June 2004

Extra dimensions

Last night at a jazz club I was talking to a graduate student at the UofC Divinity School, trying to explain the concept of extra dimensions of spacetime. The possibility of extra dimensions is one of the most exciting ideas in modern physics, but also the one I’ve had the most trouble elucidating to non-experts. (For noble attempts, see here, here, here, here, here.) I’m not completely sure why this is the one thing that is hardest to understand.

How do we know there are three dimensions of space? The simplest way is to take a set of meter sticks and tie them together, such that every one is perpendicular to every other one. What is the largest number of sticks for which you can do that? Three. If we lived in a world with two spatial dimensions, it would only be two, but if there were extra large dimensions it would be some bigger number. Given that we have developed mathematical techniques for describing the geometry of one-dimensional curves, two-dimensional surfaces, and three-dimensional spaces (not to mention four-dimensional spacetime), it shouldn’t be too surprising that we can straightforwardly generalize to higher numbers of dimensions. But people who spend their free time doing something other than studying mathematics don’t want to hear that — they want to know how you can visualize all these extra dimensions. We try our best, but ultimately you can’t really do it, and you have to resort to metaphor.

When trying to explain extra dimensions, there are a few standard analogies we always trot out. One is a straw, or garden hose. We can idealize a straw as a two-dimensional cylinder, but if you look at it from very far away it looks essentially one-dimensional. This is supposed to capture the idea that there can be extra compact dimensions at each point in space. I think this analogy is perfectly transparent, and everyone who hears it should instantly comprehend this otherwise difficult concept. But the actual reactions run the gamut from blank stares to gently-furrowed brows. (A very tiny gamut.) When I’m trying to explain this in a radio interview, it’s even worse, as the complete lack of visual aids renders me helpless. Is there some better metaphor lurking out there?

If string theory is right and there are seven extra dimensions curled up at every point in our apparently three-dimensional space, we are actually smeared out uniformly throughout these dimensions. This smearing can ultimately be traced back to our status as relatively low-energy phenomena in the universe. Something physicists take for granted is the connection between energy and distance: to access phenomena at very small scales (like a tiny curled-up extra dimension) requires the focusing of extremely high energies. That’s why we’re hoping to find evidence for extra dimensions at particle accelerators. It’s a long shot, though; we’re gradually increasing our reach in energy, but it wouldn’t be a surprise if the extra dimensions were well beyond our currently conceivable experiments.

Probably the best way to explain extra dimensions is to imagine that there were fewer dimensions, and how inhabitants of these lower-dimensional worlds could be convinced of the existence of three spatial dimensions. This was the strategy taken in Edwin Abbott’s classic social satire Flatland. Let’s not forget, however, that once the protagonist is convinced of the existence of extra dimensions and starts spreading the word, he’s thrown into jail for his subversive ideas.

Although I didn’t really succeed in conveying much understanding about extra dimensions, I did learn something about the divinity school: many, if not most, if its faculty members don’t believe in God. “Pretty skeptical about religion” was the description offered. I wonder if this phenomenon is widespread in divinity schools elsewhere?

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First impressions

Jarhead by Anthony Swofford is an account of Swofford’s experiences as a young Marine in the first Gulf War. It’s a riveting book, well worth reading, especially for the description of the training and culture of the Marines. There is not much combat in the book, largely because the combat phase of the war was so short. But there is some interesting insight about the relations between the U.S. forces and the local population. This story takes place in Saudi Arabia, after a small group of Marines have encountered a tribe of Bedouins who were complaining that someone had been using their camels for target practice.

We drive back to the Triangle on the superhighway and I sit in the back of the Hummer with Dettmann and Crocket and tell them what occurred with the Bedouins. They think the story is funny, and they both laugh and make jokes about “camel jockeys.” I’m not happy to be in the Triangle, and I’m even less happy about going to war as a hired man for another government, but I find their heartlessness particularly disturbing. I want to defend the Bedouins against this assault from these ignoramuses.

