This post is once again inspired by a Ted Chiang short story. This time, it’s “The Evolution of Human Science”, which imagines a world in which super-intelligent “metahumans” have become incomprehensible to the ordinary humans they’ve left behind. Human scientists in that world practice “hermeneutics“: instead of original research, they try to interpret what the metahumans are doing, reverse-engineering their devices and observing their experiments.

It’s a thought-provoking view of what science in the distant future could become. But it’s also oddly familiar.

You might think I’m talking about machine learning here. It’s true that in recent years people have started using machine learning in science, with occasionally mysterious results. There are even a few cases of physicists using machine-learning to suggest some property, 更改ip地址就可以连外网了, and then figuring out how to prove it. It’s not hard to imagine a day when scientists are reduced to just interpreting whatever the AIs throw at them…but I don’t think we’re quite there yet.

Instead, I’m thinking about my own work. I’m a particular type of theoretical physicist. I calculate scattering amplitudes, formulas that tell us the probabilities that subatomic particles collide in different ways. We have a way to calculate these, Feynman’s famous diagrams, but they’re inefficient, so researchers like me look for shortcuts.

How do we find those shortcuts? Often, it’s by doing calculations the old, inefficient way. We use older methods, look at the formulas we get, and try to find patterns. Each pattern is a hint at some new principle that can make our calculations easier. Sometimes we can understand the pattern fully, and prove it should hold. Other times, we observe it again and again and tentatively assume it will keep going, and see what happens if it does.

Either way, this isn’t so different from the hermeneutics scientists practice in the story. Feynman diagrams already “know” every pattern we find, like the metahumans in the story who already know every result the human scientists can discover. But that “knowledge” isn’t in a form we can understand or use. We have to learn to interpret it, to read between the lines and find underlying patterns, to end up with something we can hold in our own heads and put into action with our own hands. The truth may be “out there”, but scientists can’t be content with that. We need to get the truth “in here”. We need to interpret it for ourselves.

I’ve got unification on the brain.

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Physics admits of a lovely unification, not just at the level of fundamental forces, but when considering its extent and implications. Classifications like ‘optics’ or ‘thermodynamics’ are just straitjackets, preventing physicists from seeing countless intersections.

This passage sounds nice enough, but I feel like there’s a misunderstanding behind it. When physicists seek after unification, we’re talking about something quite specific. It’s not merely a matter of two topics intersecting, or describing them with the same math. We already plumb intersections between fields, 能爆粗吗？联通将我公网IP改成内网了。。。 - 网络设备 ...:2021-1-8 · 昨天下午家里的黑裙NAS开始登陆不上了，花生壳，3322都不行。心想不是俩都没解析地址吧？回家一看路由，我艹！WAN口IP成100开头了。心中一万个草泥马飞过。。已经联系1001 ... 能爆粗吗？联通将我公网IP改成内网了。。。 ,KoolShare. When we hope to find a unified theory, we do so because it does something. A real unified theory doesn’t just aid our calculations, it gives us new ways to alter the world.

To show you what I mean, let me start with something physicists already know: electroweak unification.

There’s a nice series of posts on the old Quantum Diaries blog that explains electroweak unification in detail. I’ll be a bit vaguer here.

You might have heard of four fundamental forces: gravity, electromagnetism, the strong nuclear force, and the weak nuclear force. You might have also heard that two of these forces are unified: the electromagnetic force and the weak nuclear force form something called the electroweak force.

What does it mean that these forces are unified? How does it work?

Zoom in far enough, and you don’t see the electromagnetic force and the weak force anymore. Instead you see two different forces, I’ll call them “W” and “B”. You’ll also see the Higgs field. And crucially, you’ll see the “W” and “B” forces interact with the Higgs.

The Higgs field is special because it has what’s called a 怎么更改手机外网ip value. Even in otherwise empty space, there’s some amount of “Higgsness” in the background, like the color of a piece of construction paper. This background Higgs-ness is in some sense an accident, just one stable way the universe happens to sit. In particular, it picks out an arbitrary kind of direction: parts of the “W” and “B” forces happen to interact with it, and parts don’t.

