Summer Informal Seminar

No, I haven’t been off on vacation in the Caribbean—but I have seen the third pirates movie. It was great. But I wanted to let anyone out their who is interested that I’m going to lead an informal seminar on general relativity at UMass/Boston this summer starting June 4th. Here are the details.

What: An informal seminar on differential geometry and general relativity
When: MTh 5–6:30pm
June 4th — early-August
Where: Taffee Tanimoto Conference Room
Science Center
Third Floor, Room 180

Words and Meanings

Freshman year of college my friend Rebecca tried to explain to me the literary school of deconstruction. After some time I tried to sum up what I had heard in a phrase that (be it my own or not, and whether it be accurate or not) I have kept with me six years later.

Words have meanings, but meanings don’t have words.

Now I’m still not sure what that means, but I do know it has to be true. My friend’s grandmother, sage that she is, disagrees entirely. Meanings are the words they mean—sometimes people misuse words—but that doesn’t detract from their instrinsic definitions. But if that were true, we wouldn’t have any need for dictionaries. If words were their meanings, then words couldn’t be defined in terms of other words. That’d be silly. The other words have their own (other) meanings, after all. Imagine what a dictionary entry might look like in this alternate semantic universe:

apple, n., apple. What don’t you understand? Apple means apple.

Of course, maybe I’m taking too naive an approach. DJ’s grandmother might be onto something. How can you sufficiently define terms like ‘this’, or ‘I’, or ‘you’? This is what it is. It’s nothing else. It’s this. I am who I am. Or am I? Words, like people, take on a meaning that emerges from their use. How words are used, though, follows from larger, guiding principles. Culture helps define who we are. So, too, culture—which is really no more than a vast set of complex and subtle rules—defines what are words mean. So, words do have meaning. But only in relationship to other things (that have meaning). It’s sort of like music.

In music syncopated rhythms accent the beats which normally go unaccented. But without some concept of normal, syncopation doesn’t exist. But it does because in our music there is a structured sense of normal. And if we let loose the structure, we loose some of the meaning. Syncopation just disappears. Ironically, the tighter a straight-jacket we put on rhythm the freer we can be within its constraints: we get things like syncopation back.

In mathematics, too, Kahler manifolds are surfaces that exhibit a rich geometry. It’s thought that the physics of our universe is actually encoded on one of a special class of these surfaces known as Calabi-Yau manifolds. The thing about Kalher manifolds, though, is that their geometry is so highly structured that the surfaces are almost flat. Flat surfaces are the simplest to investigate. It turns out that these guys, by comparison, are notoriously difficult to analyze. There may be something to that—that the most useful, interesting cases often lie just on the cusp between simple and intractable—but I’m not sure what it is.

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Book Reviews

Since I started a new job and classes at just about the exact same time, I haven’t had much time to sit down and write. Because my boss took the day off, I can put a whole day’s worth of work into this thing—the problem is, though, I’m out of the blog zone and I’m not sure how to get back in. When DJ and I play tennis, the one who lost the point has to sprint around the court. At first, the loser of a single point continued to lose several points. Running made it hard to concentrate on the game. But as we played on, we got better. The interpoint sprints actually honed our mental and physical stamina. I don’t know of an analogous blogging exercise.

So, without any prepared material, I write on. Hoping that you’ll keep reading. And while I haven’t been writing lately, I have been reading. In the past week I’ve started four books. You’ll see that three of them fall into an obvious theme. Maybe you can guess it by the first’s title:

Social Learning and Cognition, by Rosenthal and Zimmerman, was written in 1978. I don’t know how much of the book is still current, but what they say seems to make sense. Like the other books I’ll mention, I haven’t made it very far: I’m only in the first chapter. To be fair, this one only has three, individually long chapters. Basically, social learning combines information processing—which came about once people began that quest for artificial intelligence—with a behavioral twist. As far as I can tell, this sort of thing has been applied mostly to criminology. What I’m reading smacks of Vygotsky, who, due to political barriers, never made it big in the West. Bandura, the guy who sort pioneered this sort of thing, applied his work most closely to violent behavior. Hence the trajectory towards criminology. However, just about anyone—folks in public service, education, corporate training, and community building at large—should know about this stuff. We learn from each other all the time.

