Wednesday, May 25, 2011
Steve Jones gets unnatural
I’ve just discovered a review of Unnatural in the Lancet by Steve Jones. As one might expect, he has an interesting and quite particular take on it. It’s one with which, happily, I agree.
Monday, May 23, 2011
Belated Prospect
I realise that I meant to put up earlier my May column from Prospect. Almost time for the June column now, but here goes.
________________________________________________________
The notion that God has an inordinate fondness for beetles, credited to the biologist J. B. S. Haldane, retains a whiff of solipsism. For beetles are not so unlike us: multicellular, big enough to see, and legged. But God surely favours single-celled organisms far more. Beetles and humans occupy two nearby tips on the tree of life, while single-celled life forms have two of the three fundamental branches all to themselves: bacteria and archaea, so alike that it was only in the 1970s that the latter were awarded their own branch. Archaea have a different biochemistry to bacteria – their metabolism usually produces methane – and they are found everywhere, including the human gut.
Our place on the ‘tree of life’ now looks like it may be even more insignificant, for a team at the University of California, working with genomics pioneer Craig Venter, claims to have found hints of a fourth major branch in the tree, again populated only by single-celled organisms. These branches, called domains, are the most basic divisions in the Linnaean system of biological classification. We share our domain, the eukaryotes (distinguished by the way their cells are structured), with plants, fungi and yet more monocellular species.
Like most things Venter is involved in, the work is controversial. But perhaps not half so controversial as Venter’s belief, expressed in a panel debate titled ‘What is life?’ in Arizona in February, that all life on Earth might not even have a common origin. “I think the tree of life is an artefact of some early scientific studies, which are not really holding up”, he said, to the alarm of fellow panellist Richard Dawkins. His suggestion that there may be merely a “bush of life” only made matters worse.
Drop in the ocean
Despite the glee of creationists, there was nothing in Venter’s speculative remark that need undermine the case for Darwinian evolution. The claim of a fourth domain is backed by a little more evidence, but remains highly tentative. The data were gathered on a now famous round-the-world cruise that Venter undertook between 2003 and 2007 on his yacht to gather genomic information about the host of unknown microorganisms in the oceans. The rapid gene-analysing techniques that he helped to develop allow the genes of different organisms to be rapidly compared in order to identify evolutionary relationships between them. By looking at the same group of genes in two different organisms, one can deduce where in the tree of life they shared a common ancestor.
Using Venter’s data, Jonathan Eisen in California discovered that two families of genes in these marine microbes each seem to show a branch that doesn’t fit on the conventional tree of life. It’s possible that these genes might have been acquired from some unknown forms of virus (viruses are excluded from the tree altogether). The more exciting alternative is that they flag up a new domain. If so, its inhabitants would seem so far to be quite rare – a minor anomaly, like the Basque language, that has persisted quietly for billions of years. But since we are ignorant about perhaps 99 per cent of species on the planet, who knows?
Thinking big
The European Union is looking for big ideas. Really big ones. Its Flagship programme offers to fund two scientific projects to the tune of €1 bn over the next ten years. These must be “ambitious large-scale, science-driven, visionary research initiatives that aim to achieve a scientific breakthrough, provid[ing] a strong and broad basis for future technological innovation and economic exploitation in a variety of areas, as well as novel benefits for society.” In other words, they’ve got to achieve a heck of a lot, and will have truckloads of money to do so.
Six of the applications – all of them highly collaborative, international and interdisciplinary – have now been selected for a year of pilot funding, starting in May. They range from the highly technical to the borders of science fiction.
One promises to develop graphene, the carbon material that won last year’s physics Nobel prize, into a practical fabric for information technologies. Another proposes to truly figure out how the brain works; a third will integrate information technology with medicine to realise the much-advertised ‘personalized medicine’. But these things will all be pursued regardless of the Flagship scheme. More extraordinary, and therefore both more enticing and more risky, are two proposals to develop intelligent, sensitive artificial agents – characterized here as Guardian Angels or Robot Companions – that will help us individually throughout our lives. The sixth proposal (which received the highest rating) is to develop massive computer-simulation systems to model the entire ‘living Earth’, offering a ‘crisis observatory’ that will forecast global problems ranging from wars to economic meltdowns to natural disasters – the latter now all too vivid. The two initiatives to receive full funding will be selected in mid-2012 for launch in 2013.
________________________________________________________
The notion that God has an inordinate fondness for beetles, credited to the biologist J. B. S. Haldane, retains a whiff of solipsism. For beetles are not so unlike us: multicellular, big enough to see, and legged. But God surely favours single-celled organisms far more. Beetles and humans occupy two nearby tips on the tree of life, while single-celled life forms have two of the three fundamental branches all to themselves: bacteria and archaea, so alike that it was only in the 1970s that the latter were awarded their own branch. Archaea have a different biochemistry to bacteria – their metabolism usually produces methane – and they are found everywhere, including the human gut.
Our place on the ‘tree of life’ now looks like it may be even more insignificant, for a team at the University of California, working with genomics pioneer Craig Venter, claims to have found hints of a fourth major branch in the tree, again populated only by single-celled organisms. These branches, called domains, are the most basic divisions in the Linnaean system of biological classification. We share our domain, the eukaryotes (distinguished by the way their cells are structured), with plants, fungi and yet more monocellular species.
Like most things Venter is involved in, the work is controversial. But perhaps not half so controversial as Venter’s belief, expressed in a panel debate titled ‘What is life?’ in Arizona in February, that all life on Earth might not even have a common origin. “I think the tree of life is an artefact of some early scientific studies, which are not really holding up”, he said, to the alarm of fellow panellist Richard Dawkins. His suggestion that there may be merely a “bush of life” only made matters worse.
Drop in the ocean
Despite the glee of creationists, there was nothing in Venter’s speculative remark that need undermine the case for Darwinian evolution. The claim of a fourth domain is backed by a little more evidence, but remains highly tentative. The data were gathered on a now famous round-the-world cruise that Venter undertook between 2003 and 2007 on his yacht to gather genomic information about the host of unknown microorganisms in the oceans. The rapid gene-analysing techniques that he helped to develop allow the genes of different organisms to be rapidly compared in order to identify evolutionary relationships between them. By looking at the same group of genes in two different organisms, one can deduce where in the tree of life they shared a common ancestor.
Using Venter’s data, Jonathan Eisen in California discovered that two families of genes in these marine microbes each seem to show a branch that doesn’t fit on the conventional tree of life. It’s possible that these genes might have been acquired from some unknown forms of virus (viruses are excluded from the tree altogether). The more exciting alternative is that they flag up a new domain. If so, its inhabitants would seem so far to be quite rare – a minor anomaly, like the Basque language, that has persisted quietly for billions of years. But since we are ignorant about perhaps 99 per cent of species on the planet, who knows?
Thinking big
The European Union is looking for big ideas. Really big ones. Its Flagship programme offers to fund two scientific projects to the tune of €1 bn over the next ten years. These must be “ambitious large-scale, science-driven, visionary research initiatives that aim to achieve a scientific breakthrough, provid[ing] a strong and broad basis for future technological innovation and economic exploitation in a variety of areas, as well as novel benefits for society.” In other words, they’ve got to achieve a heck of a lot, and will have truckloads of money to do so.
Six of the applications – all of them highly collaborative, international and interdisciplinary – have now been selected for a year of pilot funding, starting in May. They range from the highly technical to the borders of science fiction.
One promises to develop graphene, the carbon material that won last year’s physics Nobel prize, into a practical fabric for information technologies. Another proposes to truly figure out how the brain works; a third will integrate information technology with medicine to realise the much-advertised ‘personalized medicine’. But these things will all be pursued regardless of the Flagship scheme. More extraordinary, and therefore both more enticing and more risky, are two proposals to develop intelligent, sensitive artificial agents – characterized here as Guardian Angels or Robot Companions – that will help us individually throughout our lives. The sixth proposal (which received the highest rating) is to develop massive computer-simulation systems to model the entire ‘living Earth’, offering a ‘crisis observatory’ that will forecast global problems ranging from wars to economic meltdowns to natural disasters – the latter now all too vivid. The two initiatives to receive full funding will be selected in mid-2012 for launch in 2013.
Friday, May 20, 2011
The chief designer
I have a review of the RSC’s play Little Eagles in Nature this week. Here it is. Too late now to catch the play, I fear, but I thought it was impressive – even though Andrew Billen has some fair criticisms in the New Statesman.
____________________________________________________________________________
Little Eagles
A play by Rona Munro, directed by Roxana Silbert
Hampstead Theatre, London, until 7 May
It is a curious year of anniversaries for the former Soviet military-industrial complex. Fifty years ago the cosmonaut Yuri Gagarin became the first person in space, orbiting the world for 108 minutes in the Vostok spacecraft. And 25 years ago, Reactor 4 of the Chernobyl nuclear plant exploded and sent a cloud of radioactive debris across northern Europe.
One triumph, one failure; each has been marked independently. But while Little Eagles, Rona Munro’s play commissioned by the Royal Shakespeare Company for the Gagarin anniversary, understandably makes no mention of the disaster in Ukraine a quarter of a century later, the connections assert themselves throughout. Most obviously, both events were the fruits of the Cold War nuclear age. The rockets made by Sergei Korolyov, the chief architect of the Soviet space programme and the play’s central character, armed President Khrushchev with intercontinental ballistic missiles before they took Gagarin to the stars.
But more strikingly, we see the space programme degenerate along the same lines that have now made an exclusion zone of Chernobyl. Impossible demands from technically clueless officials and terror at the consequences of neglecting them eventually compromise the technologies fatally – most notably here in the crash of Soyuz 1 in 1967, killing cosmonaut Vladimir Komarov. Gagarin was the backup pilot for that mission, but it was clear that he was by then too valuable a trophy ever to be risked in another spaceflight. All the same, he died a year later during the routine training flight of a jet fighter.
Callous disregard for life marks Munro’s play from beginning to end. We first see Korolyov in the Siberian labour camp where he was sent during Stalin’s purge of the officer class just before the Second World War. As the Soviets developed their military rocket programme, the stupidity of sending someone so brilliant to a virtual death sentence dawned on the regime, and he was freed to resume work several years later. During the 1950s Korolyov wrested control of the whole enterprise, becoming known as the Chief Designer.
Munro’s Korolyov seems to offer an accurate portrait of the man, if the testimony of one of his chief scientists is anything to go by: “He was a king, a strong-willed purposeful person who knew exactly what he wanted… he swore at you, but he never insulted you. The truth is, everybody loved him.” As magnetically played by Darrell D’Silva, you can see why: he is a swaggering, cunning, charming force of nature, playing the system only to realise his dream of reaching the stars. He clearly reciprocates the love of his ‘little eagles’, the cosmonauts chosen with an eye on the Vostok capsule’s height restrictions.
But for his leaders, rocketry was merely weaponry, or a way of demonstrating superiority over their foes in the West. Korolyov becomes a hero for beating the Americans with Sputnik, and then with Vostok. But when the thuggish, foul-mouthed Khrushchev (a terrifying Brian Doherty) is retired in 1964 in favour of the icily efficient Leonid Brezhnev, the game changes. The new leader sees no virtue in Korolyov’s dream of a Mars mission, and is worried instead that the Americans will beat them to the moon. The rushed and bungled Soyuz 1, launched after Korolyov’s death in 1966, was the result.
Out of this fascinating but chewy material, Munro has worked wonders to weave a tale that is intensely human and, aided by the impressive staging, often beautiful and moving. Gagarin’s own story is here a subplot, and not fully worked through – we start to see his sad descent into the vodka bottle, grounded as a toy of the Politburo, but not his ignominious end. There is just a little too much material here for Munro to shoehorn in. But that is the only small complaint in this satisfying and wise production.
What it becomes in the end is a grotesque inversion of The Right Stuff, Tom Wolfe’s account of the US space programme made into an exhilarating movie in 1983. Wolfe’s celebration was a fitting tribute to the courage and ingenuity that ultimately took humans to the moon, but an exposure of the other side of the coin was long overdue. There is something not just awful but also grand and awesome in the grinding resolve of the Soviets to win the space race relying on just the Chief Engineer “and convicts and some university students”, as Korolyov’s doctor puts it.
Little Eagles shows us the mix of both noble and ignoble impulses in the space race that the US programme, with its Columbus rhetoric, still cannot afford to acknowledge. It recognizes the eye-watering glory of seeing the stars and the earth from beyond the atmosphere, but at the same time reveals the human spaceflight programmes as utterly a product of their tense, cheat-beating times, a nationalistic black hole for dollars and roubles (and now, of yuan too). Crucially, it leaves the final judgement to us. “They say you changed the whole sky and everything under it”, Korolyov’s doctor (and conscience) says to him at the end. “What does that mean?”
