Business sense

Even in a land where money is valued and Lakshmi is worshipped, Dilip’s experience with online tourism firm ExtendedStay is breathtaking. Go read.

If John Cleese had met Vishwas Tiwari and not Donald Sinclair, he’d have done something much funnier than Fawlty Towers.

(On the other hand, Dilip has nice things to say about Apple Inc and their customer service, as do many of my colleagues.

Magnetic monopoles from classical physics

Much recent media attention has been showered on a recent paper by Bramwell et al, that observes the motion of “particles” in a solid that behave like carriers of “magnetic charge”, or magnetic monopoles. This is an experimental confirmation of a theoretical prediction made by Castelnovo, Moessner and Sondhi nearly two years ago, and other recent experiments have added corroboration. The solid in question is an exotic rare-earth compound called dysprosium titanate.

Magnetic monopoles don’t, as far as we know, exist in nature. There is no such thing as a “magnetic charge”. An ordinary “bar magnet” behaves much the same way as an “electric dipole”, that is, two electric charges placed close together, but if you break an electric dipole you get two electric charges (“monopoles”) while if you break a bar magnet you get two bar magnets. This is because magnetism is not produced by static “magnetic charges” but is produced by moving electric charges (that is, currents). In an electromagnet, the the movement is of conducting electrons along a coiled conducting wire; in a bar magnet, the movement is the quantum-mechanical “angular momentum” of electrons, which is not very similar to classical “rotation” but has the same effect. In particular, electrons have an “intrinsic angular momentum” or “spin” that cannot be explained as an analogue of any classical quantity; but this spin, too, contributes to a magnetic dipole moment for each electron. Nuclei, too, can have their own magnetic dipole moments.

The recent experiments have not discovered a new phenomenon of nature — the laws of physics don’t need to be rewritten. What they have found is something that would behave exactly as a collection of magnetic monopoles would behave, if observed at not too fine a scale. The explanation is really quite simple. I myself worked on this system long ago: we published the basic physics of this compound in 1999 and, between then and 2008 (when Castelnovo and colleagues published their prediction), hundreds of papers on the subject have been published. I’m sure lots of those authors are kicking themselves for not having thought of it first.

These systems have a rather exotic geometry that has become widely known as the pyrochlore lattice, after an otherwise unrelated mineral. This is a lattice of tetrahedra (solids with four triangular faces) joined at their corners, such that two tetrahedra share a corner. Here is a picture (click on it for source page).

The dysprosium atoms (which are the main players here) sit at the red dots. Each carries a large magnetic moment arising mainly from electrons in the f shell. In free space, this magnetic moment could point everywhere, but in the presence of electrostatic fields of neighbouring atoms (in particular, the oxygen ions), it turns out that the preferred direction is along the lines joining the centres of the adjoining tetrahedra. Quantum-mechanically, the possible components of the angular momentum along this direction are discrete, and it turns out that the state where the angular momentum is entirely in this direction is about 200 kelvin lower in energy than other states. So at low temperatures (these experiments are performed at temperatures close to liquid helium, that is, less than ten kelvin), the atoms behave like magnets that point along the lines joining adjoining tetrahedral centres, in either direction. And because the angular momenta are relatively large, they can be treated as classical magnets. They interact primarily via the long-ranged “magnetostatic” interaction of two classical dipoles, but their nearest-neighbour interaction is somewhat reduced by a quantum-mechanical “superexchange” effect (but is still the dominant interaction).

And that is the only entry of quantum mechanics into this discussion. The physics henceforth is entirely classical and would have been understood in the 19th century, which is part of what makes it all so remarkable.

If the nearest-neighbour interaction were all, the “ground state” of these systems — the lowest-energy state — would be any state where each tetrahedron had two “magnets” (which we will call spins) pointing in and two pointing out. There is a macroscopic number of such states, leading to a non-zero entropy in the ground state (which is what we observed in 1999, and there is a remarkable analogy with the entropy of ice, which led to these systems being called “spin ice” — but that is another story). Remarkably, the addition of long-ranged interactions does not seem to affect this picture much. Strictly speaking, the true ground state in the presence of long-ranged interactions is a fully-ordered state, unique apart from rotations. But experimental probes have only shown small signs of this form of ordering.

