The (2, 0) Theory: What does it mean?

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Part Two of a Series on the (2, 0) Theory

Apologies in advance. This is going to be a long one.

So now that you know that the (2, 0) theory is the world-volume theory of an M5-brane, you might be asking what the hell (2, 0) means. Why is this theory labeled with an arcane bunch of numbers rather than words like any sensible theory?

To explain that, we have to talk a bit about how we count supersymmetries. As I talked about with N=4 super Yang-Mills, supersymmetry is a relationship between particles of different spins, and since one particle can be related in this way to more than one other particle, we indicated the number of different related particles by the number N. (I’d recommend reading those posts to understand this one. If you need a quick summary, spin is a way of categorizing particles, with spin 1 corresponding to forces of nature like electromagnetism and the Yang-Mills forces in general, while spin ½ corresponds to the types of particles that make up much of everyday matter, like electrons and quarks.)

As it turns out, we count the number of supersymmetries N differently in different dimensions. The reasons are fairly technical, and are related to the fact that spin ½ particles are more complicated in higher dimensions. The end result is that while super Yang-Mills has N=4 in four dimensions (three space one time), in six dimensions it only has N=2 (in case you’re curious, it goes all the way down to N=1 in ten dimensions).

The “2” in the (2, 0) theory means the same thing as that N=2. However, the (2, 0) theory is very different from super Yang-Mills, and that’s where the other number in the pair comes in. To explain this, I have to talk a bit about something called chirality.

Chirality is a word for handedness. If you’re given a right-handed glove, no matter what you do you can’t rotate it to turn it into a left-handed glove. The only way you could change a right-handed glove into a left-handed glove would be to flip it through a mirror, like Alice through the looking glass.

Particles often behave similarly. While they don’t have fingers to flip, they do have spin.

I told you earlier to think of spin as just a way to classify particles. That’s still the best way for you to think about it, but in order to explain chirality I have to mention that spin isn’t just an arbitrary classification scheme, it’s a number that corresponds to how fast a particle is “spinning”.

Here I have to caution that the particle isn’t necessarily literally spinning. Rather, it acts as if it were spinning, interacting with other objects as if it were spinning with a particular speed. If you’ve ever played with a gyroscope, you know that a spinning object behaves differently from a non-spinning one: the faster it spins, the harder it is to change the direction in which it is spinning.

Suppose that a particle is flying at you head-on. If you measured the particle’s spin, it would appear to be spinning either clockwise or counterclockwise, to the left or to the right. This choice, left or right, is the particle’s chirality.

L for left, R for right, V and p show which way the particle is going.

The weird thing is that there are some particles that only spin one way. For example, every neutrino that has been discovered has left-handed chirality. In general when a fermion only spins one way we call it a chiral fermion.

What does this have to do with the (2, 0) theory?

Supersymmetry relates particles of spin X to particles of spin X-½.  As such, you can look at supersymmetry as taking the original particle, and “subtracting” a particle of spin ½. These aren’t really particles, but they share some properties, and those properties can include chirality. You can have left-supersymmetry, and right-supersymmetry.

So what does (2, 0) mean? It means that not only is the (2, 0) theory an N=2 theory in six dimensions, but those two supersymmetries are chiral. They are only left-handed (or, if you prefer, only right-handed). By contrast, super Yang-Mills in six dimensions is a (1, 1) theory. It has one left-handed supersymmetry, and one right-handed supersymmetry.

We can now learn a bit more about the sorts of particles in the (2, 0) theory.

As I said when discussing N=4 super Yang-Mills, N=4 is the most supersymmetry you can have in Yang-Mills in four dimensions. Any more, and you need to include gravity.  Recall that the (2, 0) theory comes from the behavior of M5-branes in M theory. M theory includes gravity, which means that it can go higher than N=4.

How high? As it turns out, the maximum including gravity (which I will explain a bit more when I do a series on supergravity) is N=8. That’s in four dimensions, however. In M theory’s native eleven dimensions, this is just N=1. In six dimensions, where the (2, 0) theory lives, this becomes N=4. More specifically, including information about chirality, its supersymmetry is (2, 2).

