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While looking through old physics books for alternate takes on my quals problems, I found a copy of Sir James Jeans’ Electricity and Magnetism (5th edition, 1925). It’s a fascinating time capsule of early views on relativity and what we know call the “old quantum theory,” that is, the attempt to understand atomic and molecular phenomena by adding some constraints to fundamentally classical physics. Jeans builds up Maxwellian electromagnetism starting from the assumption of the aether. Then, in chapter 20, which was added in the fourth edition (1919), he goes into special relativity, beginning with the Michelson–Morley experiment. Only after discussing many examples in detail does he, near the end of the chapter, say
If, then, we continue to believe in the existence of an ether we are compelled to believe not only that all electromagnetic phenomena are in a
conspiracy to conceal from us the speed of our motion through the ether, but also that gravitational phenomena, which so far as is known have nothing to do with the ether, are parties to the same conspiracy. The simpler view seems to be that there is no ether. If we accept this view, there is no conspiracy of concealment for the simple reason that there is no longer anything to conceal.
…because nothing says “stable platform for mission-critical applications” like “from the makers of Mathematica!”
Carl Zimmer linked to this VentureBeat piece on Wolfram Language with the remark, “Always interesting to hear what Stephen Wolfram is up to. But this single-source style of tech reporting? Ugh.” I’d go further: the software may well eventually provide an advance in some respect, but the reporting is so bad, we’d never know.
We’re told “a developer can use some natural language.” What, like the GOTO command? That’s English. Shakespearean, even. (“Go to, I’ll no more on’t; it hath made me mad.” Hamlet, act 3, scene 1.) We’re told that “literally anything” will be “usable and malleable as a symbolic expression”—wasn’t that the idea behind LISP? We’re told, awkwardly, that “Questions in a search engine have many answers,” with the implication that this is a bad thing (and that Wolfram Alpha solved that problem). We are informed that “instead of programs being tens of thousands of lines of code, they’re 20 or 200.” Visual Basic could claim much the same. We don’t push functionality “out to libraries and modules”; we use the Wolfram Cloud. It’s very different!
(Mark Chu-Carroll points out, “What’s scary is that he thinks that not pushing things to libraries is good!”)
The “wink, wink, we’re not not comparing Wolfram to Einstein” got old within a sentence, too.
“I am my own reality check.” — Stephen Wolfram (1997)
Prompted by this review of Colin McGinn’s Basic Structures of Reality (2011), I read a chapter, courtesy the uni library. It was endumbening. To the extent that he ever has a point, he says in many words what others have said more clearly in few. He confuses the pedagogy of a particular introductory book with the mature understanding of a subject, displays total ignorance of deeper treatments of his chosen topic, blunders into fallacies, and generally leaves one with the impression that he has never done a calculation in all the time he spent “studying physics”. Truly an amazing achievement.
A few years ago, I might have blogged my way through the whole darn book. I must be getting old (“REALLY? NO WAY!” declares my weak knee). But is it a healthy and mature sense of priorities, or a senescent academic crustiness? Have I become one of those people, concerned with my vita to the exclusion of all else? Dark thoughts for this cold autumn evening, dark as our current season of superhero movies—Fimbulwinter 3: Flame of Despair….
Lately, I’ve found my thoughts returning to a passage of Carl Sagan which I first read years and years ago.
The business of skepticism is to be dangerous. Skepticism challenges established institutions. If we teach everybody, including, say, high school students, habits of skeptical thought, they will probably not restrict their skepticism to UFOs, aspirin commercials, and 35,000-year-old channelees. Maybe they’ll start asking awkward questions about economic, or social, or political, or religious institutions. Perhaps they’ll challenge the opinions of those in power. Then where would we be?
That’s from The Demon-Haunted World, chapter 24, page 416. I read that book as a child. I still remember the sensation of coming-to-wakefulness which that reading brought. Since then, I’ve grown taller and greyer and just a touch more bitter. I broke my heart a couple times, got my name into the learned journals here and there, and witnessed more than a few laudatory invocations of St. Carl of Ithaca.
I should have been less surprised to learn that skeptical institutions, fancy ones with Inquiry and Education in their names, belong on that list too.
It is difficult to have patience for those who restrict their community-building to those who need it least.
EDIT TO ADD: Basically, this.
If you want an effective movement with a broad reach, this is roughly the dumbest move you could make. However, if your goal is to reinforce the public’s belief that secularism and atheism particularly is nothing but a bunch of misanthropic white guys whose only real goal is feeling superior to believers but who don’t care about making real change in the world, well job well done. And fuck you.
A post today by PZ Myers nicely expresses something which has been frustrating me about people who, in arguing over what can be a legitimate subject of “scientific” study, play the “untestable claim” card.
