Currently Reading

Xiaotie Denga and Li-Sha Huang (2006), “On the complexity of market equilibria with maximum social welfare” Information Processing Letters 97, 1: 4–11 [DOI] [PDF].

We consider the computational complexity of the market equilibrium problem by exploring the structural properties of the Leontief exchange economy. We prove that, for economies guaranteed to have a market equilibrium, finding one with maximum social welfare or maximum individual welfare is NP-hard. In addition, we prove that counting the number of equilibrium prices is #P-hard.

Found by citation-hopping from here.

Pretentious Document Format

I Love the Blogosphere!I love the Interblagotubes.

Where else could you dump thousands of grumpy and disaffected words on unsuspecting readers and have them come back asking for more, and in a more easily printable format? Seriously: if you know a better venue for long-winded, gloomy rambles, I’ll go there instead.

Recently, Scott Hatfield asked me if I could convert one of my lengthier essays into a PDF or some other such format. In the spirit of excessive and unwanted generosity, I did a quick-and-dirty conversion job on not one, but two posts. Here they are:

The next time I need to procrastinate on something dreadfully important, I might try this again.

Friday Geek Update

My aged and broken laptop is still broken and has not grown any younger. Moreover, the USB key on which I had a decently recent backup of my work appears to have died as well. Furthermoreover, the server on which I also had my work backed up is suffering from a bum RAID array. Mission for today is to extract the drive from the old laptop and wire it directly into the dilithium recrystallization coils — er, I mean, connect it to my new Sony VAIO C420. I note that Micro Center sold me a laptop with Windows Vista on it, but I forgive them, since Ubuntu gutsy (the installation disc I had on hand) installed without any trouble. Audio, wireless and all those goodies worked without extra effort; I haven’t yet had much success with the Bluetooth support it automagically detected, but the only device I’ve had to test it with has been a cell phone which doesn’t play well with anything else, either. I found a status-bar tool which displays the current weather conditions as reported on the Intertubes, and unlike the previous version I’d used, this one can display temperature in kelvins. A year in Lyon followed by a change to my laptop settings went a long way to making me “internally metric”; this may be the logical next step.

(By the way, I booted into Vista just once — so I could say I knew the enemy, and all — and it sucked. It took the duration of an entire Pinky and the Brain episode just to decide how best to phone in to the mothership and report the music library I hadn’t yet put on the blasted thing because I’d just taken it out of the box. Neil Gaiman was right to consider XP an upgrade.)

All that aside, it is now Friday afternoon in Cambridge, Mass. (which is across and down the river from Newton, Mass. — there’s gotta be a physics joke in that). Outside, it’s a partly cloudy 302 kelvins. Inside, it’s time for the Dandy Warhols, with “I am a Scientist.”

Incidentally, we like to have music playing while we cook dinner here at Château Sunclipse, and this was the song we had going when we discovered that enchilada sauce with a dash of hoisin made an excellent base for beef soup.

What Science Blogs Can’t Do

No cosmic law says that when you gaze into your navel, you have to like what you find.

My thesis is that it’s not yet possible to get a science education from reading science blogs, and a major reason for this is because bloggers don’t have the incentive to write the kinds of posts which are necessary. Furthermore, when we think in terms of incentive and motivation, the limitations upon the effects of online science writing become disquietingly clear. The problem, phrased without too much exaggeration, is that science blogs cannot teach science, nor can they change the world.


Notice how short the “basic concepts in science” list is, compared to the “basic concepts” which we know are the foundation of our fields? It has eleven entries — count them — for all of physics. Translated into lectures, that might be a couple weeks of class time. Chemistry is even worse off, and while the biology section is big, it’s also remarkably scatter-shot. Such introductory lessons as get written don’t get catalogued, and thus become damnably difficult to find again.

And, the problem hardly stops there. As the magician Andrew Mayne recently pointed out,

People only know what they can understand. There’s a lot of great information out there, but not enough is being doing to make it widely accessible to the masses. Most science entries in Wikipedia read like they’re written by graduate students for other graduate students. Even the basic science stuff is written that way.

We need to put ourselves into the perspective of someone who hasn’t had the science exposure that we’ve had and find ways to help make this information more accessible.

Why is introductory material so poorly represented?

