Category Archives: Life as a Physicist

Why I Spent Convergence Working

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Convergence is basically Perimeter Institute Christmas.

This week, the building was dressed up in festive posters and elaborate chalk art, and filled with Perimeter’s many distant relations. Convergence is like a hybrid of an alumni reunion and a conference, where Perimeter’s former students and close collaborators come to hear talks about the glory of Perimeter and the marvels of its research.

Sponsored by the Bank of Montreal

And I attended none of those talks.

I led a discussion session on the first day of Convergence (which was actually pretty fun!), and I helped out in the online chat for the public lecture on Emmy Noether. But I didn’t register for the conference, and I didn’t take the time to just sit down and listen to a talk.

Before you ask, this isn’t because the talks are going to be viewable online. (Though they are, and I’d recommend watching a few if you’re in the mood for a fun physics talk.)

It’s partly to do with how general these talks are. Convergence is very broad: rather than being focused on a single topic, its goal is to bring people from very different sub-fields together, hopefully to spark new ideas. The result, though, are talks that are about as broad as you can get while still being directed at theoretical physicists. Most physics departments have talks like these once a week, they’re called colloquia. Perimeter has colloquia too: they’re typically in the room that the Convergence talks happened in. Some of the Convergence talks have already been given as colloquia! So part of my reluctance is the feeling that, if I haven’t seen these talks before, I probably will before too long.

The main reason, though, is work. I’ve been working on a fairly big project, since shortly after I got to Perimeter. It’s an extension of my previous work, dealing with the next, more complicated step in the same calculation. And it’s kind of driving me nuts.

The thing is, we had almost all of what we needed around January. We’ve accomplished our main goal, we’ve got the result that we were looking for. We just need to plot it, to get actual numbers out. And for some reason, that’s taken six months.

This week, I thought I had an idea that would make the calculation work. Rationally, I know I could have just taken the week to attend Convergence, and worked on the problem afterwards. We’ve waited six months, we can wait another week.

But that’s not why I do science. I do science to solve problems. And right here, in front of me, I had a problem that maybe I could solve. And I knew I wasn’t going to be able to focus on a bunch of colloquium talks with that sitting in the back of my mind.

So I skipped Convergence, and sat watching the calculation run again and again, each time trying to streamline it until it’s fast enough to work properly. It hasn’t worked yet, but I’m so close. So I’m hoping.

Physics Is a Small World

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Earlier this week, Vilhelm Bohr gave a talk at Perimeter about the life of his grandfather, the famous physicist Niels Bohr. The video of the talk doesn’t appear to be up on the Perimeter site yet, but it should be soon.

Until then, here is a picture of some eyebrows.

This was especially special for me, because my family has a longstanding connection to the Bohrs. My great grandfather worked at the Niels Bohr Institute in the mid-1930’s, and his children became good friends with Bohr’s grandchildren, often visiting each other even after my family relocated to the US.

These kinds of connections are more common in physics than you might think. Time and again I’m surprised by how closely linked people are in this field. There’s a guy here at Perimeter who went to school with Jaroslav Trnka, and a bunch of Israelis at nearby institutions all know each other from college. In my case, I went to high school with an unusually large number of mathematicians.

While it’s fun to see familiar faces, there’s a dark side to the connected nature of physics. So much of what it takes to succeed in academia involves knowing unwritten rules, as well as a wealth of other information that just isn’t widely known. Many people don’t even know it’s possible to have a career in physics, and I’ve met many who didn’t know that science grad schools pay your tuition. Academic families, and academic communities, have an enormous leg up on this kind of knowledge, so it’s not surprising that so many physicists come from so few sources.

Artificially limiting the pool of people who become physicists is bound to hurt us in the long run. Great insights often come from outsiders, like Hooke in the 17th century and Noether in the early 20th. If we can expand the reach of physics, make the unwritten rules written and the secret tricks revealed, if we work to make physics available to anyone who might be suited for it, then we can make sure that physics doesn’t end up a hereditary institution, with all the problems that entails.

Calculus Is About Pokemon

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Occasionally, people tell me that calculus was when they really gave up on math. It’s a pity, because for me calculus was the first time math really started to become fun. After all, it’s when math introduces the Pokemon.

