Friday, May 1, 2015

Art, Physics & Beauty: An Interview with Jacob Barandes

Sit back... this is a more lengthy piece than my usual blog posts with lots of pictures and minimal text.  Jacob Barandes is a member of the physics teaching faculty at Harvard and the one who initially had the idea of bringing me in to 'do something' at Harvard.  We've since enjoyed many thought provoking exchanges over art, physics and beauty.  He regularly sends along great math and physics links, filled with inspiring visuals that have creative potential.  His mind works faster than I can keep up with, but it's totally worth the effort!

Bio: Jacob Barandes grew up in New York City and Westchester. He graduated from Columbia University with a bachelor's degree in physics and math, and completed a PhD in physics at Harvard. As Associate Director of Graduate Studies for the Harvard physics department, Jacob teaches graduate-level courses and advises students in the physics PhD program, in addition to administrative work and software development for the department. He lives with his wife Shelley, a letterpress printer and graphics designer, and their two children Sadie (age 6) and Emily (age 2) in Cambridge, MA. (Website:

Kim Bernard - Can you explain what initially drew you into the field of physics?

Jacob Barandes - Growing up, I was the sort of person who could always explain why I was interested in whatever I was interested in at the time, but the reasons I'd tell people definitely changed over the years. I'm not sure whether my reasons for doing physics have changed fundamentally since the end of high school, or whether it's just because I've had a lot of time to think about them.
I think my childhood interest in physics was somewhat typical for a nerdy kid, and was rolled into a larger interest in science. I had some beautiful astronomy and dinosaur books when I was little, and remember spending long hours reading them over and over and marveling at the pictures. I also watched science shows on TV with my parents. (My parents aren't scientists, but they both appreciate science very much.) I lived in New York City until I was about 10, so we also took lots of trips to the American Museum of Natural History. I played a lot of chess, which was popular in New York City schools at the time. (Our school had an amazing chess teacher, Svetozar Jovanovic.) After fourth grade, I moved an hour north of the city to Westchester, where I went to a public middle and high school.
One of my most cherished possessions in middle school was a handwritten report I did on atoms in science class in 6th grade. (It's one of the few things I've kept from my early years of school.) In 10th grade I took a class in chemistry, and found the mathematical parts to be intuitive and enjoyable. On the other hand, I was pretty awful at anything involving lab work.
I had a really amazing experience taking physics in 11th grade. It was a standard, non-honors physics class, which was all my high school had available at the time. (The school later added an AP physics class, but I never took it.) There was no calculus in the course, which was fine for me because I had jumped around so much between math classes in high school that I hadn't really learned calculus by that point.
But there was something very elegant and clean about physics -- in retrospect, almost Platonic. There were these perfect entities -- point particles, trajectories, magnetic fields, light beams, elegant thought experiments -- that seemed so much less messy and complicated than everything else I was learning about in my other classes. It was definitely that aesthetic element that drew me in, rather than a desire (or ability) to build useful things for the world.
And I really loved manipulating equations. It was like formulating magic spells that the world mysteriously had to obey. I remember doing an extra-credit project with my physics teacher (Douglas Bartel, since retired) in which I had to derive a complicated formula to predict where a laser beam would end up going, and when we set up the apparatus and started up the laser it precisely matched my prediction to all the decimal places. That was just marvelous. Is there any other human endeavor like that?
I also loved doing the homework in the class! Doing physics was the first time I felt like I wasn't wasting time that I should have been spending working on something more important.
At around the same time, a close friend of mine (Etan Harwayne-Gidansky) who was interning at the biology department at the museum of natural history got me a connection to the museum, and after moving around between departments, I was eventually able to get an internship at their astrophysics department. I learned some programming and developed code to sift through data for their Digital Galaxy project, whose goal was to visualize the distribution of stars in our galaxy on their mainframe computer.

I also started attending a free weekly Saturday morning science class (the Science Honors Program) at Columbia, where I'd later end up going to college. So I'd take the train into the city from Westchester every Friday, work that afternoon at the astrophysics department at the museum, and then stay with my grandfather overnight before going to Columbia in the morning for classes on astrophysics, cosmology, relativity, quantum theory, and particle physics. I still have all my old course notes from those classes in a little gray binder on my office bookshelf, and it took me all my years of college before I understood everything I had originally written down in it.
