programs made by others to implement Laporta’s algorithm, each with many uses in its own right.
All that, just from one of Laporta’s papers.
His ten-year magnum opus is more recent, and has fewer citations: checking now, just 139. Still, there are stories to tell there too.
I mentioned earlier 1,100 digits, and this might confuse some of you. The most precise prediction in particle physics has ten digits of precision, the magnetic behavior of the electron. Laporta’s calculation didn’t change that, because what he calculated isn’t the only contribution: he calculated Feynman diagrams with four “loops”, which is its own approximation, one limited in precision by what might be contributed by more loops. The current result has Feynman diagrams with five loops as well (known to much less than 1,100 digits), but the diagrams with six or more are unknown, and can only be estimated. The result also depends on measurements, which themselves can’t reach 1,100 digits of precision.
So why would you want 1,100 digits, then? In a word, mathematics. The calculation involves exotic types of numbers called periods, more complicated cousins of numbers like pi. These numbers are related to each other, often in complicated and surprising ways, ways which are hard to verify without such extreme precision. An older result of Laporta’s inspired the physicist David Broadhurst and mathematician Anton Mellit to conjecture newrelations between this type of numbers, relations that were only later proven using cutting-edge mathematics. The new result has inspired mathematicians too: Oliver Schnetz found hints of a kind of “numerical footprint”, special types of numbers tied to the physics of electrons. It’s a topic I’ve investigated myself, something I think could lead to much more efficient particle physics calculations.
In addition to being inspired by Laporta’s work, Broadhurst has advocated for it. He was the one who first brought my attention to Laporta’s story, with a moving description of welcoming him back to the community after his ten-year silence, writing a letter to help him get funding. I don’t have all the details of the situation, but the impression I get is that Laporta had virtually no academic support for those ten years: no salary, no students, having to ask friends elsewhere for access to computer clusters.
When I ask why someone with such an impact didn’t have a professorship, the answer I keep hearing is that he didn’t want to move away from his home town in Bologna. If you aren’t an academic, that won’t sound like much of an explanation: Bologna has a university after all, the oldest in the world. But that isn’t actually a guarantee of anything. Universities hire rarely, according to their own mysterious agenda. I remember another colleague whose wife worked for a big company. They offered her positions in several cities, including New York. They told her that, since New York has many universities, surely her husband could find a job at one of them? We all had a sad chuckle at that.
For almost any profession, a contribution like Laporta’s would let you live anywhere you wanted. That’s not true for academia, and it’s to our loss. By demanding that each scientist be able to pick up and move, we’re cutting talented people out of the field, filtering by traits that have nothing to do with our contributions to knowledge. I don’t know Laporta’s full story. But I do know that doing the work you love in the town you love isn’t some kind of unreasonable request. It’s a request academia should be better at fulfilling.
I was chatting with an astronomer recently, and this quote by Arthur Eddington came up:
“Never trust an experimental result until it has been confirmed by theory.”
Arthur Eddington
At first, this sounds like just typical theorist arrogance, thinking we’re better than all those experimentalists. It’s not that, though, or at least not just that. Instead, it’s commenting on a trend that shows up again and again in science, but rarely makes the history books. Again and again an experiment or observation comes through with something fantastical, something that seems like it breaks the laws of physics or throws our best models into disarray. And after a few months, when everyone has checked, it turns out there was a mistake, and the experiment agrees with existing theories after all.
You might remember a recent example, when a lab claimed to have measured neutrinos moving faster than the speed of light, only for it to turn out to be due to a loose cable. Experiments like this aren’t just a result of modern hype: as Eddington’s quote shows, they were also common in his day. In general, Eddington’s advice is good: when an experiment contradicts theory, theory tends to win in the end.
This may sound unscientific: surely we should care only about what we actually observe? If we defer to theory, aren’t we putting dogma ahead of the evidence of our senses? Isn’t that the opposite of good science?
To understand what’s going on here, we can use an old philosophical argument: David Hume’s argument against miracles. David Hume wanted to understand how we use evidence to reason about the world. He argued that, for miracles in particular, we can never have good evidence. In Hume’s definition, a miracle was something that broke the established laws of science. Hume argued that, if you believe you observed a miracle, there are two possibilities: either the laws of science really were broken, or you made a mistake. The thing is, laws of science don’t just come from a textbook: they come from observations as well, many many observations in many different conditions over a long period of time. Some of those observations establish the laws in the first place, others come from the communities that successfully apply them again and again over the years. If your miracle was real, then it would throw into doubt many, if not all, of those observations. So the question you have to ask is: it it more likely those observations were wrong? Or that you made a mistake? Put another way, your evidence is only good enough for a miracle if it would be a bigger miracle if you were wrong.
