Sunday, December 23, 2012

The prospects for economics? Don't bank on them

Perhaps I am simply trying to discharge all my rants before Christmas. But I did get a bit peeved at the rather mindless way in which the Queen’s ‘briefing’ on the financial crisis during her visit to the Bank of England was reported by all and sundry – which triggered this blog piece for Prospect. The comment from Peter Whipp is priceless. I’m not sure even Milton Friedman would have gone quite that far.

Thursday, December 20, 2012

Maths of the pop-up tent

Here’s my latest news story for Nature. This image shows a wood sculpture made by the paper’s authors to illustrate their principles. It’s worth seeing the video of the folding process on the Nature site too – this is one of those problems that is much more easily expressed in images than in words.


Ever wrestled with a pop-up tent, trying to fold it back up to fit in the bag? Help is at hand, in the form of a mathematical theory to describe the shapes adopted by the kinds of stressed flexible rings from which these tents are made [1]. As a result, says team leader Alain Jonas of the Catholic University of Louvain in Belgium, “we have found the best way to fold rings”.

Rings buckled into three-dimensional shapes crop up in many everyday contexts. They are used not just for pop-up tents but to make laundry baskets, small soccer goals, and some wood and creased-origami sculptures, as well as appearing inadvertently in bicycle wheels with too-tight spokes.

Jonas and his collaborators also report microscopic versions made from rings less than a millimetre across carved by electron beams out of thin double-layer films of aluminium and silicon nitride. Because the packing of atoms in the two materials doesn’t match, the films become strained when stuck back to back, inducing buckling.

In all these cases, the shapes adopted by the rings look rather similar. Typically, two opposite edges might buckle upwards, producing a kind of saddle shape. In pop-up tents, these buckles can be bent further by hand to fold the single large ring into a coil of smaller rings.

The researchers show that all these shapes can be predicted accurately with a theory that invokes a single key mathematical concept: what they call ‘overcurvature’, which is the amount by which a circular ring is made more curved than a perfect circle. For a folded, coiled pop-up tent, for example, the final coils have more total curvature than the unfolded single ring would have.

Equivalently, one can introduce overcurvature by adding segments of arc to a circle. The researchers do this experimentally by cutting out coils of a Slinky spring and joining them together in a single ring. This allows them to study the shapes that overcurvature produces, and compare it to their mathematical theory describing the stresses that appear in such a ring and make it buckle. They can figure out, say, how many arcs need to be joined together to guarantee buckling into a specific shape – just the thing that a bent-wood sculptor might like to know.

“They find a universal family of shapes that can be produced in frustrated rings”, explains Basile Audoly of the Institute de Mécanique d’Alembert in Paris. “This is why the folded tent looks like the Slinky and the creased origami.”

The results can be used to work out the easiest folding pathways to collapse a single overcurved ring into a small coil – the problem of folding a pop-up tent. “It’s not trivial to find this pathway empirically”, says Jonas. “You naturally start by deforming the ring in two lobes, since this is easiest. But then you have to deform the ring further into shapes that require a lot of energy.”

In contrast, he says, “if you take the pathway we propose, you have to use more energy at the start, but then have to cross lower energy barriers to reach the energy valley of the ring coiled in three” – you don’t get trapped by following the path of initial least resistance. The researchers provide a detailed route for how best to reach the three-ring compact form.

They also show that such a ring can be made even more compact, folded into five rings instead of three. “This is more difficult, because the energy barriers are higher”, Jonas admits, saying that for a tent it would be best to have three people on the job. He sees no reason why this shouldn’t work for real tents, provided that the pole material is flexible and strong enough.

Jonas thinks that the results might also apply on the molecular scale to the shapes of some relatively stiff molecular rings, such as small, circular bacterial chromosomes called plasmids. Their shapes look similar to those predicted for some ring-shaped polymers squashed into spherical shells [2].

“There is a lot of interest currently in this kind of fundamental mechanical problem”, says Audoly, who points out that rather similar and related findings have been reported by several others [3-7]. For example, he says, the same question has been related to the buckled fringes at the edges of plant leaves, where tissue growth can outstrip the overall growth rate of the leaf to create excess ‘edge’ that must become folded and rippled as a result [3,4]. However, Jonas says that, compared to earlier work on such problems, finding that just the single parameter of overcurvature will describe the mechanical problem “has the virtue of allowing us to find general laws and provide easy-to-use designing tools.”