Wednesday, May 18, 2011
The Achilles' heel of biological complexity
Here’s the pre-edited version of my latest news story for Nature. This is such an interesting issue that I plan to write a more detailed piece on it for Chemistry World soon.
_____________________________________________________________________________
The complex web of protein interactions in our cells may be masking an ever-worsening problem.
Why are we so complicated? You might imagine that we’ve evolved that way because it conveys adaptive benefits. But a new study in Nature [1] suggests that the complexity in the molecular ‘wiring’ of our genome – the way our proteins talk to each other – may be simply a side effect of a desperate attempt to stave off problematic random mutations in the proteins’ structure.
Ariel Fernández, working at Chicago University and now at the Mathematics Institute of Argentina in Buenos Aires, and Michael Lynch of Indiana University in Bloomington argue that complexity in the network of our protein interactions arises because our relatively small population size, compared with single-celled organisms, makes us especially vulnerable to ‘genetic drift’: changes in the gene pool due to the reproductive success of certain individuals by chance rather than by superior fitness.
Whereas natural selection tends to weed out harmful mutations in genes and their related proteins, genetic drift does not. Fernández and Lynch argue that the large number of physical interactions between our proteins – now a crucial component of how information is transmitted in our cells – compensates for the reduction in protein stability wrought by drift. But this response comes at a cost.
It might mask the accumulation of structural weaknesses in proteins to a point where the problem can no longer be contained. Then, say Fernández and Lynch, proteins might be liable to misfold spontaneously – as they do in so-called diseases such as Alzheimer’s, Parkinson’s and prion diseases, caused by misfolded proteins in the brain.
If so, this means we may be fighting a losing race. Genetic drift may eat away at the stability of our proteins until they are overwhelmed, leaving us a sickly species.
This would imply that Darwinian evolution isn’t necessary benign in the long run. By finding a short-term solution to drift, it might merely be creating a time-bomb. “Species with low population are ultimately doomed by nature’s strategy of evolving complexity”, says Fernández.
The work provides “interesting and important news”, according to William Martin, a specialist in molecular evolution at the University of Düsseldorf in Germany. Martin says it shows that evolution of eukaryotes – relatively complex organisms like us, with a cellular ‘nucleus’ that houses the chromosomes – “can be substantially affected by drift.”
Drift is a bigger problem for small populations – those of multicelled eukaryotic organisms – than for large ones, because survival by chance rather than by fitness is statistically more likely for small numbers. Many random mutations in a gene, and thus in the protein made from it, will harm the protein’s resistance to unfolding: the protein’s folded-up shape becomes more apt to loosen as water molecules intrude into it. This loss of shape weakens the protein’s ability to function.
Such problems can be avoided if proteins stick loosely to one another so as to shelter the regions vulnerable to water. Fernández and Lynch say that these associations between proteins – a key feature of the cell biology of eukaryotes – may have therefore initially been a passive response to genetic drift. Over time, certain protein-protein interactions may be selected by evolution for useful functions, such as sending molecular signals across cell membranes.
Using protein structures reported in the Protein Data Bank, the two researchers verified that disruption of the interface between proteins and water, caused mostly by exposure of ‘sticky’ parts of the folded peptide chain [full disclosure: these are actually parts of the chain that hydrogen-bond to one another; exposure to water enables the water molecules to compete for the hydrogen bonding. Ariel Fernández has previously explored how such regions may be ‘wrapped’ in hydrophobic chain segments to keep water away], leads to a greater propensity for a protein to associate with others. They also showed that drift could account for this ‘poor wrapping’ of proteins.
On this view, genome complexity doesn’t offer intrinsic evolutionary advantages, but is a kind of knee-jerk response to the chance appearance of ‘needy proteins’ – which ends up exposing us to serious risks.
“I believe prions are indicators of this gambit gone too far”, says Fernandez. “The proteins with the largest accumulation of structural defects are the prions, soluble proteins so poorly wrapped that they relinquish their functional fold and aggregate”. Prions cause disease by triggering the misfolding of other proteins.
“If genetic variability resulting from random drift keeps increasing, we as a species may end up facing more and more fitness catastrophes of the type that prions represent”, Fernandez adds. “Perhaps the evolutionary cost of our complexity is too high a price to pay in the long run.”
However, Martin doubts that drift alone can account for the difference in complexity between prokaryotes (single-celled organisms without a cell nucleus) and eukaryotes. His previous work has indicated that bioenergetics also plays a strong role [2]. For example, says Martin, prokaryotes with small population sizes are symbiotic, which tend to degenerate, not to become complex. “Population genetics is just one aspect of the complexity issue”, he says.
References
1. Fernandez, A. & Lynch, M. Nature doi:10.1038/nature09992 (2011).
2. Lane, N. & Martin, W. Nature 467, 929-934 (2010).
_____________________________________________________________________________
The complex web of protein interactions in our cells may be masking an ever-worsening problem.
Why are we so complicated? You might imagine that we’ve evolved that way because it conveys adaptive benefits. But a new study in Nature [1] suggests that the complexity in the molecular ‘wiring’ of our genome – the way our proteins talk to each other – may be simply a side effect of a desperate attempt to stave off problematic random mutations in the proteins’ structure.
Ariel Fernández, working at Chicago University and now at the Mathematics Institute of Argentina in Buenos Aires, and Michael Lynch of Indiana University in Bloomington argue that complexity in the network of our protein interactions arises because our relatively small population size, compared with single-celled organisms, makes us especially vulnerable to ‘genetic drift’: changes in the gene pool due to the reproductive success of certain individuals by chance rather than by superior fitness.
Whereas natural selection tends to weed out harmful mutations in genes and their related proteins, genetic drift does not. Fernández and Lynch argue that the large number of physical interactions between our proteins – now a crucial component of how information is transmitted in our cells – compensates for the reduction in protein stability wrought by drift. But this response comes at a cost.
It might mask the accumulation of structural weaknesses in proteins to a point where the problem can no longer be contained. Then, say Fernández and Lynch, proteins might be liable to misfold spontaneously – as they do in so-called diseases such as Alzheimer’s, Parkinson’s and prion diseases, caused by misfolded proteins in the brain.
If so, this means we may be fighting a losing race. Genetic drift may eat away at the stability of our proteins until they are overwhelmed, leaving us a sickly species.
This would imply that Darwinian evolution isn’t necessary benign in the long run. By finding a short-term solution to drift, it might merely be creating a time-bomb. “Species with low population are ultimately doomed by nature’s strategy of evolving complexity”, says Fernández.
The work provides “interesting and important news”, according to William Martin, a specialist in molecular evolution at the University of Düsseldorf in Germany. Martin says it shows that evolution of eukaryotes – relatively complex organisms like us, with a cellular ‘nucleus’ that houses the chromosomes – “can be substantially affected by drift.”
Drift is a bigger problem for small populations – those of multicelled eukaryotic organisms – than for large ones, because survival by chance rather than by fitness is statistically more likely for small numbers. Many random mutations in a gene, and thus in the protein made from it, will harm the protein’s resistance to unfolding: the protein’s folded-up shape becomes more apt to loosen as water molecules intrude into it. This loss of shape weakens the protein’s ability to function.
Such problems can be avoided if proteins stick loosely to one another so as to shelter the regions vulnerable to water. Fernández and Lynch say that these associations between proteins – a key feature of the cell biology of eukaryotes – may have therefore initially been a passive response to genetic drift. Over time, certain protein-protein interactions may be selected by evolution for useful functions, such as sending molecular signals across cell membranes.
Using protein structures reported in the Protein Data Bank, the two researchers verified that disruption of the interface between proteins and water, caused mostly by exposure of ‘sticky’ parts of the folded peptide chain [full disclosure: these are actually parts of the chain that hydrogen-bond to one another; exposure to water enables the water molecules to compete for the hydrogen bonding. Ariel Fernández has previously explored how such regions may be ‘wrapped’ in hydrophobic chain segments to keep water away], leads to a greater propensity for a protein to associate with others. They also showed that drift could account for this ‘poor wrapping’ of proteins.
On this view, genome complexity doesn’t offer intrinsic evolutionary advantages, but is a kind of knee-jerk response to the chance appearance of ‘needy proteins’ – which ends up exposing us to serious risks.
“I believe prions are indicators of this gambit gone too far”, says Fernandez. “The proteins with the largest accumulation of structural defects are the prions, soluble proteins so poorly wrapped that they relinquish their functional fold and aggregate”. Prions cause disease by triggering the misfolding of other proteins.
“If genetic variability resulting from random drift keeps increasing, we as a species may end up facing more and more fitness catastrophes of the type that prions represent”, Fernandez adds. “Perhaps the evolutionary cost of our complexity is too high a price to pay in the long run.”
However, Martin doubts that drift alone can account for the difference in complexity between prokaryotes (single-celled organisms without a cell nucleus) and eukaryotes. His previous work has indicated that bioenergetics also plays a strong role [2]. For example, says Martin, prokaryotes with small population sizes are symbiotic, which tend to degenerate, not to become complex. “Population genetics is just one aspect of the complexity issue”, he says.
References
1. Fernandez, A. & Lynch, M. Nature doi:10.1038/nature09992 (2011).
2. Lane, N. & Martin, W. Nature 467, 929-934 (2010).
Monday, May 09, 2011
Unnatural happenings
There is a smart review of Unnatural in The Age by Damon Young. I don’t just say it is smart because it is positive – he engages intelligently with the issues. This bit made me smile: “Because he's neither a religious nor scientific fundamentalist, Ball's ideas may draw flak from both.” Well, indeed.
And I recently spoke to David Lemberg about the book for a podcast on the very nice Alden Bioethics blog run out of Albany Medical Center in New York. It’s available here.
And I recently spoke to David Lemberg about the book for a podcast on the very nice Alden Bioethics blog run out of Albany Medical Center in New York. It’s available here.
Sunday, May 08, 2011
Are scientific reputations boosted artificially?
Here’s my latest Muse for Nature News.
_________________________________________________________
Scientific reputations emerge in a collective manner. But does this guarantee that fame rests on merit?
Does everyone in science get the recognition they deserve? Well obviously, your work hasn’t been sufficiently appreciated by your peers, but what about everyone else? Yes, I know he is vastly over-rated, and it’s a mystery why she gets invited to give so many keynote lectures, but that aside – is science a meritocracy?
How would you judge? Reputation is often a word-of-mouth affair; grants, awards and prizes offer a rather more concrete measure of success. But increasingly, scientific excellence is measured by citation statistics, not least by the ubiquitous h-index [1], which seeks to quantify the impact of your total oeuvre. Do all or any of these things truly reflect the worth of one’s scientific output?
Many would probably say: sort of. Most good work gets recognized eventually, and most Nobel prizes are applauded and deemed long overdue, rather than denounced as undeserved. But not always. Sometimes important work doesn’t get noticed in the author’s lifetime, and it’s a fair bet that some never comes to light at all. There’s surely an element of chance and luck in the establishment of reputations.
A new paper in PLoS ONE by Santo Fortunato of the Institute for Scientific Interchange in Turin, Italy, Dirk Helbing of ETH in Zurich, Switzerland, and coworkers aims to shed some light on the mechanism by which citations are accrued [2]. They have found that some landmark papers of Nobel laureates quite quickly give their authors a sudden boost in citation rate – and that this boost extends to the author’s earlier papers too, even if they were in unrelated areas.
For example, citations to a pivotal 1989 paper by chemistry Nobel laureate John Fenn on electrospray ionization mass spectrometry [3] took off exponentially, but also raised the citation profile of at least six of Fenn’s older papers. These peaks in citation rate stand out remarkably clearly for several laureates (some of whom have more than one peak), and might be a useful indicator both of important breakthroughs and of scientific performance.
This behaviour could seem reassuring or disturbing, depending on your inclination. On the one hand, some of these researchers were not particularly well known before they published their landmark papers – and yet the value of the work does seem to have been recognized, overcoming the rich-get-richer effect by which those already famous tend more easily to accrue more fame [4]. This boost could help innovative new ideas to take root. On the other hand, such a rise to prominence brings a new rich-get-richer effect, for it awards ‘unearned’ citations to the researcher’s other papers.
And the findings seem to imply that citations are sometimes selected not because they are necessarily the best or most appropriate but to capitalize on the prestige and presumed authority of the person cited. This further distorts a picture that already contains a rich-get-richer element among citations themselves. An earlier analysis suggested that some citations become common largely by chance, benefitting from a feedback effect in which they are chosen simply because others have chosen them before [5].