I still wouldn't have described myself as being primarily interested in physics, though. Maybe astronomy. The next year, in 12th grade, I took AP chemistry in high school (my lab work was probably even worse than in 10th grade chemistry), switched over to psychology classes at the Columbia Saturday program, and didn't take any more math.
When I got to college, I was planning on studying neuroscience, and maybe some computer science. (I had done a lot of computer programming and web design in high school.) Then I took some math classes and really learned calculus for the first time while also taking the standard physics track for physics majors.
I was completely blown away. It was love. There was no other way to explain it -- I couldn't have given an objective reason why I enjoyed it so much. (Can a person give an objective reason for falling in love with anyone or anything?) I just loved what I was learning and relished solving physics and math problems. I would work all day on problems, and for the very difficult ones, I'd mull over them in my head when I went to sleep. The other students in my dorm said that they'd scarcely ever seen anyone so happy.
But I felt like I was way behind all the "very serious" people who were studying math and physics. (Some of them even told me outright that I had no shot at getting anywhere.) In my sophomore year, I enrolled in the standard introductory course in microbiology while also still taking some physics.
I had become friends with a student in one of my physics classes, and he and I got dinner across the street from school one evening. We were talking about studying physics and how we both felt like despite enjoying it, we were probably not going to become very successful at it in the long run. He told me that he didn't really care -- he said we would be stupid to give up doing something we really loved doing just because we were afraid we wouldn't end up getting to the top of the field some day. What he said really stuck with me.
A few months later, I had a very late night working on biology homework, and the next day I realized I wasn't doing what I wanted to be doing with my life. So I dropped the biology class and never took another one, or any other electives. I just started loading up my schedule with as many physics and math classes as I could. I was taking 5 or 6 classes a term and getting very little sleep, but it was thrilling. I studied physics every summer, and taught myself my school's undergraduate course in quantum mechanics from the textbook and homework sets that had been posted on the course website. I took nearly all the undergraduate and graduate-level physics courses available, and essentially finished a master's degree in physics in addition to my major in math.
I spent every minute thinking about physics or math and talking about physics or math. Apart from the time I spent with Shelley (now my wonderful wife), my only extracurricular activities in college were the Society of Physics Students and the Undergraduate Math Society. I was extremely fortunate to get into Harvard's PhD program in physics, and decided that I wanted to go into high-energy theory.
I benefited tremendously from the mentorship of the director of undergraduate studies in physics at Columbia, Prof. Allan Blaer, who, in addition to running the Saturday Columbia program I had attended in high school, was one of the most patient and kind human beings I've ever known -- and a brilliant teacher. I also got to know an incredible group of students in physics. One student in particular, David Kagan, quickly became one of my very closest friends, and we spent countless hours discussing physics and philosophy during my college years. (We still do!)
As you and I discussed when we spoke last in person, I think what keeps me in love with physics (despite the many ups and downs along the way) is that it gives me access to a whole aesthetic realm that would otherwise have been unavailable to me. There are certain concepts and ideas in physics that are among the most beautiful things I know about, and I am grateful that I learned enough physics that I was able to get to see them. I wish everyone could see them. There are lots of great reasons why people study physics, but I hope everyone in the field gets a chance to experience that kind of beauty.
Like lots of other physicists, I've also been motivated by a desire to understand the world a little better. When I was first learning physics years ago, the subject seemed limitless, but now I appreciate that physics does have an outer boundary, and that there are aspects of existence outside of physical reality that go beyond what physics could ever tell us and that lie more properly in the realm of philosophy. Nonetheless, it's been amazing to follow along with the progress physicists have made in elucidating the nature of physical reality, and it would be a wonderful privilege to see that adventure continue and continue sharing it with people who are just starting their own careers in physics.
KB - You speak about the elegance and beauty of physics, and the aesthetic realm.  I'm also intrigued by the "aspects of existence outside of physical reality that go beyond what physics could ever tell us and that lie more properly in the realm of philosophy".   Can you elaborate?
JB - In short, science has turned out to be a marvelous tool for developing a description of empirical data and making highly nontrivial predictions about as-yet-unknown real-world phenomena, not to mention leading the way to important inventions and technologies that have changed the way we all live our lives. And, as I've emphasized throughout our conversations, the structure, models, and applications of science often possess a great deal of beauty.
But the moment one begins asking what it all means -- what the results of our scientific work actually tell us about the way the world really is -- one has moved beyond the reach of experiments and into the realm of philosophy.
There are people both in science and outside it who would rather not spend their precious time grappling with such concerns, and that's very much all right with me. We don't generally get to choose what interests us, and the world is a better place for all of our diverse interests. But these concerns cannot simply be dismissed as nonexistent, whether we like it or not, and so I'm happy that some people (some scientists, some not) spend their time taking them seriously. I should also say that I go back and forth on a lot of this stuff myself -- I'm far from settled in my opinions here.
There's a lot of formal terminology that arises in these kinds of discussions (ontology, epistemology, logical positivism, falsifiability, scientific realism, foundationalism, reification, instrumentalism, structural realism, phenomenology, Platonism, etc.), and I'll do my best to avoid it. To summarize, the folk tale we often hear is that a philosophical consensus was reached in scientific communities in the early part of the 20th century in which certain broad kinds of questions were deemed acceptable and the rest were cast aside as meaningless. Statements that made operational, nontrivial predictions about the world and that were falsifiable (that is, in principle, there was a conceivable way in which they could be demonstrated empirically to be false), as well as mathematical corollaries of such statements, were regarded as sensible, and all other statements were branded by some (though not all) as being a waste of time.
In practice, however, many scientists practice a kind of implicit belief system in which their models and theories are literally describing what reality actually is. In this picture, there really are electrons and quarks zipping around and popping into and out of existence, energy is really a physical thing that's out there (beyond being merely a mathematical device), and there is a true sense in which we can say that the laws of nature and maybe even wave functions are really out there; our models are accurate depictions of the underlying reality of nature. Of course, statements like these go beyond the conservative restrictions I mentioned before (valid statements must be operational and falsifiable, or must be mathematical corollaries of statements that are), and so truthfully require some kind of philosophical justification. And, indeed, when pressed, most scientists will often admit as much.
However, I think the urge on the part of so many scientists to make those kinds of claims about our scientific models is not a surprise, and shouldn't be so readily dismissed. Ultimately, many of us got into science in the first place not just because we wanted to make austere nontrivial predictions about future empirical data (ten more decimal places -- hurray!), but because we were interested in trying to learn something about the actual underlying reality of the world. That was certainly part of what drew me into science, apart from the sheer love of doing it and the appeal of its hidden beauty. And early on in my studies, I figured that science was a more reliable way to pursue this goal than other ways, like philosophy or religion, would have been.
But what I learned over the years is that science simply can't tell us whether or not our models and theories are truly telling us the actual underlying reality of the world -- that would require a leap beyond what science can do. Even this very discussion is something beyond the bounds of science.
It's true that the sorts of models we often use in the safe and familiar territory of classical mechanics are fairly transparent, and one might therefore decide to take a philosophical leap and identify them with reality. After all, in classical mechanics, my model might consist of pendulums and rolling cylinders and tennis balls, and those are certainly things we see around us all the time. In this framework, maybe notions like energy and momentum are just convenient mathematical devices, but particles are real, velocities are real, etc. Those things show up in our models because our models are just reflecting the underlying reality.
But quantum theory upends this picture dramatically. Yes, it has had astounding empirical success as a framework for predicting the outcomes of measurements. Indeed, many of our theoretical calculations in quantum theory agree with experimental data to countless decimal places. (Note that Prof. Gerald Gabrielse, who comes up in the article for his outstanding accomplishments in high-precision experiments, is on our faculty here at Harvard.)
Nonetheless, physicists have been unable thus far to find a formulation of quantum theory in such a way that we can identify a sensible picture of what actual reality could be like. So to the question "What could the world really be like such that quantum theory turns out to be the ideal theoretical description?", we don't have an answer -- certainly not with any consensus -- and may never have one.