1. Mouthuy, P.-O., Coulombier, M., Pardoen, T., Raskin, J.-P. & Jonas, A. M. Nat. Commun. 3, 1290 (2012).
2. Ostermeir, K., Alim, K. & Frey, E. Phys. Rev. E 81, 061802 (2010).
3. Sharon, E., Roman, B., Marder, M., Shin, G.-S. & Swinney, H. L. Nature 419, 579 (2002).
4. Marder, M., Sharon, E. Smith, S. & Roman, B. Europhys. Lett. 62, 498-504 (2003).
5. Moulton, D. E., Lessinnes, T. & Goriely, A. J. Mech. Phys. Solids doi/10.1016/j.jmps.2012.09.017 (2012).
6. Audoly, B. & Boudaoud, A. Comptes Rendus Mecanique 330, 831-836 (2002).
7. Dias, M. A., Dudte, L. H., Mahadevan, L. & Santangelo, C. D. Phys. Rev. Lett. 109, 114301 (2012).

Tuesday, December 18, 2012

The problem with opera

I have been enjoying David Moser’s classic rant about the difficulties of learning Chinese, to which Alan Mackay directed me, presumably after my recent piece for Nature on how reading ideograms and alphabetical words use essentially the same parts of the brain. A lot of what Moser says rings bells – my Chinese teachers too occasionally forget how to write (rare) characters, and more often make little slips with the pinyin system (so is that tan or tang?). And I too had tended to dismiss these as just universal lapses of memory, rather overlooking the fact that this was their language, not mine. I’m glad Moser agrees that abolishing characters isn’t a viable solution, not least because the Chinese orthographic system is so beautiful. But what chimes most is that this is a problem that simply doesn’t register with Chinese people.

And that, it strikes me – and to change the subject rather lurchingly – is just how it is too with fans of opera. Reading a nice review by Philip Hensher of a new history of opera by Carolyn Abbate and Roger Parker, the penny dropped that this is how I struggle with opera. It has its moments, but in musical, theatrical and literary terms opera as we have received it has some very deep-seated problems that seem to remain utterly invisible to aficionados. That is why it was a huge relief to see Hensher, who is evidently an avid opera buff, bring these out into the open. Ask many fans what they love in opera, and they are likely to start talking about how it brings together the highest art forms – music, literature and theatre – in one glorious package. It astounds me that they remain oblivious to the profound difficulties that union presents – if not inevitably, then certainly in practice.

For a start: opera traditionally has crap plots and terrible acting. It’s not, I think, ignorant philistinism that prompts me to say this, since the view is shared by Jonathan Miller, who says that 90 percent of operas aren’t worth bothering with. Miller makes no bones about the efforts he has had to make, in directing operas, to suppress the ridiculous gestures that his performers would insist on making. His comments remind me of once watching a trained dancer in an acting class. The chap was asked to walk across the stage in a neutral way. He couldn’t do it. His body insisted on breaking into the most contrived and stylized preening, even though he’d walk down the corridor after the class just like anyone else. His training, like that of opera singers, was doubtless exquisite. It was, however, a training evidently bent on obliterating his ability to move like a normal human being. Now, opera lovers will insist that things have got better over the past several decades – opera singers actually learn something about acting now, not simply a catalogue of absurd symbolic gestures – and this is true. But it’s a slow process, and in some ways you could regard it as a ‘de-operafication’ of opera.

The same with voice. Even Hensher seems to regard opera singing as the highest pinnacle of refinement in the use of the human voice. It’s very, very hard, to be sure, but it is also utterly stylized. This is not how people sing, it is how opera is sung. That seems abundantly obvious, but opera buffs seem to have no notion of it, even though no one sings that way until they have been trained to. There are reasons for it (which I’m coming to) – but operatic singing is a highly contrived, artificial form of human vocal performance, and as such it is emotionally constrained as much as it is expressive – the emotions, like the physical gestures, are stylized conventions. That’s not necessarily a bad thing, but it is bizarre that this evident fact is not even noticed by most opera lovers. Hensher puts it, gnomically, like this: “Opera survives in a safe, hermetic, sealed condition of historic detachment, where emotion can be expressed directly because it is incomprehensible, remote and stylised.” I’m still working on that sentence – how can emotion can be especially ‘direct’ precisely because it is ‘remote’ and ‘stylised’?