What Pokemon? Why, the special functions of course.

By special functions I mean things like \sin x, \cos x, e^x, and \ln x. Like Pokemon, these guys come in a bewildering variety. And in calculus, you learn that they, like Pokemon, can evolve.

x integrates into \frac{1}{2}x^2!

\frac{1}{x} integrates into \ln x!

\sin x integrates into -\cos x, and \cos x integrates into…\sin x.

Ok, the analogy isn’t perfect. Pokemon don’t evolve back into themselves. But the same things that make Pokemon so appealing are precisely why calculus was such a breath of fresh air. Suddenly, there was a grand diversity of new things, and those new things were related.

College gave me new Pokemon, in the form of the Bessel functions. Nowadays, I work with a group of functions called Polylogarithms, and they’re even more like Pokemon. Logarithms are like the baby Pokemon of the Polylogarithms, integrating into Dilogarithms. Dilogarithms integrate into Trilogarithms, and so on.

062poliwrath

Polylogarithms, in turn, evolve into Poliwrath

To this day, the talks I enjoy the most are those that show me new special functions, or new relations between old ones. If a talk shows me a new use of multiple zeta values, or new types of Polylogarithm, it’s not just teaching me new physics or mathematics: it’s expanding my Pokemon collection.

The Cycle of Exploration

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Science is often described as a journey of exploration. You might imagine scientists carefully planning an expedition, gathering their equipment, then venturing out into the wilds of Nature, traveling as far as they can before returning with tales of the wonders they discovered.

Is it capybaras? Please let it be capybaras.

Is it capybaras? Please let it be capybaras.

This misses an important part of the story, though. In science, exploration isn’t just about discovering the true nature of Nature, as important as that is. It’s also about laying the groundwork for future exploration.

Picture our explorers, traveling out into the wilderness with no idea what’s in store. With only a rough idea of the challenges they might face, they must pack for every possibility: warm clothing for mountains, sunscreen for the desert, canoes to ford rivers, cameras in case they encounter capybaras. Since they can only carry so much, they can only travel so far before they run out of supplies.

Once they return, though, the explorers can assess what they did and didn’t need. Maybe they found a jungle, full of capybaras. The next time they travel they’ll make sure to bring canoes and cameras, but they can skip the warm coats. This lets them free up more room, letting them bring more supplies that’s actually useful. In the end, this lets them travel farther.

Science is a lot like this. The more we know, the better questions we can ask, and the further we can explore. It’s true not just for experiments, but for theoretical work as well. Here’s a slide from a talk I’m preparing, about how this works in my sub-field of Amplitudeology.

Unfortunately not a capybara.

Unfortunately not a capybara.

In theoretical physics, you often start out doing a calculation using the most general methods you have available. Once you’ve done it, you understand a bit more about your results: in particular, you can start figuring out which parts of the general method are actually unnecessary. By paring things down, you can figure out a new method, one that’s more efficient and allows for more complicated calculations. Doing those calculations then reveals new patterns, letting you propose even newer methods and do even more complicated calculations.

It’s the circle of exploration, and it really does move us all, motivating everything we do. With each discovery, we can go further, learn more, than the last attempt, keeping science churning long into the future.

My Travels, and Someone Else’s

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I arrived in São Paulo, Brazil a few days ago. I’m going to be here for two months as part of a partnership between Perimeter and the International Centre for Theoretical Physics – South American Institute for Fundamental Research. More specifically, I’m here as part of a program on Integrability, a set of tricks that can, in limited cases, let physicists bypass the messy approximations we often have to use.

I’m still getting my metaphorical feet under me here, so I haven’t had time to think of a proper blog post. However, if you’re interested in hearing about the travels of physicists in general, a friend of mine from Stony Brook is going to the South Pole to work on the IceCube neutrino detection experiment, and has been writing a blog about it.

Where do you get all those mathematical toys?

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I’m at a conference at Caltech this week, so it’s going to be a shorter post than usual.

The conference is on something call the Positive Grassmannian, a precursor to Nima Arkani-Hamed’s much-hyped Amplituhedron. Both are variants of a central idea: take complicated calculations in physics and express them in terms of clean, well-defined mathematical objects.