Well, what do we science bloggers write about, anyway? This is how I caricature what I see:

0. Fun posts about random non-science stuff — entertaining, humanizing, but not the subject I’m focusing on right now.

1. Reactions to creationists and other pseudo-scientists.

2. Reactions to stories in the mainstream media, often in the “My God, how did they screw up so badly” genre.

3. Reports on peer-reviewed research.
Continue reading What Science Blogs Can’t Do


Las Vegas is a town of bottled water, not just because they’re hawking it on the street corners, but on general principles: the city takes things which should not be encapsulated — risk, chance, sex, scenery — packages them and sells them at exorbitant prices. I’m glad I’m out of it, except that on the way home, I was caught in a monsoon downpour which lasted almost exactly the duration of the walk from the T station to my front door. The next day, my trusty laptop developed an interesting new behavior: when I turned it on, it turned itself off. I suspect the containment around it failed, to use a Star Trek-ism, and its power supply had a delayed allergic reaction to the rainwater. It remains to be seen whether I can extract the data from its hard drive.

Fortunately, the so-called social circle in which I move is a giant geek support system.

While I try to get my act together, Maria Brumm has a couple good posts on the troubles mathphobia causes in a geology education. To an aspiring high-school science teacher, she writes,
Continue reading Woe

The Laplace-Runge-Lenz Vector

Greetings from The Amaz!ng Meeting!

This is the happiest I have yet been, here in the city I am learning to hate, the city with nothing to offer me and nothing to enjoy — except Joshua, Rebecca, PZ, Phil and nine hundred other friends. Yes, Gentle Reader, you know me well enough to guess that my most truly recreational experience here in Las Vegas has been sleeping late, eating a Toblerone in bed, tidying up a blag post from my drafts pile, and missing Michael Shermer’s talk. Joshua just “texted” me, as the kids say, with the following message: “Ok. Shermer needs his Powerpoint privileges revoked. How many text-dump slides is he going to use?”

Call me psychic, Gentle Reader, or at least give me a little credit for remembering what I read. . . .

Anyway, because I’m here to have fun, it’s time to talk physics. With equations.

When we studied the hydrogen atom, we found that an interaction potential which fell off inversely with distance was shape-invariant, implying all sorts of nice symmetry properties of the hydrogen atom’s state space. The classical analogue of this situation would be two objects interacting via an inverse-square force (remember that force is given by the derivative of the potential). Having recently taken a rather madcap tour of the history of classical mechanics, we can probe a little more deeply and investigate one item in more technical detail. Today’s subject will be defining and appreciating the Laplace-Runge-Lenz vector, which as we said earlier was not discovered by Laplace, Runge or Lenz. After finding out that this vector quantity is conserved, we’ll take a quick look at equations which define ellipses and then show that an inverse-square law of gravity can yield elliptical orbits. If any portion of this post is in error, please return the unused portion for a full refund.
Continue reading The Laplace-Runge-Lenz Vector

Sagan on Eratosthenes

After getting himself all grumpy about the ways in which statistics are abused, Joshua Hall decided to relax with a little Carl Sagan.

Fun fact: the philosopher Poseidonios of Apameia (c. 135–51 BCE) repeated Eratosthenes’s experiment about a century and a half later. He observed that on the island of Rhodes, the bright star Canopus was just touching the horizon, while at the same time in Alexandria, the star was a few degrees above the horizon. Because the Earth curves between the two places, the star was seen from different vantage points, and thus the angle between Rhodes and Alexandria could be found. Poseidonios was luckier than he knew: both his figure for the distance between Rhodes and Alexandria and his measurement of Canopus’s position were wrong, but the two wrongnesses canceled each other out, giving a reasonable final answer.

(And yes, I employ BCE/CE dating just to irritate people.)

The Necessity of Mathematics

Today, everything from international finance to teenage sexuality flows on a global computer network which depends upon semiconductor technology which, in turn, could not have been developed without knowledge of the quantum principles of solid-state physics. Today, we are damaging our environment in ways which require all our fortitude and ingenuity just to comprehend, let alone resolve. More and more people are becoming convinced that our civilization requires wisdom in order to survive, the sort of wisdom which can only come from scientific literacy; thus, an increasing number of observers are trying to figure out why science has been taught so poorly and how to fix that state of affairs. Charles Simonyi draws a distinction between those who merely “popularize” a science and those who promote the public understanding of it. We might more generously speak of bad popularizers and good ones, but the distinction between superficiality and depth is a real one, and we would do well to consider what criteria separate the two.

Opinions on how to communicate science are as diverse as the communicators. In this Network age, anyone with a Web browser and a little free time can join the conversation and become part of the problem — or part of the solution, if you take an optimistic view of these newfangled media. Certain themes recur, and tend to drive people into one or another loose camp of like-minded fellows: what do you do when scientific discoveries clash with someone’s religious beliefs? Why do news stories sensationalize or distort scientific findings, and what can we do about it? What can we do when the truth, as best we can discern it, is simply not politic?

