When I was a kid, there were no toys I treasured more than magnets. I had dozens of them: horseshoes, bars, a couple of powerful alnico cylinders salvaged from old loudspeakers. The invisible but very palpable forces acting between these objects—pushing like poles apart, drawing unlike together—were signs to me that mystery still exists in the universe. And yet magnetism also taught me that mysteries can be unraveled and understood. In some book I borrowed from the public library (maybe it was a biography of William Gilbert?) I read an explanation of magnetism that seemed to make sense. Imagine an array of many thousands of magnetic compass needles, all packed tightly together, the book suggested. Each such needle will tug on its neighbors as the magnetic fields interact, and so the needles throughout the array will all tend to line up in parallel. This is how a permanent magnet (or ferromagnet) works, the book said; the imagined tiny compass needles represent individual atoms in magnetic materials such as iron.

There are two problems with this story. First, it fails to explain where the atomic magnetic fields come from. Are we to imagine inside each atom an array of even tinier compass needles? Second, the explanation is just plain wrong. The atomic-scale magnetic dipoles in a ferromagnet do not line up because of magnetic interactions like those between compass needles. The actual interatomic forces are quite different; they are short-range, quantum-mechanical interactions that have no direct counterpart in the world of macroscopic objects.

I have known the truth about ferromagnets for some time, but the debunking of the many-tiny-compass-needles story leaves another question still murky. If an array of compass needles is not a good model of a ferromagnet, what does happen when you bring a bunch of magnetic compasses close together? A recent paper by six authors in Japan, India and the U.S. answers this question in the most direct way possible—through experiments with real compasses. They used small, spherical, liquid-filled compasses meant for mounting on a car windshield.

Before reading on, you might try to guess the outcome of their experiments.

When the compasses are arranged in a line—a one-dimensional array—the needles do tend to line up head-to-tail, all parallel to the line. Even with as few as two compasses, this interaction is strong enough to overcome the influence of the earth’s magnetic field.

But a two-dimensional, square array behaves differently, and not at all like a ferromagnet. In fact, the square lattice of compasses is an antiferromagnet, with nearby elements pointing in opposite directions. Even more surprising, the antiferromagnetic lattice is twisted 45 degrees with respect to the underlying lattice of compass needles. If the edges of the compass array are parallel to the east-west and north-south axes, then the compass needles all point along the diagonals. Sets of four adjacent compasses form a sort of loop, with needles pointing northeast, southeast, southwest, northwest. The paper explains this curious structure as a superposition of two simpler antiferromagnetic states: In one of these states, alternating rows of the latttice are oriented east and west; in the other, alternating columns are directed north and south.

The paper, Ferroics: magnetic-compass lattice and optical phonon dispersions of dipolar crystals, is available from the arXiv and has been submitted to The American Journal of Physics. The authors are Takeshi Nishimatsu, Umesh V. Waghmare, Yoshiyuki Kawazoe, Benjamin Burton, Kazutaka Nagao and Yoshihiko Saito.

In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case for reelection.

I wrote about spam three years ago in the May-June 2003 issue of American Scientist. Since then, my unhealthy fascination with the stuff has been dulled somewhat by overexposure, but I continue to keep an eye on the subject. The volume of spam reaching my mailbox is now about 10 megabytes per month, almost all of it silently skimmed off into a “Junk” folder by the simple filter built into the Eudora software that I use for reading my e-mail. Much of the spam includes countermeasures intended to fool such filters. For example, many messages have gobs of random text, generated by plucking words or phrases from some arbitrary source. Here’s a sample:

He laughed as he ran his hand through the clustering curls of his hair and said us a long time therell be a pretty kettle of fish In pursuance of my aunts kind scheme I was shortly afterwards and jungle fevers and agues and every kind of thing you can mention As to his liverand sorry and so reliant upon me to be so too that nothing she could have said would have

As it happens, I have also written about algorithms for producing this sort of nonsense (”Computer Recreations: A progress report on the fine art of turning literature into drivel,” Scientific American, November 1983, pages 18-28.) It’s not impossible that the spammers learned how to create this blancmange from me. So perhaps the 10 megabytes per month that now comes my way is only fitting retribution.