It's not just quantum theory that might shake someone's confidence that science is ever going to be able to tell us what underlying reality actually consists of. When I was little, I hoped that science, unlike philosophy or theology, might be able to teach me definitive things about the world, at least up to some given level of certainty (e.g., 99% confidence). But all logical arguments consist of premises (i.e., axioms, that is, assumptions), followed by sound logical deductions or inferences that lead to conclusions. In that sense, all knowledge is ultimately contingent on premises or axioms, and eventually there are just some axioms that we cannot derive from anything else, nor even assign probabilities to. (There isn't consensus, by the way, on rigorously defining what probability means!)
When you think about it, that unavoidable contingency of knowledge is a really profound thing. Seemingly every scientific, philosophical, linguistic, theological, or moral fact -- no matter how "objective" -- is ultimately contingent on axioms that cannot be derived from anything deeper or even assigned probabilities (whatever probabilities rigorously mean). At best, one could say that objective knowledge does not consist of facts themselves, but only of inter-relations between axioms and their logical consequences, although we might hope that we could reduce our knowledge at least approximately to a parsimonious set of mutually consistent axioms.
It goes without saying that this discussion is yet again outside the bounds of science, but reaches down into some of the very most important things in our lives -- our very concept of what it means to "know" something.
The rabbit hole goes deeper, of course, because the rules of logic themselves are impossible to derive from anything else. And there are intriguing alternative logical frameworks out there -- frameworks that do not agree with our default Aristotelian framework. How does one pick among logical frameworks, or compare their merits? One can't rely on Aristotelian logic -- that would be begging the question!
And yet -- there are some things about reality that manage to escape this whole morass altogether. When I experience the color blue, for example, I know it -- and at a level that doesn't depend on axioms or logic or anything else. Now, the cause isn't certain -- it could be that I'm seeing a bluebird, or a blue butterfly, or I'm having a bizarre neurological event. The cause of my experience of blue is uncertain and falls into the class of "objective" knowledge statements I made before, with all its ambiguities about premises and choice of logical system. ("Given the premise that blue birds are blue, the existence of a blue bird in my field of view is a logically possible explanation for my experience of blue.") But my very direct experience of blue itself is completely outside this whole system and all its ambiguities and subtleties. I know it with absolute certainty, even as I may be uncertain as to its cause. (Or even uncertain about whether "cause" is ultimately a sensible property of things in the world.)
How can it be that "subjective" things like the experience of blue, or pain, or love are 100% certain to me and free of any dependence on axioms, whereas "objective" things like blue birds, knives, F=ma, etc., are never known with certainty, and are furthermore ultimately contingent on unprovable axioms? Doesn't that upend everything we're taught about objective statements being better or more reliable than subjective ones? And if subjective experiences truly exist, then what does that even mean? In any event, science isn't going to be able to answer any of these questions -- even though they're understandably very important to me.
I mean, perhaps the most important thing that has ever happened to me (and here I'm borrowing from some of the musings of Scott Aaronson) was that somehow "I" got assigned to this particular physical body, so that its experiences would be my experiences. The reality of my perspective and presumably its attachment as an irreducible thing to this physical body are just as real to me as "blue", and more real to me than essentially anything that one might call an "objective" fact. It's as though some cosmic recording needle landed on a particular human body and declared "There -- that's going to be you." Science will never be able to tell me how that happened, or even make any sense of the question itself, despite its obviously huge personal significance!
Once one starts to look for more examples of things outside the bounds of what science can reach, one starts to see them everywhere. F=ma appears to be an excellent approximation for many systems in classical mechanics, and appears to be just as "objectively" true as the existence of the book sitting on my desk. But where is F=ma, and what would it mean to say that it's real or that it exists? If some of our mathematical laws of nature exist, then in what sense? Is there some other plane of reality, beyond physical reality, where true mathematical equations and theorems and statements exist, as Plato would have imagined, with the "real" physical world just a grotesque gallery of imperfect reflections of that Platonic realm? Or does the Pythagorean theorem exist only in the same way that objective-fact-statements exist -- that is, as contingent statements following from axioms, in this case the standard axioms of mathematics? Or maybe all logical relations between axioms and consequences (including all mathematical facts) live together with mathematics someplace. One thing is for sure -- science can never tell us.
Now, although lots of scientists I know enjoy talking about these things, the reaction of some people to these wonderings is to declare them undefined and meaningless -- to declare that we should just "un-ask" these kinds of questions. But why? Sure -- it may be difficult or impossible to answer them, or even to formulate them very sharply to begin with. But the moment one begins to make some sort of argument that they are meaningless, one is literally engaging in philosophy, not science, and one is furthermore implicitly assuming as premises lots of things that are supposed to be proven in the argument.
I sometimes feel like science has given us this circle filled with rich and miraculous things, but beyond its edge we see a vast and incomprehensibly huge void that may lie forever beyond our reach. One attitude is to declare that we should ignore the void, and maybe declare that it isn't there. (That's called scientism.) But I feel like it's more honest to learn to live humbly with the void and just accept our limitations.
KB – Can you give me (and my artist friends) some visual examples of beauty in physics?
JB - I can't speak for all physicists, but I've always found deep beauty in many aspects of electromagnetism.
For example, ever since I can remember, I've found lightning to be extremely beautiful. When I was a kid, my parents got me a little plasma sphere from RadioShack, and I recall spending many nights in bed staring at it in the dark. There are lots more lovely examples of what one can do with electrical discharges, such as this. (It's a remarkable thing about nature that we see these sorts of patterns appear in strikingly different contexts -- those are plant roots in the picture!)
Back in the 1800s, Michael Faraday popularized the notion of flux lines to explain and describe the influences of electric charges and magnetic dipoles. One can sketch the flux lines produced by a bar magnet (as Rene Descartes did in 1644!) or by a current-carrying wire by scattering around some iron filings and tracing the patterns they make. (The amazing folks who run our instructional labs can provide you with the necessary materials if you'd like to try it yourself.) Later in the 1800s, a theoretical physicist named James Clerk Maxwell explained how to derive these flux lines mathematically from his eponymous equations. The results are extremely beautiful. The Maxwell equations can now be used together with computers to produce staggeringly complex examples.
​There are so many more things to mention. One example is turbulence in fluids, which shows up in countless phenomena, including cups of water and plumes of smoke.
Phase space is a graphical way for physicists to visualize the trajectories of physical systems. One axis is position and the other is momentum, and if the system's behavior is chaotic, one obtains dazzling complex figures.
The tracks left by high-energy particles on old photographic plates are another marvelous example of beauty in physics, and partly inspired Feynman's beautiful diagrammatic recipe for representing the various ways that particle-physics processes can occur. These Feynman diagrams, which provide a mnemonic for remembering the various numerical factors that are necessary for calculating the rates at which various scattering and decay processes occur, are ubiquitous on chalkboards in physics departments.
Atomic physicists have become extremely adept at manipulating and visualizing individual atoms, and their scanning tunneling microscopes (we have working examples in our department) have produced beautiful images, some of which, like these "quantum corrals", clearly capture the rippling wavelike nature of subatomic particles.
Astronomy and astrophysics have provided countless images of incredible beauty, from spectral lines, which are literally bar codes that reveal the chemical ingredients of bright faraway objects, to the Hubble telescope's famous "deep field" consisting of countless individual galaxies, to the magnetic fields that are generated by planets like our own, to the growing recognition of our place in the larger cosmos, to the faint echo of leftover microwave radiation from the moment 380,000 years after the Big Bang when our universe finally became cool enough to be transparent to light. (Take a look at this stunning graph to see the agreement between theoretical prediction -- the curve -- and experimental data -- the dots. Isn't that beautiful?)
Many additional examples from one of the most beautiful physical theories known today, Einstein's brilliant theory of general relativity, in which gravity manifests itself through the warping of the very fabric of spacetime. Among the phenomena predicted by general relativity are black holes, gravitational lensing, and, in more exotic cosmological contexts, cosmic strings.
A lot of physics technology is itself beautiful. A while back, the Big Picture blog at the Boston Globe did a breathtaking photo set of the Large Hadron Collider (the LHC), which is where a lot of our particle-physics faculty do their research. It really boggles the mind that human beings (including some of our faculty) have created these machines.
