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.

I’ve met, corresponded with and in a couple cases collaborated with authors of these papers, but I’ve had no input on writing or peer-reviewing any of them.

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.

6. He won’t kill his uncle first because he wants to be crowned, not executed; and second, because he wants Claudius damned, not just dead.

T. Biancalani, D. Fanelli and F. Di Patti (2010), “Stochastic Turing patterns in the Brusselator modelPhysical Review E 81, 4: 046215, arXiv:0910.4984 [cond-mat.stat-mech].

Abstract:

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.

“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!”

“Perfect!”

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.

I suggest the following: scrap “precalculus” and replace it with a year-long statistics course. This plan has several advantages:

“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:

In the appendix to a paper I am currently co-authoring, I recently wrote the following within a parenthetical excursus:

When talking of dynamical systems, our probability assignments really carry two time indices: one for the time our betting odds are chosen, and the other for the time the bet concerns.

A parenthesis in an appendix is already a pretty superfluous thing. Treating this as the jumping-off point for further discussion merits the degree of obscurity which only a lengthy post on a low-traffic blog can afford.

Need to cite Twitter posts in your LaTeX documents? Of course you do! Want someone else to modify the utphys BibTeX style to add a “@TWEET” option so you don’t have to do it yourself? Of course you do!

Style file:

Example document:

\documentclass[aps,amsmath,amssymb]{revtex4}
\usepackage{amsmath,amssymb,hyperref}

\begin{document}
\bibliographystyle{utphystw}

\title{Test}
\author{Blake C. Stacey}
\date{\today}

\begin{abstract}
Only a test!
\end{abstract}

\maketitle

As indicated, this is only
a test.\cite{stacey2011,sfi2011}

\bibliography{twtest.bib}

\end{document}


And the example bibliography file:

@TWEET{stacey2011,
author={Blake Stacey},
authorid={blakestacey},
year={2011},
month={July},
day={25},
tweetid={95521600597786624},
tweetcontent={I find it hard to tell, in some
areas of science, whether I am

@TWEET{sfi2011,
author={anon},
authorid={OverheardAtSFI},
year={2011},
month={June},
day={23},
tweetid={84018131441422336},
tweetcontent={The brilliance of the word
Complexity'' is that it
to anybody.}}
`

PDF output:

You know what I’d like to see? I’d like to have all the course materials necessary for a good, solid undergraduate physics degree available online, free to access and licensed in a way which permits reuse and remixing. I’d like it all in one place, curated, with paths through it mapped out to define a curriculum. When I say all the course materials, I mean that this webzone should have online textbooks; copies of, or at least pointers to, relevant primary literature; video lectures; simulation codes; sample datasets on which to practice analysis; homework and exam problems with worked-out solutions; interactive quizzes, so we can be trendy; and ways to order affordable experimental equipment where that is possible, e.g., yes on diffraction gratings, but probably no on radioactive sources. I’m talking about physics, because that’s what I nominally know about, but I’d like this to encompass the topics which I got sent to other departments to learn about, like the Mathematics Department’s courses in single- and multivariable calculus, differential equations, linear algebra, group theory, etc.

One way to think about it is this: suppose you had to teach a physics class to first- or second-year undergraduates. Could you get all the textual materials you need from Open-Access sources on the Web? Would you know where to look?

What with Wikipedia, OpenCourseWare, review articles on the arXiv, science blogs, the Khaaaaaan! Academy and so forth, we probably already have a fair portion of this in various places. But the operative word there is various. I, at least, would like it gathered together so we can know what’s yet to be done. With a project like, say, Wikipedia, stuff gets filled in based on what people feel like writing about in their free time. So articles grow by the cumulative addition of small bits, and “boring” content — parts of the curriculum which need to be covered, but are seldom if ever “topical” — doesn’t get much attention.

I honestly don’t know how close we are to this ideal. And, I don’t know what would be the best infrastructure for bringing it about and maintaining it. Idle fantasies and pipe dreams!

I’d like to have this kind of resource, not just for the obvious practical reasons, but also because it would soothe my conscience. I’d like to be able to tell people, “Yes, physics and mathematics are difficult, technical subjects. The stuff we say often sounds like mystical arcana. But, if you want to know what we know, all we ask is time and thinking — we’ve removed every obstacle to your understanding which we possibly can.”

I don’t think this would really impact the physics cranks and crackpots that much, but that’s not the problem I’m aiming to (dreaming that we will) solve. Disdain for mathematics is one warning sign of a fractured ceramic, yes: I’ve lost count of the number of times I’ve seen websites claiming to debunk Einstein “using only high-school algebra!” We could make learning the mathematical meat of physics easier, but that won’t significantly affect the people whose crankishness is due to personality and temperament. Free calculus lessons, no matter how engaging, won’t help those who’ve dedicated themselves to fighting under the banner of Douche Physik.

Alchemists work for the people. —Edward Elric

I’ve received several invitations to be listed in a “Who’s Who”, over the years. As far as academic spam goes, it’s been slightly more common than the invitations to attend fraudulent conferences or to publish in fee-gouging, unrefereed vanity journals. (Memo to academic vanity publishers: I know LaTeX. I’ve wrangled two volumes of conference proceedings into shape. I’ve done six books through three different print-on-demand services. I handled the production editing and the typesetting for two editions of The Open Laboratory. I can do your job myself, and I can do it better than you.) I’ve gotten several e-mails with basically identically repeated verbiage in recent weeks. Take a look:

Now and then, one hears physicist stories of uncertain origin. Take the case of Niels Bohr and his horseshoe. A short version goes like the following:

It is a bit like the story of Niels Bohr’s horseshoe. Upon seeing it hanging over a doorway someone said, “But Niels, I thought you didn’t believe horseshoes could bring good luck.” Bohr replied, “They say it works even if you don’t believe.” [source]

I find it interesting that nobody seems to know where this story comes from. The place where I first read it was a jokebook: Asimov’s Treasury of Humor (1971), which happens to be three years older than the earliest appearance Wikiquote knows about. In this book, Isaac Asimov tells a lot of jokes and offers advice on how to deliver them. The Bohr horseshoe, told at slightly greater length, is joke #80. Asimov’s commentary points out a difficulty with telling it:

To a general audience, even one that is highly educated in the humanities, Bohr must be defined — and yet he was one of the greatest physicists of all time and died no longer ago than 1962. But defining Bohr isn’t that easy; if it isn’t done carefully, it will sound condescending, and even the suspicion of condescension will cool the laugh drastically.

Note the light dusting of C. P. Snow. Asimov proposes the following solution.

If you despair of getting the joke across by using Bohr, use Einstein. Everyone has heard of Einstein and anything can be attributed to him. Nevertheless, if you think you can get away with using Bohr, then by all means do so, for all things being equal, the joke will then sound more literate and more authentic. Unlike Einstein, Bohr hasn’t been overused.

I find this, except for the last sentence, strangely appropriate in the context of quantum-foundations arguments.

The question came up while discussing the grand canonical ensemble the other day of just where the word fugacity came from. Having a couple people in the room who received the “benefits of a classical education” (Gruber 1988), we guessed that the root was the Latin fugere, “to flee” — the same verb which appears in the saying tempus fugit. Turns out, the Oxford English Dictionary sides with us, stating that fugacity was formed from fugacious plus the common +ty suffix, and that fugacious (meaning “apt to flee away”) goes back to the Latin root we’d guessed.

Gilbert N. Lewis appears to have introduced the word in “The Law of Physico-Chemical Change”, which appeared in the Proceedings of the American Academy of Arts and Sciences 37 (received 6 April 1901).