But at root, what this finding underscores is that science is a social enterprise, with all the consequent quirks and nonlinearities. That has potential advantages, but also drawbacks. In an ideal world, every researchers would reach an independent judgement about the value of a paper or a body of work, and the sum of these judgements should then reflect something fundamental about its worth.
That, however, is no longer an option, not least because there is simply too much to read – no one can hope to keep up with all that happens in their field, let alone in related ones. As a result, the scientific community must act as a collective search engine that hopefully alights on the most promising material. The question is whether this social network is harnessed efficiently, avoiding blind alleys while not overlooking gems.
No one really knows the answer to that. But some social-science studies highlight the possible consequences. For example, it seems that selections made ostensibly on merit are somewhat capricious when others’ choices are taken into account: objectively ‘good’ and ‘bad’ material still tends on average to be seen as such, but feedbacks can create a degree of randomness in what succeeds and fails [6]. Doubtless the same effects operate in the political sphere – so that democracy is a somewhat compromised meritocracy – and also in economics, which is why prices frequently deviate from their ‘fundamental’ value.
But Helbing suggests that there is probably an optimal balance between independence and group-think. A computer model of people exiting a crowded room in an emergency shows that it empties most efficiently when there is just the right amount of follow-the-crowd herding [7]. Are scientific reputations forged in this optimal regime? And if not, what would it take to engineer more wisdom into this particular crowd?
References
1. Hirsch, J. E. Proc. Natl Acad. Sci. USA 102, 16569-16572 (2005).
2. Mazloumian, A., Eom, Y.-H., Helbing, D., Lozano, S. & Fortunato, S. PLoS ONE 6(5), e18975 (2011).
3. Fenn, J. B., Mann, M., Meng, C. K., Wong, S. F. & Whitehouse, C. M., Science 246, 64-71 (1989).
4. Merton, R. K. Science 159, 56-63 (1968).
5. Simkin, M. V. & Roychowdhury, V. P. Ann. Improb. Res. 11, 24-27 (2005).
6. Salganik, M. J., Dodds, P. S. & Watts, D. J. Science 311, 854-856 (2006).
7. Helbing, D., Farkas, I. & Vicsek, T. Nature 407, 487-490 (2000).
_________________________________________________________
Scientific reputations emerge in a collective manner. But does this guarantee that fame rests on merit?
Does everyone in science get the recognition they deserve? Well obviously, your work hasn’t been sufficiently appreciated by your peers, but what about everyone else? Yes, I know he is vastly over-rated, and it’s a mystery why she gets invited to give so many keynote lectures, but that aside – is science a meritocracy?
How would you judge? Reputation is often a word-of-mouth affair; grants, awards and prizes offer a rather more concrete measure of success. But increasingly, scientific excellence is measured by citation statistics, not least by the ubiquitous h-index [1], which seeks to quantify the impact of your total oeuvre. Do all or any of these things truly reflect the worth of one’s scientific output?
Many would probably say: sort of. Most good work gets recognized eventually, and most Nobel prizes are applauded and deemed long overdue, rather than denounced as undeserved. But not always. Sometimes important work doesn’t get noticed in the author’s lifetime, and it’s a fair bet that some never comes to light at all. There’s surely an element of chance and luck in the establishment of reputations.
A new paper in PLoS ONE by Santo Fortunato of the Institute for Scientific Interchange in Turin, Italy, Dirk Helbing of ETH in Zurich, Switzerland, and coworkers aims to shed some light on the mechanism by which citations are accrued [2]. They have found that some landmark papers of Nobel laureates quite quickly give their authors a sudden boost in citation rate – and that this boost extends to the author’s earlier papers too, even if they were in unrelated areas.
For example, citations to a pivotal 1989 paper by chemistry Nobel laureate John Fenn on electrospray ionization mass spectrometry [3] took off exponentially, but also raised the citation profile of at least six of Fenn’s older papers. These peaks in citation rate stand out remarkably clearly for several laureates (some of whom have more than one peak), and might be a useful indicator both of important breakthroughs and of scientific performance.
This behaviour could seem reassuring or disturbing, depending on your inclination. On the one hand, some of these researchers were not particularly well known before they published their landmark papers – and yet the value of the work does seem to have been recognized, overcoming the rich-get-richer effect by which those already famous tend more easily to accrue more fame [4]. This boost could help innovative new ideas to take root. On the other hand, such a rise to prominence brings a new rich-get-richer effect, for it awards ‘unearned’ citations to the researcher’s other papers.
And the findings seem to imply that citations are sometimes selected not because they are necessarily the best or most appropriate but to capitalize on the prestige and presumed authority of the person cited. This further distorts a picture that already contains a rich-get-richer element among citations themselves. An earlier analysis suggested that some citations become common largely by chance, benefitting from a feedback effect in which they are chosen simply because others have chosen them before [5].
But at root, what this finding underscores is that science is a social enterprise, with all the consequent quirks and nonlinearities. That has potential advantages, but also drawbacks. In an ideal world, every researchers would reach an independent judgement about the value of a paper or a body of work, and the sum of these judgements should then reflect something fundamental about its worth.
That, however, is no longer an option, not least because there is simply too much to read – no one can hope to keep up with all that happens in their field, let alone in related ones. As a result, the scientific community must act as a collective search engine that hopefully alights on the most promising material. The question is whether this social network is harnessed efficiently, avoiding blind alleys while not overlooking gems.
No one really knows the answer to that. But some social-science studies highlight the possible consequences. For example, it seems that selections made ostensibly on merit are somewhat capricious when others’ choices are taken into account: objectively ‘good’ and ‘bad’ material still tends on average to be seen as such, but feedbacks can create a degree of randomness in what succeeds and fails [6]. Doubtless the same effects operate in the political sphere – so that democracy is a somewhat compromised meritocracy – and also in economics, which is why prices frequently deviate from their ‘fundamental’ value.
But Helbing suggests that there is probably an optimal balance between independence and group-think. A computer model of people exiting a crowded room in an emergency shows that it empties most efficiently when there is just the right amount of follow-the-crowd herding [7]. Are scientific reputations forged in this optimal regime? And if not, what would it take to engineer more wisdom into this particular crowd?
References
1. Hirsch, J. E. Proc. Natl Acad. Sci. USA 102, 16569-16572 (2005).
2. Mazloumian, A., Eom, Y.-H., Helbing, D., Lozano, S. & Fortunato, S. PLoS ONE 6(5), e18975 (2011).
3. Fenn, J. B., Mann, M., Meng, C. K., Wong, S. F. & Whitehouse, C. M., Science 246, 64-71 (1989).
4. Merton, R. K. Science 159, 56-63 (1968).
5. Simkin, M. V. & Roychowdhury, V. P. Ann. Improb. Res. 11, 24-27 (2005).
6. Salganik, M. J., Dodds, P. S. & Watts, D. J. Science 311, 854-856 (2006).
7. Helbing, D., Farkas, I. & Vicsek, T. Nature 407, 487-490 (2000).
Friday, May 06, 2011
A discourse on method
Actually (to pick up from the previous post), I’d meant to put my last Crucible column up here too. So here it is now.
__________________________________________________
What’s wrong with this claim? “Replication of results is a crucial part of the scientific method. Experimental errors come rapidly to light when researchers prove unable to reproduce the claims of others. In this way, science has a built-in mechanism for self-correction.”
The insistence on replication – as the motto of the Royal Society puts it, ‘take no one’s word for it’ (Nullius in verba) – has indeed long been one of science’s great strengths. It explains why pathological science such as cold fusion and polywater was rather quickly consigned to the dustbin while equally striking claims such as high-temperature superconductivity have entered the textbooks.
But too often this view of the ‘scientific method’ – itself a slippery concept – is regarded as a regular aspect of science in action, rather than an expression of the ideal. Rather few experiments are replicated verbatim, as it were, not least because science is too competitive and busy to spend one’s time doing what someone has already done. Important claims are bound to get checked as others rush to follow up on the work, but mundane stuff will probably never be tested – it will simply sink unheeded into the literature.
No one should be surprised or unduly alarmed at that – if work isn’t important enough to warrant replication, it matters little if it is flawed. And although the difficulty of publishing negative results probably hinders the correction process and favours exaggerated claims, information technologies might now offer solutions.1 What matters more is that replication isn’t just a problem in practice; it’s a problem in theory.
The concept emerged along with experimental science itself in the late sixteenth century. Before that, experiments – when they were done at all – were typically considered not a test of your hypothesis but a demonstration that it was right. If ‘experience’ didn’t fit with theory, no one felt a compelling urge to modify the theory, not least because the world was not considered law-bound it quite the same way it is today. Even though the early experimentalists, often working outside the academic mainstream, decided they needed to filter recipes and reports by attempting to verify them before recording them as fact, the tradition of experiment-as-demonstration persisted for a long time. Many of the celebrated trials shown to the Fellows of the Royal Society were like that.
But in any case, it would be wrong to suppose that the failure of an experiment to verify a hypothesis or to replicate a prior claim should be grounds for their rejection. Robert Boyle appreciated this in his ‘Two Essays, concerning the Unsuccessfulness of Experiments’ (1661). There are many reasons, he wrote, why an experiment might not work as anticipated: the equipment might be faulty, or the reagents not fresh, for example. That was amply borne out (albeit in reverse) by the recent discovery that a crucial step (first reported in 1918) in the alleged total synthesis of quinine by Robert Woodward and William Doering in 1944 depended on a catalyst being aged.2 The very fact that it took 90 years to test that step is itself a comment on how replication really functions in science.
The problem of replication was highlighted by Boyle’s own famous experiments with the air pump. By raising the possibility of a vacuum, these studies posed a serious challenge to the prevailing Aristotelian philosophy. So the stakes were very high. But because of the imperfections of the apparatus, it was no easy matter even for Boyle to reproduce some of his findings. And because the air pump was a hugely sophisticated piece of scientific kit– it has been dubbed the cyclotron of its age – it was very expensive, so very few others were in a position to try the experiments. Even if they did, the designs differed, so one couldn’t be sure that the same procedures were being followed.3 That essentially no replications could be attempted without first-hand experience of Boyle’s instrument reflects today’s situation, in which hardly any complicated experimental procedure can be replicated reliably without direct contact between the labs involved. Even then, the only way to calibrate your apparatus may be against that whose results you’re trying to test.
Which raises the question: if your attempted replication ‘fails’, where is the error? Have you neglected something? Or was the original claim wrong? Or was it right for the wrong reasons? The possibilities are endless. Indeed, the philosophers Pierre Duhem and Willard Van Orman Quine have independently pointed out that, from a strictly logical perspective, no hypothesis can ever be tested or an experimental replication assayed, because the problem is under-determined: discrepancies can never be logically localized to a particular cause. Science makes progress regardless, and what is perhaps surprising is that the ‘scientific method’ remains so effective when it is in truth ramshackle, makeshift and logically shaky.
These issues seem more pertinent than ever. Who, for example, is going to check the findings from the Large Hadron Collider?
References
1. J. Schooler, Nature 470, 437 (2011).
2. A. C. Smith & R. M. Williams, Angew. Chem. Int. Edn 47, 1736–1740 (2008).
3. S. Shapin & S. Schaffer, Leviathan and the Air-Pump (Princeton University Press, Princeton, 1985).
__________________________________________________
What’s wrong with this claim? “Replication of results is a crucial part of the scientific method. Experimental errors come rapidly to light when researchers prove unable to reproduce the claims of others. In this way, science has a built-in mechanism for self-correction.”
The insistence on replication – as the motto of the Royal Society puts it, ‘take no one’s word for it’ (Nullius in verba) – has indeed long been one of science’s great strengths. It explains why pathological science such as cold fusion and polywater was rather quickly consigned to the dustbin while equally striking claims such as high-temperature superconductivity have entered the textbooks.
But too often this view of the ‘scientific method’ – itself a slippery concept – is regarded as a regular aspect of science in action, rather than an expression of the ideal. Rather few experiments are replicated verbatim, as it were, not least because science is too competitive and busy to spend one’s time doing what someone has already done. Important claims are bound to get checked as others rush to follow up on the work, but mundane stuff will probably never be tested – it will simply sink unheeded into the literature.
No one should be surprised or unduly alarmed at that – if work isn’t important enough to warrant replication, it matters little if it is flawed. And although the difficulty of publishing negative results probably hinders the correction process and favours exaggerated claims, information technologies might now offer solutions.1 What matters more is that replication isn’t just a problem in practice; it’s a problem in theory.