Now let’s zoom back out. We could, if we wanted, keep our eyes on the “W” and “B” forces. But that gets increasingly silly. As we zoom out we won’t be able to see the Higgs field anymore. Instead, we’ll just see different parts of the “W” and “B” behaving in drastically different ways, depending on whether or not they interact with the Higgs. It will make more sense to talk about mixes of the “W” and “B” fields, to distinguish the parts that are “lined up” with the background Higgs and the parts that aren’t. It’s like using “aft” and “starboard” on a boat. You could use “north” and “south”, but that would get confusing pretty fast.

What are those “mixes” of the “W” and “B” forces? Why, they’re the weak nuclear force and the electromagnetic force!

This, broadly speaking, is the kind of unification physicists look for. It doesn’t have to be a “mix” of two different forces: most of the models physicists imagine start with a single force. But the basic ideas are the same: that if you “zoom in” enough you see a simpler model, but that model is interacting with something that “by accident” picks a particular direction, so that as we zoom out different parts of the model behave in different ways. In that way, you could get from a single force to all the different forces we observe.

That “by accident” is important here, because that accident can be changed. That’s why I said earlier that real unification lets us alter the world.

To be clear, we can’t change the background Higgs field with current technology. The biggest collider we have can just make a tiny, temporary fluctuation (that’s what the Higgs boson is). But one implication of electroweak unification is that, with enough technology, we could. Because those two forces are unified, and because that unification is physical, with a physical cause, it’s possible to alter that cause, to change the mix and change the balance. This is why this kind of unification is such a big deal, why it’s not the sort of thing you can just chalk up to “interpretation” and ignore: when two forces are unified in this way, it 怎么更改手机外网ip.

Mathematical unification is valuable. It’s great when we can look at different things and describe them in the same language, or use ideas from one to understand the other. But it’s not the same thing as physical unification. When two forces really unify, it’s an undeniable physical fact about the world. When two forces unify, it does something.

There are two kinds of theoretical physicists. Some, called phenomenologists, make predictions about the real world. Others, the so-called “formal theorists”, don’t. They work with the same kinds of theories as the phenomenologists, quantum field theories of the sort that have been so successful in understanding the subatomic world. But the specific theories they use are different: usually, toy models that aren’t intended to describe reality.

Most people get this is valuable. It’s useful to study toy models, because they help us tackle the real world. But they stumble on another point. Sure, they say, you can study toy models…but then you should call yourself a mathematician, not a physicist.

I’m a “formal theorist”. And I’m very much not a mathematician, I’m definitely a physicist. Let me explain why, with an analogy.

As an undergrad, I spent some time working in a particle physics lab. The lab had developed a new particle detector chip, designed for a future experiment: the International Linear Collider. It was my job to test this chip.

Naturally, I couldn’t test the chip by flinging particles at it. For one, the collider it was designed for hadn’t been built yet! Instead, I had to use simulated input: send in electrical signals that mimicked the expected particles, and see what happens. In effect, I was using a kind of toy model, as a way to understand better how the chip worked.

I hope you agree that this kind of work counts as physics. It isn’t “just engineering” to feed simulated input into a chip. Not when the whole point of that chip is to go into a physics experiment. This kind of work is a large chunk of what an experimental physicist does.

As a formal theorist, my work with toy models is an important part of what a theoretical physicist does. I test out the “devices” of theoretical physics, the quantum-field-theoretic machinery that we use to investigate the world. Without that kind of careful testing on toy models, we’d have fewer tools to work with when we want to understand reality.

Ok, but you might object: an experimental physicist does eventually build the real experiment. They don’t just spend their career on simulated input. If someone only works on formal theory, shouldn’t that at least make them a mathematician, not a physicist?

Here’s the thing, though: after those summers in that lab, I didn’t end up as an experimental physicist. After working on that chip, I didn’t go on to perfect it for the International Linear Collider. But it would be rather bizarre if that, retroactively, made my work in that time “engineering” and not “physics”.