Since the three-dimensional lattice is hard to visualise, at this point let us consider instead a two-dimensional “square lattice”, as shown below.

The constraint is that each shaded square must have two spins pointing in and two pointing out. This leads to results very much analogous to the pyrochlore case (in fact, this lattice, with all pairwise interactions within the shaded squares being of equal strength, is often called the “square pyrochlore” lattice). An example ground state satisfying this constraint is shown. Again, there is a large (macroscopic) number of such states.

Now how do we visualise excitations? The simplest excitation is a “spin flip” — reversing the direction of a single arrow. This upsets the balance of arrows: one square has three arrows pointing in (with a net “north charge”) and another has three arrows pointing out (with a net “south charge”). It is like placing a little magnet locally in an otherwise magnetically-neutral material.

But the key point is that the “north charge” and “south charge” can now migrate and separate, via a series of spin flips. Click on the above figure for an animation.

Viewed on a coarse scale, what this looks like is two magnetic “monopoles” that can move around freely. Castelnovo et al. examined the dynamics of this process theoretically, and now Bramwell et al. have measured it in the laboratory.

It is a simple idea, and a remarkable experimental observation. Whether it is just a curiosity or has further scientific or technological importance, only time will tell.

It should once again be emphasised that these “monopoles” are not elementary particles. People familiar with semiconductors will think of an analogy with “particle-hole excitations”, where a electron gets excited and leaves behind a positively-charged “hole” that behaves like a particle in its own right. But that is a quantum-mechanical phenomenon which cannot be understood classically. The magnetic “monopoles” here, however, are purely a phenomenon of classical physics. If you could build a model with wires, springs and magnets, designed to mimic the geometry of the system and enforce the constraints of the allowed magnet directions, it should behave in exactly the same way. That in itself is of interest: I’m not aware of any other examples of “quasiparticles” or “particle-hole excitations” that can be described purely classically.

Happy birthday, Martin Gardner

Martin Gardner is 95, and the New York Times has a great article about the man and his new book.

For those who don’t know the name, Gardner wrote the column “Mathematical Games” in Scientific American for a quarter of a century. The following quote from the NYT article summarises the impact of those columns perfectly: “Martin has turned thousands of children into mathematicians, and thousands of mathematicians into children.”

I am not a mathematician, but perhaps close enough to be counted. I first read him as a child — it was my mother’s yellowing copy of Mathematical Puzzles and Diversions, a collection of Scientific American columns that began with the “Hexaflexagons” column mentioned in the NYT article above — and was hooked. I collected several more of those volumes over the years.

Almost equally delightful has been his debunking, over the years, of various forms of pseudoscience. I say “almost” because I think he sometimes went a bit overboard, to the detriment of his argument. But perhaps I will leave that to another blog post.

And then there are gems like “The Annotated Alice” and “The Annotated Snark”, which will teach you more about the hidden layers in the Lewis Carroll books than you ever believed existed…

Fouad al-Rabiah, Obama and peace

I linked the case of Fouad al-Rabiah in my last post, but didn’t provide any details. I think it is worth talking about more. First, here is Andy Worthington’s original article on the subject. It is a long and disturbing read. If you want a shorter and equally disturbing one, here is a new article by Andrew Sullivan in The Times.

From Sullivan’s article:

We know that an American interrogator, operating under the authority of the US government, said the following words to a detainee: “There is nothing against you. But there is no innocent person here. So, you should confess to something so you can be charged and sentenced and serve your sentence and then go back to your family and country, because you will not leave this place innocent.”