The concept emerged along with experimental science itself in the late sixteenth century. Before that, experiments – when they were done at all – were typically considered not a test of your hypothesis but a demonstration that it was right. If ‘experience’ didn’t fit with theory, no one felt a compelling urge to modify the theory, not least because the world was not considered law-bound it quite the same way it is today. Even though the early experimentalists, often working outside the academic mainstream, decided they needed to filter recipes and reports by attempting to verify them before recording them as fact, the tradition of experiment-as-demonstration persisted for a long time. Many of the celebrated trials shown to the Fellows of the Royal Society were like that.
But in any case, it would be wrong to suppose that the failure of an experiment to verify a hypothesis or to replicate a prior claim should be grounds for their rejection. Robert Boyle appreciated this in his ‘Two Essays, concerning the Unsuccessfulness of Experiments’ (1661). There are many reasons, he wrote, why an experiment might not work as anticipated: the equipment might be faulty, or the reagents not fresh, for example. That was amply borne out (albeit in reverse) by the recent discovery that a crucial step (first reported in 1918) in the alleged total synthesis of quinine by Robert Woodward and William Doering in 1944 depended on a catalyst being aged.2 The very fact that it took 90 years to test that step is itself a comment on how replication really functions in science.
The problem of replication was highlighted by Boyle’s own famous experiments with the air pump. By raising the possibility of a vacuum, these studies posed a serious challenge to the prevailing Aristotelian philosophy. So the stakes were very high. But because of the imperfections of the apparatus, it was no easy matter even for Boyle to reproduce some of his findings. And because the air pump was a hugely sophisticated piece of scientific kit– it has been dubbed the cyclotron of its age – it was very expensive, so very few others were in a position to try the experiments. Even if they did, the designs differed, so one couldn’t be sure that the same procedures were being followed.3 That essentially no replications could be attempted without first-hand experience of Boyle’s instrument reflects today’s situation, in which hardly any complicated experimental procedure can be replicated reliably without direct contact between the labs involved. Even then, the only way to calibrate your apparatus may be against that whose results you’re trying to test.
Which raises the question: if your attempted replication ‘fails’, where is the error? Have you neglected something? Or was the original claim wrong? Or was it right for the wrong reasons? The possibilities are endless. Indeed, the philosophers Pierre Duhem and Willard Van Orman Quine have independently pointed out that, from a strictly logical perspective, no hypothesis can ever be tested or an experimental replication assayed, because the problem is under-determined: discrepancies can never be logically localized to a particular cause. Science makes progress regardless, and what is perhaps surprising is that the ‘scientific method’ remains so effective when it is in truth ramshackle, makeshift and logically shaky.
These issues seem more pertinent than ever. Who, for example, is going to check the findings from the Large Hadron Collider?
References
1. J. Schooler, Nature 470, 437 (2011).
2. A. C. Smith & R. M. Williams, Angew. Chem. Int. Edn 47, 1736–1740 (2008).
3. S. Shapin & S. Schaffer, Leviathan and the Air-Pump (Princeton University Press, Princeton, 1985).
Thursday, May 05, 2011
Science and religion - even chemists aren't immune
Oh, it’s risky, I know. But I offer the following mild observations about the recent Templeton Prize in my Crucible column in Chemistry World. When I wrote it, on the day of the announcement, I didn’t realise quite what a lot of shrieking the award would elicit. There is, by the way, a sentence in the final para, omitted in the published version, that makes the meaning of my final sentence a little more apparent. Herein lies a tale.
_______________________________________________________________________
The astronomer Martin Rees, until recently President of the Royal Society, seems nonchalant, even bemused, about receiving this year’s Templeton Prize for work at the interface of science and religion. Not only has he seemingly little idea to what to do with the £1m prize money, but he confesses to knowing little about the Templeton Foundation beyond what appeared in a recent Nature article [1], and wasn’t sure why he had been selected.
According to the Pennsylvania-based Templeton Foundation, set up by the late billionaire John Templeton to develop links between science and spirituality, the prize is awarded to people who have “expanded our vision of human purpose and ultimate reality”. In giving it to Rees, the foundation says that his “profound insights on the cosmos have provoked vital questions that speak to humanity’s highest hopes and worst fears”.
One thing Rees must have known, however, is that his award would be controversial. Some scientists see it as an attempt to buy respectability for the Foundation through the names of illustrious scientists. In its early days the award went to religious figures such as Billy Graham and Mother Teresa. But Rees joins a list of winners that now includes cosmologists George Ellis and John Barrow, physicists Paul Davies, Freeman Dyson and Charles Townes, and biologist Francisco Ayala. This reflects the Foundation’s energetic determination over the past two decades to focus on interactions between science and religion – topics that some sceptics say have no shared ground. Chemistry Nobel laureate Harry Kroto, one of those who has condemned Rees’ acceptance of the prize, suggests that to qualify you just have to be an eminent scientist prepared to be nice – or at least not rude – about religion.
Rees is no stranger to this disputed territory. He presided over the sacking of the Royal Society’s director of education Michael Riess, an ordained Church of England minister, after remarks that were construed as defending the teaching of creationism in schools. Rees also drew fire from the inclusion of a service at St Paul’s Cathedral, led by the Archbishop of Canterbury, in the Royal Society’s 350th anniversary celebrations last year. Rees has said publicly that he has no religious beliefs but occasionally attends church services and recognizes their social role. He takes the pragmatic view that, in battling the anti-scientific extremes of religious fundamentalism, he’d rather have the Archbishop and other moderates on his side. For others, the distance between evidence-based science and faith-based religion is too great to make common cause.
Chemistry might seem too remote from the Templeton Foundation’s goals for the issue of whether to accept its ‘tainted’ money ever to arise. Historically, of course, many chemists were profoundly religious. For Robert Boyle, investigating all aspects of nature was a holy duty that deepens our reverence for God’s works. Michael Faraday had to juggle his science and his profound non-conformist Christian beliefs.
Yet surely chemical research can’t directly speak to religious questions today? Don’t be so sure. In 2005 I took part in a Templeton-funded symposium called “Water of Life: Counterfactual Chemistry and Fine-Tuning in Biochemistry”. While I won’t pretend to have been indifferent to the venue on the shore of Lake Como, I would have declined were it not for the stellar list of other delegates. The meeting was motivated by Harvard biologist Lawrence Henderson’s 1913 book The Fitness of the Environment, in which he suggested that water is ‘biophilic’, with physical and chemical properties remarkably fine-tuned to support life. The question put to the gathering was: are they really?
Among the many contributions, Ruth Lynden-Bell and Pablo Debenedetti described computer simulations of ‘counterfactual water’ in which the properties of the molecule were slightly altered to see if it retained its unique liquid properties [2]. For example, the tetrahedral hydrogen-bonded motif remains, in distorted form, if the H-O-H bond angle is changed from 109.5 degrees to 90 degrees, but the structure becomes more like that of a ‘normal’ liquid as the hydrogen-bond strength is decreased. This notion of a ‘modified chemistry’ thus may probe how far the chemical world is contingent and how far it is inevitable. Of course, one could say that there is no contingence: things are as they are and not otherwise. But fine-tuning arguments in cosmology confront the mystery of why the laws of nature seem geared to enable our existence. If there’s plenty of slack, there’s no mystery to explain. Counterfactual scenarios can also explore the supposed uniqueness of water as life’s solvent, irrespective of any metaphysical implications.
If you want to know what the meeting concluded, you’ll have to read the book [3]. It has only recently been published, in part because some university presses seemed nervous of the association with the Templeton Foundation. Wary at the outset of an underlying agenda, I saw no evidence of it at the meeting: it was good science all the way. Sceptics are right to ask questions about the Foundation’s motives, but they need to be open-minded about the answers. When such scepticism stands in the way of solid science, we are all the losers.
1. M. M. Waldorp, Nature 470, 323 (2011).
2. R. M. Lynden-Bell & P. G. Debenedetti, J. Phys. Chem. B 109, 6527 (2005).
3. R. M. Lynden-Bell, S. Conway Morris, J. D. Barrow, J. L. Finney & C. L. Harper (eds). Water and Life: the Unique Properties of H2O. CRC Press, Boca Raton, 2010.
_______________________________________________________________________
The astronomer Martin Rees, until recently President of the Royal Society, seems nonchalant, even bemused, about receiving this year’s Templeton Prize for work at the interface of science and religion. Not only has he seemingly little idea to what to do with the £1m prize money, but he confesses to knowing little about the Templeton Foundation beyond what appeared in a recent Nature article [1], and wasn’t sure why he had been selected.
According to the Pennsylvania-based Templeton Foundation, set up by the late billionaire John Templeton to develop links between science and spirituality, the prize is awarded to people who have “expanded our vision of human purpose and ultimate reality”. In giving it to Rees, the foundation says that his “profound insights on the cosmos have provoked vital questions that speak to humanity’s highest hopes and worst fears”.
One thing Rees must have known, however, is that his award would be controversial. Some scientists see it as an attempt to buy respectability for the Foundation through the names of illustrious scientists. In its early days the award went to religious figures such as Billy Graham and Mother Teresa. But Rees joins a list of winners that now includes cosmologists George Ellis and John Barrow, physicists Paul Davies, Freeman Dyson and Charles Townes, and biologist Francisco Ayala. This reflects the Foundation’s energetic determination over the past two decades to focus on interactions between science and religion – topics that some sceptics say have no shared ground. Chemistry Nobel laureate Harry Kroto, one of those who has condemned Rees’ acceptance of the prize, suggests that to qualify you just have to be an eminent scientist prepared to be nice – or at least not rude – about religion.
Rees is no stranger to this disputed territory. He presided over the sacking of the Royal Society’s director of education Michael Riess, an ordained Church of England minister, after remarks that were construed as defending the teaching of creationism in schools. Rees also drew fire from the inclusion of a service at St Paul’s Cathedral, led by the Archbishop of Canterbury, in the Royal Society’s 350th anniversary celebrations last year. Rees has said publicly that he has no religious beliefs but occasionally attends church services and recognizes their social role. He takes the pragmatic view that, in battling the anti-scientific extremes of religious fundamentalism, he’d rather have the Archbishop and other moderates on his side. For others, the distance between evidence-based science and faith-based religion is too great to make common cause.
Chemistry might seem too remote from the Templeton Foundation’s goals for the issue of whether to accept its ‘tainted’ money ever to arise. Historically, of course, many chemists were profoundly religious. For Robert Boyle, investigating all aspects of nature was a holy duty that deepens our reverence for God’s works. Michael Faraday had to juggle his science and his profound non-conformist Christian beliefs.
Yet surely chemical research can’t directly speak to religious questions today? Don’t be so sure. In 2005 I took part in a Templeton-funded symposium called “Water of Life: Counterfactual Chemistry and Fine-Tuning in Biochemistry”. While I won’t pretend to have been indifferent to the venue on the shore of Lake Como, I would have declined were it not for the stellar list of other delegates. The meeting was motivated by Harvard biologist Lawrence Henderson’s 1913 book The Fitness of the Environment, in which he suggested that water is ‘biophilic’, with physical and chemical properties remarkably fine-tuned to support life. The question put to the gathering was: are they really?
Among the many contributions, Ruth Lynden-Bell and Pablo Debenedetti described computer simulations of ‘counterfactual water’ in which the properties of the molecule were slightly altered to see if it retained its unique liquid properties [2]. For example, the tetrahedral hydrogen-bonded motif remains, in distorted form, if the H-O-H bond angle is changed from 109.5 degrees to 90 degrees, but the structure becomes more like that of a ‘normal’ liquid as the hydrogen-bond strength is decreased. This notion of a ‘modified chemistry’ thus may probe how far the chemical world is contingent and how far it is inevitable. Of course, one could say that there is no contingence: things are as they are and not otherwise. But fine-tuning arguments in cosmology confront the mystery of why the laws of nature seem geared to enable our existence. If there’s plenty of slack, there’s no mystery to explain. Counterfactual scenarios can also explore the supposed uniqueness of water as life’s solvent, irrespective of any metaphysical implications.
If you want to know what the meeting concluded, you’ll have to read the book [3]. It has only recently been published, in part because some university presses seemed nervous of the association with the Templeton Foundation. Wary at the outset of an underlying agenda, I saw no evidence of it at the meeting: it was good science all the way. Sceptics are right to ask questions about the Foundation’s motives, but they need to be open-minded about the answers. When such scepticism stands in the way of solid science, we are all the losers.