Hume’s argument always struck me as a little bit too strict: if you rule out miracles like this, you also rule out new theories of science! A more modern approach would use numbers and statistics, weighing the past evidence for a theory against the precision of the new result. Most of the time you’d reach the same conclusion, but sometimes an experiment can be good enough to overthrow a theory.
Still, theory should always sit in the background, a kind of safety net for when your experiments screw up. It does mean that when you don’t have that safety net you need to be extra-careful. Physics is an interesting case of this: while we have “the laws of physics”, we don’t have any established theory that tells us what kinds of particles should exist. That puts physics in an unusual position, and it’s probably part of why we have such strict standards of statistical proof. If you’re going to be operating without the safety net of theory, you need that kind of proof.
This post was also inspired by some biological examples. The examples are politically controversial, so since this is a no-politics blog I won’t discuss them in detail. (I’ll also moderate out any comments that do.) All I’ll say is that I wonder if in that case the right heuristic is this kind of thing: not to “trust scientists” or “trust experts” or even “trust statisticians”, but just to trust the basic, cartoon-level biological theory.
I remember, a while back, visiting a friend in his office. He had just became a professor, and was still setting things up. I noticed a list on the chalkboard, taking up almost one whole side. Taking a closer look, I realized that list was a list of projects. To my young postdoc eyes, the list was amazing: how could one person be working on so many things?
There’s an idiom in English, “too many irons in the fire”. You can imagine a blacksmith forging many things at once, each piece of iron taking focus from the others. Too many, and a piece might break, or otherwise fail.
Perhaps the irons in the fire are fire irons
In theoretical physics, a typical PhD publishes three papers before they graduate. That usually means one project at a time, maybe two. For someone used to one or two irons in the fire, so many at a time seems an impossible feat.
Scientists grow over their careers, though, and in more than one way. What seems impossible can eventually be business as usual.
First, as your skill grows, you become more efficient. A lot of scientific work is a kind of debugging: making mistakes, and figuring out how to fix them. The more experience you have, the more you know what kinds of mistakes you might make, and the better you will be at avoiding them. (Never perfect, of course: scientists always have to debug something.)
Second, your collaborations grow. The more people you work with, the more you can share these projects, each person contributing their own piece. With time, you start supervising as well: Masters students, PhD students, postdocs. Each one adds to the number of irons you can manage in your fire. While for bad supervisors this just means having their name on lots of projects, the good supervisors will be genuinely contributing to each one. That’s yet another kind of growth: as you get further along, you get a better idea of what works and what doesn’t, so even in a quick meeting you can solve meaningful problems.
Third, you grow your system. The ideas you explore early on blossom into full-fledged methods, tricks which you can pull out again and again when you need them. The tricks combine, forming new, bigger tricks, and eventually a long list of projects becomes second nature, a natural thing your system is able to do.
As you grow as a scientist, you become more than just one researcher, one debugger at a laptop or pipetter at a lab bench. You become a research program, one that manifests across many people and laptops and labs. As your expertise grows, you become a kind of living exchange of ideas, concepts flowing through you when needed, building your own scientific world.
Each year, the Niels Bohr International Academy has a series of public talks. Part of Copenhagen’s Folkeuniversitet (“people’s university”), they attract a mix of older people who want to keep up with modern developments and young students looking for inspiration. I gave a talk a few days ago, as part of this year’s program. The last time I participated, back in 2017, I covered a topic that comes up a lot on this blog: “The Quest for Quantum Gravity”. This year, I was asked to cover something more unusual: “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”.
Some of you might notice that title is already taken: it’s a famous lecture by the physicist Wigner, from 1959. Wigner posed an interesting question: why is advanced mathematics so useful in physics? Time and time again, mathematicians develop an idea purely for its own sake, only for physicists to find it absolutely indispensable to describe some part of the physical world. Should we be surprised that this keeps working? Suspicious?
I talked a bit about this: some of the answers people have suggested over the years, and my own opinion. But like most public talks, the premise was mostly a vehicle for cool examples: physicists through history bringing in new math, and surprising mathematical facts like the ones I talked about a few weeks back at Culture Night. Because of that, I was actually a bit unprepared to dive into the philosophical side of the topic (despite it being in principle a very philosophical topic!) When one of the audience members brought up mathematical Platonism, I floundered a bit, not wanting to say something that was too philosophically naive.
Well, if there’s anywhere I can be naive, it’s my own blog. I even have a label for Amateur Philosophy posts. So let’s do one.
Mathematical Platonism is the idea that mathematical truths “exist”: that they’re somewhere “out there” being discovered. On the other side, one might believe that mathematics is not discovered, but invented. For some reason, a lot of people with the latter opinion seem to think this has something to do with describing nature (for example, an essay a few years back by Lee Smolin defines mathematics as “the study of systems of evoked relationships inspired by observations of nature”).