Because of this, this conference is attended not just by physicists, but by mathematicians as well, and it’s been interesting watching how the two groups interact.

From a physics perspective, mathematicians are great because they give us so many useful tools! Many significant advances in my field happened because a physicist talked to a mathematician and learned that a problem that had stymied the physics world had already been solved in the math community.

This tends to lead to certain expectations among physicists. If a mathematician gives a talk at a physics conference, we expect them to present something we can use. Our ideal math talk is like when Q presents the gadgets at the beginning of a Bond movie: a ton of new toys with just enough explanation for us to use them to save the day in the second act.

Pictured: Mathematicians, through Physicist eyes

You may see the beginning of a problem here, once you realize that physicists are the James Bond in this analogy.

Physicists like to see themselves as the protagonists of their own stories. That’s true of every field, though, to some degree or another. And it’s certainly true of mathematicians.

Mathematicians don’t go to physics conferences just to be someone’s supporting cast. They do it because physics problems are interesting to them: by hearing what physicists are working on they hope to get inspiration for new mathematical structures, concepts jury-rigged together by physicists that represent corners that mathematics hasn’t yet explored. Their goal is to take home an idea that they can turn into something productive, gaining glory among their fellow mathematicians. And if that sounds familiar…

Pictured: Physicists, through Mathematician eyes

While it’s amusing to watch the different expectations go head-to-head, the best collaborations between physicists and mathematicians are those where both sides respect that the other is the protagonist of their own story. Allow for give-and-take, paying attention not just to what you find interesting but to what the other person does, without assuming a tired old movie script, and it’s possible to make great progress.

Of course, that’s true of life in general as well.

Research or Conference? Can’t it be both?

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“If you’re there for two months, for sure you’ll be doing research.”

I wanted to be snarky. I wanted to point out that, as a theoretical physicist, I do research wherever I go. I wanted to say that I even did research on the drive over. (This may not have been true, I think I mostly thought about Magic the Gathering cards.)

More than any of those, though, I wanted to get my travel visa. So instead I said,

“That’s fair.”

“Mmhmm, that’s fair.” Looking down at the invitation letter, she triumphantly pointed to the name of the inviting institution: “South American Institute for Fundamental Research.”

A bit of background: I’m going to Brazil this winter. Partly, this is because winter in Canada is not especially desirable, but it’s also because Sao Paulo’s International Center for Theoretical Physics is running a Program on Integrability, the arcane set of techniques that seeks to bypass the approximate perturbations we often use in particle physics and find full, exact results.

What do I mean by a Program? It’s not the sort of scientific program I’ve talked about before, though the ideas are related. When an institute holds a Program, they’re declaring a theme. For a certain length of time (generally from a few months to a whole semester), there will be a large number of talks at the institute focused on some particular scientific theme. The institute invites people from all over the world who work on that theme. Those people are there to give and attend talks, but they’re also there to share ideas with each other, to network and collaborate and do research.

This is where things get tricky. See, Brazil has multiple types of visas. A Tourist Visa can be used, among other things, for attending a scientific conference. On the other hand, someone coming to Brazil to do research uses Visa 1.

A Program is essentially a long conference…but it’s also an opportunity to do research. So are most short conferences, though! In theoretical physics we have workshops, short conferences explicitly focused on collaboration and research, but even if a conference isn’t a workshop you can bet that we’ll be doing some research there, for sure. We don’t need labs, and some of us don’t even need computers, research can happen whenever the inspiration strikes. The distinction between conferences and research, from our perspective, is an arbitrary one.

In physics, we like to cut through this sort of ambiguity by looking at what’s really important. I wanted to figure out what about research makes the Brazilian government use a different visa for it, whether it was about motivating people to enter the country for specific reasons or tracking certain sorts of activities. I wanted to understand that, because it would let me figure out whether my own research fell under those reasons, and thus figure out objectively which type of visa I ought to have.

I wanted to ask about all of this…but more than any of that, I wanted to get my travel visa. So I applied for the visa they told me to, and left.

Science is Debugging

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What do I do, when I get to work in the morning?

I debug programs.