So if M theory in six dimensions has (2, 2) symmetry, how to we get to (2, 0)? What happens to the other ( ,2)?

As I talked about in the last post, the varying position of the M5-brane in the other five dimensions gives rise to five scalar fields. In a way, we have broken the symmetry between the eleven dimensions of M theory, treating five of them differently from the other six.

It turns out that supersymmetry is closely connected to the symmetry of space and time. What this means in practice is that when you break the symmetry of space-time, you can also break supersymmetry, reducing the number N of symmetries. Here, the M5-brane breaks supersymmetry from (2, 2) to (2, 0), so two of the supersymmetries are broken.

Just like the position of the M5-brane can vary, so too can the specific supersymmetries broken. What this means is that just like the numbers for the positions become scalar fields, the choices of supersymmetry to be broken become new fermion fields. Because supersymmetry is broken in a chiral way, these new fermion fields are chiral, which for technical reasons ends up meanings that because of the two broken supersymmetries, there are four new chiral fermions.

So far, we know that the (2, 0) theory has five scalar fields, and four chiral fermions. But scalar fields and chiral fermions are pretty ordinary, surely not as mysterious as the Emperor, or even Mara Jade. What makes the (2, 0) theory so mysterious, so difficult to deal with? What makes it, in a word, sexy? Tune in next week to find out!

The (2, 0) Theory: Where does it come from?

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Part One of a Series on the (2, 0) Theory

By semi-popular demand, I’m doing a guide on the (2, 0) theory. Over the course of this guide I’ll try to explain where the (2, 0) theory comes from, what its name means, and, more elusively, what it’s actually about.

The (2, 0) theory doesn’t get much press coverage, and when it does, it’s a bit silly. The article I just linked compares it to Star Wars’ Emperor Palpatine, in analogy with what George Musser and perhaps others call the Darth Vader theory, or N=4 super Yang-Mills.

The metaphor, as far as I can parse it, is the following: while N=4 super Yang-Mills is solid, powerful, and important (like Darth Vader), the (2, 0) theory is mysterious and yet somehow even more central (like the Emperor).

The thing is, while the (2, 0) theory is indeed sexy and mysterious, it isn’t especially central. Laymen haven’t heard of it for good reason: it’s really only specialists in the field who have a reason to be interested in it. So really, it’s more like the Mara Jade theory.

If you don’t know who this is, that’s my point

The (2, 0) theory is very much a theory, in the same sense as N=4 super Yang-Mills. It isn’t a “theory of everything”, and it isn’t supposed to describe the real world. With that in mind, let’s talk about the sort of world it does describe.

There are two ways to “define” the (2, 0) theory. One of them is to take a particular type of string theory (type IIB) with ten dimensions (nine space dimensions and one dimension for time), and twist four of those dimensions into a particular shape (called a K3 surface). There are six dimensions left (five space, one time), and in those six dimensions the world obeys the (2, 0) theory.

That definition may not seem particularly illuminating, and it really isn’t. You can get almost any theory in physics by taking some type of string theory and twisting up some of the dimensions in a particular way, so unless you’re familiar with that particular type of string theory or the particular shape of the dimensions, you don’t learn anything from that definition.

The second definition, though, is more appealing. The (2, 0) theory can be defined as the world-volume theory of a five-dimensional object called an M5-brane.

A world-volume theory is a theory that describes what it is like to live inside of the volume of some object, so that the object is your whole world. To understand what that means, think about Flatland.

Think upward, not northward

In Edwin A. Abbott’s Flatland, the characters are two-dimensional shapes living in a two-dimensional world. Because their whole world is two-dimensional, they cannot imagine a third dimension. Despite that, there is a third dimension, as demonstrated by a sphere who floats through the world one day and upsets the main character’s life. The theory of physics in Flatland, then, is the world-volume theory of a two-dimensional plane in three-dimensional space.