Rather than trying to find a new and juicy angle on these oft-repeated questions, this essay will attempt to explore another direction, one which I believe has received insufficient attention. We might grandiosely call this a foray into the philosophy of science popularization. The topic I wish to explore is the role mathematics plays in understanding and doing science, and how we disable ourselves if our “explanations” of science do not include mathematics. The fact that too many people don’t know statistics has already been mourned, but the problem runs deeper than that. To make my point clear, I’d like to focus on a specific example, one drawn from classical physics. Once we’ve explored the idea in question, extensions to other fields of inquiry will be easier to make. To make life as easy as possible, we’re going to step back a few centuries and look at a development which occurred when the modern approach to natural science was in its infancy.

Our thesis will be the following: that if one does not understand or refuses to deal with mathematics, one has fatally impaired one’s ability to follow the physics, because not only are the ideas of the physics expressed in mathematical form, but also the relationships among those ideas are established with mathematical reasoning.

This is a strong assertion, and a rather pessimistic one, so we turn to a concrete example to investigate what it means. Our example comes from the study of planetary motion and begins with Kepler’s Three Laws.


Johannes Kepler (1571–1630) discovered three rules which described the motions of the planets. He distilled them from the years’ worth of data collected by his contemporary, the Danish astronomer Tycho Brahe (1546–1601). The story of their professional relationship is one of clashing personalities, set against a backdrop of aristocracy, ruin and war. From that drama, we boil away the biography and extract some items of geometry:
Continue reading The Necessity of Mathematics

Hydrogen Atoms in Motion

Still working on diagrams. . . Cairochemist, who has just recently started co-blogging at Skulls in the Stars, presents us a video showing hydrogen atoms migrating across a copper-palladium surface. Yes, understanding how catalysts work might help in arranging reactions for new energy sources, but even if it didn’t, being able to watch atoms move has a certain appeal of its own.

Oh, and Skulls in the Stars also points us to The Giant’s Shoulders, which we’re all hoping will become a new monthly event.

Who’s Next?

Drawing diagrams for my next post. . . I begin to procrastinate. . . and find that Dana is now embedding Tom Lehrer videos. Given my background, this one has particular resonance for me:

The Tom Lehrer songbook — yes, I own the Tom Lehrer songbook — has alternate lyrics which include the couplet, “Japan will have its own device / transistorized at half the price.”

Help, Help, I’m Being Oppressed!

I just noticed a post at Michael White’s Adaptive Complexity entitled, “Bad Science Journalism and the Myth of the Oppressed Underdog” (9 March 2008). It’s good. Go read it.

[I]n our culture we love the underdog, who sticks to his or her guns, in spite of heavy opposition. In this narrative, we have heroes, villains, and a famous, brilliant scientist proven wrong.

I’m sure you could pick out instances in science history where this story is true, but more often it is not. You wouldn’t know this from the pages of our major news media though; in fact you’d probably get the impression that the underdog narrative is the way science works. And many journalists may think that too; after all, most of them read (or misread) Thomas Kuhn when they were in college, and Kuhn brought this kind of narrative to a new high.

This is the narrative which I called the “David vs. Goliath of Scientific Establishment” story. White gives a specific example, concerning the public presentation of evolutionary biology; in physics, the problem can be even more fun, since the actual relationship between David’s revolutionary idea and Goliath’s orthodoxy often requires a hefty dose of mathematical reasoning to understand. When a typical statement by a physicist trying to sort the mess out might read, “Any embedding of your gauge group in either noncompact real form of E8 will always give you a nonchiral fermion spectrum,” well. . . the temptation will always be to plump for the “social” angle and emphasize the personalities of the physicists involved. The “oppressed underdog” story emerges quite naturally.

To be fair, or at least spread the misery around, biology can suffer from Popularizer Mathophobia, too. White’s example comes from sexual selection theory and relates to the role game theory might play in understanding the dynamics of a population. Oooh! Math! Scary!

(My “typical statement” is a paraphrase of Jacques Distler, who pointed out this problem almost six years ago.)

Please Her With Your Genome

One of the nice things about science blogs is that they can help transmit the “life stories” of the scientific lifestyle, making a written record of the hitherto unwritten folklore our community generates. In an earlier epoch, each student had to learn the hard way the lesson that whatever you do in lab will not work the first time. Now, the student can receive a tiny foretaste of the pain which awaits and thus, perhaps, live better for it. So, in that spirit, I offer the “life lesson” for this week:

Do not oversleep and miss a meeting because the meeting announcement was sent to the e-mail address you don’t use because it’s continually broken, or else you too may draw the short straw in absentia and find yourself in charge of assembling a volume of conference proceedings. I enjoy working with the written word, perhaps more so than many of my fellow physics boffins, but I can easily think of more interesting things to edit than an overpriced book which nobody will buy and fewer will read. Hooray, academia.