Plot – oh, don’t get me started. It’s too easy a target. Even opera lovers admit that most of the plots suck. Now, it’s often said that this is one of the necessary sacrifices of the art: if all the lines are sung, the action must be pretty simple. If that is so, we must already then concede that there’s some erosion of the theatrical substance. However, it doesn’t have to be that way. People can sing complex dialogue quite audibly in principle. They do it in musicals all the time. If you want to hear complex, incredibly moving emotion sung, you need only listen to Billie Holliday (or Nina Simone) singing "Strange Fruit". The fact is, however, that these things can’t be done if sung operatically, in particular because the operatic voice reduces the audibility of the words. As Hensher asks, “why harness a drama to music of such elaboration that it will always get in the way of understanding?” (though actually it’s not the music but the vocalization). He doesn’t answer that question, but I’m mighty glad he raises it. Composers themselves have acknowledged this problem, even if indirectly: it has been shown, for example, that Wagner seems to have intentionally matched the pitch of vowels in his (self-penned) libretti to the frequencies at which the vocal tract resonates when they are spoken in normal speech, making them somewhat more intelligible. (At the very highest frequencies of a female soprano, all vowels tend to sound like ‘ah’.) In other words, Wagner was wrestling with the limitations on communication that opera had chosen to impose on itself.

Why did it do that? Because of a misconceived idea, in the early development of opera in the sixteenth century, that the cadences of speech can be rendered in music. They can’t: the irregular rhythms, indefinite contours and lack of melody make it unlike musical melody, even if there are other intriguing parallels. Opera has kind of accepted this, which is why, as Hensher points out, the form became one “in which lyric utterances of a single significance alternate with brisk, less melodic passages”. Or to put it another way, we get some fabulous arias in which nothing much is said beyond “I’m heartbroken” or “I love you”, interrupted by unmusical recitative which audiences have so much learned to put up with that they barely seem to register that they are at such times not having a ‘musical’ experience at all, but rather, an operatic one. The nineteenth century music critic Eduard Hanslick puts it delicately: “in the recitative music degenerates into a mere shadow and relinquishes its individual sphere of action altogether.” To put it another way, as “music” those parts are gibberish.

Again, this is a choice. It is one that has historical reasons, of course – but for many opera fans it seems again simply to have become invisible, which strikes me as at least a little odd. Hensher says it nicely: “If you were going to design an art form from scratch, you'd be able to improve in a good few ways on opera as we have inherited it.” And I accept that we don’t have the option of starting again from scratch – but we do have the luxury of acknowledging the room for improvement.

In her review of the same book in Prospect, Wendy Lesser seems initially to be demonstrating the same refreshing sensibility: “Opera must be one of the weirdest forms of entertainment on the planet. Its exaggerated characters bear little relation to living people, and its plots are often ludicrous.” But it soon becomes clear that Lesser doesn’t really get the point at all. She quotes Abbate and Parker as saying “the whole business is in so many ways fundamentally unrealistic, and can’t be presented as a sensible model for leading one’s life or understanding human behaviour.” Hang on – you are going to the opera for that? Is that why we go to the theatre either, for goodness’ sake? Lesser soon shows that her talent for ducking the issue is remarkable; she becomes just like the Chinese people who frustrate Moser with their pride at the sheer difficulty of the language – “Yes, it’s the hardest in the world!” But, he longs to say, doesn’t that strike you as a problem? Ludicrous plots, exaggerated characters – hey, aren’t we strange to like this stuff? Well no, it’s just that there seems no particular reason to celebrate those flaws, even if you like opera in spite of them. Lesser presents the “huge acoustic force” of the opera voice as another lovable oddity, but doesn’t seem to recognize that the historical necessity of attaining such volume creates a distance from regular human experience and compromises intelligibility.

I know people who have large collections of opera recordings. Perhaps they use them to compile collections of their favourite arias – why not? But my impression is that they hardly ever put on an opera and listen to it all the way through, as we might a symphony. Now, call me old-fashioned, but I still have this notion that music is something you want to listen to because it works as a coherent whole. Opera is something else: a thing to be experienced in the flesh, as stylized and refined as Noh or Peking opera (but a fair bit more expensive). Opera is indeed an experience, and Hensher encapsulates the intensity and romance of that experience brilliantly. I only ask that, especially since opera dominates the classical music reviews to such a degree, we remember to ask: what sort of experience is it, exactly? Neither primarily musical, nor lyrical, nor theatrical – but operatic.