1. M. M. Waldorp, Nature 470, 323 (2011).
2. R. M. Lynden-Bell & P. G. Debenedetti, J. Phys. Chem. B 109, 6527 (2005).
3. R. M. Lynden-Bell, S. Conway Morris, J. D. Barrow, J. L. Finney & C. L. Harper (eds). Water and Life: the Unique Properties of H2O. CRC Press, Boca Raton, 2010.
Sunday, April 24, 2011
The Information - a review
I have a review of James Gleick's new book in the Observer today. Here it is. He does an enviable job, on the whole - this is better than Chaos.
________________________________________________________________
The Information: A History, a Theory, a Flood
James Gleick
Fourth Estate, 2011
ISBN 978-0-00-722573-6
Too much information: the complaint du jour, but also toujours. Alexander Pope quipped that the printing press, “a scourge for the sins of the learned”, would lead to “a deluge of Authors [that] covered the land”. Robert Burton, the Oxford anatomist of melancholy, confessed in 1621 that he was drowning in books, pamphlets, news and opinions. All the twittering and tweeting today, the blogs and wikis and apparent determination to archive even the most ephemeral and trivial thought has, as James Gleick observes in this magisterial survey, something of the Borgesian about it. Nothing is forgotten; the world imprints itself on the informatosphere at a scale approaching 1:1, each moment of reality creating an indelible replica.
But do we gain from it, or was T. S. Eliot right to say that “all our knowledge brings us nearer to our ignorance”? Gleick is refreshingly upbeat. In the face of the information flood that David Foster Wallace called Total Noise, he says, “we veer from elation to dismay and back”. But he is confident that we can navigate it, challenging the view of techno-philosopher Jean-Pierre Dupuy that “ours is a world about which we pretend to have more and more information but which seems to us increasingly devoid of meaning”. Yet this relationship between information and meaning is the crux of the matter, and it is one that Gleick juggles but does not quite get to grips with. I’ll come back to that.
This is not, however, a book that merely charts the rising tide of information, from the invention of writing to the age of Google. To grasp what information truly means – to explain why it is shaping up as a unifying principle of science – he has to embrace linguistics, logic, telecommunications, codes, computing, mathematics, philosophy, cosmology, quantum theory and genetics. He must call as witnesses not only Charles Babbage, Alan Turing and Kurt Gödel, but also Borges, Poe and Lewis Carroll. There are few writers who could accomplish this with such panache and authority. Gleick, whose Chaos in 1987 helped to kick-start the era of modern popular science and who has also written acclaimed biographies of Richard Feynman and Isaac Newton, is one.
At the heart of the story is Claude Shannon, whose eclectic interests defy categorization today and were positively bizarre in the mid twentieth century. Having written a visionary but ignored doctoral thesis on genetics, Shannon wound up in the labs of the Bell Telephone Company, where electrical logic circuitry was being invented. There he worked (like Turing, who he met in 1943) on code-breaking during the Second World War. And in 1948 he published in Bell’s obscure house journal a theory of how to measure information – not just in a phone-line signal but in a random number, a book, a genome. Shannon’s information theory looms over everything that followed.
Shannon’s real point was that information is a physical entity, like energy or matter. The implications of this are profound. For one thing, manipulating information in a computer then has a minimum energy cost set by the laws of physics. This is what rescues the second law of thermodynamics (entropy or disorder always increases) from the hypothetical ‘demon’ invoked by James Clerk Maxwell in the nineteenth century to undermine it. By observing the behaviour of individual molecules, Maxwell’s demon seemed able to engineer a ‘forbidden’ decrease in entropy. But that doesn’t undo the sacrosanct second law, since processing the necessary information (more precisely, having to discard some of it – forgetting is the hard part) incurs a compensating entropic toll. In effect the demon instead turns information to energy, something demonstrated last year by a group of Japanese physicists – sadly too late for Gleick.
In quantum physics the role of information goes even deeper: at the level of fundamental particles, every event can be considered a transaction in information, and our familiar classical world emerges from the quantum by the process of erasing information. In quantum terms, Gleick says, “the universe is computing its own destiny.” By this point we are a long way from cuneiform and Morse code, though he makes the path commendably clear.
Moreover, Gleick does so with tremendous verve, which is mostly exhilarating, sometimes exhausting and occasionally coy. He is bracingly ready to use technical terms without definition – nonlinear, thermodynamic equilibrium – rightly refusing any infantilizing hand-holding. What impresses most is how he delves beneath the surface narrative to pull out the conceptual core. Written language, he explains, did not simply permit us to make thoughts permanent – it changed thinking itself, enabling abstraction and logical reasoning. Language is a negotiation whose currency is information. A child learning to read is not simply turning letters into words but is learning how to exploit (often recklessly) the redundancies in the system. She reads ‘this’ as ‘that’ not because she confuses the phonemes but because she knows that only a few of them may follow ‘th’, and it’s less effort to guess. Read the whole word, we tell her, but we don’t do it ourselves. That’s why we fail to spot typos: we’ve got the message already. Language elaborates to no informational purpose; the ‘u’ after ‘q’ could be ditched wholesale. Text messaging now lays bare this redundancy: we dnt nd hlf of wht we wrt.
Shannon’s take on language is disconcerting. From the outset he was determined to divorce information from meaning, making it equivalent to something like surprise or unpredictability. That’s why a random string of letters is more information-rich, in Shannon’s sense, than a coherent sentence. There is a definite value in his measure, not just in computing but in linguistics. Yet to broach information in the colloquial sense, somewhere meaning must be admitted back into all the statistics and correlations.
Gleick acknowledges the tension between information as Shannon’s permutation of bits and information as agent of meaning, but a reconciliation eludes him. When he explains the gene with reference to a Beethoven sonata, he says that the music resides neither in acoustic waves nor annotations on paper: ‘the music is the information’. But where and what is that information? Shannon might say, and Gleick implies, that it is in the pattern of notes that Beethoven conceived. But that’s wrong. The notes become music only in the mind of a listener primed with the cognitive, statistical and cultural apparatus to weave them into coherent and emotive forms. This means there is no bounded information set that is the music – it is different for every listener (and every performance), sometimes subtly, sometimes profoundly. The same for literature.
Lest you imagine that this applies only to information impinging on human cognition, it is equally true of the gene. Gleick too readily accepts the standard trope that genes – the abstract symbolic sequence – contain the information needed to build an organism. That information is highly incomplete. Genes don’t need to supply it all, because they act in a molecular milieu that fills in the gaps. It’s not that the music, or the gene, needs the right context to deliver its message – without that context, there is no message, no music, no gene. An information theory that considers just the signal and neglects the receiver is limited, even misleading.
It is the only serious complaint about what is otherwise a deeply impressive and rather beautiful book.
________________________________________________________________
The Information: A History, a Theory, a Flood
James Gleick
Fourth Estate, 2011
ISBN 978-0-00-722573-6
Too much information: the complaint du jour, but also toujours. Alexander Pope quipped that the printing press, “a scourge for the sins of the learned”, would lead to “a deluge of Authors [that] covered the land”. Robert Burton, the Oxford anatomist of melancholy, confessed in 1621 that he was drowning in books, pamphlets, news and opinions. All the twittering and tweeting today, the blogs and wikis and apparent determination to archive even the most ephemeral and trivial thought has, as James Gleick observes in this magisterial survey, something of the Borgesian about it. Nothing is forgotten; the world imprints itself on the informatosphere at a scale approaching 1:1, each moment of reality creating an indelible replica.
But do we gain from it, or was T. S. Eliot right to say that “all our knowledge brings us nearer to our ignorance”? Gleick is refreshingly upbeat. In the face of the information flood that David Foster Wallace called Total Noise, he says, “we veer from elation to dismay and back”. But he is confident that we can navigate it, challenging the view of techno-philosopher Jean-Pierre Dupuy that “ours is a world about which we pretend to have more and more information but which seems to us increasingly devoid of meaning”. Yet this relationship between information and meaning is the crux of the matter, and it is one that Gleick juggles but does not quite get to grips with. I’ll come back to that.
This is not, however, a book that merely charts the rising tide of information, from the invention of writing to the age of Google. To grasp what information truly means – to explain why it is shaping up as a unifying principle of science – he has to embrace linguistics, logic, telecommunications, codes, computing, mathematics, philosophy, cosmology, quantum theory and genetics. He must call as witnesses not only Charles Babbage, Alan Turing and Kurt Gödel, but also Borges, Poe and Lewis Carroll. There are few writers who could accomplish this with such panache and authority. Gleick, whose Chaos in 1987 helped to kick-start the era of modern popular science and who has also written acclaimed biographies of Richard Feynman and Isaac Newton, is one.
At the heart of the story is Claude Shannon, whose eclectic interests defy categorization today and were positively bizarre in the mid twentieth century. Having written a visionary but ignored doctoral thesis on genetics, Shannon wound up in the labs of the Bell Telephone Company, where electrical logic circuitry was being invented. There he worked (like Turing, who he met in 1943) on code-breaking during the Second World War. And in 1948 he published in Bell’s obscure house journal a theory of how to measure information – not just in a phone-line signal but in a random number, a book, a genome. Shannon’s information theory looms over everything that followed.
Shannon’s real point was that information is a physical entity, like energy or matter. The implications of this are profound. For one thing, manipulating information in a computer then has a minimum energy cost set by the laws of physics. This is what rescues the second law of thermodynamics (entropy or disorder always increases) from the hypothetical ‘demon’ invoked by James Clerk Maxwell in the nineteenth century to undermine it. By observing the behaviour of individual molecules, Maxwell’s demon seemed able to engineer a ‘forbidden’ decrease in entropy. But that doesn’t undo the sacrosanct second law, since processing the necessary information (more precisely, having to discard some of it – forgetting is the hard part) incurs a compensating entropic toll. In effect the demon instead turns information to energy, something demonstrated last year by a group of Japanese physicists – sadly too late for Gleick.
In quantum physics the role of information goes even deeper: at the level of fundamental particles, every event can be considered a transaction in information, and our familiar classical world emerges from the quantum by the process of erasing information. In quantum terms, Gleick says, “the universe is computing its own destiny.” By this point we are a long way from cuneiform and Morse code, though he makes the path commendably clear.
Moreover, Gleick does so with tremendous verve, which is mostly exhilarating, sometimes exhausting and occasionally coy. He is bracingly ready to use technical terms without definition – nonlinear, thermodynamic equilibrium – rightly refusing any infantilizing hand-holding. What impresses most is how he delves beneath the surface narrative to pull out the conceptual core. Written language, he explains, did not simply permit us to make thoughts permanent – it changed thinking itself, enabling abstraction and logical reasoning. Language is a negotiation whose currency is information. A child learning to read is not simply turning letters into words but is learning how to exploit (often recklessly) the redundancies in the system. She reads ‘this’ as ‘that’ not because she confuses the phonemes but because she knows that only a few of them may follow ‘th’, and it’s less effort to guess. Read the whole word, we tell her, but we don’t do it ourselves. That’s why we fail to spot typos: we’ve got the message already. Language elaborates to no informational purpose; the ‘u’ after ‘q’ could be ditched wholesale. Text messaging now lays bare this redundancy: we dnt nd hlf of wht we wrt.
Shannon’s take on language is disconcerting. From the outset he was determined to divorce information from meaning, making it equivalent to something like surprise or unpredictability. That’s why a random string of letters is more information-rich, in Shannon’s sense, than a coherent sentence. There is a definite value in his measure, not just in computing but in linguistics. Yet to broach information in the colloquial sense, somewhere meaning must be admitted back into all the statistics and correlations.
Gleick acknowledges the tension between information as Shannon’s permutation of bits and information as agent of meaning, but a reconciliation eludes him. When he explains the gene with reference to a Beethoven sonata, he says that the music resides neither in acoustic waves nor annotations on paper: ‘the music is the information’. But where and what is that information? Shannon might say, and Gleick implies, that it is in the pattern of notes that Beethoven conceived. But that’s wrong. The notes become music only in the mind of a listener primed with the cognitive, statistical and cultural apparatus to weave them into coherent and emotive forms. This means there is no bounded information set that is the music – it is different for every listener (and every performance), sometimes subtly, sometimes profoundly. The same for literature.
Lest you imagine that this applies only to information impinging on human cognition, it is equally true of the gene. Gleick too readily accepts the standard trope that genes – the abstract symbolic sequence – contain the information needed to build an organism. That information is highly incomplete. Genes don’t need to supply it all, because they act in a molecular milieu that fills in the gaps. It’s not that the music, or the gene, needs the right context to deliver its message – without that context, there is no message, no music, no gene. An information theory that considers just the signal and neglects the receiver is limited, even misleading.