And here’s another thing: the downside of working in an “interdisciplinary” environment (other than the episodic crises of “I’m not doing real science!” conscience and the assertions from specialists in field X that they can solve problems and lead revolutions in field Y without actually having the ground-level knowledge of Y) is that you might be one of the select few who know LaTeX. This is a death sentence: much as being the guy/girl who knows how the Web server works means that all the Web-related tasks fall onto your lap, being the one who knows LaTeX brings all sorts of “little,” er, “action items” your way.

But it’s not all bad. Even digging through the conference e-mail pile for the revised papers people have sent in has a few compensations. There’s the Big Name who doesn’t want to bother with the “Procrustean bed requirements” imposed by the publisher and forgoes inclusion, but even better, there’s the entertaining spam attracted to an e-mail address which was, after all, publicly announced on the conference Web site without the slightest bit of preventive obfuscation.

“We offer the clone-by-phone service of your dreams,” proclaims the e-mail. In just twelve days, their company will “synthesize and clone a 1 kb gene, with all mutations, deletions, fusions, epitope tags and codon optimizations you can think of.” Increase the size of your DNA by four micrograms in only two weeks!

The same firm — which, on casual investigation, looks otherwise legitimate — has been spamming other addresses. The linguist Mark Liberman got a similar message, for example. (“I expect they got my name and email address from some bioinformatics conference I attended, or something like that,” he notes.)

MEMO TO GEN SCRIPT: Mass, unsolicited mailings are not the way to generate good will or impress the world with your netiquette. Thanks for the laugh, though.

Upon reflection, this opens an entire new avenue of exploration. What other scientific services can be hawked by spam, and what would the messages sound like?

Brain Damage and Journalism

Dan Hurley writes of Katherine P. Rankin’s neurological research on sarcasm,

To her surprise, though, the magnetic resonance scans revealed that the part of the brain lost among those who failed to perceive sarcasm was not in the left hemisphere of the brain, which specializes in language and social interactions, but in a part of the right hemisphere previously identified as important only to detecting contextual background changes in visual tests.

That’s from a New York Times piece, “The Science of Sarcasm (Not That You Care),” 3 June 2008. The abstract for Rankin et al.‘s presentation says, in part,

This study provides lesion data suggesting that the right posterior temporal lobe and dorsomedial frontal cortex are associated with recognizing and interpreting sarcastic irony using paralinguistic vocal and facial cues, consistent with functional imaging research examining neural correlates of voice prosody, facial emotion recognition, and perspective taking.

Trust the alchemy of science journalism to turn a result consistent with prior research into a great surprise. As Vaughan Bell points out, by the early 1980s people had already found out that damage to the brain’s right hemisphere can cause “disorders of affective language,” i.e., problems with recognizing emotion in speech. More recently, Shamay-Tsoory et al. (2005) found that lesions in the ventromedial section of the right prefrontal cortex impaired test subjects’ abilities to handle tasks which required understanding sarcasm.

This is the sort of gaffe which makes neurocurmudgeons file a story under “chaff” instead of “wheat.” I wonder: can fMRI detect a cortical lesion which makes all interesting and worthwhile research be perceived as revolutionary? The problem is not just restricted to neuro-journalism, of course — revolution disease is a general trope, right up there with “Think of the children!” and “David vs. the Scientific Goliath.” One begins to appreciate why Eric Roston, author of The Carbon Age (2008), said of his research practices, “I wanted to avoid secondary literature, media,” even though this meant a masochistic journey through peer-reviewed articles.

As for the research itself. . . . To my knowledge (and that of the Neurocritic), Rankin et al.‘s results have not yet appeared in a journal, only at an American Academy of Neurology conference, so pickings are as yet rather thin. No doubt more details will be available anon.

Shifting Standards of Inclusion

SILVER SPRING, MD — Tommy Thayer, 30, is quoted by the Washington Post as saying the following:

It’s a damn shame there hasn’t already been a black president as far as I’m concerned. We are so used to all the presidents being all whites and all men. That’s like telling everyone we are a racist nation. I think people are robbing themselves if they don’t get to know other cultures.

Thayer identifies himself as “all white, 100 percent white, Irish, Italian if you want specifics.” Irish and Italians as members of a cultural or ethnic majority: discuss. Have we as a nation outgrown Grandmother’s fears that Kennedy was taking his orders from the Pope? Would latter-day incarnations of Sacco and Vanzetti be regarded as white troublemakers?