Imagine that the two-dimensional plane of Flatland was flexible, that is, more like a two-dimensional membrane. Such a membrane could move back and forth in the third dimension, rippling up and down.

Now remember that, in Flatland, nobody can imagine a third dimension. So if you are within Flatland, and the world around you is bouncing up and down, can you notice?

The answer is a counter-intuitive yes. It’s easy if there is gravity in the third dimension: when the world curves up, it would get harder to climb up, while if the world curves down, it would be easier. Even if there isn’t gravity, though, you can still notice the changes in energy. It takes energy to set the world vibrating, and that energy has to come from somewhere. That energy can come from movement within your dimension. What a Flatlander would observe, then, would be processes that seem to violate conservation of energy, by losing more energy than they put in: instead, that energy would go to making the world wiggle.

What a Flatland scientist would observe, then, would be a world in which there is some number that can change from place to place, and that can oscillate, carrying energy as it does so. Those of you who remember my older posts might recognize what’s going on here: this is precisely the way in which you discover the existence of a scalar field!

An M5-brane is a five-dimensional membrane that lives in M theory, a theory with eleven dimensions (ten space and one time). The world-volume theory of an M5-brane, then, is the theory of what it is like to have your whole world inside the five dimensions of the M5-brane, just like a person in Flatland has their whole world within the two dimensions of Flatland. And just like the two-dimensional Flatland would have one scalar field corresponding to its ability to vibrate in the third dimension, the five space dimensions of the (2, 0) theory have five scalar fields, corresponding to the five other directions (ten minus five) in which the M5-brane can move.

So the (2, 0) theory is the theory of what it’s like to live on a five-dimensional membrane in a ten-dimensional space, and because of that, the theory contains five scalar fields. But if it was just five scalar fields, it would hardly be mysterious. What else does the theory contain? And what does “(2, 0)” mean anyway? Tune in next week to find out!

Edit: I am informed by George Musser (@gmusser on twitter) that the Darth Vader thing was apparently all Nima Arkani-Hamed’s idea. So don’t blame him for the somewhat misleading metaphor!

Hexagon Functions – or, what is my new paper about?

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I’ve got a new paper up on arXiv this week.

(For those of you unfamiliar with it, arXiv.org is a website where physicists, mathematicians, and researchers in related fields post their papers before submitting them to journals. It’s a cultural quirk of physics that probably requires a post in its own right at some point. Anyway…)

What’s it about? Well, the paper is titled Hexagon functions and the three-loop remainder function. Let’s go through that and figure out what it means.

When the paper refers to hexagon functions, it’s referring to functions used to describe situations with six particles involved. An important point to clarify here is that when counting the number of “particles involved”, we add together both the particles that go in and the particles that go out. So if three particles arrive somewhere, interact with each other in some complicated way, and then those three particles leave, that’s a six-particle process. Similarly, if two particles collide and four particles emerge, that’s also a six-particle process. (If you find the idea of more particles coming out than went in confusing, read this post.) Hexagon functions, then, can describe either of those processes.

What, specifically, are these functions being used for? Well, they’re being used to find the three-loop remainder function of N=4 super Yang-Mills.

N=4 super Yang-Mills is my favorite theory. If you haven’t read my posts on the subject, I encourage you to do so.

N=4 super Yang-Mills is so nice because it is so symmetric, and because it takes part in so many dualities. These two traits ended up being enough for Zvi Bern, Lance Dixon, and Vladimir Smirnov to propose an ansatz for all amplitudes in N=4 super Yang-Mills, called the BDS ansatz. (Amplitudes are how we calculate the probability of events occurring: for example, the probability of that “two particles going to four particles” situation I talked about earlier.)

Unfortunately, their formula was incomplete. While it was possible to prove that the formula was true for four-particle and five-particle processes, for six or more particles the formula failed. As it turned out though, it failed in a predictable way. All that was needed to fix it was to add something called the remainder function, the remaining part of the formula beyond the BDS ansatz.