It is the only serious complaint about what is otherwise a deeply impressive and rather beautiful book.
Tuesday, April 19, 2011
Universal blues
I have written a news story and a leader for Nature on a new paper examining the notion that there are universal grammatical principles in language. Here they are, in that order. But I must say that, much as the results reported by Dunn et al. chime with my instinctive resistance to universal theories of anything, the comments I’ve received on the paper make me a little sceptical that it does what it claims. Time will tell, I suppose.
__________________________________________________________________________
Linguists debate whether languages share universal grammatical features.
Languages evolve in their own idiosyncratic fashion, rather than being governed by universal rules. That’s the conclusion of a new study which compares the grammar of several hundred languages in the light of their evolutionary trees.
Psychologist Russell Gray of the University of Auckland in New Zealand and his coworkers examine the relationships between traits such as the ordering of verbs and nouns in four families representing more than 2,000 languages, and find no sign of any persistent, universal guiding principles [1].
It’s already proving to be a controversial claim. “There is nothing in the paper that brings into question the views that they are arguing against”, says linguist Matthew Dryer of the State University of New York at Buffalo.
There is thought to be around 7,000 languages in the world, which show tremendous diversity in structure. Some have complex ways of making composite words (such as Finnish), others have simple, short and invariant words (such as Mandarin Chinese). Some put verbs first in a sentence, others in the middle and others at the end.
But many linguists suspect there be some universal logic behind this bewildering variety – common cognitive factors that underpin grammatical structures. Two of the most prominent ‘universalist’ theories of language have been proposed by American linguists Noam Chomsky and Joseph Greenberg.
Chomsky tried to account for the astonishing rapidity with which children assimilate complicated and subtle grammatical rules by supposing that we are all born with an innate capacity for language, presumably housed in brain modules specialized for language. He suggested that this makes children able to generalize the grammatical principles of their native tongue from a small set of ‘generative rules’.
Chomsky supposed that languages change and evolve when children reset the parameters of these rules. A single change should induce switches in several related traits in the language.
Greenberg took a more empirical approach, enumerating many observed shared traits between languages. Many of these concerned word order. For example, a conditional clause normally precedes its conclusion: “if he’s right, he’ll be famous.” Greenberg argued that these universals reflect fundamental biases, probably for cognitive reasons. “The Greenbergian word order universals have the strongest claim to empirical validity of any universalist claim about language”, says Gray’s coauthor Michael Dunn of the Max Planck Institute for Psycholinguistics at Nijmegen.
Both of these ideas have implications for the family tree of language evolution. In Chomsky’s case, as languages evolve, certain features should co-vary because they are products of the same underlying parameter. Greenberg’s idea also implies co-dependencies between certain grammatical features of a language but not others. For example, the word order for verb-subject pairs shouldn’t depend on that for object-verb pairs.
To test these predictions, Gray and colleagues used the methods of phylogenetic analysis developed for evolutionary biology to reconstruct four family trees representative of more than 2,000 languages: Austronesian, Indo-European, Bantu and Uto-Aztecan. For each family they looked at eight word-order features and used statistical methods to calculate the changes that each pair of features had evolved independently or in a correlated way. This allowed them to deduce the webs of co-dependence among the features and compare them to what the theories of Chomsky and Greenberg predict.
They found that neither of these two models matched the evidence. Not only do the co-dependencies differ from those expected from Greenberg’s word-order ‘universals’, but they are different for each family. In other words, the deep grammatical structure of each family is different from that of each of the others: each family has evolved its own rules, so there is no reason to suppose that these are governed by universal cognitive factors.
What’s more, even when a particular co-dependency of traits was shared by two families, the researchers could show that it came about in different ways for each – that the commonality may be coincidental. They conclude that the languages – at least in their word-order grammar – have been shaped in culture-specific ways and not by universals.
Other experts express some skepticism about the new results, albeit for rather different reasons. Martin Haspelmath at the Max Planck Institute for Evolutionary Anthropology in Leipzig, Germany, says he agrees with the conclusions but that “for specialists they are nothing new”. “It’s long been known that grammatical properties and dependencies are lineage-specific”, he says.
Meanwhile, Dryer, who has previously presented evidence that supports Greenberg’s position, is not persuaded that the results make a convincing case. “There are over a hundred language families that the authors ignore but which provide strong support for the views they are arguing against”, he says. There is no reason to expect a consistent pattern of word-order relationships within families, he adds, regardless of whether they are shaped by universal constraints.
Haspelmath feels it may be more valuable to look for what languages share in common than how they (inevitably) differ. Even if cultural evolution is the primary factor in shaping them, he says, “it would be very hard to deny that cognitive biases play no role at all.”
“Comparative linguists have focused on the universals and cognitive explanations because they wanted to explain something”, he adds. “Saying that cultural evolution is at play basically means that we can’t explain why languages are the way they are – which is largely true, but it’s not the whole truth.”
1. Dunn, M., Greenhill, S. J., Levinson, S. C & Gray, R. D. Nature 10.1038/nature089923 (2011).
*********************
A search for universals has characterized the scientific enterprise at least since Aristotle. In some ways, this quest for common principles underlying the diversity of the universe defines science: without it there is no order and pattern, but merely as many explanations as there are things in the world. Newton’s laws of motion, the oxygen theory of combustion and Darwinian evolution each united a host of different phenomena in a single explicatory framework.
One view takes this impulse for unification to its extreme: to find a Theory of Everything that offers a single generative equation for all we see. It is becoming ever less clear, however, that such a theory – if it exists – can be considered a simplification, given the proliferation of dimensions and universes it might entail. Nonetheless, unification of sorts remains a major goal.
This tendency in the natural sciences has long been evident in the social sciences too. Darwinism seems to offer justification: if all humans share common origins, it seems reasonable to suppose that cultural diversity must also be traceable to more constrained origins. Just as the bewildering variety of courtship rituals might all be considered forms of sexual selection, so perhaps the world’s languages, music, social and religious customs and even history could be governed by universal features. Filtering out what is contingent and unique from what is shared in common might enable us to understand how complex cultural behaviours arose and what ultimately guides them in evolutionary or cognitive terms.
That, at least, is the hope. But a comparative study of linguistic traits by Dunn et al. (online publication doi:10.1038/nature09923) supplies a sharp reality check on efforts to find universality in the global spectrum of languages. The most famous of these was initiated by Noam Chomsky, who postulated that humans are born with an innate language-acquisition capacity – a brain module or modules specialized for language – that dictates a universal grammar. Just a few generative rules are then sufficient to unfold the entire fundamental structure of a language, which is why children can learn it so quickly. Languages would diversify through changes to the ‘parameter settings’ of the generative rules.
In contrast, Joseph Greenberg took a more empirical approach to universality, identifying a long list of traits (particularly in word order) shared by many languages, which are considered to represent biases that result from cognitive constraints. Chomsky’s and Greenberg’s are not by any means the only theories on the table for how languages evolve, but they make the strongest predictions about universals. Dunn et al. have put them to the test by using phylogenetic methods to examine the four family trees that between them represent over 2,000 languages. A generative grammar should show patterns of language change that are independent of the family tree or the pathway tracked through it, while Greenbergian universality predicts strong co-dependencies between particular types of word-order relations (and not others). Neither of these patterns is borne out by the analysis, suggesting that the structures of the languages are lineage-specific and not governed by universals.
This doesn’t mean that cognitive constraints are irrelevant, nor that there are no other universals dictated by communication efficiency. It’s surely inevitable that cognition sets limits on, say, word length or the total number of phonemes. But such ‘universals’ seem likely to be relatively trivial features of languages, just as may be the case for putative universals in music and other aspects of culture. We should perhaps learn the lesson of Darwinism: a ‘universal’ mechanism of adaptation says little of interest, in itself, about how a particular feature got to be the way it is, or how it works. This truth has dawned on physicists too: universal equations are all very well, but particular solutions are what the world actually consists of, and those particulars are generally the result of contingent history.
__________________________________________________________________________
Linguists debate whether languages share universal grammatical features.
Languages evolve in their own idiosyncratic fashion, rather than being governed by universal rules. That’s the conclusion of a new study which compares the grammar of several hundred languages in the light of their evolutionary trees.
Psychologist Russell Gray of the University of Auckland in New Zealand and his coworkers examine the relationships between traits such as the ordering of verbs and nouns in four families representing more than 2,000 languages, and find no sign of any persistent, universal guiding principles [1].
It’s already proving to be a controversial claim. “There is nothing in the paper that brings into question the views that they are arguing against”, says linguist Matthew Dryer of the State University of New York at Buffalo.
There is thought to be around 7,000 languages in the world, which show tremendous diversity in structure. Some have complex ways of making composite words (such as Finnish), others have simple, short and invariant words (such as Mandarin Chinese). Some put verbs first in a sentence, others in the middle and others at the end.
But many linguists suspect there be some universal logic behind this bewildering variety – common cognitive factors that underpin grammatical structures. Two of the most prominent ‘universalist’ theories of language have been proposed by American linguists Noam Chomsky and Joseph Greenberg.
Chomsky tried to account for the astonishing rapidity with which children assimilate complicated and subtle grammatical rules by supposing that we are all born with an innate capacity for language, presumably housed in brain modules specialized for language. He suggested that this makes children able to generalize the grammatical principles of their native tongue from a small set of ‘generative rules’.
Chomsky supposed that languages change and evolve when children reset the parameters of these rules. A single change should induce switches in several related traits in the language.
Greenberg took a more empirical approach, enumerating many observed shared traits between languages. Many of these concerned word order. For example, a conditional clause normally precedes its conclusion: “if he’s right, he’ll be famous.” Greenberg argued that these universals reflect fundamental biases, probably for cognitive reasons. “The Greenbergian word order universals have the strongest claim to empirical validity of any universalist claim about language”, says Gray’s coauthor Michael Dunn of the Max Planck Institute for Psycholinguistics at Nijmegen.
Both of these ideas have implications for the family tree of language evolution. In Chomsky’s case, as languages evolve, certain features should co-vary because they are products of the same underlying parameter. Greenberg’s idea also implies co-dependencies between certain grammatical features of a language but not others. For example, the word order for verb-subject pairs shouldn’t depend on that for object-verb pairs.
To test these predictions, Gray and colleagues used the methods of phylogenetic analysis developed for evolutionary biology to reconstruct four family trees representative of more than 2,000 languages: Austronesian, Indo-European, Bantu and Uto-Aztecan. For each family they looked at eight word-order features and used statistical methods to calculate the changes that each pair of features had evolved independently or in a correlated way. This allowed them to deduce the webs of co-dependence among the features and compare them to what the theories of Chomsky and Greenberg predict.
They found that neither of these two models matched the evidence. Not only do the co-dependencies differ from those expected from Greenberg’s word-order ‘universals’, but they are different for each family. In other words, the deep grammatical structure of each family is different from that of each of the others: each family has evolved its own rules, so there is no reason to suppose that these are governed by universal cognitive factors.
What’s more, even when a particular co-dependency of traits was shared by two families, the researchers could show that it came about in different ways for each – that the commonality may be coincidental. They conclude that the languages – at least in their word-order grammar – have been shaped in culture-specific ways and not by universals.
Other experts express some skepticism about the new results, albeit for rather different reasons. Martin Haspelmath at the Max Planck Institute for Evolutionary Anthropology in Leipzig, Germany, says he agrees with the conclusions but that “for specialists they are nothing new”. “It’s long been known that grammatical properties and dependencies are lineage-specific”, he says.
Meanwhile, Dryer, who has previously presented evidence that supports Greenberg’s position, is not persuaded that the results make a convincing case. “There are over a hundred language families that the authors ignore but which provide strong support for the views they are arguing against”, he says. There is no reason to expect a consistent pattern of word-order relationships within families, he adds, regardless of whether they are shaped by universal constraints.
Haspelmath feels it may be more valuable to look for what languages share in common than how they (inevitably) differ. Even if cultural evolution is the primary factor in shaping them, he says, “it would be very hard to deny that cognitive biases play no role at all.”
“Comparative linguists have focused on the universals and cognitive explanations because they wanted to explain something”, he adds. “Saying that cultural evolution is at play basically means that we can’t explain why languages are the way they are – which is largely true, but it’s not the whole truth.”