The Bedouins are not our enemy, and the Bedouins will not try to kill us whenever the Coalition decides to act. I’ve just experienced a human moment with the Bedouin, free of profanity and anger and hate. Because they are ignorant and young and have been well trained by the Corps, Dettmann and Crocket are afraid of the humanity of the Bedouin, unable to see through their desert garb into the human.

Before I have a chance to tell Dettmann and Crocket the reasons they are wrong, before I have an opportunity to explain the difference between the Bedouin and the Iraqis, a Mercedes sedan approaches from the rear, traveling at high speed. We occasionally see large Mercedes sedans on the superhighway, a Saudi male driving with a female or a few females in the backseat, each wearing a hijab, the traditional Muslim head covering. These brief, high-speed glances are our only exposure to the citizens of the country we’re protecting (the Bedouins are less citizens of the country than denizens of the land). We’re sure the Saudis prefer this arrangement. We are the ghost protectors. As the car closes in, Crocket stands in the back of the Humvee, holds the crossbar with one hand, and puts his other hand to his mouth, flicking his tongue between the two fingers. The driver of the Mercedes turns his head slowly, a little late to see Crocket, but one covered woman sits alone in the backseat of the car, and I watch her eyes follow Crocket’s rude gesture. I don’t know if she’s registering shock or confusion or disgust, but I know I will always remember her eyes, locked on the crude young American.

The Mercedes blows past and Crocket and Dettmann yell profanities and excitedly slap each other on the back. Dettmann calls Crocket a “ballsy motherfucker,” and Crocket says, “That bitch will never forget me. She wanted me.”

It’s not hard to see why sending our armed forces into a foreign country tends not to be an effective way to capture hearts and minds. The Marines are nineteen-year-old kids, far from home and trained in the difficult and specialized arts of winning wars. They are not a skilled cadre of career diplomats. And that’s the way it should be; empathy for the Other is not a skill that helps soldiers win battles, and might even help you get killed. Being a fighter is different than being a negotiator or statesman. If we are going to make a habit of nation-building in countries that aren’t fully convinced of our benevolence, we’re going to have to figure out better ways to manage the transition from battle to rebuilding.

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Democracy is coming

Here’s hoping that all goes relatively well for the people of Iraq, who were graciously handed their sovereignty a couple of days early. Even if their new government arose out of the fevered imaginations of crypto-imperialist neoconservatives, we should all wish that the experiment with democracy turns out to be a true success. I don’t have much reason to believe that a real government by the people has a better chance of taking hold in Iraq than it does in, say, Russia, but I absolutely hope I’m wrong.

Meanwhile, the rule of law seems to be catching on in the United States as well, as the Supreme Court has used their combined legal acumen to determine that the President does not have the right to detain people for years without bringing charges or any access to the court system. It feels like a Leonard Cohen song is breaking out.

(Sorry for not linking to any other clever blogospherical thoughts on these weighty matters — still running around in headless-chicken mode.)

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Modern cool

Occasionally the demands of the tangible world — unpacking after a recent move, for example, or even trying to be a good scientist — make it hard to indulge in blogging. Fortunately, wiser minds than my own have developed all sorts of coping strategies, such as the Sunday Song Lyrics you’ll find at the Volokh Conspiracy.

So here is a Sunday Song Lyric of my own. In honor of moving, I’ll offer up the first song that really struck me upon moving to Chicago five years ago: Patricia Barber’s Postmodern Blues (punctuation as in original liner notes):