The task, then, was to compute this remainder function.

I’ve talked before about how in quantum field theory, we calculate probabilities through increasingly complicated diagrams, keeping track of the complexity by counting the number of loops. The remainder function had already been computed up to two loops by working out these diagrams, but three looked to be considerably more difficult.

Luckily, we (myself, Lance Dixon, James Drummond, and Jeffrey Pennington) had a trick up our sleeves.

Formulas in N=4 super Yang-Mills have a property called maximal transcendentality. I’ve talked about transcendentality before:  essentially, it’s a way of counting how many powers of pi and logarithms are in your equations. Maximal transcendentality means that every part of the formula has a fixed, maximum number for its degree of transcendentality. In the case of the remainder function, this is two times the number of loops. Thus, the two-loop remainder function has degree of transcendentality four, so it can have pi to the fourth power in it, while the three-loop remainder function (the one that we calculated) has degree of transcendentality six, so it can have pi to the sixth power.

Of course, it can have lots of other expressions as well, which brings us back to the hexagon functions. By classifying the sort of functions that can appear in these formulas at each level of transcendentality, we find the basic building blocks that can show up in the remainder function. All we have to do then is ask what combinations of building blocks are allowed: which ones make good physics sense, for example, or which ones allow our formula to agree with the predictions of other researchers.

As it turns out, once you apply all the restrictions there is only one possible way to put the building blocks together that gives you a functioning formula. By process of elimination, this formula must be the correct three-loop six-point remainder function. Every extra constraint then serves as a check that nothing went wrong and that the formula is sound. Without calculating a single Feynman diagram, we’ve gotten our result!

Just to give you an idea of how complicated this result is, in order to write the formula out fully would take 800 pages. We’ve got shorter ways to summarize it, but perhaps it would be better to give a picture. The formula depends on three variables, called u, v, and w. To show how the formula behaves when all three variables change, here’s a plot of the formula in the variables u and v, for a series of different values of w.

wstacksheaves

Without our various shortcuts to generate this formula, it would have taken an extraordinarily long amount of time. Luckily, N=4 super Yang-Mills’s nice properties save the day, and allow us to achieve what I hope you won’t mind me calling a truly impressive result.

New Guide, Taking Suggestions

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Hello readers!

Some of you have probably read the guide to N=4 super Yang-Mills theory linked at the top of my blog’s home page. A few of you even discovered this blog via the guide.

I’m thinking about doing another series of posts, like those, explaining a different theory. I’d like to get an idea of which theory you guys are most interested in seeing described. Whichever I choose, it will be largely along the same lines as the N=4 posts, so focused less on technical details and more on presenting something that a layman can understand.

Here are some of the options I’m considering:

  • N=8 Supergravity: Very broadly speaking, this is gravity’s equivalent of N=4 super Yang-Mills. It’s connected to N=4 in a variety of interesting ways, and it’s something I’d like to work more with at some point.
  • The (2,0) Theory: This was the motivation behind my first paper. It’s harder to explain than some of the other theories because it doesn’t have an easy analogy with the particles of the real world. It’s also even harder to work with, to the point that saying something rigorous about it is often worthy of a paper on its own.
  • String Theory/M Theory: This is a big topic, and there are many sites out there already that cover aspects of it. What I might try to do is look for an angle of approach that others haven’t covered, and try to explain some slightly more technical aspects of the situation in a popularly approachable way.

I could also give a more detailed description of some method from amplitudeology, like generalized unitarity or symbology.

Finally, I could always just keep posting like I have been doing. But this seems like a good time to add to my site’s utility. So what do you think? What should I talk about?

Dammit Jim, I’m a Physicist not a Graphic Designer!

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Over the last week I’ve been working with a few co-authors to get a paper ready for publication. For my part, this has mostly meant making plots of our data. (Yes, theorists have data! It’s the result of calculations, not observations, but it’s still data!)