Oh, I should also mention that the International Linear Collider might not ever be built. So, there’s that.

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I avoid talking politics on this blog. There are a few issues, though, where I feel not just able, but duty-bound, to speak out. Those are issues affecting graduate students.

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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, 更改ip地址就可以连外网了 (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.

It feels like the people who made this decision didn’t think about any of this. That they don’t think grad students matter, or forgot they exist altogether. It seems frustratingly common for policy that affects grad students to be made by people who know nothing about grad students, and that baffles me. PhDs are a vital part of the academic career, without them universities in their current form wouldn’t even exist. Ignoring them is like if hospital policy ignored residencies.

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.

Sabine Hossenfelder had an explainer video recently on 【查看虚拟机网络是否通】-博文推荐-CSDN博客:2021-6-7 · csdn已为您找到关于查看虚拟机网络是否通相关内容，包含查看虚拟机网络是否通相关文档代码介绍、相关教学视频课程，以及相关查看虚拟机网络是否通问答内容。为您解决当下相关问题，如果想了解更详细查看虚拟机网络是否通内容，请点击详情链接进行了解，或者注册账号与客服人员联系给您 .... This is a famously difficult problem, so naturally we have different opinions. I actually think the picture she draws is reasonably sound. But while it is a good criterion to tell whether you yourself are doing pseudoscience, it’s surprisingly tricky to apply it to other people.

Hossenfelder argues that science, at its core, is about explaining observations. To tell whether something is science or pseudoscience you need to ask, first, if it agrees with observations, and second, if it is simpler than those observations. In particular, a scientist should prefer models with fewer parameters. If your model has so many parameters that you can fit any observation, you’re not being scientific.

This is a great rule of thumb, one that as Hossenfelder points out forms the basis of a whole raft of statistical techniques. It does rely on one tricky judgement, though: how many parameters does your model actually have?

Suppose I’m one of those wacky theorists who propose a whole new particle to explain some astronomical mystery. Hossenfelder, being more conservative in these things, proposes a model with no new particles. Neither of our models fit the data perfectly. Perhaps my model fits a little better, but after all it has one extra parameter, from the new particle. If we want to compare our models, we should take that into account, and penalize mine.

Here’s the question, though: how do I know that Hossenfelder didn’t start out with more particles, and got rid of them to get a better fit? If she did, she had more parameters than I did. She just fit them away.

The problem here is closely related to one called the look-elsewhere effect. Scientists don’t publish everything they try. An unscrupulous scientist can do a bunch of different tests until one of them randomly works, and just publish that one, making the result look meaningful when really it was just random chance. Even if no individual scientist is unscrupulous, a community can do the same thing: many scientists testing many different models, until one accidentally appears to work.

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The normal way to deal with the look-elsewhere effect is to consider, not just whatever tests the scientist claims to have done, but all tests they could reasonably have done. You need to count all the parameters, not just the ones they say they varied.

This works in some fields. If you have an idea of what’s reasonable and what’s not, you have a relatively manageable list of things to look at. You can come up with clear rules for which theories are simpler than others, and people will agree on them.

Physics doesn’t have it so easy. We don’t have any pre-set rules for what kind of model is “reasonable”. If we want to parametrize every “reasonable” model, the best we can do are what are called Effective Field Theories, theories which try to describe every possible type of new physics in terms of its effect on the particles we already know. Even there, though, we need assumptions. The most popular effective field theory, called SMEFT, assumes the forces of the Standard Model keep their known symmetries. You get a different model if you relax that assumption, and even that model isn’t the most general: for example, it still keeps relativity intact. Try to make the most general model possible, and you end up waist-deep in parameter soup.

Subjectivity is a dirty word in science…but as far as I can tell it’s the only way out of this. We can try to count parameters when we can, and use statistical tools…but at the end of the day, we still need to make choices. We need to judge what counts as an extra parameter and what doesn’t, which possible models to compare to and which to ignore. That’s going to be dependent on our scientific culture, on fashion and aesthetics, there just isn’t a way around that. The best we can do is own up to our assumptions, and be ready to change them when we need to.

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Recently, this has all been jeopardized. A reporter at the New York Times, writing an otherwise positive article, told Scott he was going to reveal his real name publicly. In a last-ditch effort to stop this, Scott deleted his blog.

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I don’t know why the Times thinks revealing Scott’s name is a good idea. I do know that there are people out there who view anyone under a pseudonym with suspicion. Compared to Scott, my pseudonym is paper-thin: it’s very easy to find who I am. Still, I have met people who are irked just by that, by the bare fact that I don’t print my real name on this blog.

I think this might be a generational thing. My generation grew up alongside the internet. We’re used to the idea that very little is truly private, that anything made public somewhere risks becoming public everywhere. In that world, writing under a pseudonym is like putting curtains on a house. It doesn’t make us unaccountable: if you break the law behind your curtains the police can get a warrant, similarly Scott’s pseudonym wouldn’t stop a lawyer from tracking him down. All it is, is a filter: a way to have a life of our own, shielded just a little from the whirlwind of the web.

I know there are journalists who follow this blog. If you have contacts in the Times tech section, or know someone who does, please reach out. I want to hope that someone there is misunderstanding the situation, that when things are fully explained they will back down. We have to try.

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 “怎么更换外网ip“, 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.

Scientific programming was in the news lately, when doubts were raised about a coronavirus simulation by researchers at Imperial College London. While the doubts appear to have been put to rest, doing so involved digging through some seriously messy code. The whole situation seems to have gotten a lot of people worried. If these people are that bad at coding, why should we trust their science?

I don’t know much about coronavirus simulations, my knowledge there begins and ends with a talk I saw last month. But I know a thing or two about bad scientific code, because I write it. My code is atrocious. And I’ve seen published code that’s worse.

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In part, it’s a matter of training. Some scientists have formal coding training, but most don’t. I took two CS courses in college and that was it. Despite that lack of training, we’re expected and encouraged to code. Before I took those courses, I spent a summer working in a particle physics lab, where I was expected to pick up the C++-based interface pretty much on the fly. I don’t think there’s another community out there that has as much reason to code as scientists do, and as little training for it.

Would it be useful for scientists to have more of the tools of a trained coder? Sometimes, yeah. Version control is a big one, I’ve collaborated on papers that used Git and papers that didn’t, and there’s a big difference. There are coding habits that would speed up our work and lead to fewer dead ends, and they’re worth picking up when we have the time.

But there’s a reason we don’t prioritize “proper coding”. It’s because the things we’re trying to do, from a coding perspective, are 怎么更改手机外网ip.

What, code-wise, is a coronavirus simulation? A vector of “people”, really just simple labels, all randomly infecting each other and recovering, with a few parameters describing how likely they are to do so and how long it takes. What do I do, code-wise? Mostly, giant piles of linear algebra.

These are not some sort of cutting-edge programming tasks. These are things people have been able to do since the dawn of computers. These are things that, when you screw them up, become quite obvious quite quickly.

Compared to that, the everyday tasks of software developers, like making a reliable interface for users, or efficient graphics, are much more difficult. They’re tasks that really require good coding practices, that just can’t function without them.

For us, the important part is not the coding itself, but what we’re doing with it. Whatever bugs are in a coronavirus simulation, they will have much less impact than, for example, the way in which the simulation includes superspreaders. Bugs in my code give me obviously wrong answers, bad scientific assumptions are much harder for me to root out.

There’s an exception that proves the rule here, and it’s that, when the coding task is actually difficult, scientists step up and write better code. Scientists who want to run efficiently on supercomputers, who are afraid of numerical error or need to simulate on many scales at once, these people learn how to code properly. The code behind the LHC still might be jury-rigged by industry standards, but it’s light-years better than typical scientific code.

I get the furor around the Imperial group’s code. I get that, when a government makes a critical decision, you hope that their every input is as professional as possible. But without getting too political for this blog, let me just say that whatever your politics are, if any of it is based on science, it comes from code like this. Psychology studies, economic modeling, polling…they’re using code, and it’s jury-rigged to hell. Scientists just have more important things to worry about.

In the past, what did we know about eel reproduction? What do we know now?

The answer to both questions is, surprisingly little! For those who don’t know the story, I recommend this New Yorker article. Eels turn out to have a quite complicated life cycle, and can only reproduce in the very last stage. Different kinds of eels from all over Europe and the Americas spawn in just one place: the Sargasso Sea. But while researchers have been able to find newborn eels in those waters, and more recently track a few mature adults on their migration back, no-one has yet observed an eel in the act. Biologists may be able to infer quite a bit, but with no direct evidence yet the truth may be even more surprising than they expect. The details of eel reproduction are an ongoing mystery, the “eel question” one of the field’s most enduring.

But of course this isn’t an eel blog. I’m here to answer a different question.

In the past, what did we know about the Higgs boson? What do we know now?

Ask some physicists, and they’ll say that even before the LHC everyone knew the Higgs existed. While this isn’t quite true, it is certainly true that something like the Higgs boson had to exist. Observations of other particles, the W and Z bosons in particular, gave good evidence for some kind of “Higgs mechanism”, that gives other particles mass in a “Higgs-like-way”. A Higgs boson was in some sense the simplest option, but there could have been more than one, or a different sort of process instead. Some of these alternatives may have been sensible, others as silly as believing that eels come from horses’ tails. Until 2012, when the Higgs boson was observed, we really didn’t know.

We also didn’t know one other piece of information: the Higgs boson’s 更改ip地址就可以连外网了. That tells us, among other things, 淘宝地址经验-淘宝地址填错了怎么办-315货源网:2021-6-15 · 找淘宝地址信息？315货源网淘宝地址经验专题精选了多个受用户欢迎的相关信息，包含淘宝地址经验、货源、延伸阅读、问答、排行等信息，是您了解和查找同类信息的理想平台。. Physicists were pretty sure the LHC was capable of producing a Higgs boson, but they weren’t sure where or how they’d find it, or how much energy would ultimately be involved.

Now thanks to the LHC, we know the mass of the Higgs boson, and we can rule out some of the “alternative” theories. But there’s still quite a bit we haven’t observed. In particular, we haven’t observed many of the Higgs boson’s couplings.

The couplings of a quantum field are how it interacts, both with other quantum fields and with itself. In the case of the Higgs, interacting with other particles gives those particles mass, while interacting with itself is how it itself gains mass. Since we know the masses of these particles, we can infer what these couplings should be, at least for the simplest model. But, like the eels, the truth may yet surprise us. Nothing guarantees that the simplest model is the right one: what we call simplicity is a judgement based on aesthetics, on how we happen to write models down. Nature may well choose differently. All we can honestly do is parametrize our ignorance.

In the case of the eels, each failure to observe their reproduction deepens the mystery. What are they doing that is so elusive, so impossible to discover? In this, eels are different from the Higgs boson. We know why we haven’t observed the Higgs boson coupling to itself, at least according to our simplest models: we’d need a higher-energy collider, more powerful than the LHC, to see it. That’s an expensive proposition, much more expensive than using satellites to follow eels around the ocean. Because our failure to observe the Higgs self-coupling is itself no mystery, our simplest models could still be correct: as theorists, we probably have it easier than the biologists. But if we want to verify our models in the real world, we have it much harder.

During Zoomplitudes (my field’s big yearly conference, this year on Zoom) I didn’t have time to write a long blog post. I said a bit about the format, but didn’t get a chance to talk about the science. I figured this week I’d go back and give a few more of my impressions. As always, conference posts are a bit more technical than my usual posts, so regulars be warned!

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After Shadmi’s talk was a brace of talks on 更改ip地址就可以连外网了, featuring 更改ip地址就可以连外网了 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 recent collaboration. Julio Parra-Martinez discussed some interesting behavior shared by both 怎么更换外网ip 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.