as the century ends and tradition turns in on itself

as Boulez screams and yells his music is put on the shelf

repetition is back, a rose is a rose, said herself

Bill Gates has won

i’ve got the postmodern blues

1900 began the obsession with function as form

with a hammer and nail and a paintbrush and camera they storm

in Russia the Bolsheviks conquer, the masses want more

Karl Marx has gone,

i’ve got the postmodern blues

line is fragmented, Isadora invented modern dance

philosophers ponder while communists squander their chance

illusion is captured in Cubism’s reign over france

Picasso’s gone

i’ve got the postmodern blues

the stock market rallies as futures are tallied and sold

pensions are raided and parachutes painted in gold

conformism packaged to save us all from the cold

Cezanne is gone

i’ve got the postmodern blues

I love Barber’s lyrics, but they’re not her strong suit — take your pick from singing, composing, and playing the piano, she’s fantastic at all of them. Although “jazz” would be the idiom you’d squeeze her into if you were so inclined, she is heavily influenced by classical music (her original training) and is somewhat celebrated for startling interpretations of pop tunes (both “Light My Fire” and “Ode to Billy Joe” are personal favorites of mine). The All-Music Guide sums her up pretty well: “Quirky, Cerebral, Ambitious, Playful, Melancholy, Sophisticated, Stylish, Intimate, Bittersweet, Freewheeling.”

Best of all, she plays (most) Monday’s at the Green Mill here in Chicago, five dollar cover in a cozy and historic venue. Another reason this is the world’s greatest city.

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Homeward bound

No time for blogging, I’ve just become a homeowner. Yesterday was closing — the first time in my life I have ever hired an attorney. (Before, I just knew them as those really competitive people in the intramural basketball league.) Today I actually moved, although much remains to be done. A phone/DSL line, for example; this is being typed from an internet cafe, where I have escaped to after discovering that none of my telecommunication services were working yet.

Another change wrought by my new status: until recently, I’m pretty sure I had never actually set foot inside a Home Depot. Now I am practically friends with all the staff. And I have designed a truly ingenious way to use my bookshelves as a CD rack, of which I am undeservedly proud.

The whole process involves so many failure modes that it’s very frightening to contemplate. (For example, don’t just park in the alley and leave your hazard lights flashing for too long, as you might drain your battery and be unable to start your car — not that I know from experience, you understand.) The key is a good real estate agent, and I was lucky enough to have a true genius on my side — Ed Jelinek, whom I heartily recommend to anyone looking to buy property in Chicago. Putting yourself in the hands of someone who really knows what they are doing, and makes extra efforts to look out for you and set you straight when you are about to make a horrible mistake, makes an intimidating process immeasurably less scary.

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Vacuum popularity

Okay, folks out there in internet-land, help me out here. Did vacuum energy just surge in popularity all of a sudden? If you look for “cosmological constant” in Google or other search engines, one of the first things that comes up is a short article I wrote for the Encyclopedia of Astronomy and Astrophysics some time back. On an average day there might be ten or so hits on that web page; but thus far today there have been well over two hundred, from a collection of different search engines. Did the cosmological constant get mentioned on Oprah or something? (And, more importantly, how can I make money off of this?)

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Precognition

You knew it, right? There was something inside you, as you read just yesterday about the startling evidence of an actual link between Iraq and Al Qaida, maybe even a direct tie to Sept. 11? There was some nagging feeling that it couldn’t be true. There’s been no evidence worth talking about for any such connection, and it would be very strange for it to suddenly pop up now. Who knows, maybe they did something incredibly bone-headed yet again, like mixing up two kinda-Arabic-sounding names. Ha, ha! Wouldn’t that be ridiculous? Any idiot would have cleared something like that up a long time ago.

I’m sure glad this stuff isn’t important, so we can all just enjoy a good laugh about it.

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What would Shelly do?

A gaggle of Nobel Laureates in Chemistry, Physics, and Medicine have endorsed John Kerry for President, on the (sensible) grounds that the Bush administration is undermining science in countless ways, from cutting funding for basic research to ignoring honest input on bioethics issues. Probably most of these folks are good liberal academics who would have voted Democratic anyway, but the administration’s specific affronts to science are what made them get together to sign the letter.

Like Chris C. Mooney, I wonder how much impact such a letter will have. It got a good amount of play on the news, and polls typically indicate that the public has a high regard for the honesty and ethical standards of scientists (compared to journalists, prostitutes, car salesmen, politicians, etc.). But as Chris says, people don’t turn to scientists for policy guidance the way they used to (or we imagine they used to, anyway).