Certainly a lot of theoretical physicists and mathematicians find many of the most important questions in physics to be profoundly beautiful. ("I've spent three years studying mathematics at university, and Lagrangian mechanics is the most beautiful thing I've seen.") Physicists love the way our equations look so much that they often decorate things with them. Here's the formula for the Standard Model, which is our most complete empirically tested theory of fundamental particle physics. Here are some chocolate bars decorated with more equations. And here's a whole art gallery dedicated to equation-covered chalkboards.
One more example of beautiful equations: Take a look at Laplace's Treatise on Celestial Mechanics from 1799(!). (Here's Volume 2.) If you scroll through the pages, you'll see some equations that many physicists find deeply beautiful. (What's especially amazing is how similar many college-level textbooks on classical mechanics look to Laplace's masterpiece from over two centuries ago.)
I haven't even touched more frontier areas of theoretical physics, including string theory, which inspired a famous book by a top string theorist whose actual title is "The Elegant Universe." If you drop by a physics library and pick up any textbook on string theory, you'll find countless pictures and diagrams that are extremely beautiful just to look at.
But a lot of the most beautiful things in physics are hard to visualize at all, including many of the deeply important symmetries that underlie a lot of our models. Indeed, one of the very most beautiful ideas in all of physics is Noether's theorem, named for mathematician Emmy Noether. Her theorem establishes a profound connection between the symmetries of a physical model's basic rules and the existence of conserved quantities. Prominent examples: If a model's rules are symmetric under shifts in space, then momentum will be conserved; symmetry under shifts in time implies energy conservation; and symmetry under rotations implies conservation of angular momentum.
Just for fun, I'll end with this nice (and beautiful!) video by artist Asa Lucander that covers all of physics up through Einstein in four minutes. Enjoy!
KB - Can you briefly describe YOUR creative process?
JB - The most successful physicists out there are tremendously creative, producing not just new ideas in existence fields but creating entirely new fields altogether.
Personally, my creative process involves looking for good questions, which are ideally not just intriguing and appealing to my interests but also sufficiently clearly defined. Some questions come from reading papers or books, attending seminars, or talking to other people, but, for me, the best questions come from my teaching. Looking for ways to re-organize topics to improve their logical order and pedagogical coherence often leads me to new questions.
John Preskill, a renowned theoretical physicist at Caltech, captured this idea marvelously in a recent speech in which he declared that "we learn by teaching." As he put it:
"Well, when I contemplate my own career, I realize I could never have accomplished what I have as a research scientist if I were not also a teacher. And it's not just because the students and postdocs have all the great ideas. No, it's more interesting than that. Most of what I know about physics, most of what I really understand, I learned by teaching it to others. When I first came to Caltech 30 years ago I taught advanced elementary particle physics, and I'm still reaping the return from what I learned those first few years. Later I got interested in black holes, and most of what I know about that I learned by teaching general relativity at Caltech. And when I became interested in quantum computing, a really new subject for me, I learned all about it by teaching it.

"Part of what makes teaching so valuable for the teacher is that we're forced to simplify, to strip down a field of knowledge to what is really indispensable, a tremendously useful exercise. Feynman liked to say that if you really understand something you should be able to explain it in a lecture for the freshman. Okay, he meant the Caltech freshman. They're smart, but they don't know all the sophisticated tools we use in our everyday work. Whether you can explain the core idea without all the peripheral technical machinery is a great test of understanding."
When I have to teach something, I'm forced to probe my own understanding far more deeply than I would otherwise, and I often uncover lots of interesting questions along the way. (Sometimes prompted by my students!)

Once I have a good question in mind -- perhaps a physics problem, or maybe just the search for a better approach to explaining an important concept in one of my classes -- I read everything I can about it to see if it's been solved already, and I try to talk to others who might know more than me or who are at least willing to be confused along with me. I write down everything in as organized a way as possible. If the problem hasn't been resolved already, or if I think there's a new angle for looking at an existing solution, then I try to find some time just to sit and think about it, maybe taking some long walks or thinking about the problem when I go to sleep. (Once I have a gripping problem in my head, I find that it's often very hard to put it aside.) I like to sketch out calculations or various approaches to making sense of the problem as I think through it. If I really don't know how to proceed, then I may just let the problem sit in the back of my head for a while in case inspiration eventually hits.