The other morning, though, I received some spam with an unusual flavor. The “payload” — the part the spammer wanted me to read — is perfectly ordinary and not worth reproducing, but here is the block of filter-foiling random text (slightly reformatted for presentation here in HTML):

John was enjoying sleeping near the tree..
That dentist is not enjoying writing near my home..
Luke is missing jumping today..
That carpenter is practicing running at this time..
Weren’t those plumbers practicing talking last month?.
But this is where you come in: Between now and November, you, the American people, you can reject the tired, old, hateful, negative politics of the past. And instead you can embrace the politics of hope, the politics of what’s possible because this is America, where everything is possible..
I don’t miss jumping for three or four weeks..
That computer programmer isn’t enjoying swimming behind the post office right at this time.
I was missing jumping..
I don’t miss jumping for three or four weeks..
Is the scientist missing praying?.
I was missing jumping..
3.
Is the manager missing walking?.
Joe’s girlfriend generally misses laughing..
Did Alfred’s niece like playing well?.

This is not mere random text; it is random grammatical text. That is, the method for creating it is not to choose words at random but to generate sentences at random with a generative grammar of English. And the grammatical structures are nontrivial; those participles governing gerunds (”I was missing jumping”) are the sort of thing that give a computational linguist fits. The proper handling of such embedded sentences was one of the problems that led Noam Chomsky and his colleagues to abandon simple phrase-structure grammars and try transformational grammars. Someone has been working hard to get this right. They say that pornography has inspired and sustained many innovations in both technology and business practices; maybe spam will have similar effects on the little academic field of computational linguistics.

How interesting that with all the work the spammers have invested in grammar, they couldn’t get the punctuation right. Every sentence has two trailing marks.

Note that the paragraph in the middle (”But this is where you come in….”) is obviously something else entirely. Google reveals that it is lifted from John Edwards’s speech nominating John Kerry in 2004. A Google search for some of the other phrases in this message shows that I’m definitely not the first or the only one to notice the new style in spam. “Is the manager missing walking?” turns up in several collections of spam poetry (e.g., here and here).

Why do spam “authors” include this kind of glop in their messages? I think it can be understood as part of an arms race between spammers and filterers. When spamming began (and before filtering began), the spammer could send out millions of copies of the same message. But it’s easy to block such mass-produced prose; the filter can simply search for the specific, known text. Adding random gibberish lets the spammer send out millions of messages with no two alike. But then the filterer escalates: Genuine language can be distinguished from random text by a statistical analysis; a string of words such as “of his hair and said us a long time therell be” is highly unlikely in real speech. With the advent of random grammars I think we may be seeing the next round in this conflict.

It is by no longer having to think about things that civilisation progresses.

Scribble, scribble, scribble. As if the world didn’t get enough of my writing already, with a bimonthly column in American Scientist, now I’m equipped to publish my every thought on a momen’t notice.

The bit-player weblog will cover much the same territory as the Computing Science column in American Scientist, but with greater frequency and with less fuss and formality. The main theme here (though not the only one) is the computational approach to understanding the world we live in, using algorithmic methods to explore, experiment, and explain.

The computer is sometimes described as a “tool for thought”—and I would not quarrel with that statement. At the same time, though, the computer is also a tool for not thinking, a device that allows us to find answers even to problems that we don’t fully or deeply understand. If you have keen mathematical intuition, you don’t need a computer; you can just prove the theorem and solve the equation, capturing the state of the universe in a concise formula that’s true for all time. I am full of admiration—or is it envy?—for that kind of genius. Sadly, however, I am seldom visited by mathematical inspiration. I haven’t a theorem or a lemma to my name. What I can do is write a program—a dumb, brute-force procedure that tries to get at the truth of nature by starting with simple rules and applying them over and over again, tracing the evolution of a system from moment to moment. It’s not always pretty, but sometimes it works.

It’s an article of faith for those who adopt a scientific worldview that the universe is ultimately comprehensible. Sooner or later, it yields its secrets to human ingenuity. But it’s really not enough just to say that the universe is “comprehensible,” if all we mean by that is that someone somewhere, possessing all the right mental equipment, can hope to make sense of it. Far better for each of us to be able to say: “I can understand; I can work it out for myself.” This is where the computer has been such a liberating and democratizing influence. It’s mathematics for the rest of us.

In the bit-player weblog I’ll be reporting on my own occasional, casual, amateur forays into computational science; more often, I’ll be giving pointers to the work of many others.