1. Dunn, M., Greenhill, S. J., Levinson, S. C & Gray, R. D. Nature 10.1038/nature089923 (2011).
*********************
A search for universals has characterized the scientific enterprise at least since Aristotle. In some ways, this quest for common principles underlying the diversity of the universe defines science: without it there is no order and pattern, but merely as many explanations as there are things in the world. Newton’s laws of motion, the oxygen theory of combustion and Darwinian evolution each united a host of different phenomena in a single explicatory framework.
One view takes this impulse for unification to its extreme: to find a Theory of Everything that offers a single generative equation for all we see. It is becoming ever less clear, however, that such a theory – if it exists – can be considered a simplification, given the proliferation of dimensions and universes it might entail. Nonetheless, unification of sorts remains a major goal.
This tendency in the natural sciences has long been evident in the social sciences too. Darwinism seems to offer justification: if all humans share common origins, it seems reasonable to suppose that cultural diversity must also be traceable to more constrained origins. Just as the bewildering variety of courtship rituals might all be considered forms of sexual selection, so perhaps the world’s languages, music, social and religious customs and even history could be governed by universal features. Filtering out what is contingent and unique from what is shared in common might enable us to understand how complex cultural behaviours arose and what ultimately guides them in evolutionary or cognitive terms.
That, at least, is the hope. But a comparative study of linguistic traits by Dunn et al. (online publication doi:10.1038/nature09923) supplies a sharp reality check on efforts to find universality in the global spectrum of languages. The most famous of these was initiated by Noam Chomsky, who postulated that humans are born with an innate language-acquisition capacity – a brain module or modules specialized for language – that dictates a universal grammar. Just a few generative rules are then sufficient to unfold the entire fundamental structure of a language, which is why children can learn it so quickly. Languages would diversify through changes to the ‘parameter settings’ of the generative rules.
In contrast, Joseph Greenberg took a more empirical approach to universality, identifying a long list of traits (particularly in word order) shared by many languages, which are considered to represent biases that result from cognitive constraints. Chomsky’s and Greenberg’s are not by any means the only theories on the table for how languages evolve, but they make the strongest predictions about universals. Dunn et al. have put them to the test by using phylogenetic methods to examine the four family trees that between them represent over 2,000 languages. A generative grammar should show patterns of language change that are independent of the family tree or the pathway tracked through it, while Greenbergian universality predicts strong co-dependencies between particular types of word-order relations (and not others). Neither of these patterns is borne out by the analysis, suggesting that the structures of the languages are lineage-specific and not governed by universals.
This doesn’t mean that cognitive constraints are irrelevant, nor that there are no other universals dictated by communication efficiency. It’s surely inevitable that cognition sets limits on, say, word length or the total number of phonemes. But such ‘universals’ seem likely to be relatively trivial features of languages, just as may be the case for putative universals in music and other aspects of culture. We should perhaps learn the lesson of Darwinism: a ‘universal’ mechanism of adaptation says little of interest, in itself, about how a particular feature got to be the way it is, or how it works. This truth has dawned on physicists too: universal equations are all very well, but particular solutions are what the world actually consists of, and those particulars are generally the result of contingent history.
Newton's Rainbow
Here’s the pre-edited text of my review for Nature of a new play about Isaac Newton, which I saw recently at the Royal Society and enjoyed more than I thought I might. But you’ll only catch it now if you’re in Toronto or Boston, I believe.
__________________________________________________________
Let Newton Be!
A play by Craig Baxter, directed by Patrick Morris and produced by the Menagerie Theatre Company
Touring until 30 April
Isaac Newton perplexes and fascinates not just because he was a transitional figure in the history of science but because he was a very odd man. The difficulty has been in distinguishing those two things. The temptation to portray him as a man torn between science and religion, or flitting from mathematical physics to superstitious alchemy, is the modern legacy of a tradition of positivistic science history that today’s historians are still working to dispel. In his passion for none of these things was Newton particularly unusual in his time. What made him odd was not so much what he believed but how he lived: isolated from intimate relationships, sensitive to every slight, at the same time vain and yet so indifferent to adulation that he could barely be persuaded to write the Principia.
All that, quite apart from his towering status in science, naturally makes him an attractive figure for biographers. Among those who have grappled with his story are the leading science historians Richard Westfall (whose 1980 biography is still the standard reference) and A. Rupert Hall, and the science writer James Gleick. It also supplies fertile soil for more inventive explorations of his life, of which Let Newton Be! is one. This new play by Craig Baxter was commissioned by the Faraday Institute for Science and Religion at Cambridge University, and has benefited from the input of, among others, Rob Iliffe, the head of the Newton Project to place all of Newton's writings online, and the astrophysicist John Barrow.
To conjure up this mercurial man, Baxter elected to use almost entirely Newton’s own words, or those of some of his contemporaries, such as his rival and critic Gottfried Leibniz. Moreover, Newton – the only character in the piece, apart from brief appearances by the likes of Leibniz and Edmond Halley – is played here simultaneously by three actors, one of them a woman. It sounds like a gimmick, but isn’t: the device allows us to see different facets of the man, though happily not as reductively conflicting voices.
The play’s structure is largely chronological. We see Newton as a boy in the family home at Woolsthorpe, an undergraduate at Trinity College Cambridge, then as Lucasian professor of mathematics (appointed in 1669 at the age of 27). We see him take his retractable telescope to the Royal Society and, stung by what he perceived as the antagonism of the London virtuosi, retreat into religious exegesis, until Halley cajoles him to write down his proof of elliptical planetary orbits – a treatise that expands into the Principia. Feted and now somewhat pompous, he becomes Warden of the Royal Mint and the President of the Royal Society.
The original material is well used. There is a reconstruction of Newton’s famous prism experiment (or roughly so – his experimentum crucis of around 1666, when he reconstituted white light from the spectrum, is notoriously difficult to reproduce). But we also get Newton’s sometimes surreal, obsessive lists of sins committed (“I lied about a Louse”), and the only time we are lectured to is in one of the real lectures on optics that Newton was obliged to provide in the Lucasian chair, at which he proves to be hilariously inept.
In such ways, the play delivers an impressive quantity of Newton’s thought. In particular, it sets out to emphasize just how much of his work was religious – as Iliffe confirmed in a post-performance panel discussion, Newton considered this his central mission, with the seminal scientific works on light, motion and gravity being almost tossed off before breakfast. The natural theology that motivated much of the science – the idea that by exploring the natural world we deepen our appreciation of God’s wisdom and power – was the conventional position of most seventeenth-century scientists, most notably Robert Boyle, and was their defence against accusations of materialistic atheism. Newton was anything but a materialist: that his gravity was an occult force acting at a distance was precisely what Leibniz considered wrong with it, while for Newton this force was actively God’s doing.
But I’m not sure how much would be comprehensible to anyone coming new to Newton. It is characteristic of the play’s intelligence that we don’t get any nonsense with falling apples, but neither are we really told what distinguished Newton’s ideas on gravity from the many that went before (especially Descartes’ vortices and the belief that it is a form of magnetism, both of which ideas Newton shared at some point). His work on the additive colour mixing of light is beautifully illustrated but not actually alluded to; likewise his laws of motion. Moreover, the play lacks a real narrative – there is no tension, nothing to be resolved, for in the end it is a biography, however inventively told. But that was, after all, its brief, and it is probably a more enjoyable hour and a half with Newton than anyone ever had in his lifetime.
Tuesday, April 12, 2011
The Naked Oceans
The Naked Scientists is (are?) running a series of podcasts called The Naked Oceans. The latest one has an interview with me about Ernst Haeckel and his images of radiolarians.
Monday, April 11, 2011
Chaos promotes prejudice
Here’s my latest news story for Nature, pre-editing.
_______________________________________________________________
A disorderly environment makes people more inclined to put others in boxes.
Messy surroundings make us more apt to stereotype people, according to a new study by a pair of social scientists in the Netherlands.
Diederik Stapel and Siegwart Lindenberg of Tilburg University asked subjects to complete questionnaires that probed their judgements about certain social groups while in everyday environments (a street and a railway station) that were either messy or clean and orderly. They found small but significant and systematic differences in the responses: there was more stereotyping in the former cases than the latter.
The researchers say that social discrimination could therefore be counteracted by diagnosing and removing signs of disorder and decay in public environments. They report their findings in Science today [1].
Psychologist David Schneider of Rice University in Houston, Texas, a specialist in stereotyping, calls this “an excellent piece of work which speaks not only to a possibly important environmental cause, but also supports a major potential theoretical explanation for some forms of prejudice.”
The influence of environment on behaviour has long been suspected by social scientists and criminologists. The ‘broken windows’ hypothesis of sociologists James Q. Wilson and George Kelling supposes that people are more likely to commit criminal and anti-social acts when they see evidence of others having done so – for example, in public places with signs of decay and neglect.
This idea motivated the famous zero-tolerance policy on graffiti on the New York subway in the late 1980s (on which Kelling acted as a consultant), which is credited with a role in improving the safety of the network. Lindenberg and his coworkers conducted experiments in Dutch urban settings in 2008 that supported an influence of the surroundings on people’s readiness to act unlawfully or antisocially [2].
But could evidence of social decay, even at the mild level of littering, also affect our unconscious discriminatory attitudes towards other people? To test that possibility, Stapel and Lindenberg devised a variety of disorderly environments in which to test these attitudes.
In their questionnaires, participants were asked for example to rate Muslims, homosexuals and Dutch people according to various positive, negative and unrelated stereotypes. For example, the respective stereotypes for homosexuals were (creative, sweet), (strange, feminine) and (impatient, intelligent).
In one experiment, passers-by in the busy Utrecht railway station were asked to participate by coming to sit in a row of chairs, for the reward of a candy bar or an apple. The researchers took advantage of a cleaners’ strike, which had left the station dirty and litter-strewn. They then returned to do the same testing after the strike was over and the station was clean.
As well as probing these responses, the experiment examined unconscious negative responses to race. All the participants were white, while one place at the end of the row of chairs was already taken by a black or white Dutch person. In the messy station, people sat on average further from the black person than the white one, while in the clean station there was no statistical difference in these distances.
In another experiment, the researchers aimed to eliminate differences in cleanliness of the environments while preserving the disorder. The participants were approached on a street in an affluent Dutch city. But in one case the street had been made more disorderly by the removal of a few paving slabs and the addition of a badly parked car and an ‘abandoned’ bicycle. Again, disorder boosted stereotyping.
Stapel and Lindenberg suspect that stereotyping may be an attempt to compensate for mess: it could be, they say, “a way to cope with chaos, a mental cleaning device” that partitions other people neatly into predefined categories.
In support of that idea, they showed participants pictures of disorderly and orderly situations, such as a bookcase with dishevelled and regularly stacked books, before asking them to complete both the stereotyping survey and another one that probed their perceived need for structure, including questions such as “I do not like situations that are uncertain”. Both stereotyping and the need for structure were higher in people viewing the disorderly pictures.
Sociologist Robert Sampson of Harvard University says that the study is “clever and well done”, but is cautious about how to interpret the results. “Disorder is not necessarily chaotic’, he says, “and is subject to different social meanings in ongoing or non-manipulated environments. There are considerable subjective variations within the same residential environment on how disorder is rated – the social context matters.”
Therefore, Sampson says, “once we get out of the lab or temporarily induced settings and consider the everyday contexts in which people live and interact, we cannot simply assume that interventions to clean up disorder will have invariant effects.”
Schneider agrees that the implications of the work for public policy are not yet clear. “One question we’d need to answer is how long these kinds of effects last”, he says. “There is a possibility that people may quickly adapt to disorder. So I would be very wary of concluding that people who live in unclean and disordered areas are more prejudiced because of that.” Stapel acknowledges this: “people who constantly live in disorder get used to it and will not show the effects we find. Disorder in our definition is something that is unexpected.”
References
1. D. A. Stapel & S. Lindenberg, Science 332, 251-253 (2011).
2. K. Keizer, S. Lindenberg & L. Steg, Science 322, 1681 (2008).
Tuesday, April 05, 2011
Fattening up Schrödinger's cats
Here’s my latest story for Nature News.
__________________________________________________________
Huge molecules can show the wave-particle duality of quantum theory.
Researchers in Austria have made what they call the “fattest Schrödiner cats realized to date”. They have demonstrated quantum superpositions – objects in two or more states simultaneously – of molecules with up to 430 atoms each, several times larger than those used in previous experiments of this sort [1].
In the famous thought experiment conceived by Erwin Schrödinger in 1935 to illustrate the apparent paradoxes of quantum theory, a cat will be poisoned or not depending on the state of an atom, governed by quantum rules. Because the recently developed quantum theory insisted that these rules allowed for superpositions, it seemed that Schrödinger’s cat could itself be placed in a superposition of ‘live’ and ‘dead’ states.