Maybe I’m just frustrated that in the end I know it is my loss that I sit entranced through the Prelude of Tristan and Isolde and then roll my eyes when the singing starts. I know from enough people whose judgement I trust what delights await in the operatic repertoire (you’re pushing at an open door as far as Peter Grimes is concerned). It’s just the failure of opera lovers to notice the high cost of entry (in all respects) that confounds me.

Friday, December 14, 2012

New articles

I have an article in Nature on thermal management of computers, which is also available online via Scientific American. Before I spoke to folks at IBM about this, I’d have imagined it to be deadly dull. I hope you’ll agree that it isn’t at all – in fact, it strikes me as perhaps the big potential roadblock for computing, though talked about far less than the question of how to keep on miniaturizing.

I also have an article on supercapacitors in MRS Bulletin, which can be seen here. But I have just put a longer version on my website (under Materials) which contains the references chopped out of the published version. This follows on from an article in the MRS Bulletin September Energy Quarterly on the use of supercapacitors in transport in Germany, which can be downloaded here.

In fact I have just put a few new articles up on my web site, hopefully with more to follow. Oh, and as well as writing for the ultra-nerdy MRS Bulletin, I have done a piece on emotion in music for the ‘supermarket magazine’ The Simple Things, for which you can see a sampler here. Nothing like variety. I’ll stick the pdf up on my website soon.

Tuesday, December 11, 2012

Crystallography's fourth woman?

Here is a book review just published in Nature, with some bits reinserted that got lost in the edit.


I Died For Beauty: Dorothy Wrinch and the Cultures of Science by Marjorie Senechal
Oxford University Press
3 Dec 2012 (UK Jan 2013)
304 pages

X-ray crystallography and the study of biomolecular structure was one of the first fields of modern science in which women scientists came to the fore. Dorothy Hodgkin, Rosalind Franklin and Kathleen Lonsdale are the best known of the women who made major contributions in the face of casual discrimination and condescension. In I Died for Beauty Marjorie Senechal suggests that there was nearly a fourth: Dorothy Wrinch, a name that few now recognize and that is often derided by those who do.

The late protein chemist Charles Tanford, for instance, has poured scorn on Wrinch’s best-known work, the ‘cyclol theory’ of protein structure, proposed in the 1930s. It was, he said, “not really worth more than a footnote, a theory built on nothing, no training, no relevant skills”, which gained visibility only thanks to the “sheer bravura (chutzpah) of the author”. Of Wrinch herself, he proclaimed “she was arrogant and felt persecuted when criticized, but in retrospect her miseries seem self-inflicted.”

In an attempt to rebalance such attacks, Senechal, a former assistant of Wrinch’s at Smith College in Massachusetts and now coeditor of The Mathemetical Intelligencer, has written no hagiography, but rather, a sympathetic apologia. Whatever one feels about Wrinch and her research, she is a fascinating subject. Her circle of friends, colleagues and correspondents reads like a who’s who of early twentieth-century science and philosophy. Wrinch, a Cambridge-trained mathematician, was a student of Bertrand Russell, was championed by D’Arcy Thompson and Irving Langmuir, worked alongside Robert Robinson and knew Niels Bohr, G. H. Hardy, Kurt Gödel and John von Neumann. Several of them considered her brilliant, although one wonders how much this reflected her ambition and force of personality than actual achievements. Nonetheless, calling for mathematicians to interest themselves in biology, Thompson says in 1931 that “I do not know of anyone so well qualified as Dr Wrinch.” The polymathic mathematician and geophysicist Harold Jeffreys developed some of his ideas on statistical reasoning in collaboration with Wrinch at Cambridge, and wrote in Nature in 1976 of “the substantial contribution she made to this [early] work, which is the basis of all my later work on scientific inference.”

Senechal’s central question is: what went wrong? Why did so apparently promising a figure, a member of the pioneering Theoretical Biology club that included Joseph Needham, J.D.Bernal and Conrad Waddington, end up relegated to obscurity?

The too-easy answer is: Linus Pauling. When Pauling, in a 1939 paper, comprehensively destroyed Wrinch’s cyclol theory – which argued that globular proteins are polyhedral shells, in which amino acids link into a lattice of hexagonal rings – he finished her career too. Senechal clearly feels Pauling was bullying and vindictive, although her attempt at revenge via Pauling’s cavalier dismissal of Dan Schechtman’s quasicrystals doesn’t make him any less right about proteins.