I debug programs literally, in that most of the calculations I do are far to complicated to do by hand. I write programs to do my calculations, and invariably these programs have bugs. So, I debug.

I debug programs in a broader sense, too.

In science, a research program is a broad approach, taken by a number of people, used to make progress on some set of important scientific questions. Someone suggests a way forward (“Let’s try using an ansatz of transcendental functions!” “Let’s try to represent our calculations with a geometrical object!”) and they and others apply the new method to as many problems as they can. Eventually the program loses steam, and a new program is proposed.

The thing about these programs is, they’re pretty much never fully fleshed out at the beginning. There’s a general idea, and a good one, but it usually requires refinement. If you just follow the same steps as the first person in the program you’re bound to fail. Instead, you have to tweak the program, broadening it and adapting it to the problem you’re trying to solve.

It’s a heck of a lot like debugging a computer program, really. You start out with a hastily written script, and you try applying it as-is, hoping that it works. Often it doesn’t, and you have to go back, step by step, and figure out what’s going wrong.

So when I debug computer programs at work, I’m doing it with a broader goal. I’m running a scientific program, looking for bugs in that. If and when I find them, I can write new computer programs to figure out what’s going wrong. Then I have to debug those computer programs…

I’ll just leave this here.

The Near and the Far: Motivations for Physics

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When I introduce myself, I often describe my job like this:

“I develop mathematical tools to make calculations in particle physics easier and more efficient.”

However, I could equally well describe my job like this:

“I’m looking for a radical new way to reformulate particle physics in order to solve fundamental problems in space and time.”

These may sound very different, but they’re both correct. That’s because in theoretical physics, like in many branches of science, we have two types of goals: near-term and far-term.

In the near-term, I develop mathematical tools and tricks, which let me calculate things I (and others) couldn’t calculate before. Pushing the tricks to their limits gives me more proficiency, making the tools I develop more robust. In the future, I can imagine applying the tools to more types of calculations, and specifically to more “important” calculations.

All of that still involves relatively near-term goals, though. Develop a new trick, and you can already envision what it might be used for. The far-term goals are generally deeper.

End of the road, not just the next tree.

In the far term, the new techniques that I and others develop might lead to fundamentally new ways to understand particle physics. That’s because a central feature of most of the tricks we develop is that they rephrase the calculation in a way that leaves out something that used to be thought of as fundamental. They’re “revolutions”, overthrowing some basic principle of how we do things. The hope is that the right “revolution” will help us solve problems that our current understanding of physics seems incapable of solving.

Most scientists have both sorts of goals. Someone who studies quantum mechanics might talk about developing a quantum computer, but in the near-term be interested in perfecting some algorithm. A biologist might study how information is stored in a cell, but introduce themself as someone trying to cure cancer.

For some people, the far-term goals are a big component of how they view themselves. Nima Arkani-Hamed, for example, has joked that believing that “spacetime is doomed” is what allows him to get out of bed in the morning. (For a transcript of the relevant parts, see here.) There are plenty of others with similar perspectives, people who need a “big” goal to feel motivated.

Myself, I find it harder to identify with these kinds of goals, because the payoff is so uncertain. Rephrasing particle physics in a new way might be the solution to a fundamental problem…but it could also just be another way to say the same thing. There’s no guarantee that any one project will be that one magical solution. In contrast, for me, near term goals are something I can feel confident I’m making real progress on. I can envision each step along the way, and see the part my work plays in a larger picture, led along by the satisfaction of solving each puzzle as it comes.

Neither way is better than the other, and both are important parts of science. Some people do better with one, some do better with the other, and in the end, everyone can view themselves as accomplishing something they care about.

Perimeter!

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I’m moving in at Perimeter this week, so I don’t have time to write a long post. For those who aren’t familiar with it, the Perimeter Institute for Theoretical Physics is an independent research institute, not affiliated with any university. Instead, it’s funded by a combination of government and private sources (for why private sources might fund theoretical physics, read my discussion here). Because it’s not a university they have budgets to do things like hire people to make the transition process easier, so everything has been really nice and well-organized.

The postdoc offices are really nice, with a view of the nearby park, shown below.

On the Perimeter...of Waterloo Park

On the Perimeter…of Waterloo Park