The second book I’m reading for class. In fact, I found Social Learning only because it was near Uncommon Genius on the shelf. The author, Shekerjian, tries to figure out what creativity is through interviews with forty of MacArthur fellows: those men and women given a cool half mil from what has been popularly dubbed the “genius award.” Sadly, she didn’t interview the two MacArthur fellows I know. To be fair, Zaldarriaga, the guy who co-taught a course on cosmology I took last year, neither knows me nor had received the award before the time of this book’s publication. It’s an enjoyable read. Don’t expect any research, though. Sheekerjian warns you from the outset that her book isn’t rigorous investigation of creative thought. The anecdotes are apt and her writing is smooth. Her analysis falls into same linear model of thought as much of the research literature on creativity, though. Pick it up if you have a short flight and you’re bored.

The last book hasn’t been published yet. The Emotion Machine is Marvin Minsky’s soon to be released follow up to Society of Mind. If you can’t wait until November to read it, you can find a draft online on his personal website, though I’m not sure for how much longer. Minsky, who you can tell is a trained mathematician by his style, gives a very easy introduction into the basics of artificial intelligence, which, by the way, doesn’t preclude its telling us something about human intelligence along the way. Minsky writes in a semi-dialogue form, injecting objections and commentary by invented philosopher, student, and citizen characters. They move along the discussion in an informal way which hides its unusual directness. If you had to choose among these three, you should probably choose this one.

The fourth book, which I only started about an hour ago, is Sakurai’s Modern Quantum Mechanics. I started this one based on a recommendation of one of my college roommates, who’s gone on to do her PhD in physics. She says that everyone agrees, Sakurai’s exposition is wonderfully clear though advanced. I guess they use this in a graduate-level QM course either at Harvard or MIT. (She cross-registers a lot.) Being an undergraduate mathematician, I missed out on quantum mechanics. As a high schooler, I thought that it would be my ultimate achievement. In the meantime, my dad has started spending a lot of money on some heinous line of products based on the study of so-called biophotons. This ever-authoritative Wikipedia entry sums it up nicely:

The field of biophoton related study also appears to have recently become rife with new age, complementary and alternative medicine, and quantum mysticism claims from those wishing to exploit such clams [sic] for financial benefit. Numerous claims are even made that by “harnessing the energy of biophotons” that supposed natural cures for cancer are guaranteed. Mainstream medicine and science strongly reject these claims as outright fraud and a dangerous diversion from actual medical treatment for someone who is suffering from such disease.

I figure if I can master the basics of QM, maybe I can have my dad ask questions that will confuse his prophets—because that’s what this has become. He defends these guys as if they were his gods.—and demonstrate that they’re just out to get his money. Even if that’s not your aim, you should read Sakurai, especially if you have a strong background in linear algebra (including Fourier analysis).

Out of a Job Even Before I Get Out of School

In the fifth or sixth grade, I had to do a report. And much like my fifth grade science fair project, which I do remember: I passed in a paper on resistors with a small experiment that my dad all but typed up for me, I had no idea what I was writing. The topic was Einstein’s special relativity. The whole thing was lifted from the appropriate volume of Encyclopedia Britannica kept in my dad’s home office. But what was so special about special relativity? The encyclopedia article explained that the theory was the result of a simplifying assumption or something in Einstein’s general theory, and that this whole thing was really about gravity. I have to admit, I still find the entire enterprise of relativity and gravity mystifying. One of the more outrageous predictions of classical GR are those objects popularized by scary movies like Event Horizon and other popular science fiction called black holes.