I’m not a mathematical Platonist. I don’t even like to talk about which things do or don’t “exist”. But I also think that describing mathematics in terms of nature is missing the point. Mathematicians aren’t physicists. While there may have been a time when geometers argued over lines in the sand, these days mathematicians’ inspiration isn’t usually the natural world, at least not in the normal sense.
Instead, I think you can’t describe mathematics without describing mathematicians. A mathematical fact is, deep down, something a mathematician can say without other mathematicians shouting them down. It’s an allowed move in what my hazy secondhand memory of Wittgenstein wants to call a “language game”: something that gets its truth from a context of people interpreting and reacting to it, in the same way a move in chess matters only when everyone is playing by its rules.
This makes mathematics sound very subjective, and we’re used to the opposite: the idea that a mathematical fact is as objective as they come. The important thing to remember is that even with this kind of description, mathematics still ends up vastly less subjective than any other field. We care about subjectivity between different people: if a fact is “true” for Brits and “false” for Germans, then it’s a pretty limited fact. Mathematics is special because the “rules of its game” aren’t rules of one group or another. They’re rules that are in some sense our birthright. Any human who can read and write, or even just act and perceive, can act as a Turing Machine, a universal computer. With enough patience and paper, anything that you can prove to one person you can prove to another: you just have to give them the rules and let them follow them. It doesn’t matter how smart you are, or what you care about most: if something is mathematically true for others, it is mathematically true for you.
Some would argue that this is evidence for mathematical Platonism, that if something is a universal truth it should “exist”. Even if it does, though, I don’t think it’s useful to think of it in that way. Once you believe that mathematical truth is “out there”, you want to try to characterize it, to say something about it besides that it’s “out there”. You’ll be tempted to have an opinion on the Axiom of Choice, or the Continuum Hypothesis. And the whole point is that those aren’t sensible things to have opinions on, that having an opinion about them means denying the mathematical proofs that they are, in the “standard” axioms, undecidable. Whatever is “out there”, it has to include everything you can prove with every axiom system, whichever non-standard ones you can cook up, because mathematicians will happily work on any of them. The whole point of mathematics, the thing that makes it as close to objective as anything can be, is that openness: the idea that as long as an argument is good enough, as long as it can convince anyone prepared to wade through the pages, then it is mathematics. Nothing, so long as it can convince in the long-run, is excluded.
If we take this definition seriously, there are some awkward consequences. You could imagine a future in which every mind, everyone you might be able to do mathematics with, is crushed under some tyrant, forced to agree to something false. A real philosopher would dig in to this corner case, try to salvage the definition or throw it out. I’m not a real philosopher though. So all I can say is that while I don’t think that tyrant gets to define mathematics, I also don’t think there are good alternatives to my argument. Our only access to mathematics, and to truth in general, is through the people who pursue it. I don’t think we can define one without the other.
It’s time for my yearly Halloween post. My regular readers know what to expect: a horror trope and a physics topic, linked by a tortured analogy. And this year, the pun is definitely intended.
Horror movies have a fascination with serial killers. Over the years, they’ve explored every possible concept: from gritty realism to the supernatural, crude weapons to sophisticated traps, motivations straightforward to mysterious, and even killers who are puppets.
Yes I know Billy is not actually the killer in the Saw films
One common theme of all fictional serial killers is power. Serial killers are scary because they have almost all the power in a situation, turned to alien and unpredictable goals. The protagonists of a horror film are the underdogs, never knowing whether the killer will pull out some new ability or plan that makes everything they try irrelevant. Even if they get the opportunity to negotiate, the power imbalance means that they can’t count on getting what they need: anything the killer agrees will be twisted to serve their own ends.
Academics tell their own kind of horror stories. Earlier this month, the historian Brett Deveraux had a blog post about graduate school, describing what students go through to get a PhD. As he admits, parts of his story only apply to the humanities. STEM departments have more money, and pay their students a bit better. It’s not a lot better (I was making around $20,000 a year at Stony Brook), but it’s enough that I’ve never heard of a student taking out a loan to make ends meet. (At most, people took on tutoring jobs for a bit of extra cash.) We don’t need to learn new languages, and our degrees take a bit less time: six or seven years for an experimental physicist, and often five for a theoretical physicist. Finally, the work can be a lot less lonely, especially for those who work in a lab.
Still, there is a core in common, and that core once again is power. Universities have power, of course: and when you’re not a paying customer but an employee with your career on the line, that power can be quite scary. But the person with the most power over a PhD student is their advisor. Deveraux talks compellingly about the difference that power can make: how an advisor who is cruel, or indifferent, or just clueless, can make or break not just your career but your psychological well-being. The lucky students, like Deveraux and me, find supportive mentors who help us survive and move forward. The unlucky students leave with scars, even if those scars aren’t jigsaw-shaped.