This man had worked at Kuwait Airways for 20 years; he was also a humanitarian volunteer in Afghanistan, who got caught up in the war and found his entry route (via Iran) blocked for exit. Trying to leave via Pakistan, he was caught by US troops and sent to Guantanamo. But even after initial interrogators concluded he was innocent, he was kept there and tortured — because he couldn’t be allowed to leave Guantanamo.

This happened mostly under the Bush administration, but the Obama administration continued to pursue the case despite knowing he was innocent. Says Sullivan (who was, and in some ways still is, one of Obama’s strongest supporters):

Shockingly, although Barack Obama’s justice department knew the details of this case, it persisted with the Bush administration’s attempt to prosecute him. Last week, the Obama administration also backed a legal provision to withhold permanently all unreleased photographic evidence of torture in sites and prisons far away from Guantanamo and Abu Ghraib. And some of us believed we were voting for change.

And a President who defends the torture of a man known to be innocent is rewarded with the Nobel Peace Prize. Tom Lehrer once said that satire died when Henry Kissinger won the peace prize. But was it necessary to stab the dead body again?

Nobel thoughts

As I type this, the winners of the five original Nobel prizes have been named for this year; only the winner of the Bank of Sweden (Nobel memorial) prize in economics remains to be announced. It is usually the case that the science awards are noncontroversial, while the literature, peace and economics awards attract much discussion.

The Physiology and Medicine and the Chemistry awards are richly deserved this year. The Chemistry award has of course attracted lots of interest in India because of the origins of one of its recipients. But I found another point interesting: while there was originally no Nobel prize in “biology”, these days there are, in practice, two in molecular biology: the Physiology and Medicine prize, and the Chemistry prize. This year’s chemistry prize was awarded for improved understanding of the structure and functioning of the ribosome. Last year, it was awarded for discovering the green fluorescent protein and developing it as an important tool. In 2006, it was awarded for a better understanding of the transcription process; in 2004, for ubiquitin-mediated protein degradation; in 2003, for determining the structure of ion channels.

The Physics prize this year went not to fundamental discoveries, but to inventions: fibre optics and CCDs. But there is a spot of controversy in the award for Charles Kao: the “father of fibre optics” is widely held to be Narinder Singh Kapany, whose work preceded Kao’s by over a decade. Kapany’s work focussed on imaging, while Kao’s Nobel award was specifically for developing fibres that could carry signals over 100 kilometres; both innovations were extremely significant, and both were technological rather than fundamental.

The literature prize went to Herta Mueller, whom I hadn’t heard of. But this must be the hardest prize to give: there are more deserving candidates than prizes available, and unlike in the sciences, it doesn’t make sense to share it among multiple candidates. I had never heard of Wisława Szymborska, the 1996 winner, until two weeks ago (well, I suppose I’d heard her name in 1996, but it did not stick in my memory); having been introduced to her poetry, I find it extremely interesting.

That leaves the peace prize, announced today. I personally think it is a laughable idea giving it to Barack Obama at this stage of his career, when he has absolutely no concrete achievements, has backtracked from many of his earlier promises, has had his Justice Department defend the torture of innocent people by the previous administration, is prolonging the war in Afghanistan, and is achieving little success in his domestic agenda.

Perhaps the future will vindicate this prize; but giving a prize for future achievements requires extraordinary clairvoyance.

It remains to be seen what surprises are sprung by the award committee for the Economics prize. We will know soon.

Non-Bollywood cinema from Maharashtra

Apparently not everything is song and dance. The Beeb has a feature on Marathi-language films that deal with the gritty issues of rural hardship and farmer suicides in Maharashtra, especially the Vidarbha region. Apparently locally-themed films, in local languages, exposing local problems, do have a market. We have all been reading about Vidarbha’s problems (and similar problems in Andhra Pradesh and many other places) for a while now, though few of us have actually seen it for ourselves. Hopefully such films will raise awareness.

(I know, these days, suggesting that it is a good idea to support the local language wins you accusations from eminent scientist bloggers of being a Shiv Sena fellow-traveller. So be it.)