Black holes are tricky to define mathematically. Physically, they’re a place where mass becomes “infinitely” dense. [The quotes are there because infinite anything is a physical no-no. If you were to squeeze the mass of the earth into a ball a few millimeters across, then the force of gravity would take over and compress it even further. The math predicts a formation of singularity — the thing at the center of a black hole.] The space around such points acts funny. Because of the strong gravity associated with these objects, if something, a rocket, a lampshade, or a photon of light, for example, gets too close, then it gets drawn in ever closer until it meets collides with the singularity. Then all bets are off, and nobody can say with any amount of certainty what happens. The boundary in space beyond which nothing can return is called the event horizon of the black hole. Because not even light can escape, the structure will look, well, black; hence the name.

Black holes have always made people feel a little uneasy. First off, they’re scary. When I was small, I hated the drain in the bath tub. It was only a matter of time, I thought, before it took me down with the bath water. Black holes evocate the same sort of fear. And according to the big bang, there are tons of tiny, primeval black holes floating around the universe. The thought of it petrifies me. Secondly, black holes cause a few problems. Most notable is the information paradox, something that Stephen Hawking both proposed and recently resolved. The old saying goes that black holes have no hair. To avert the paradox, it turns out that black holes must be fuzzy, that things can escape. The problem stems from a butting of general relativity against quantum mechanics. They both work in their regimes, so what gives?

George Chapline has an answer: there is no such thing as a black hole. Instead, he proposes something whose geometry looks outwardly very similar to a black hole. He calls this something a dark energy star. I met him last spring when he came to give one of the Friday colloquium talks. He motivated his quantum critical points — a concept which neither I nor the New Scientist article I link explains — with the following scenario. [Okay, I will a little: usually we think of temperature as the master of phase transitions. Cool down a gas, like water vapor, and you get a liquid, like water. Cool down further, freeze it, even, and you get a solid, say, ice. Now keep going, cool it down all the way to just above absolute zero. When things that cold, quantum mechanical effects are the dominating factor in phase transitions, not temperature. In this condition weird things can happen, like superconductivity.]

Consider a long cylinder filled with a superfluid. The pressure gradient will be small nearer to the top, at the bottom, it will be large. At the top of the tube attach a speaker which sends out a sound wave. As the wave travels through the liquid it will slow down as the gradient increases. At some height, the wave should stop. What happens, he asks, as the wave meets this surface? If you’re a classical general relativist, you might look at the math and think, “Ah, ha! That’s just like the event horizon of a black hole. So, nothing, the wave will just pass through.” Classical GR lets anything just fall into a black hole. Once you’re inside you can’t send emails or make outgoing phone calls, but outside of that, nothing happens. You wouldn’t feel a thing. The earth could’ve just passed through the event horizon of a super, ultra massive black hole right now and you wouldn’t even know it. But Chapline does some quantum mechanics and says that’s not what happens. Instead, we might expect the magical height at which the wave stops really to represent a quantum critical surface. And the phase transition effects are wild.

In his talk he explained that a sort of Georgi-Glashow process could occur, causing quarks to split into an electron and a positron. This could account for all the anti-matter we see at the centers of galaxies. Using the liquid superconductor analogy, he conjectured that the vortices like those that form when liquid helium might also explain relativistic jets we observe spitting out anti-matter, too. The exciting [or threatening] implication of Chapline’s idea is that there is no singularity, no black hole, just lots of dead stars.

On the other hand, Penrose and Hawking have their names attached to the famed Singularity Theorems. They say that given certain assumptions on the causal structure of a universe, assumptions that we think our universe satisfy, then there needs be a singularity some where in that space-time. What of that? I’m not sure, and I’m not sure I care. Luckily, mathematical general relativity is replete with really interesting questions that are completely divorced of whatever’s going on in this universe. As I like to say, “Physics is the study of this universe, mathematics is the study of all possible universes.”