As it turns out, making the actual plots is only the first and easiest step. We have a huge number of data points, which means the plots ended up being very large files. To fix this I had to smooth out the files so they don’t include every point, a process called rasterizing the images. I also needed to make sure that the labels of the plots matched the fonts in the paper, and that the images in the paper were of the right file type to be included, which in turn meant understanding the sort of information retained by each type of image file. I had to learn which image files include transparency and which don’t, which include fonts as text and which use images, and which fonts were included in each program I used. By the end, I learned more about graphic design than I ever intended to.

In a company, this sort of job would be given to a graphic designer on-staff, or a hired expert. In academia, however, we don’t have the resources for that sort of thing, so we have to become experts in the nitty-gritty details of how to get our work in publishable form.

As it turns out, this is part of a wider pattern in academia. Any given project doesn’t have a large staff of specialists or a budget for outside firms, so everyone involved has to become competent at tasks that a business would parcel out to experts. This is why a large part of work in physics isn’t really physics per se; rather, we theorists often spend much of our time programming, while experimentalists often have to build and repair their experimental apparatus. The end result is that much of what we do is jury-rigged together, with an amateur understanding of most of the side disciplines involved. Things work, but they aren’t as efficient or as slick as they could be if assembled by a real expert. On the other hand, it makes things much cheaper, and it’s a big contributor to the uncanny ability of physicists to know about other peoples’ disciplines.

Talks, and what they’re good for

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It’s an ill-kept secret that basically everyone in academia is a specialist. Nobody is just a “physicist”, or just a “high energy theorist”, or even just a “string theorist”. Even when I describe myself as something as specific as an “amplitudeologist”, I’m still over-generalizing: there’s a lot of amplitudes work out there that I would be hard-pressed to understand, and even harder-pressed to reproduce.

In the end, each of us is only going to understand a small subset of the vastness of our subject. This is problematic when it comes to attending talks.

Rarely, we get to attend talks about something we completely understand. Generally, we’re the ones giving those talks. The rest of the time, even at conferences for people of our particular specialty, we’re going to miss some fraction of the content, either because we don’t understand it or because we don’t find it interesting.

The question then becomes, why attend the talk in the first place? Why spend an hour of your time when you’re not getting an hour’s worth of content?

There are a couple reasons, of varying levels of plausibility.

One is that it’s always nice to know what other subfields are doing. It lets one feel connected to one’s compatriots, and it helps one navigate one’s career. That said, it’s unclear whether going to talks is really the best way of doing this. If you just want to know what other people are doing, you can always just watch to see what they publish. That doesn’t take an hour, unless you’re really dedicated to wasting time.

A more important benefit is increasing levels of familiarity. These days, I can productively pay attention to the first quarter of a talk, half if it’s particularly good. When I first got to grad school, I’d probably tune out after the first five minutes. The more talks you see on a subject, the more of the talk makes sense, and the more you get out of it. That’s part of why even fairly specialized people who are further along in their careers can talk on a wide range of subjects: often, they’ve intentionally kept themselves aware of what’s going on in other subfields, going to talks, reading papers, and engaging in conversation. This is a valuable end goal, since there is some truth to the hype about the benefits of interdisciplinarity in providing unconventional solutions to problems. That said, this is a gradual process. The benefit of one individual talk is tiny, and it doesn’t seem worth an hour of time. Much like exercise, it’s the habit that provides the benefit, not any individual session.

So in the end, talks are almost always unsatisfying. But we keep going to them, because they make us better scientists.

Duality: Find out what it means to me

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There’s a cute site out there called Why String Theory. Started by Oxford and the Royal Society, Why String Theory contains lots of concise and well-illustrated explanations of string theory, and it even wades into some of the more complex topics like AdS/CFT and string dualities in general. Their explanation of dualities is a nice introduction to why dualities matter in string theory, but I don’t think it does a very good job of explaining what a duality actually is or how one works. As your fearless host, I’m confident that I can do better.

Why String Theory defines dualities as when “different mathematical theories describe the same physics.” How does that work, though? In what sense are the theories different, if they describe the same thing? And if they describe the same thing, why do we need both of them?

1563px-face_or_vase_ata_01.svg_

You’ve probably seen the above image before, or one much like it. Look at it one way, and you see a goblet. Another, and you see two faces.

Now imagine that instead of a flat image, these are 3D objects, models you have in your house. You’ve got a goblet, and a pair of clay faces. You’re still pretty sure they fit together like they do in the image, though. Maybe they said they fit together on the packaging, maybe you stuck them together and it didn’t look like there were any gaps. Whatever the reason, you’re confident enough about this that you’re willing to assume it’s true.

Now suppose you want to figure out how long the noses on the faces are. In case you’ve never measured a human nose, I can let you know that it’s tricky. You could put a ruler along the nose, but it would be diagonal rather than straight, so you wouldn’t get an accurate measurement. Even putting the ruler beneath the nose doesn’t work for rounded noses like these.

That said, measuring the goblet is easy. You can run measuring tape around the neck of the goblet to find the circumference, and then calculate the diameter. And if you measure the goblet in this way, you also know how long the faces’ noses are.

You could go further, and build up a list of things you can measure on one object that tell you about the other one. The necks match up to the base of the goblet, the foreheads to the mouth, etc. It would be like a dictionary, translating between two languages: the language of measurements of the faces, and the language of measurements of the goblet.

That sort of “dictionary” is the essence of duality. When two theories have a duality (are dual to each other), you can make a “dictionary” to translate measurements in one theory to measurements in the other. That doesn’t mean, however, that the theories are clearly connected: like 3D models of the faces and the goblet, it may be that without looking at the particular “silhouette” defined by duality the two views are radically different. Rather than physical objects, the theories compare mathematical “objects”, so rather than physical obstructions like the solidity of noses we have to deal with mathematical ones, situations where one quantity or another is easier or harder to calculate depending on how the math is set up. For example, many dualities relate things that require calculations at very high loops to things that can be calculated with fewer loops (for an explanation of loops, check out this post).

As Why String Theory points out, one of the most prominent dualities is called AdS/CFT, and it relates N=4 super Yang-Mills (a Conformal Field Theory, or CFT) to string theory in something called Anti-de Sitter (AdS) space (tricky to describe, but essentially a world in which space is warped like a hyperbola). Another duality relates N=4 super Yang-Mills Feynman diagrams with n particles coming in from outside to diagrams with an n-sided shape and particles randomly coming in from the edges of the shape (these latter diagrams are called Wilson loops). In general N=4 super Yang-Mills is involved in many, many dualities, which is a big part of why it’s so dang cool.

Shout-Out for a Fellow Blogger

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This is a blog about explaining science. Science is for everybody!

In particular, science is not just for geeks/those into geek culture. Nevertheless, I’m willing to bet that a substantial fraction of you are into something nerdy, whether sci-fi, fantasy, or one of the many genres and subgenres that have sprung up in the crazy genre jungles of the internet.

As such, some of you may be aware of Geek and Sundry, the Felicia Day-headed geek media mini-empire. They’re adding a set of new Vloggers (like bloggers but with video), and they’re running a contest to determine their lineup. And of these Vloggers, you should definitely vote for Kiri Callaghan.

I know Kiri as a kickass director from way back when I used to do community theatre stuff. These days, she’s running an extra-mini geek media empire of her own, centered around her blog. This blog somehow manages to update every weekday (and used to update every day), which as someone who updates once a week I can tell you is physically impossible, especially while also holding down a real job which she apparently does. She almost certainly owns a Time Turner or something.  So yeah, very impressive, and the high quality nerd stuff attached (check out some of her parody songs, in particular I Dreamed a Dream of Firefly) adds to the picture.

So for those in the audience who are into this sort of thing, vote for her! Comment on the video (apparently the scoring for this stage is based on interaction with commenters)! Join the facebook group to keep tabs on the competition!

You get paid to learn. How bad can that be?

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In my “who am I” post, I describe being a grad student as like being an apprentice. I’d like to elaborate on that.

Ph.D. programs in the sciences are different at every school, but they have a few basic features. Generally you enter them with a bachelor’s degree from another university. The program lasts for somewhere between four and six years, longer for particularly unfortunate cases. Sometimes you get a Master’s degree after the first two years, sometimes you don’t, but you don’t usually have to get it from another school. Generally the first two years mostly involve taking courses while the later years are mostly research, but this can vary as well. And in general, once you’re in the program, you get paid: either as a Teaching Assistant, in which case you help grade papers, lead lab sections, and sometimes give lectures, or as a Research Assistant, in which you are paid to do research.

This last is occasionally confusing to people. If a Ph.D. student learns by doing research, then why are they also paid to do research? That sounds like not just getting your education for free, but being paid for it, which sounds at the very least like a very good deal.

There are two ways to think about the situation. One, as I mentioned in my “who am I” post, is as an apprenticeship. An apprentice is expected to learn on the job, and provided they learn enough they are eventually certified to work on their own. Despite this, an apprenticeship is still very much a job. An apprentice is subservient to their master, and can generally be counted upon to work on the master’s projects and help the master in their job. In much the same way, a Ph.D. student is not certified to work on their own until they graduate from the program and obtain their Ph.D. In the meantime they are subservient to their advisor, and they have to take their advisor’s desires into account when choosing research projects. In general, most of a grad student’s research projects will be part of their advisor’s research in one way or another, furthering their advisor’s goals. Beyond the research itself, grad students will often have other duties, depending on the nature of their advisor’s work, especially if their advisor has a lab with complicated equipment that needs to be maintained.

The other thing to realize is that grad students are, ostensibly, part-time workers. The university pays me for 20 hours a week of work. The thing is, though, I don’t just work part-time. I work full-time. I also work at home, on the weekends…whenever I can make progress on my research (and I’m not doing some side project like this blog or taking a needed sanity break), I work. So if I work 40 hours a week and am paid for 20, that means I am effectively spending half my income on education.

Not so free, is it?

It’s not as if any of us could just work less and take on another part-time job, either. Apart from the fact that many grad students are international students on visas that don’t allow them to get other jobs, it is research itself: keeping up, making progress, working towards graduating, that takes up so much of our time. To get any education out of the process at all, we have to be involved as much as possible.  So we are, inevitably, paying for our education. And hopefully, we’re getting something out of it.

Blackboards

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As a college student, I already knew that theoretical physicists weren’t like how they were portrayed in movies. They didn’t wear lab coats, or have universally frizzy, unkempt white hair. I knew they didn’t have labs, or plot to take over the world. And I was pretty sure that they didn’t constantly use blackboards.

After all, blackboards are a teaching tool. They’re nice for getting equations up so that the guy way in the back can see them. But if you were actually doing a real calculation, surely you’d prefer paper, or a computer, or some other method that doesn’t involve an unkempt scrawl and a heap of loose white dust all over your clothing.

Right?

Right?

Over the last few years I’ve come to appreciate the value of blackboards. Blackboards actually can be used for calculations. You don’t want to use them all the time, but there are times when it’s useful to have a lot of room on a page, to be able to make notes and structure the board around concepts. More importantly, though, there is a third function that I didn’t even consider back in college. Between calculation and teaching, there is collaboration.

Go to a physics or math department, and you’ll find blackboards on the walls. You’ll find them not just in classrooms, but in offices, and occasionally in corridors. Go to a high-class physics location like the Perimeter Institute or the Simons Center, and they’ll brag to you about how many blackboards they have strewn around their common areas.

The purpose of these blackboards is to facilitate conversation. If you want to explain your work to someone else and you aren’t using a blog post, you need space to write in a way that you can both see what you’re doing. Blackboards are ideal for that sort of conversation, and as such are essential for collaboration and communication among scientists.

What about whiteboards? Well, whiteboards are just evil, obviously.