I think the laureates are doing the right thing by intervening, though. If Sheldon Glashow wants to give his opinion about globalization or literary theory, his expertise as a particle physicist don’t count for very much; but in a letter focused sharply on science policy, they have every reason to stick their noses in the debate. And in a society that takes your opinion about world peace seriously once you simply demonstrate your ability to carry a tune or look good on screen, why shouldn’t people with actual expert knowledge about a field make their judgments known?

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Rawls

Brian Leiter points at a memorial notice for the late John Rawls, one of the leading (probably the leading) American political philosopher of the twentieth century. I got to know Rawls just a little bit, when as a graduate student I sat in on one of his classes. He was both one of the warmest and one of the most intelligent people I have ever had the privilege to meet.

The class I took was offered both to undergraduates and graduate students; there were twice-weekly lectures, plus weekly discussion sections. The sections for undergrads were led by philosophy grad students, while Rawls himself led the session for grad students. I asked whether I could sit in on the grad-student section, given that I was an astronomy grad student who was merely auditing the class; being the paragon of fairness that he was, he said that since I was a grad student, I should go to the section for grad students, simple as that.

Unfortunately, I almost never got to talk with him about philosophy; once he found out that I was interested in cosmology and the early universe, he was always asking me questions about that. He had wide-ranging interests in math and science, and would often use metaphors in the lectures that I’m sure nobody but me could appreciate. The best was when he said that deriving his two principles of justice should be like proving Stokes’ theorem in differential geometry on an arbitrary manifold: it required a large investment to set up the definitions and axioms, but then the proof was almost immediate. He also had a standing offer of $100 to anyone who could find a “mistake” in his theory of justice as fairness, in the sense of an incorrect conclusion drawn from his premises. He believed that good philosophy should be like good mathematics; it need not be “right” (if you didn’t believe in the premises), but it could be free of mistakes.

He influenced my own views a great deal, moving me from a confused utilitarianism to a fervent social-contractarianism. A rare combination of genius and genuine humanity.

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God: threat, or menace?

I’ve learned from experience that the way to get a lot of comments is to claim that God doesn’t exist. Some of the comments, unfortunately, seemed to imply that the statements in my post were naive, simplistic, patronizing, etc. My response was basically that the post was indeed simplistic, but not naive (patronizing I will leave as a judgment call); I was just blurting out some things I believe are true, in a rhetorically oversimplified fashion, and not trying to give any sophisticated arguments just then. But it wouldn’t hurt to be more careful and explain what I actually do believe, even if restrictions of space, time, and interest mean that I’ll still be pretty superficial about the reasoning.

One problem with “God” is that nobody agrees on the definition. Of course it’s useless to argue about the “correct” definition, but we should agree on what we’re talking about. So, when I say “God”, I am thinking of something we would recognize as a conscious being, unique in the universe and playing some important role in its creation and/or maintenance, with apparently supernatural abilities (maybe omnipotence or some similar degree of ability, but certainly way above anything we’re familiar with in everyday life). For many academic theologians (although certainly not all), the sticking point there is likely to be the “conscious being” part. In particular, I don’t want to use “God” to refer to nature itself, or to a feeling we get in certain sacred situations, or to the abstract laws of physics, or to our capacity for joy and love, or anything so insentient. Those things might be interesting to talk about in their own rights, but I don’t see why we should call them “God” — they are quite different from the God of classical Abrahamic monotheism, as well as from an Aristotelian unmoved mover responsible for creating the universe. Nor are they what 90% of the 90% of Americans who profess belief in God really mean when they profess that belief, I’d be willing to wager. Whatever most people have in mind when they speak of God, it must be some being that is able to care about we humans. (If you’d like to define God as all of nature or as our love for our fellow persons, then fine, I agree that God exists. But as a good pragmatist who sees no practical consequences flowing from such an identification, I wonder why we should bother. Why not just use a different word?)

So, do we have reason to believe that God exists? There are two possibilities: either the existence of God is a logical inevitability and can be demonstrated through pure reason, or God is possible but not necessary and we must turn to experience, revelation, or something otherwise more contingent.