Their ideal is the experiment that, in one session, shoots down a claim cleanly and neatly. So let’s bring in dowsers who claim to be able to detect water flowing underground, set up control pipes and water-filled pipes, run them through their paces, and see if they meet reasonable statistical criteria. That’s science, it works, it effectively addresses an individual’s very specific claim, and I’m not saying that’s wrong; that’s a perfectly legitimate scientific experiment.
I’m saying that’s not the whole operating paradigm of all of science.
Plenty of scientific ideas are not immediately testable, or directly testable, or testable in isolation. For example: the planets in our solar system aren’t moving the way Newton’s laws say they should. Are Newton’s laws of gravity wrong, or are there other gravitational influences which satisfy the Newtonian equations but which we don’t know about? Once, it turned out to be the latter (the discovery of Neptune), and once, it turned out to be the former (the precession of Mercury’s orbit, which required Einstein’s general relativity to explain).
There are different mathematical formulations of the same subject which give the same predictions for the outcomes of experiments, but which suggest different new ideas for directions to explore. (E.g., Newtonian, Lagrangian and Hamiltonian mechanics; or density matrices and SIC-POVMs.) There are ideas which are proposed for good reason but hang around for decades awaiting a direct experimental test—perhaps one which could barely have been imagined when the idea first came up. Take directed percolation: a simple conceptual model for fluid flow through a randomized porous medium. It was first proposed in 1957. The mathematics necessary to treat it cleverly was invented (or, rather, adapted from a different area of physics) in the 1970s…and then forgotten…and then rediscovered by somebody else…connections with other subjects were made… Experiments were carried out on systems which almost behaved like the idealization, but always turned out to differ in some way… until 2007, when the behaviour was finally caught in the wild. And the experiment which finally observed a directed-percolation-class phase transition with quantitative exactness used a liquid crystal substance which wasn’t synthesized until 1969.
You don’t need to go dashing off to quantum gravity to find examples of ideas which are hard to test in the laboratory, or where mathematics long preceded experiment. (And if you do, don’t forget the other applications being developed for the mathematics invented in that search.) Just think very hard about the water dripping through coffee grounds to make your breakfast.
The following is a selection of interesting papers on the theory of evolutionary dynamics. One issue addressed is that of “levels of selection” in biological evolution. I have tried to arrange them in an order such that the earlier ones provide a good context for the ones listed later.
Reading today’s Saturday Morning Breakfast Cereal, I got all “someone is WRONG about HAMLET on the INTERNET!”
1. Hamlet couldn’t have said anything much before the play starts, because he was off at school in Wittenberg.
2. He sees the ghost on the night of the first day in the play where he appears. Not a long delay there. And his reaction to being told “The serpent that did sting thy father’s life now wears his crown” is, “O my prophetic soul!” Or, in a different idiom, “Called it!”
3. He has every reason not to act rashly, because (a) he wants to be King (Claudius “popp’d in between the election and my hopes”), and (b) he can’t trust that the ghost is really his father. “The devil hath power to assume a pleasing shape”, etc. Watch your Star Trek, people! Emo!Hamlet is a comparatively recent invention. Prior to the late 1700s, the standard was to play Hamlet as a chessmaster, a brilliant young man trying to turn a bad situation to his advantage, facing a shrewd opponent.
4. It’s the characters in the play who remark on Hamlet’s “transformation”. That’s why Claudius sends for Rosencrantz and Guildenstern.
Welcome, dear Rosencrantz and Guildenstern!
Moreover that we much did long to see you,
The need we have to use you did provoke
Our hasty sending. Something have you heard
Of Hamlet’s transformation; so call it,
Sith nor the exterior nor the inward man
Resembles that it was.
5. He’s so antisocial that he…has a girlfriend? And, as Claudius says, is beloved by the general populace of Denmark? Indeed, that’s a big part of why Claudius doesn’t have Hamlet killed for stabbing Polonius. As he tells Laertes, he doesn’t want to hurt Gertrude, and in addition…
The other motive,
Why to a public count I might not go,
Is the great love the general gender bear him;
Who, dipping all his faults in their affection,
Would, like the spring that turneth wood to stone,
Convert his gyves to graces; so that my arrows,
Too slightly timber’d for so loud a wind,
Would have reverted to my bow again,
And not where I had aim’d them.
T. Biancalani, D. Fanelli and F. Di Patti (2010), “Stochastic Turing patterns in the Brusselator model” Physical Review E 81, 4: 046215, arXiv:0910.4984 [cond-mat.stat-mech].
A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining the Turing condition for instability, we pay particular attention to the role of cross-diffusive terms, often neglected in the heuristic derivation of reaction-diffusion schemes. Stochastic fluctuations are shown to give rise to spatially ordered solutions, sharing the same quantitative characteristic of the mean-field based Turing scenario, in term of excited wavelengths. Interestingly, the region of parameter yielding to the stochastic self-organization is wider than that determined via the conventional Turing approach, suggesting that the condition for spatial order to appear can be less stringent than customarily believed.
See also the commentary by Mehran Kardar.
“We need someone to direct the new Star Wars. Who’s hot?”