Moving Out Sluggishly.

In seven minutes my Harvard ID should not, if what they threaten is true, allow me into Leverett any longer. Even so, I can’t muster the necessary fear that would otherwise inspire me to get the last few things out of my room so the next kid can take it. Instead, I’d like to post this very silly graphic explaining the three possible geometries of the universe without much introduction or explanation. Notice that it is unduly funny. [I stole it from NASA’s WMAP page.]

Putting the Simple in Supergravity.

Despite the title of this entry, I am not going to talk about supergravity outside of this: Cabot recently purchased a book I may’ve used for my thesis. However they processed my order over a week late. I’ve got it with me now, just for kicks — personal edification and so that I can impress you, the reader, and the people who see me with it at lunch, like Luke and Lixin. On my way back from the Science Center, I flipped through the table of contents, I came across a chapter called “Geometrical Gravitational Theories,” which is why I asked the library buy the book in the first place. This book,Geometry, Spinors, and Applications, makes heavy use of — wait for it — spinors. There are lots of books on geometry; tons on applications; a sizable number on both geometry and applications. But there are surprisingly few on geometry, application, and special mention of spinors. And under that chapter on gravity, there’s a subheading: Simple supergravity. It reminded me of a conversation I had with Eda a few weeks ago. She finds that mathematicians are superficially humble, but in an oblivious and therefore endearing way. The idea of supergravity ever being simple is sort like a slap in my face, but in an endearing kind of way.

I quit you now to take up a programming assignment Paul has given me. He has resurrected that automated inspection-announcement-general purpose-web-based-email-program-thing project for me. He doesn’t like me to admit to him that I can’t do things, like, we’ll say for example, program. I’ve got a copy of PHP3: Programming Browser-Based Applications to my right. Somehow I think the supergravity would be simpler.


Kirkland wrecked me, and the Leverett team at large, tonight at IMs. David showed me how to alter my swing to get more power without using more. This came only minutes before my match, allowing little time to perfect my new technique. Even still, I’m not sure it would’ve helped much. My opponent had excellent court position and placement. I am encouraged, therefore, to take private lessons from the varsity coach once I graduate, find a job, and determine the feasibility based on time and money.

In the meantime, I took this quiz on the NOVA website about that silly E=mc^2 equation that everyone talks about. I was tricked by one of the questions.

Einstein appears to be the theme today. I met with Professor Strain to talk about possible final paper topics. After rejecting his initial offer (a proof of the previously thought impossible global solution to the vaccuum field equations by wave coordinates; they were thought — reasonably, it seems —, to diverge at inifinity.), we mulled over a casuality theorem due to Jacobi fields, or applications of PDE to mean curvature, finally arriving at the Hamiltonian formulation of GR. This is something that I really ought to understand. ADM mass, a quantity I now know and love, was originally proposed as a good definition of total mass because of its appearance by variational techniques. When explaining it, I like to use the nonlinearity of the field equations to eek out the self-interaction of gravitation. (This amounts to linearizing the theory and noting that these equations obey a linearized Bianchi identity, suggesting a conserved quantity.) I don’t know the calculus of variations, and, as a geometer, I should. And since I want to go into GR, this couldn’t make more sense.

Also, it seems, as my grandmother mentioned to me today, that Newton was an alchemist! I can’t but believe she’ll soon be concocting her own Philosopher’s Stone before long.

And mom, dad, and Janice, you can, if you want, purchase the complete DVD set of Sportsnight for me for Christmas.

A Breaktime Blog.

It’s been a dead sprint to the end today. The end, however, is Monday. Having finished — the definition of finished is a bit flexible, so I revise — having started a new section, the last section, of the third chapter, I have decided to take a break. Rest-time activities include push-ups, showering, and looking at graphs of Ian’s thesis.

Ian lives down the hall and also does general relativity-type things. While I’m wrestling with mass of gravitationally bound systems, he’s trying to detect isolated black holes through gravitational lensing effects.

Lensing works something like this: a heavy object, like a neutron star or a giant loaf of bread, causes space to dip down. Light from an object behind the bread, like a neon sign, travels in all directions, including toward the loaf of bread. Light rays which were very close to each other but hit the bend around the loaf on opposite sides cross in front of it. If we’re just the right distance away from all this wacky bending, we see not one, but TWO copies of the neon sign. This is how lensing works, roughly.

But that’s not really what I meant to write about. It was this:

Tonight Eda and I went to Adams’ dining hall for dinner. She suggested that we eat out, but I told her I couldn’t. “Broke?” she asked. And that got me thinking, I need a job. I’m broke because I don’t work. So, because I’m broke, I should work. And then I thought some more. Idioms just don’t respect causation. Funny.

Even String Theorists Can Be Nice.

I just emailed Clifford Johnson, a professor at USC who specializes in string theory and gravity. More importantly he is one of the permanent bloggers at Cosmic Variance. Recently he recounted a story from his advisor at the University of Southampton. So, I started thinking, hey! that probably means Clifford, who teaches in the States, probably got his degree in England.

Previously I had had some reservations about postgraduate degrees from abroad. But I had also had the feeling that most of the big general relativity things happen in England. After all, it’s tradition.

Sir Arthur Eddington, a pacifist, quaker, humanitarian, and Chief Astronomer at the Observatory of Cambridge University, single-handedly brought Einstein’s relativity to the Allied World — proving that science transcends political boundaries even in a time of war. Anyway, it was Eddington who made Einstein famous. He not only understood and explained the theory — which, at the time, was a remarkable feat in and of itself — he also gathered the money and manpower to execute two expeditions to put GR to its first experimental test. Eddington himself led the team in South America, while another headed to Africa, both to observe the bending of light by the sun during a solar eclipse.

The rest, as they say, is history. England has continued to produce excellent relativists, and not just in the philosophical sense. Hawking and Penrose are, perhaps, the most famous. But there are also Gibbons, d’Inverno, Tod, Geroch, and so many more!

After reading Clifford’s post, I decided to email him about his Southampton experience. Minutes later I received a response.

Add Warwick, Durham, and Southampton to my English school list.

Revise Your Textbooks.

There’s a tenth planet out there in our solar system. At least according to some American astronomers. Coming just days after the Spanish announce their discovery of some other celestial body navigating our sun.

Excited by the news, I immediately sent an email to two of my astronomer friends to guage their reaction.

The first maintains “that we live in a system populated by only 8 wanderers.” And, flatly, that “the largest objects of the Kuiper belt should hardly be considered planets.” The second declined to comment.

Which made me wonder, what makes a planet a planet? Pluto is small. But this thing is at least more than double Pluto’s size. The orbital plane is offset 44 degrees to the rest of the solar system. But Pluto, which we commonly accept as a planet, is off, according to an unreliable and somewhat confusing source on the web, orbits at 32 degrees due to a myseterious twelfth planet. But the repulsive magnetic forces of the sun are righting the planet. Given enough time, I suspect similar mechanisms would operate on our new eleventh. (The chronology is a bit fuzzy here. We just found a tenth; where’d this well-established twelfth come from?) Maybe this will renew interest in, and funding to NASA.

But I’m getting myself into some dangerous territory, and I don’t want the guys on This American Life to accuse me of being a modern jackass. So I’ll admit my ignorance and get off the planet here.

In other news, I suddenly remembered that I don’t have to snoop around the internet to find new music. Instead, I can just walk over to one of our music and media libraries and borrow new stuff.

Because I missed the reenactment today, I got me a CD of period music from the American revolution. Since I was in the area, I picked up some Duke Ellington and Jim McNeely, too.

Perhaps jazz isn’t the healthiest thing for me. It makes staying up in the middle of the night really, really tolerable.