Dizzy and Louis

Here are two of the three most influential jazz trumpeters ever: Dizzy Gillespie and Louis Armstrong.

I don’t know who the pianist and others are, what the year is (certainly post-1953 since Dizzy’s trumpet is bent) and whether these two made any other recordings together. But this pairing is particularly interesting since Dizzy, with Charlie Parker, was the founder of bebop, and Louis never embraced that style of jazz, with its “weird” chords and complicated melodies and rhythms. By 1953, however, the debate was over: bebop was mainstream jazz and Louis had become more a popular entertainer than a cutting-edge jazz musician. This song is popular entertainment, and good fun.

The third great jazz trumpeter was, of course, Miles Davis. Miles played with Dizzy in his early days, but I don’t know whether he ever played with Louis.

Famous people who support a child-rapist

So Bernard-Henri Levy, Salman Rushdie, Milan Kundera, Mike Nichols, Isabelle Adjani, William Shawcross, Pedro Almodovar, Martin Scorsese, Terry Gilliam, Harvey Weinstein, Tilda Swinton, Monica Bellucci and dozens of other celebrities have attached their names to petitions deploring the recent arrest of director Roman Polanski in Switzerland. Polanski was arrested because he plied a 13-year-old with alcohol and a drug (Quaalone), made her strip, and raped her. He did this in 1977, pled guilty to a lesser charge (sex with a minor), and before he could be sentenced, fled the USA in 1978, never to return.

I knew little about Polanski before recent events: I had seen one film (Chinatown) which was brilliant, and disturbing; and I knew his wife had been murdered by the Manson cult. I now know that he escaped the Nazis at seven, and his mother died in Auschwitz. He had claimed that the encounter with the 13-year-old was consensual. Though that doesn’t excuse it, I had not thought much about it one way or another, even when he was in the news in 2005 for winning an Oscar.

So when news of the arrest broke, my reaction was roughly: “What he did was wrong and criminal, but it was 30 years ago, and he’d had a very disturbed life, from fleeing the Nazis as a 7-year-old to the murder of his pregnant wife by the Manson cult… Perhaps we should be asking why the French didn’t extradite him back in 1978 when his crime was fresh. They had no treaty obligations but they could certainly decide on a case-by-case basis.” (In fact that’s what I posted in a comment on a facebook thread.)

Since then, despite the victim’s wishes, the details of the incident have become widely known and her testimony to the jury is available on the internet. It is indeed stomach-churning. It was not “statutory rape”. It was rape, committed on a girl who had been drugged and fed alcohol but was still capable of repeatedly asking him to stop, and even feigning asthma in an attempt to make him stop and let her leave. If she had been over 18, it would still have been rape. But the “statutory rape” charge was easier to prove: there was evidence of sexual contact, and there was no doubt about her age. So Polanski got away with a plea bargain. Then when he had doubts about the judge’s intentions of honouring the bargain, he skipped.

Was he remorseful? Not in 1979: take a look at this excerpt of an interview that year with Martin Amis. I don’t know of any expression of remorse since. He seems not only to think he had done nothing wrong, but to have persuaded many well-known people that he was the victim in the matter.

So my opinion has hardened now. Let him stay in jail — Swiss or American — for life.

The bulk of the US-based opinion that I have been reading seems to agree on that. In fact I have seen no coherent defence of letting Polanski go. It seems to come down to his tragic past, the length of elapsed time since the crime, and the victim’s views. But none of these should be relevant. Millions of people suffer personal tragedies without becoming child rapists. He was free for 30 years because he was a fugitive, not because law enforcement was lax. And violent crimes are prosecuted regardless of the victim’s wishes (in many cases, though probably not in this one, the victim is too scared to talk).

Even in France, according to the NYT, the public is not favourably disposed to Polanski, and the elite are having second thoughts about supporting him.

But I wonder about all those eminent signatories of petitions. Many of them knew Polanski and surely knew something about the case before they signed; but if they didn’t when they signed, they certainly would have since. Do they still support letting someone who drugged and raped a child go free?