Archive for June, 2006

More on category theory

June 30, 2006

While reading this mildly entertaining discussion (among mathematicians) on the merits and misdemeanours of category theory, i’ve stumbled upon this sci.physics.research thread (also available here) with the subject How does category theory help?. The thread starts with a skeptic tone, as exemplified by this fun quote:

is almost impossible for me to read contemporary mathematicians who, instead of saying Petya washed his hands,” write simply: There is a t1 < 0 such that the image of t1 under the natural mapping t1 -> Petya(t1) belongs to the set of dirty hands, and a t2, t1 < t2 <= 0, such that the image of t2 under the above-mentioned mapping belongs to the complement of the set defined in the preceding sentence.”

but of course there’s many a post defending CT, as well as a lot of (i’m actually tempted to say, every single one you’ll ever need) references to papers, books and everything categorical [1]. You’ll find in there all the usual suspects (Baez, Weiss, …) engaged in a very civilized and informative exchange about virtually every single topic related to CT (including lambda calculus and its application to physics!) and then more, like comments on Arnol’d’s geometrical way of thinking (to name a random issue that caught my eye).

As for me, the jury’s still out, although the more time i spend far from (theoretical) computer science, the less i find CT appealing in physics. On the other hand, when i’m just trying to play some maths, CT is really fun in its own sake and i have the nagging suspicion that i like it because it is sometimes posed as the unified theory of math. Whatever.


[1] If you just want a quick link to references to get started, follow this one to a post by Chris Hillman (author of his own Categorical Primer).

Litmus test for QM interpretations

June 29, 2006

Chances are that, if you are interested in the foundations of Quantum Mechanics, you already now about Matt Leifer and his excellent blog, Quantum Quandaries. But just in case, i wanted to point out (and strongly recommend) his latest post about the criteria that any interpretation of QM should meet to be considered as a worthy contender in this crowded arena.

Matt makes his points so well that i won’t belabour further on what he says, but just comment his mentioning one of the issues that have been worrying me as of late, namely, the correct interpretation of probability in QM (or what he calls the great probabilty debate). The issue is also discussed in other recent post by Matt himself, which mentions a recent and interesting paper (also discussed over at Guide to Reality) sort of making the case for Bayesian approaches and debunking frequentist ones. The post goes on to tackle a (to me) intriguing issue: the connection between many-worlds interpretations and probability. For many years i had been reading popular accounts about Everett’s interpretation without realizing that nobody was explaining me a fundamental issue: how does the constant unfolding of new worlds account for Born’s rule of probability distribution? What makes some words more probable than others if all of them exist? When later on i read more technical descriptions i found the, so to speak, interpretations of the interpretation less than compeling. But, again, i don’t need to further comment on them: Matt is already giving a pretty good account, with pointers to further reading.

Parenthetical geometry

June 25, 2006

sicmIf i were asked for my preferred field in physics, i’d have a really hard time choosing just one, but it would surely relate in one way or the other to differential geometry. Picking up a programming language, on the other hand, would be far easier, for i feel at home among Scheme’s lots of infuriating, silly parenthesis. Jack Wisdom and Gerry Sussman have managed to bring together the best of both worlds in their book Structure and Interpretation of Classical Mechanics, freely available on-line. The book, aptly dedicated to the Principle of Least Action, is an amazing journey through modern classical mechanics, using two apparently different languages: differential geometry and scheme. There you’ll find all the expected topics: Lagrangian and Hamiltonian formulations, the rigid body, phase space structure, canonical transformations and a very complete treatment of perturbation theory in non-linear systems. What makes this book different (and extremely fun) is what one may call its computational stance: in the authors’ words,

Computational algorithms are used to communicate precisely some of the methods used in the analysis of dynamical phenomena. Expressing the methods of variational mechanics in a computer language forces them to be unambiguous and computationally effective. Computation requires us to be precise about the representation of mechanical and geometric notions as computational objects and permits us to represent explicitly the algorithms for manipulating these objects. Also, once formalized as a procedure, a mathematical idea becomes a tool that can be used directly to compute results.[...]
Our requirement that our mathematical notations be explicit and precise enough that they can be interpreted automatically, as by a computer, is very effective in uncovering puns and flaws in reasoning.

As i mentioned, the computer language chosen is Scheme, for pretty good reasons (besides the obvious one of Sussman being one of the language’s inventors). To begin with, Scheme’s syntax is so simple that one can learn it on the go, although that simplicity does not preclude in any way powerful abstraction means and natural expression of symbolic computations. As a matter of fact, it favours it, as testified by the book’s accompanying library, scmutils. Thanks to it,
expressing mathematical equations in a way understandable by a computer is often a natural exercise. On the other hand, Scheme is an interpreted language, which means that you have at your disposal an interactive environment to play with. The convenience of it for exploratory purposes is hard to overstate.

Wisdom and Sussman have been using SICM for teaching classical mechanics at MIT during several years, and you can find additional material in the course’s website. But the fun does not end there. The 2005 booklet Functional Differential Geometry is an unconventional introduction to differential geometry using SICM’s schemy approach, which is also being followed and extended to Lie Groups by Will Farr, who has started an effort to port (part of) scmutils to PowerPC architectures [1]. Finally, there’s a SICM reading group in sore need of contributions and discussion (hint, hint), but with some potentially useful tips.

Happy hacking!


[1] Those of you who enjoyed my swimming post will probably be interested in this article by Wisdom that i found in Will’s blog,

Powers of Ten

June 18, 2006

If one were to choose a classic science video, that’d probably be Powers of Ten. Now, a kind soul has posted it online:

In the states

June 17, 2006

I’ve arrived to College Park (in the Washington DC area) today, after a rather trying trip from Paris to Dulles (eight hours flight) and from there to the nearby hotel (3 (sic) hours taxi!). I’m participating in the 6th International LISA Symposium, which starts next Monday. I’ll present a poster, initially devised as a talk, giving an overview of the software aspects of Lisa Pathfinder’s development, which is currently well underway. To judge from the number of presentations (50), posters (75) and participants (250) in the symposium, there is a quite active community pushing hard to make LISA a reality, and i expect to learn a lot about the project and its prospects during the week. So the following days will probably be quiet ones here at physics musings. But i’ll be back ;)

Update: Over at Not Even Wrong, Peter Woit is reporting about some news claiming that, somehow, LISA will test string theory. My impression from the field is that nobody in the symposium is seriously talking about that, with the exception of Odylio Aguiar’s talk (mentioned here), which i couldn’t attend.

Update: Finally, there was some talk about string theory in the symposium. Yesterday morning, Craig Hogan gave a talk entitled New physics with LISA where he discussed the potential detectability of a stochastic GW background which would be a relic from an inflationary period and gave some qualitative analysis of cosmic strings as generators of gravitational waves. To be honest, i understood nearly nothing, and was left with a feeling of handwavyness, if only because in the conclusions Craig jokingly admitted that, most probably, in the next LISA Symposium he will give a talk with the same title but totally different contents!

Nobody expects the Strings Inquisition

June 13, 2006

The Spanish InquisitionThe recent comments by you-know-who against the positive press that Peter Woit’s book Not Even Wrong is receiving just reminded me (by some weird association of ideas) of this epoch-making gag by Monty Python. I was about to write an entry on my recently ordering this book and planning to read it on a trip next week, but now i’m scared of confessing having bought it! (and, anyway, Christine Dantas has recently put quite nicely almost my exact feelings on this matter). Imagine, i might even like it, and got immediately classified as a crackpot and a nincompoop by the theoretical physics community!

I’m trying hard to respect string theory and theorists (and even plan on reading Zee, Weinberg and Zwiebach’s books, already waiting on my shelf). Why, i even admire several string theorists. But it would help if someone told me that Motl is not the string community’s spokesman. Or to read every now and then a bit of self-criticism from said community (something in the vein of Smolin’s comments in, say, Three Roads to Quantum Gravity). For if the (so to speak) dialectic battles between those two are to be taken as the kind of discussion we theoretical physicists favour these days, poor Monty Python are just out of business. Paraphrasing Erwin Schrodinger, i wouldn’t like it, and i would be sorry i ever had anything to do with it.

Update: Christine’s again right on the spot. And this is much, much closer to the kind of discussion i was asking for!

GP-B video lecture

June 10, 2006

GPBAs you surely know, the Gravity Probe B experiment will check, very precisely, tiny changes in the direction of spin of four gyroscopes contained in an Earth satellite orbiting at 400-mile altitude directly over the poles, comparing their values to those predicted by General Relativity. During the 50-week science phase of the GP-B mission and the 7-week instrument calibration phase, which lasted from August 2004 – September 2005, it collected over a terabyte of experimental data. The data analysis phase currently underway will culminate, by next year, an amazing work spanning more than four decades. The GP-B Stanford site is just impressive, containing everything you’ll ever one to know about the experiment, from an introductory General Relativity Q&A or a series of beautiful litographs explaining the experiment to relevant scientific papers and directions to build your own GP-B spacecraft.

Thus, there’s really no point in duplicating that well-organized and excellently presented information here, my point being instead recommending the whole site to the few of you that didn’t knew it, and drawing the attention of everyone to a recent addition: an entertaining public lecture by the mission’s principal investigator and instigator, Francis Everitt. Targeting a non-specialist audience sitting in the aisles, Everitt covers the following ground:

  • Testing Einstein
  • The invention of many new technologies
  • Collaboration between university departments
  • Highly successful student involvement in a long-running space program
  • A remarkable range of spin-offs, some of which made possible other NASA missions, including IRAS, COBE, WMAP, and the Spitzer telescope
  • Collaboration between NASA, academia, and industry
  • The challenge of managing a flight program with a very highly integrated payload and spacecraft

Or, if you don’t feel like going to the movies, read Everitt himself explaining this amazing journey in a recent interview.

Quantum mechanical quotes

June 9, 2006

From the revamped This Quantum World site, an all but sobering quotes collection:

  • Quantum mechanics is magic. Daniel Greenberger.
  • Everything we call real is made of things that cannot be regarded as real. Niels Bohr.
  • Those who are not shocked when they first come across quantum theory cannot possibly have understood it. Niels Bohr.
  • If you are not completely confused by quantum mechanics, you do not understand it. John Wheeler.
  • It is safe to say that nobody understands quantum mechanics. Richard Feynman.
  • If [quantum theory] is correct, it signifies the end of physics as a science. Albert Einstein.
  • I do not like [quantum mechanics], and I am sorry I ever had anything to do with it. Erwin Schrödinger.
  • Quantum mechanics makes absolutely no sense. Roger Penrose.

Serendipity

June 3, 2006

Reading the recent article Electrons Act Like Waves (from the Physical Review Focus series, a highly recommended, lay[wo]man-friendly feed for your newsreader), i've discovered one of those peculiar stories that make the history of physics even more enjoyable than it would be by its purely scientific side alone.

The article tells the story of Davisson and Germer's discovery of the so-called wave-like nature of electrons. As explained in every textbook, they set up an experiment consisting in scattering electrons through a (nickel) crystal, and observed the familiar fringes that one obtains when a wave crosses a gratting with alternating slots in a wall.

SlitIt was 1927, and i always pictured Davisson and Germer as intrepid experimenters boldly trying to confirm de Broglie's 1924 ideas about the wave nature of matter [1]. (Justly enough, an idealisation of this experiment has become the de facto standard presentation of the quantum mechanical world!.) The funny thing is that this romantic picture has nearly nothing to do with what really happened. As it comes, D&G were looking for evidence of the atomic structure of metals and knew nothing about de Broglie. After the experiment had been going on for a somewhat sterile period, one of their widgets broke and overheated the nickel plaits, which crystalised and made (when used again for scattering electrons) the interference patterns apparent. The experimenters were all but bewildered, and only after Davisson discussed his results with other colleagues during a holiday in England, did they realize the importance of their discovery.

That's serendipity at its best. And, of course, it was not the first nor the last time that serendipity gave physicists a helping hand. The Oxford Dictionary gives a precise definition of this beautiful word:

serendipity noun the occurrence and development of events by chance in a happy or beneficial way.

or, even better, this one from Julius H. Comroe (as quoted by Simon Singh)

Serendipity is looking for a needle in a haystack and finding the Farmer's Daughter.

and its all too apt etymology:

ORIGIN 1754: coined by Horace Walpole, suggested by The Three Princes of Serendip, the title of a fairy tale in which the heroes “were always making discoveries, by accidents and sagacity, of things they were not in quest of.”

which in my opinion captures extremely well the kind of discoveries we're discussing. They were by chance, that's true, but not just chance: one needs to be in the quest of something, to begin with.

Another famous (and probably better known) example of serendipity at work is Penzias and Wilson's discovery of the cosmic microwave background. As explained by Ivan Kaminow,

He [Ivan] joked that Penzias was an unusually lucky guy. "Arno Penzias and Bob Wilson were trying to find the source of excess noise in their antenna, where pigeons were roosting," he said. "They spent hours searching for and removing the pigeon dung. Still the noise remained, and was later identified with the Big Bang."He laughed, "Thus, they looked for dung but found gold, which is just opposite of the experience of most of us."

The experiment was being conducted at Bell's Labs and its aim was to tune an ultra-sensitive microwave receiving system to study radio emissions from the Milky Way. It was only after Penzias talked with Robert H. Dicke (see also this nice memorial (PDF) for more on Dicke) that the misterious radiation was recognized as the relics of the Big Bang hypothesized by George Gamow some time before. I read the whole story for the first time in Weinberg's marvelous book (required reading), and I've always found a bit unfair that the Nobel prize went only to Penzias and Wilson.

My third serendipitous example comes also from the skies. In summer of 1974, Russell Hulse was a 23-year-old graduate student compiling data from the Arecibo Observatory radio telescope in Puerto Rico. The job was a little bit tedious: he was trying to detect periodic radio sources that could be interpreted as a pulsar [2]. One of the pulsar's earmarks is its extraordinary regularity (a few nanoseconds deviation per year for a period of about a second). Around 100 pulsars were known back then, all with a stable period with a extremely slow tendency to increase. At the end of the day, the data obtained by the telescope was processed by a computer program written by Russell, which selected candidate signals based on the stability of their period. Those were correlated with later or former observations of the same sky zone, to rule out earth-based, spurious sources. One night, Russell boringly noticed a very weak candidate, so weak that, had it been a mere 4 percent fainter, it would have passed unnoticed. On top of that, its period was too short (about 0,06 seconds) and, even worst, it was variable. Russell was on the verge of discarding it more than once during the following weeks, but eventually he persevered and, helped by his supervisor, Joe Taylor (a.k.a. K1JT), correctly interpreted the observation as a binary pulsar. The rest is history, and a Nobel prize [3] one. Russell tells the amazing story in his delicious Nobel lecture (PDF), which starts with these telling words:

I would like to take you along on a scientific adventure, a story of intense preparation, long hours, serendipity, and a certain level of compulsive behavior that tries to make sense out of everything that one observes.

I specially like this instance of serendipity, for it shows that, many a time, lucky strikes befall on those who work hard enough to get hit.

Update: I've just found an excellent article by Alan Lightman, Wheels of Fortune, which gives some very nice examples of serendipitous discoveries, as well as a nice discussion. After reading Michael post on serendipity in HEP, i was wondering about non-experimental lucky strikes, and Lightman gives an excellent example: Steve Weinberg's electroweak theory:

Serendipitous discovery strikes not only in the photographic plates, test tubes, and petri dishes of the laboratory. It also can strike in the pencil-and-paper world of theoretical scientists. In the fall of 1967, theoretical physicist Steven Weinberg was working out a new theory of the so-called “weak force,” one of the four fundamental forces of nature, when he discovered, to his surprise, that his new theory was actually two theories in one. Weinberg was approaching the weak force with the seminal idea that pairs of particles it acted upon, electrons and neutrinos for example, might be identical as far as the force is concerned, just as yellow and white tennis balls are identical as far as the game of tennis goes. When he cast this idea into the mathematical language of quantum physics, Weinberg found that his theory necessarily included the electromagnetic force as well as the weak force. The mathematics required the union of the two forces. As he later remarked, “I found in doing this, although it had not been my idea at all to start with, that it turned out to be a theory not only of the weak forces, based on an analogy with electromagnetism; it turned out to be a unified theory of the weak and electromagnetic forces.” 


[1] As an aside, i find the constant chatter about matter being some sort of schizophrenic mix between particles and waves misleading, if not outright wrong. As stressed (to no avail, it seems) by Feynman (see and hear him on this and much more in his Vega Lectures, for instance), electrons (and photons, for that matter) are particles. You never detect half an electron, or a pi-fold-photon. There's always ticks in a detector (a photo-multiplier, a photographic plate, or trails in a Wilson chamber, for instance). The wave function is not real (neither in the physical nor in the mathematical sense of real), and it 'oscillates' in an imaginary space which is not even 3-dimensional when more than a particle is described. The interference patterns observed (which arise from the addition of complex amplitudes which are squared afterwards) are not associated with single electrons, the only thing wavelike (with a twist) about them being the statistics of their hits on the wall. Even if you believe in Bohm's pilot waves, the particles are still particles! Of course, there's ample room for analogy, but i still find the typical discussions misleading.

[2] The discovery of pulsars had also its share of serendipity. They were found, also unexpectedly, by Jocelyn Bell and Anthony Hewish while they were looking studying scintillating radio signals from compact sources. Jocelyn has written a lively report of their discovery, including the funny story of how they were on the verge on attributing the signals to extraterrestrials, and jokingly use monikers starting with the prefix LGM (for little green men) to name the misterious radio sources. There's also a good review of the tale over at the Hitchhiker's Guide to the Galaxy funny website.

[3] The pulsar discovery also won a Nobel in 1974. But, curiously enough, the undergraduate hero of the story (Jocelyn Bell) was not awarded this time. One wonders.

Technorati Tags: , , , ,


Follow

Get every new post delivered to your Inbox.

Join 33 other followers