But a more complex reason for Wrinch’s downfall emerges as the story unfolds. Part of her undoing was her magpie mind. Seemingly unable to decide how to use her substantial abilities, Wrinch never really made important contributions to one area before flitting to another — from Bayesian statistics to seismology, topology to mitosis. Warren Weaver, the astute director for natural sciences at the Rockefeller Foundation that funded Wrinch for some years, offered an apt portrait: “W. is a queer fish, with a kaleidoscopic pattern of ideas, ever shifting and somewhat dizzying. She works, to a considerable extent, in the older English way, with heavy dependence on ‘models’ and intuitive ideas.”

Senechal presents a selection of opinions the Foundation collected on her while assessing her funding application, many deeply unflattering: she is a fool, she is mad or ‘preachy’, she dismisses facts that don’t fit and poaches others’ ideas. Frustratingly, we’re left to decide for ourselves told how much of this is justified, but even Senechal admits that a little of Wrinch went a long way. Her wearisome habits were noted by science historian George Sarton’s daughter in an account of a London tea in 1937: “Dorothy Wrinch was there in one of her strange, simpering showing off moods, talking about herself constantly.” The evidence for a problematic personality gradually piles up.

She certainly had a talent for making enemies. “Everyone in England in on or near the protein field is more than antagonistic to her,” said one of the Rockefeller interviewees. Bernal was incensed when Wrinch tried to argue that the diffraction data obtained by his student Hodgkin supported her cyclol theory – an assertion that was sloppy at best, and perhaps dishonest. In retaliation Wrinch called Bernal “jealous, brutal and treacherous”. (Hodgkin, true to form, was charitably forgiving.)

Underlying all of this is the position of Wrinch as a female scientist. Like many educated women of the 1930s, she felt motherhood as a burden and barrier that only extreme measures could relieve. Her eugenic inclinations and call, in her pseudonymous The Retreat from Parenthood (1930), for a state-run Child Rearing Services that farmed out children to professional carers reinforce the fact that Aldous Huxley was only writing what he heard. Alarming though her behaviouralist approach to parenting might now sound (Senechal rather sidesteps Wrinch’s relationship with her daughter Pamela, who died tragically in a house fire aged 48), it is shameful that the professional structures of science have hardly made it any easier for mothers some 80 years on.

Her central problem, it seems, was that, working at a time when most male scientists assumed that women thought differently from them, Wrinch seemed to conform to their stereotype: headstrong, stubborn, strident, reliant on intuition rather than facts. It is clear in retrospect that those complaints could also be made of Wrinch’s arch-enemy Pauling: Senechal rightly observes that “Dorothy and Linus were more alike than either of them ever admitted.” She sees injustice in the way Pauling’s blunders, such as denying quasicrystals, were forgiven while Wrinch’s were not.

Was there a hint of sexism here? In this case I doubt it – Pauling of course, unlike Wrinch, hit more than enough bullseyes to compensate. But Senechal’s imagined scene of braying men and their snickering wives poring over Pauling’s devastating paper has a depressing ring of truth.

Primarily a mathematician herself, Senechal doesn’t always help the reader understand what Wrinch was trying to do. Her interest in “the arrangement of genes on the chromosome” sounds tantalizingly modern, but it’s impossible to figure out what Wrinch understood by that. Neither could one easily infer, from Senechal’s criticisms of Pauling’s attack, that the cyclol theory was way off beam even then. Tanford has pointed out that it predicted protein structures that were “sterically impossible” – the atoms just wouldn’t fit (although cyclol rings have now been found in some natural products). Fundamentally, Wrinch was in love with symmetry – to which the title, from an Emily Dickinson poem, alludes. It was this that drew her to crystallography, and her 1946 book Fourier Transforms and Structure Factors is still esteemed by some crystallographers today. But such Platonic devotion to symmetrical order can become a false refuge from the messiness of life, both in the biochemical and the personal sense.

Senechal’s prose is mannered, but pleasantly so — a welcome alternative to chronological plod. Only occasionally does this grate. Presenting the battle with Pauling in the form of an operatic synopsis is fun, but muddies truth and invention. The account of Wrinch’s first husband John Nicholson’s breakdown in 1930 is coy to the point of opacity.

It’s tremendous that Senechal has excavated this story. She offers a gripping portrait of an era and of a scientist whose flaws and complications acquire a tragic glamour. It’s a cautionary tale for which we must supply the moral ourselves.