November 2010

The Pi-on

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I am in love with this comment and want to have its babies:

pi appears as a constant in many formula of physics. General relativity says that it isn’t constant. Is it the origin of the pi particle, aka pion?

A curmudgeonly literalist might, when faced with a question such as this, harrumph a simple “No.” A more loquacious sort might explain that general relativity does not say that π is not a contstant. Pi is not a parameter of physics like the fine-structure constant, which could conceivably be different or even variable from place to place. It’s a universal answer to a fixed question, to wit: what is the ratio of the circumference of a circle to its diameter, as measured in Euclidean geometry? The answer is of course 3.141592653589793…, or any number of representations in terms of infinite series.

But the point of the question is that GR says we don’t live in Euclidean space; we move through a curved spacetime manifold. That’s okay. In a curved space, we could imagine defining the “diameter” of a circle as the maximum geodesic distance connecting two of its points, and taking the ratio of the circumference with that diameter, and indeed it would typically not give us 3.14159… But that doesn’t mean π is changing from place to place; it just means that the ratio of circumference to diameter (defined this way) in a curved space doesn’t equal π. If the circumference/diameter ratio is less than π, you are in a positively curved space, such as a sphere; if it is greater than π, you are in a negatively curved space, such as a saddle. Geometry can also be much more complicated than that, with different ratios depending on how the circle is oriented in space, which is why curvature is properly measured by tensors rather than by a simple number.

Taken from Mathematics Illuminated, which says that pi really does depend on the geometry of space, which is crazy.
Taken from Mathematics Illuminated, which says that pi really does depend on the geometry of space, which is crazy.

(Parenthetically, one of the dumbest mathematical arguments ever given was put forward by the world’s smartest person, Marilyn Vos Savant. The columnist wrote an entire book criticizing Andrew Wiles’s proof of Fermat’s Last Theorem. Her argument: Wyles made use of non-Euclidean geometry, but what if geometry is really Euclidean? Touche!)

However … despite the fact that π doesn’t really change from place to place in general relativity, the geometry does change from place to place, and there is a particle associated with those dynamics — the graviton. Although the formulation of the original question isn’t accurate, the spirit is very much in the right place. And I, for one, will henceforth be perpetually sad that the physics community missed a chance by attaching the word pion to the lightest quark-antiquark bound state, rather than to the particle associated with deviations from Euclidean geometry. That would have been awesome.

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Against Space

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The Philosophy of Science Association meeting in Montreal was great fun. For one thing it was in Montreal; for another I got to hang out with Doctor Free-Ride; and as a bonus there were some interesting and provocative talks about the nature of time. I chatted with Tim Maudlin, Huw Price, Craig Callender, Nick Huggett, Chris Wuttrich, David Wallace, John Norton, and other people I always learn from when I talk to. Philosophers always force you to think hard about things.

Here are the slides from my own talk, which was supposed to be about time but ended up being more about space. Not much in the way of original research, just some ruminations on what is and is not “fundamental” about spacetime (with the caveat that this might not be a sensible question to ask). I made two basic points, which happily blended into each other: first, that the distinction between “position” (space) and “momentum” is not a fundamental aspect of classical mechanics or quantum mechanics, but instead reflects the particular Hamiltonian of our world; and second that holography implies that space is emergent, but in a very subtle and non-local way. This latter point is one reason why many of us are skeptical of approaches like loop quantum gravity, causal set theory, or dynamical triangulations; these all start by assuming that there are independent degrees of freedom at each spacetime point, and quantum gravity doesn’t seem to work that way.

Sadly the slides aren’t likely to be very comprehensible. There’s a lot of math, and the equations don’t come out completely clearly — my first time using Slideshare, so perhaps they would look better if I uploaded a pdf file rather than PowerPoint. (Hint: the slides are much more clear if you switch to full-screen mode by clicking on the bottom right.) Also I didn’t make any attempt to have the slides stand by themselves without the accompanying words. But at least this will serve as documentation that I really did give a talk at the conference, no just hang out in restaurants in Montreal.

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Food In Space

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Editor’s note: Crap. I wrote this post within milliseconds after the first of these awesome images came out, but somehow didn’t publish it. Now they are all over the place, and the message is ancient news in internet-time. But the science is timeless!

This tweet by Alicia Chang says it all: “Comet Hartley 2 looks like a peanut.”