Neither Deveraux or I have experience with PhD programs in Europe, which are quite different in structure from those in the US. But the power imbalance is still there, and still deadly, and so despite the different structure, I’ve seen students here break down, scarred in the same way.
Deveraux frames his post as advice for those who want to go to grad school, and his first piece of advice is “Have you tried wanting something else?” I try to echo that when I advise students. I don’t always succeed: there’s something exciting about a young person interested in the same topics we’re interested in, willing to try to make a life of it. But it is important to know what you’re getting into, and to know there’s a big world out there of other options. If, after all that, you decide to stick through it, just remember: power matters. If you give someone power over you, try to be as sure as you can that it won’t turn into a horror story.
I’m in Uppsala in Sweden this week, at an actual in-person conference.
With actual blackboards!
Elliptics started out as a series of small meetings of physicists trying to understand how to make sense of elliptic integrals in calculations of colliding particles. It grew into a full-fledged yearly conference series. I organized last year, which naturally was an online conference. This year though, the stage was set for Uppsala University to host in person.
I should say mostly in person. It’s a hybrid conference, with some speakers and attendees joining on Zoom. Some couldn’t make it because of travel restrictions, or just wanted to be cautious about COVID. But seemingly just as many had other reasons, like teaching schedules or just long distances, that kept them from coming in person. We’re all wondering if this will become a long-term trend, where the flexibility of hybrid conferences lets people attend no matter their constraints.
The hybrid format worked better than expected, but there were still a few kinks. The audio was particularly tricky, it seemed like each day the organizers needed a new microphone setup to take questions. It’s always a little harder to understand someone on Zoom, especially when you’re sitting in an auditorium rather than focused on your own screen. Still, technological experience should make this work better in future.
Content-wise, the conference began with a “mini-school” of pedagogical talks on particle physics, string theory, and mathematics. I found the mathematical talks by Erik Panzer particularly nice, it’s a topic I still feel quite weak on and he laid everything out in a very clear way. It seemed like a nice touch to include a “school” element in the conference, though I worry it ate too much into the time.
The rest of the content skewed more mathematical, and more string-theoretic, than these conferences have in the past. The mathematical content ranged from intriguing (including an interesting window into what it takes to get high-quality numerics) to intimidatingly obscure (large commutative diagrams, category theory on the first slide). String theory was arguably under-covered in prior years, but it felt over-covered this year. With the particle physics talks focusing on either general properties with perhaps some connections to elliptics, or to N=4 super Yang-Mills, it felt like we were missing the more “practical” talks from past conferences, where someone was computing something concrete in QCD and told us what they needed. Next year is in Mainz, so maybe those talks will reappear.
Tonight is “Culture Night” in Copenhagen, the night when the city throws open its doors and lets the public in. Museums and hospitals, government buildings and even the Freemasons, all have public events. The Niels Bohr Institute does too, of course: an evening of physics exhibits and demos, capped off with a public lecture by Denmark’s favorite bow-tie wearing weirder-than-usual string theorist, Holger Bech Nielsen. In between, there are a number of short talks by various folks at the institute, including yours truly.
In my talk, I’m going to try and motivate the audience to care about math. Math is dry of course, and difficult for some, but we physicists need it to do our jobs. If you want to be precise about a claim in physics, you need math simply to say what you want clearly enough.
Since you guys likely don’t overlap with my audience tonight, it should be safe to give a little preview. I’ll be using a few examples, but this one is the most complicated:
I’ll be telling a story I stole from chapter seven of the web serial Almost Nowhere. (That link is to the first chapter, by the way, in case you want to read the series without spoilers. It’s very strange, very unique, and at least in my view quite worth reading.) You follow a warrior carrying a spear around a globe in two different paths. The warrior tries to always point in the same direction, but finds that the two different paths result in different spears when they meet. The story illustrates that such a simple concept as “what direction you are pointing” isn’t actually so simple: if you want to think about directions in curved space (like the surface of the Earth, but also, like curved space-time in general relativity) then you need more sophisticated mathematics (a notion called parallel transport) to make sense of it.
It’s kind of an advanced concept for a public talk. But seeing it show up in Almost Nowhere inspired me to try to get it across. I’ll let you know how it goes!
By the way, if you are interested in learning the kinds of mathematics you need for theoretical physics, and you happen to be a Bachelor’s student planning to pursue a PhD, then consider the Perimeter Scholars International Master’s Program! It’s a one-year intensive at the Perimeter Institute in Waterloo, Ontario, in Canada. In a year it gives you a crash course in theoretical physics, giving you tools that will set you ahead of other beginning PhD students. I’ve witnessed it in action, and it’s really remarkable how much the students learn in a year, and what they go on to do with it. Their early registration deadline is on November 15, just a month away, so if you’re interested you may want to start thinking about it.
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