I honestly don’t know what it would mean for some aspect of reality to be logically necessary; logical necessity is a characteristic of formal statements, not of the real world. Our descriptions of the world might involve certain logical requirements, but the world is whatever it is. In particular, there is absolutely no obstacle to imagining a world without God. It is perfectly straightforward to imagine a strictly mechanistic universe, consisting of certain dynamical objects obeying a set of immutable rules. (In Aquinas and elsewhere you can find the idea that the universe requires a First Cause to keep it all moving. Everyone these days should recognize that this is a perfect example of how you can trick yourself by sloppy use of language; ever since Newton, we’ve understood that motion is a perfectly natural state of being, and doesn’t require any agent to keep it going.) I furthermore see no obstacle to imagining that some of those objects get together to form complex collections possessing what we would call “consciousness.” (The details of how it might happen remain to be worked out, but that’s not an obstacle in principle.) Such a universe could easily last forever as a self-contained entity, without the aid of any external creator or first cause. Indeed, I think our universe is really like that. And since I can perfectly well imagine it, there’s no way to use pure reason to argue that it’s not possible; we have to turn to the actual universe we find ourselves in to determine if God is playing a role.

So we need to examine our particular universe and decide whether it looks like God is a part of it or not. Of course, we ourselves are part of the universe, so we might in principle be able to look purely inside ourselves, appealing to contemplation or even revelation. Personally, I find those methods completely unreliable; we could come to all sorts of absurd conclusions by trusting them. Instead, we should be good empiricists, and try to judge as objectively as we can whether our universe makes more sense with God or without. In other words, we should consider the idea of God as any other hypothesis about how nature works, and test it using conventional scientific methods.

Although natural theology has a long history, it’s not an especially distinguished one, with the argument from design taking an especially heavy beating (from Hume even before Darwin). Consequently, a lot of people don’t like the idea that we should treat God as an hypothesis to be empirically tested. Stephen Jay Gould tried to argue that religion and science are compatible because they are strictly non-overlapping in their spheres of interest. But if you look hard at his argument, it only makes sense because his definition of “religion” is what most people would call “moral philosophy.” It’s certainly true that religion has important aspects other than a theory of the nature of reality — moral and social aspects, most obviously. But it also makes claims about how reality works, and those claims can be tested by the same criteria that other claims about reality can be tested. (Furthermore, if the claims about reality fail to be supportable, there doesn’t seem to be much reason left to put any stock in the moral or social aspects — but that’s an entirely separate kettle of fish.)

By the standards of conventional scientific reasoning, the idea that there exists a God that plays an important role in the universe does very badly as an hypothesis, as I’ve discussed in some detail elsewhere. Everything we’ve ever seen in the universe is completely compatible with a purely naturalistic description; we’ve never seen any reliable evidence of supernatural influence or design, and adding an entirely new metaphysical category to a perfectly self-sufficient universe is an unnecessarily drastic step in our attempts to fill in those gaps that remain in our understanding. (Again, plenty of people disagree; the argument from design is alive and well, and now typically refers to the exquisite perfection of the laws of nature rather than to the human eye. I just think adherents of this view are wrong.) It didn’t have to be this way; I could equally well imagine a universe in which evidence for the existence God were quite manifest, with good alternate-universe scientists who were among the most devout members of society. It’s just not the universe in which we live.

Of course mine is a minority view, if we were to take a poll among all the people in the world. That’s exactly the reason why it’s worth pressing the issue. It wouldn’t be fair to call belief in God the Big Lie, as the people who argue in its favor are generally quite sincere. But it is the Big Mistake; of all the incorrect beliefs in the modern world, this is certainly the one that combines the widest prevalence with the most significant impact. So it’s worth arguing against, gently but persistently.

Not that I expect to change anybody’s mind (although one theologian did tell me that I had convinced him to give up on the argument from design, if not on belief in God). But at least now I can point to this post if the issue arises again, so the blog can concentrate on important issues like ice cream and performance art.

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