Comet Hartley 2

This is the first close-up image from a fly-by of the comet by NASA’s Deep Impact mission. Expect more coming in. Despite the delicious appearance, however, it wouldn’t be prudent to take a bite; the comet is spewing out cyanide.

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Wicked Company

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wickedcompany
Via 3 Quarks Daily, an Economist review of what looks like a fun book: Philipp Blom’s A Wicked Company: The Forgotten Radicalism of the European Enlightenment.

It is the story of the scandalous Paris salon run by Baron Paul Thierry d’Holbach, a philosophical playground for many of the greatest thinkers of the age. Its members included Denis Diderot (most famous as the editor of the original encyclopedia, but, Mr Blom argues, an important thinker in his own right), Jean-Jacques Rousseau, the father of romanticism, and the baron himself; even David Hume, a famous Scottish empiricist, paid the occasional visit.

I have a special fondness for these guys, having taught a course about them. As much as I am a forward-thinking person, the modern mode of expression by freethinkers (pounding out passionate diatribes on our keyboards) isn’t quite as much fun as gathering in a salon among good food and drink to denounce hypocrisy and spread the Enlightenment message.

Apparently Blom’s historical account has a contemporary message:

Even today, and even in secular western Europe, the bald and confident atheism and materialism of Diderot and Holbach seems mildly shocking. We still cling stubbornly to the idea of an animating soul, a spiritual ghost in the biological machine. For Mr Blom, the modern, supposedly secular world has merely dressed up the “perverse” morality of Christianity in new and better camouflaged ways. We still hate our bodies, he says, still venerate suffering and distrust pleasure.

This is the message of Mr Blom’s book, hinted at but left unstated until the closing chapters. He believes the Enlightenment is incomplete, betrayed by its self-appointed guardians. Despite all the scientific advances of the past two centuries, magical thinking and the cultural inheritance of Christianity remain endemic.

Sounds pretty darn accurate. Let’s order some bottles of wine and get this job finished!

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Physicalist Anti-Reductionism

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In a philosophical mood at the moment, because I’m about to head to Montreal for the Philosophy of Science Association biennial meeting. Say hi if you’re in the neighborhood! I’m on a panel Thursday morning with Nick Huggett, Chris Wüthrich, and Tim Maudlin, talking about the emergence of spacetime in quantum gravity. My angle: space is obviously not fundamental, though time might be.

Here’s a Philosophy TV dialogue between John Dupré (left) and Alex Rosenberg (right). They are both physicalists — the believe that the world is described by material things (or fermions and bosons, if you want to be more specific) and nothing else. But Dupré is an anti-reductionist, which is apparently the majority view among philosophers these days. Rosenberg holds out for reductionism, and seems to me to do a pretty good job at it.

John and Alex from Philosophy TV on Vimeo.

To be honest, even though this was an interesting conversation and I can’t help but be drawn into very similar discussions, I always come away thinking this is the most boring argument in all of philosophy of science. Try as I may, I can’t come up with a non-straw-man version of what it is the anti-reductionists are actually objecting to. You could object to the claim that “the best way to understand complex systems is to analyze their component parts, ignoring higher-level structures” but only if you can find someone who actually makes that claim. You can learn something about a biological organism by studying its genome, but nobody sensible thinks that’s the only way to study it, and nobody thinks that the right approach is to break a giraffe down to quarks and leptons and start cranking out the Feynman diagrams. (If such people can be identified, I’d happily join in the condemnations.)

A sensible reductionist perspective would be something like “objects are completely defined by the states of their components.” The dialogue uses elephants as examples of complex objects, so Rosenberg imagines that we know the state (position and momentum etc.) of every single particle in an elephant. Now we consider another collection of particles, far away, in exactly the same state as the ones in the elephant. Is there any sense in which that new collection is not precisely the same kind of elephant as the original?

Dupré doesn’t give a very convincing answer, except to suggest that you would also need to know the conditions of the environment in which the elephant found itself, to know how it would react. That’s fine, just give the states of all the particles making up the environment. I’m not sure why this is really an objection.

This is purely a philosophical stance, of course; it means next to nothing for practical questions. Nor does the word “fundamental” act in this context as a synonym for
“important” or “interesting.” If I want to describe an elephant, the last thing I would imagine doing is listing the positions and momenta of all its atoms. But it’s worth getting the philosophy right. I could imagine hypothetical worlds in which reductionism failed — worlds where different substances were simply different, rather than being different combinations of the same underlying particles. It’s just not our world.