“Well, there’s this guy who made a movie about a cute farmboy in the boondocks who never knew his real father, dreams of outer space, fights in a bar full of crazy aliens and then goes up against the evil overlord who killed his father—this really nasty guy with Roman Empire trappings, favorite color black, lots of glowy green energy—and who flies around in a giant ship bigger than anything else in space blowing up planets. He blasts the home planet of one of the heroes early on, so we know he’s serious, and at the end, it’s a race with the clock to stop him blowing up the planet that’s really important. But the good guys win and there’s a flashy award ceremony to wrap it all up.”
“Sounds great! Is there stuff which only makes sense if, like, Fate or Destiny is willing it?”
“Like you wouldn’t believe!”
A. Franceschini et al. (2011), “Transverse Alignment of Fibers in a Periodically Sheared Suspension: An Absorbing Phase Transition with a Slowly Varying Control Parameter” Physical Review Letters 107, 25: 250603. DOI: 10.1103/PhysRevLett.107.250603.
Abstract: Shearing solutions of fibers or polymers tends to align fiber or polymers in the flow direction. Here, non-Brownian rods subjected to oscillatory shear align perpendicular to the flow while the system undergoes a nonequilibrium absorbing phase transition. The slow alignment of the fibers can drive the system through the critical point and thus promote the transition to an absorbing state. This picture is confirmed by a universal scaling relation that collapses the data with critical exponents that are consistent with conserved directed percolation.
Last October, a paper I co-authored hit the arXivotubes (1110.3845, to be specific). This was, on reflection, one of the better things which happened to me last October. (It was, as the song sez, a lonesome month in a rather immemorial year.) Since then, more relevant work from other people has appeared. I’m collecting pointers here, most of them to freely available articles.
I read this one a while ago in non-arXiv preprint form, but now it’s on the arXiv. M. Raghib et al. (2011), “A Multiscale maximum entropy moment closure for locally regulated space-time point process models of population dynamics”, Journal of Mathematical Biology 62, 5: 605–53. arXiv:1202.6092 [q-bio].
Abstract: The pervasive presence spatial and size structure in biological populations challenges fundamental assumptions at the heart of continuum models of population dynamics based on mean densities (local or global) only. Individual-based models (IBM’s) were introduced over the last decade in an attempt to overcome this limitation by following explicitly each individual in the population. Although the IBM approach has been quite insightful, the capability to follow each individual usually comes at the expense of analytical tractability, which limits the generality of the statements that can be made. For the specific case of spatial structure in populations of sessile (and identical) organisms, space-time point processes with local regulation seem to cover the middle ground between analytical tractability and a higher degree of biological realism. Continuum approximations of these stochastic processes distill their fundamental properties, but they often result in infinite hierarchies of moment equations. We use the principle of constrained maximum entropy to derive a closure relationship for one such hierarchy truncated at second order using normalization and the product densities of first and second orders as constraints. The resulting `maxent’ closure is similar to the Kirkwood superposition approximation, but it is complemented with previously unknown correction terms that depend on on the area for which third order correlations are irreducible. This region also serves as a validation check, since it can only be found if the assumptions of the closure are met. Comparisons between simulations of the point process, alternative heuristic closures, and the maxent closure show significant improvements in the ability of the maxent closure to predict equilibrium values for mildly aggregated spatial patterns.
Now that 2.2 metric Ages of Internet Time have passed since Andrew Hacker’s ill-advised “math is hard!!” ramble, I figure it’s a good day to propose my own way of improving high-school mathematics education. Be advised: this is a suggestion about the curriculum, not about how to train teachers, buy books and all that un-TED-friendly stuff which reformers happily gloss over. And I’ll be talking about changes late in the game, which won’t address problems at the “why can’t Johnny add?” level.
When I was in high school—at a pretty well-supported public school, out in the ‘burbs at the comparatively unimpoverished end of town—I took a “precalculus” class my eleventh-grade year. Most of the advanced-track students I knew did the same thing. (If you’d gotten yourself on the even-more-advanced track back in eigth grade, you took precalculus in tenth.) This was supposed to prepare us for taking the AP Calculus class our senior year, which would allow us to get college credit. Instead, it was a thoroughgoing waste of time. The content was a repeat of Algebra II/Trigonometry, which we’d taken the year before, with two exceptions thrown in. The first, probability, was a topic our teacher didn’t know how to teach. In fact, she admitted as much: “I don’t know how to teach probability, so you’re all going to read the book today.” The second, limits, served no purpose. I’ll explain why in a moment.
“This room smells of mathematics!
Go out and fetch a disinfectant spray!”
—A.H. Trelawney Ross, Alan Turing’s form master
It’s been a while since I’ve felt riled enough to blog. But now, the spirit moves within me once more.
First, I encourage you to read Andrew Hacker’s op-ed in The New York Times, “Is Algebra Necessary?” Then, sample a few reactions: