SUSY QM 1: Superalgebra

A couple months ago, I stumbled across an amusing bit of academic woo: “Quantum Mind and Social Science.” The misrepresentations, false dichotomies and nons sequitur of that piece prompted me to wonder what a good litmus test for knowing quantum mechanics might look like. Joshua offered a simple criterion: be able to pick the Schrödinger Equation out of a line-up. At a slightly higher level, I suggested being able to describe in the Heisenberg picture the time evolution of a harmonic oscillator coherent state, and explaining why states of the hydrogen atom with the same n but different angular momentum number l are degenerate. You can’t discuss the relationship between classical and quantum physics without bringing up coherent states eventually, and a good grounding in the basics should include the Schrödinger and Heisenberg pictures. (That’s why I wrote problem 5 in this homework assignment.)

The excited states of the hydrogen atom are our prototype for understanding how the periodic table works, and it’s often the first place one runs into the mathematics of angular momentum. Unfortunately, too many standard treatments of introductory QM say that hydrogen has “accidental degeneracies”: these states have the same energies as those states for no spectacularly interesting reason. But we are trained to associate degeneracies with symmetries — when two sets of eigenstates have the same eigenvalues, we expect some symmetry to be at work. So, is there a symmetry in the hydrogen atom above and beyond the familiar rotational kind, a symmetry which They haven’t been telling us about?

I’d like to explore this topic over a few posts. First, I’ll build up some very general machinery for solving problems, and then I’ll apply those techniques to the hydrogen atom; by that point, we should have a fair amount of knowledge with which we can move in any one of several interesting directions. To begin, let’s familiarize ourselves with the behavior of a superalgebra.
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Beyond the Hoax

Alan Sokal has written a new book, and Oxford University Press promises to get it to us in March 2008. Beyond the Hoax: Science, Philosophy and Culture expands upon his earlier work with Jean Bricmont, including that superb dark comedy Intellectual Impostures, also known as Fashionable Nonsense (1998). After treating his readers to an annotated version of his infamous “Transgressing the Boundaries” essay, Sokal moves on to examine the relationship between science and political liberalism, and he devotes a chapter to asking what his infamous experiment “does and does not prove.”

The middle portion of the book delves into the philosophy of science. In this area, Sokal — a practicing physicist with a tolerance for philosophy books — is sure to have interesting things to say. Finally, he moves into the territory which I expect to be the most controversial (at least outside the Literature Department), with the book’s final third headed off by a study of pseudoscience and postmodernism. Sokal asks if these enterprises are “antagonists or fellow-travelers.”

If you wonder why such a scholarly inquiry might provoke hot air and flying feathers, just read the appendix of Sokal’s earlier essay on the subject. (To my knowledge, this is the closest anybody has done to an academic study of quantum woo and the related pseudoscientific memes employed by medicine denialists. “As a physicist,” he says, “I am not impressed.”) Then ask yourself, “Which bloggers will get upset about this?”

Beyond the Hoax is expected to be published roughly three months after John Allen Paulos’ new book, Irreligion.

Homeopathic Killing

Occasionally, I like to indulge in a bit of blogospheric public service. A little while back, I re-keyed the leaked Dezenhall memo, so people wouldn’t have to deal with a PDF. Today, I’m going to repost an article which got pushed off its original site by litigious intimidation.

The short version is that the Society of Homeopaths are trying to silence their critics by firing out legal threats. (And all along I thought that was how Big Pharma covered up the truth about the ancient Atlantean techniques of energy aura realignment!) After Le Canard Noir of the Quackometer Blog wrote an essay pointing out how the promotion of homeopathy can easily cost lives, the SoH got some lawyers to send letters to the Quackometer’s ISP.

James Randi says, “If they’re so litigious, let them sue the JREF. We can handle it.”

The original essay of Le Canard Noir is now mirrored across the Network, and one copy is below the fold right here. Enjoy.
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What Everybody Knows

In my previous post, I tossed out the following observation:

It is, at any rate, folklore among the anti-creationist blogging community that non-American scientists are more likely to use the word “Darwinism” and its variants than American ones are, although it seems that outside academic circles, “Darwinism” and “Darwinist” may have negative connotations everywhere.

This got me thinking. There are umpty-ump science bloggers on the Net nowadays, and more commenters than one could shake a phasmatodean at. This is a big pile of people, and though it has very fuzzy boundaries, one might justifiably call it a subculture. What, then, are its cultural icons?

If your eager and curious niece finally started using the Internet for something other than MySpace and wanted to become part of this whole skeptical, scientifical shindig, what would you tell her? Who are the personalities of this world? What are their clashes, their feuds, their running jokes? Who hangs out at their places? What are the books which everybody has read, or at least pretends to? Set forth, if you can, the stuff which everybody knows — the hidden curriculum of our Network campus.

Language Logged!

UPDATE (31 October): I’ve now heard the D-word in real life.

To my considerable surprise, I found this morning that I’d been Language Logged. I’m glad to hear that Deborah Cameron’s The Myth of Mars and Venus contains a solid critique of evolutionary psychology — in Mark Liberman’s words, “a dissection, and a rather careful and limited one, not a bludgeoning.” After reading what Liberman had to say, I think I erred in my original post on Deborah Cameron and her use of the word Darwinist. I stand by the essential content of what I said before, but in two respects, I goofed. First, I should have called greater attention to the sexism of the news story which first piqued my curiosity; second, I should have been more precise in my claims about “usage.” After saying some nice things, for which I am grateful, Liberman takes issue with this part of what I’d written:

On this side of the Atlantic, hearing a person say “Darwinism” is a red flag that you’re dealing with a creationist or, at least, a person whose knowledge of science derives primarily from creationist claptrap. To me, calling evolutionary biology “Darwinism” makes as little sense as calling all modern music “Beethovenism.” The year is no longer 1859; we understand many things which Darwin did not, although we stand on his shoulders.

In British usage, “Darwinism” is much more synonymous with evolution in general. (Richard Dawkins is a prime example of this tendency.) I find this unfortunate, partly because it slights all the relevant discoveries we have made since, from Mendel’s time to the present day, and partly because it provides unwarranted ammunition to creationists over here. Still, that’s the way they talk.

Instead of talking about general “British usage,” I should have done what I did in my brief follow-up, making explicit that I meant the writings of British evolutionary biologists in particular. Mea culpa! Liberman writes of his searching Google News for “Darwinism,”
Continue reading Language Logged!

Sentiment Classification

Mark Liberman has more on that profile of Deborah Cameron which prompted me to investigate just what Cameron meant by Darwinist. He applies the notion of sentiment classification, the idea that one can gauge how a writer feels about the subject by applying an algorithmic approach. Often, this involves counting up the number of characteristic words or short word sequences: in a book review, “a must” tends to indicate a positive overall impression, whereas “don’t waste” is indicative of a negative opinion. (A breakdown of Amazon reader reviews, comparing the comment text to the numerical ranking, indicates that you’d much rather see “grisham” in the review of your novel than “predictable.”) Indicator words vary among settings, and what is negative or positive in one context is not necessarily weighted the same in another.

Liberman applies this to Ed Caesar’s profile of Cameron, noting that Caesar uses snippets like “rather prosaically,” “pet peeves,” “irked” and “bludgeoning its brains out” — all of which tend to indicate that the writer of the article has a somewhat negative view of the subject.

Of course, the same technique is applicable to whatever Cameron says, too. In fact, after working through some background material, I’d say that Darwinist and Darwinian are, for her, negative indicators, much as they seem to be for anybody outside of British evolutionary biology departments.

News from the Nervous Front

Via Encephalon #33, I learned about how microarray experiments (a high-throughput way of studying gene expression) are offering new ways to understand the evolution of the human brain. See the essay of neurobiotaxis, and the review article by Preuss et al.

The Neurocritic points to a PNAS paper which shows that the 5-HT4 receptors mediate the appetite-suppressant effect of Ecstasy. How can they tell this? Knock out the genes which produce 5-HT4 receptors in mice and feed them drugs!

This is where we play a spooky clip of Bruce Sterling saying, “Anything that can be done to a rat can be done to a human being.”

Document Typesetting Fantasy

“This is TeXnical support. How may I be of assistance?”

“Yes, I’m trying to typeset the conference book for an upcoming conference — you know, the thing we give everybody which has the abstracts of all the presentations, and so forth — and LaTeX isn’t working.”

“What seems to be the problem, sir?”

“Well, the alphabetical list of speakers, the index at the very end, isn’t displaying.”

“It doesn’t appear in the DVI output?”

“That’s right.”

“This is an alphabetical list of speakers which tells where in the conference book their abstracts will be found?”

“Yes, each abstract is given a number with the \label command, and the list refers to them with the \pageref command. The LaTeX source is actually the output of a Perl script which reads the conference data from a MySQL database, so all of this is automatically generated.”
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The Pharyngula Mutating Genre Meme

There are a set of questions below that are all of the form, “The best [subgenre] [medium] in [genre] is …”.

Copy the questions, and before answering them, you may modify them in a limited way, carrying out no more than two of these operations:

  • You can leave them exactly as is.
  • You can delete any one question.
  • You can mutate either the genre, medium, or subgenre of any one question. For instance, you could change “The best time travel novel in SF/Fantasy is…” to “The best time travel novel in Westerns is…”, or “The best time travel movie in SF/Fantasy is…:, or “The best romance novel in SF/Fantasy is…”.
  • You can add a completely new question of your choice to the end of the list, as long as it is still in the form “The best [subgenre] [medium] in [genre] is…”.

You must have at least one question in your set, or you’ve gone extinct, and you must be able to answer it yourself, or you’re not viable.

Then answer your possibly mutant set of questions. Please do include a link back to the blog you got them from, e.g. Science After Sunclipse to simplify tracing the ancestry, and include these instructions.

Finally, pass it along to any number of your fellow bloggers. Remember, though, your success as a Darwinian replicator is going to be measured by the propagation of your variants, which is going to be a function of both the interest your well-honed questions generate and the number of successful attempts at reproducing them.
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Darwi-fraggin-ists

UPDATE (11 October): After being Language Logged — wow, thanks! — I realized I had been imprecise in my talk about “British usage.” See my follow-up, which hopefully clarifies things a little. Now, for my original post:

We begin by talking about words, and words about words. From there, we go on to discuss science, words about science, and what happens when the meanings of those words get all tangled up.

Neil Gaiman tells a story about being on BBC Radio 3.

My favourite conversation about language and words was before we went on the air, when Ian told us not to swear (as Radio 3 is only allowed one serious swear word per show) and also not to answer any question with an enthusiastic “ABSOLUTELY!” (which is apparently what writers tend to do). And when I said that I thus presumed that “absofuckinglutely” was right out, Deborah Cameron (Rupert Murdoch Professor of Language and Communication at the University of Oxford) enthusiastically explained to me that swearing is the only example of infixing in the English language and I was happy, for I had learned something.

Let’s pass over the creepiness Rupert Murdoch endowing a chair in any field related to communications. Other weirdness is at work here. Specifically, something strange is afoot in this talk of expletive infixation, which is the practice of inserting an expletive, often in participial form, into the middle of another word. For example, consider Sheridan’s catchphrase in Babylon 5, “abso-fraggin’-lutely,” or Abbie Hoffman’s exclamation to Forrest Gump, “The war in Viet-fucking-nam!” Both these examples illustrate the typical situation, in which the expletive is inserted just before a stressed syllable. John McCarthy has put forward a more general model, in which syllables are organized into binary trees, and infixes can only be inserted in certain locations on the tree; this model appears to describe which constructions the listener hears as “well-formed” and which sound aberrant (fanta-fuckin’-stic just doesn’t sound right).

Infixation is rare in English, but are expletives the only things which we use as infixes? Surely, the Internet can tell us. In fact, let’s just click on the hyperlink which Gaiman provides to define infix. This page, from Answers.com, pulls information from several sources, one of which is a Wikipedia article; we read the following.

English has very few infixes, and those it does have are marginal. A few are heard in colloquial speech, and a couple more are found in technical terminology.

  • The infix <iz> or <izn> is characteristic of hip-hop slang, for example hizouse for house and shiznit for shit. Infixes occur in some language games. The <ma> infix, whose distribution was documented by linguist Alan C. L. Yu, gives a word an ironic pseudo-sophistication, as in sophistimacated, saxomaphone, and edumacation.
  • Chemical nomenclature includes the infixes <pe>, signifying complete hydrogenation (from piperidine), and <et> (from ethyl), signifying the ethyl radical C2H5. Thus from picoline is derived pipecoline, and from lutidine is derived lupetidine; from phenidine and xanthoxylin are derived phenetidine and xanthoxyletin.

I see little reason to exclude chemist-speak from the “English language,” although I’ll leave it to the professionals to decide how to classify Ned Flanders’ “Wel-diddly-elcome” and “Mur-diddly-urderer” (also an example of reduplication, I think). As for the <iz> infix, I can testify that among folks of my background — middle-class white kids from sub-frickin’-urbia — infixation is sometimes used to palliate the offensiveness of a word. When playing Halo in mixed company, for example, Shiznit! and Biyotch! are more acceptable exclamations than their uninfixated counterparts. This is clearly not the same as expletive infixation: instead of adding an expletive to an innocent word, a curse is diluted, sometimes for humorous effect.

I can also attest to edumacate and sophistimacation, not to mention alcomohol and even the variant boozeomohol.

So, no, I don’t think swearing is “the only example of infixing” which the English language provides. I wouldn’t go on at such length about it unless another linguistic issue, also related to Deborah Cameron, had come to my attention. This conundrum revolves around that old goblin of a word, Darwinism.
Continue reading Darwi-fraggin-ists

The Mathematics of Love

Or, at least, of nostalgia — who else here remembers Square One?

And no, the Phoenicians did not use Arabic numerals. Those were cooked up a couple hundred years after Rome fell, in India, and spread to Europe via the Arabs. The forms of the written digits changed over time, and the idea of “0” seems to have come around later than the use of numerals for 1 through 9.

It suddenly occurs to me that people who watched too much Square One grow up to sing about the Finite Simple Group of Order Two.