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Is Dark Matter Supernatural?

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No, it’s not. Don’t be alarmed: nobody is claiming that dark matter is supernatural. That’s just the provocative title of a blog post by Chris Schoen, asking whether science can address “supernatural” phenomena. I think it can, all terms properly defined.

This is an old question, which has come up again in a discussion that includes Russell Blackford, Jerry Coyne, John Pieret, and Massimo Pigliucci. (There is some actual discussion in between the name-calling.) Part of the impetus for the discussion is this new paper by Maarten Boudry, Stefaan Blancke, Johan Braeckman for Foundations of Science.

There are two issues standing in the way of a utopian ideal of universal agreement: what we mean by “supernatural,” and how science works. (Are you surprised?)

There is no one perfect definition of “supernatural,” but it’s at least worth trying to define it before passing judgment. Here’s Chris Schoen, commenting on Boudry et. al:

Nowhere do the authors of the paper define just what supernaturalism is supposed to mean. The word is commonly used to indicate that which is not subject to “natural” law, that which is intrinsically concealed from our view, which is not orderly and regular, or otherwise not amenable to observation and quantification.

Very sympathetic to the first sentence. But the second one makes matters worse rather than better. It’s a list of four things: a) not subject to natural law, b) intrinsically concealed from our view, c) not orderly and regular, and d) not amenable to observation and quantification. These are very different things, and it’s far from clear that the best starting point is to group them together. In particular, b) and d) point to the difficulty in observing the supernatural, while a) and c) point to its lawless character. These properties seem quite independent to me.

Rather that declare once and for all what the best definition of “supernatural” is, we can try to distinguish between at least three possibilities:

  1. The silent: things that have absolutely no effect on anything that happens in the world.
  2. The hidden: things that affect the world only indirectly, without being immediately observable themselves.
  3. The lawless: things that affect the world in ways that are observable (directly or otherwise), but not subject to the regularities of natural law.

There may be some difficulty involved in figuring out which category something fits, but once we’ve done so it shouldn’t be so hard to agree on how to deal with it. If something is in the first category, having absolutely no effect on anything that happens in the world, I would suggest that the right strategy is simply to ignore it. Concepts like that are not scientifically meaningful. But they’re not really meaningful on any other level, either. To say that something has absolutely no effect on how the world works is an extremely strong characterization, one that removes the concept from the realm of interestingness. But there aren’t many such concepts. Say you believe in an omnipotent and perfect God, one whose perfection involves being timeless and not intervening in the world. Do you also think that there could be a universe exactly like ours, except that this God does not exist? If so, I can’t see any way in which the idea is meaningful. But if not, then your idea of God does affect the world — it allows it to exist. In that case, it’s really in the next category.

That would be things that affect the world, but only indirectly. This is where the dark matter comparison comes in, which I don’t think is especially helpful. Here’s Schoen again:

We presume that dark matter –if it exists–is lawful and not in the least bit capricious. In other words, it is–if it exists–a “natural” phenomena. But we can presently make absolutely no statements about it whatsoever, except through the effect it (putatively) has on ordinary matter. Whatever it is made of, and however it interacts with the rest of the material world is purely speculative, an untestable hypothesis (given our present knowledge). Our failure to confirm it with science is not unnerving.

I would have thought that this line of reasoning supports the contention that unobservable things do fall unproblematically within the purview of science, but Chris seems to be concluding the opposite, unless I’m misunderstanding. There’s no question that dark matter is part of science. It’s a hypothetical substance that obeys rules, from which we can make predictions that can be tested, and so on. Something doesn’t have to be directly observable to be part of science — it only has to have definite and testable implications for things that are observable. (Quarks are just the most obvious example.) Dark matter is unambiguously amenable to scientific investigation, and if some purportedly supernatural concept has similar implications for observations we do make, it would be subject to science just as well.

It’s the final category, things that don’t obey natural laws, where we really have to think carefully about how science works. Let’s imagine that there really were some sort of miraculous component to existence, some influence that directly affected the world we observe without being subject to rigid laws of behavior. How would science deal with that? …

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Is Dark Matter Supernatural? Read More »

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