The paradox highlights the question of how the rules of the quantum world – where objects like atoms can be in several positions at once – give way to the ‘classical’ mechanics that governs the macroscopic world of our everyday experience, in which things must be one way or the other but not both at the same time. This is called the quantum-to-classical transition.
It is now generally thought that the ‘quantumness’ is lost in a process called decoherence, where disturbances from the surrounding environment make the quantum wavefunction describing many-state superpositions appear to collapse [note to subs: we have to keep this ‘appear to’. The precise relationship between decoherence and wavefunction collapse is complicated and too tricky fully get into here] into a well-defined and unique classical state. This decoherence tends to become more pronounced as objects get bigger and the opportunities for interacting with the environment multiply.
There is still no consensus on how Schrödinger’s thought experiment will play out if the cat-and-atom system could be perfectly protected from decoherence. Some physicists are happy to believe that in that case the cat could indeed be in a live-dead superposition. But we couldn’t see it directly because the act of looking would destroy the superposition.
One manifestation of quantum superpositions is the interference that can occur between quantum particles passing through two or more narrow slits. In the classical world the particles just pass through with their trajectories unchanged, like footballs rolling through a doorway.
But quantum particles can behave like waves, which interfere with one another as they pass through the slits, either enhancing or cancelling to produce a series of bright and dark bands. This interference of quantum particles, first seen for electrons in 1927, is effectively the result of each particles passing through more than one slit: a quantum superposition.
At some point as the experiment is scaled up in size, quantum behaviour (interference) should give way to classical behaviour (no interference). But how big can the particles be before that happens?
In 1999 a team at the University of Vienna in Austria demonstrated interference in a many-slit experiment using beams of 60-atom carbon molecules (C60) shaped like hollow spheres [2]. Now Markus Arndt, one of the researchers in that experiment, and his colleagues in Austria, Germany and Switzerland have shown much the same effect for considerably larger molecules tailor-made for the purpose, up to 6 nanometres (millionths of a millimetre) across and composed of up to 430 atoms. These are bigger than some small protein molecules in the body, such as insulin.
In their experiment, the beams of molecules are passed through three sets of slits. The first of them, made from a slice of the hard material silicon nitride patterned with a grating of 90-nm-wide slits, prepares the molecular beam in a coherent state, in which the matter waves are all in step. The second, a ‘virtual grating’ made from laser light formed by mirrors into a standing wave of light and dark, causes the inference pattern. The third grating, also of silicon nitride, acts as a mask to admit parts of the interference pattern to an instrument called a mass spectrometer, which counts the number of molecules that pass through.
The researchers report in Nature Communications that this number rises and falls periodically as the outgoing beam is scanned from left to right, showing that interference, and therefore superposition, is present.
Although this might not sound like a Schrödinger cat experiment, it probes the same quantum effects. It is essentially like firing the cats themselves at the interference grating, rather than making a single cat’s fate contingent on an atomic-scale event.
Quantum physicist Martin Plenio of the University of Ulm in Germany calls the study part of an important line of research. “We have perhaps not gained deep new insights into the nature of quantum superposition from this specific experiment”, he admits, “but there is hope that with increasing refinement of the experimental technique we will eventually discover something new.”
Arndt says that such experiments might eventually enable tests of fundamental aspects of quantum theory, such as how wavefunctions are collapsed by observation. “Predictions such as that gravity might induce wavefunction collapse beyond a certain mass limit should become testable at significantly higher masses in far-future experiments”, he says.
Can living organisms – perhaps not cats, but maybe microscopic ones such as bacteria – be placed in superpositions? That has been proposed for viruses [3], the smallest of which are just a few nanometres across – although there is no consensus about whether viruses should be considered truly alive. “Tailored molecules are much easier to handle in such experiments than viruses”, says Arndt. But he adds that if various technical issues can be addressed, “I don’t see why it should not work.”
References
1. Gerlich, S. et al., Nat. Commun. online publication doi:10.1038/ncomms1263.
2. Arndt, M. et al., Nature 401, 680-682 (1999).
3. Romero-Isart, O., Juan, M. L., Quidant, R. & Cirac, J. I. New J. Phys. 12, 033105 (2010).
Monday, March 28, 2011
Who's (still) afraid of MMR?
With the fallout from the MMR scare still with us, this programme on BBC Radio 4 is a timely reminder of the issues. “Science betrayed” indeed, but by whom? The full story is societal as much as it is biomedical. Anyway, listen while you still can.
Friday, March 25, 2011
More monster myths
I have reviewed the National Theatre’s production of Frankenstein in the latest issue of Nature. Worth seeing (though if you haven’t got a ticket already, you don’t stand much chance), but I was slightly disappointed in the end, having seen some glowing reviews. There’s another perspective here.
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Mary Shelley’s Frankenstein has been endlessly adapted and reinterpreted since it was first published, anonymously, in 1818. Aside from the iconic screen version by James Whale in 1931, there have been sequels, parodies (Mel Brooks’ Young Frankenstein, The Rocky Horror Picture Show), and postmodern interpolations (Brain Aldiss’s Frankenstein Unbound). Victor Frankenstein has become the archetypal mad scientist, unleashing powers he cannot control – in one recent remake, he became a female biologist experimenting on organ regeneration with stems cells. The ‘Franken’ label is attached to every new technology that appears to intervene in life, from genetic modification of crops to Craig Venter’s ‘synthetic’ microbe.
This reinvention is no recent phenomenon. Shelley’s book was little known until the first stage adaptations began in the 1820s, in which Frankenstein’s creature was already transformed into a mute, shambling brute based on the stock theatrical character of the Wild Man. This personification continued in the first film adaptation in 1910, simply called Frankenstein.
Some might lament how the original novel has been distorted and vulgarized. But literary critic Chris Baldick has a wiser perspective:
The truth of a myth… is not to be established by authorizing its earliest versions, but by considering all its versions… That series of adaptations allusions, accretions, analogues, parodies and plain misreadings which follows up on Mary Shelley’s novel is not just a supplementary component of the myth; it is the myth.
After all, there isn’t even a definitive version of Shelley’s story. She made small but significant changes in the third edition (1831), in particular emphasizing the Faustian themes of presumption and retribution on which the early stage versions insisted.
Besides, critics still dispute what Shelley’s message was meant to be – probably she was not fully conscious of all the themes herself. Far from offering a simplistic critique of scientific hubris, the story might instead echo Shelley’s troubled family life. Her mother, the feminist and political radical Mary Wollstonecraft, died from complications after Mary’s birth, and her father William Godwin all but disowned her after she eloped to Europe with Percy Shelley in 1814. She lost her first child, named William, that year, subsequently describing a dream in which the boy was reanimated. There is ample reason to believe Percy Shelley’s statement of the central moral of Frankenstein: ‘Treat a person ill, and he becomes wicked’.
If so, Nick Dear’s adaptation of the story for the National Theatre in London, directed by Danny Boyle of Trainspotting and Slumdog Millionaire fame, has returned to the essence of the tale. For it focuses on the plight of the creature, whose lone and awkward ‘birth’ begins the play. We see how this mumbling wretch, spurned as a hideous thing by Victor, is reviled by society until finding refuge with the blind peasant De Lacey. The kindly old man teaches the creature how to speak and read using Milton’s Paradise Lost, the story of Satan’s Promethean challenge to heaven.
Eventually De Lacey’s son and daughter-in-law return from the fields and drive out the creature in horror, whereupon he burns them in their cottage. These scenes are the moral core of Shelley’s novel, and in placing them so early Dear signals that this is very much the monster’s show.
In fact, perhaps too much. For while the creature is the most fully realised, most sympathetic and inventive incarnation I have seen, Victor Frankenstein is left with little to do but recoil from him and neglect all his other duties, martial, filial and moral. It is very clear from the outset who is the real monster.
In this production the two lead actors – Benedict Cumberbatch and Jonny Lee Miller – alternate the roles of Victor and his creature. This Doppelgänger theme is not a new idea: in the stage adaptation by Peggy Webling that formed the basis of Whale’s movie, the creature appeared dressed like Victor (there renamed Henry), who foreshadows the later confusion of creator and creature by saying ‘I call him by my own name – he is Frankenstein.’ It motivates Dear’s decision to leave the duo locked in mutual torment at the end: a vision more true to their relationship than that of the novel itself.
The scientific elements of the tale are skated over. Mary Shelley provided just enough hints for the informed reader to make the connection with Luigi Galvani’s recent work on electrophysiology; Dear has Frankenstein mention galvanism and electrochemistry (somewhat anachronistically), but that is as far as it goes. There is no serious attempt, therefore, to make the play a comment on the ‘Promethean ambitions’ of modern science (as Pope John Paul II called them in 2002) – a relief not because modern science is unblemished but because the alchemical trope of a solitary experimenter exceeding the bounds of God and nature is no longer the relevant vehicle for a critique.
The staging of this production is spectacular, and intelligent choices were made in the structure (if not always in the dialogue). Miller was extraordinary as the creature on the night I saw it; by all accounts Cumberbatch is equally so. Whether Dear adds anything new to the legend – as Whale and even Mel Brooks did – is debatable. But it is well to be reminded that the novel may be read not so much as a Gothic tale of monstrosity and presumption but as a comment on the consequences of how we treat one another.
Wednesday, March 23, 2011
Maths polymath scoops Abel Prize
Here’s a little news story I wrote for Nature on the Abel Prize. This award presents a notoriously challenging subject for science reporters each year, because it is always the devil of a job concisely to explain what on earth the recipient has done to deserve the award. I can’t deny that the same challenge applied here, but in spades, because Milnor has done so much. But it was a challenge I enjoyed. Given the choice, I’d have personally kept in the edited version the fact that holomorphic dynamics involves numbers in the complex plane, because it is the kind of thing experts will sniffily point out. But I can understand the fear that the reader will be exhausted by then. Ah, mathematics – what a wonderful, strange game it is.
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John Milnor wins the ‘Nobel of maths’ for his manifold works.
Awarding Albert Einstein a Nobel prize for his research on the photoelectric effect looks in retrospect like a somewhat arbitrary choice from among the galaxy of his contributions to all of physics.
In granting the 2011 Abel Prize in mathematics to John Milnor of Stony Brook University in New York, the committee of the Norwegian Academy of Science and Letters has wisely abandoned any such attempt to single out a particular achievement. The citation states merely that Milnor has made ‘pioneering discoveries in topology, geometry and algebra’: in effect a recognition that he has contributed to modern maths across the board.
In fact, Milnor’s work goes further: it also touches on dynamical systems, game theory, group theory and number theory. In awarding this equivalent of a Nobel prize, worth around $1m, the committee states that “All of Milnor’s works display marks of great research: profound insights, vivid imagination, elements of surprise, and supreme beauty.”
His breadth is unusual, says Professor Ragni Piene of the University of Oslo, the chair of the Abel Prize committee. “Though some of the fields he has worked in are related, he really has had to learn and develop new tools and new theory.”
Milnor “says is mainly a problem solver”, adds Piene. “But in the solving process, in order to understand the problem deeply he ends up creating new theories and opening up new fields.”
Among the most surprising of Milnor’s discoveries was the existence of so-called exotic spheres, multidimensional objects with strange topological properties. In 1956 Milnor was studying the topological transformations of smooth-contoured high-dimensional shapes – that is, shapes with no sharp edges. A so-called continuous topological transformation converts one object smoothly – as though remoulding soft clay – into another, without any tears in the fabric.
He discovered that in seven-dimensions there exist smooth objects that can be converted into the 7D equivalent of spheres only via intermediates that do have sharp kinks. In other words, the only way to get from one of these smooth objects to another is by making them not smooth. Kinks and corners in a surface are said to make it non-differentiable, which means that its curvature at the kinks has no well-defined value.
These counter-intuitive exotic spheres can exist in other dimensions too. With the French mathematician Michel Kervaire, Milnor calculated that there are precisely 28 exotic spheres in seven dimensions. But there seems at first glance little rhyme or reason to the trend for other dimensions: there is just one exotic sphere in 1, 2, 3, 5 and 6 dimensions, but 992 in 11 dimensions, 1 in 12 dimensions, 16,256 in 15D, and 2 in 16D. No one has yet figured out how many there are in four dimensions. This work spawned an entire new field of mathematics, called differential topology.
Some of Milnor’s other achievements are recognizably related to such topological conundrums, such as his work on the relationships between different triangulations (representations as networks of triangles) of mathematical surfaces called manifolds. Topology was also central to some of Milnor’s earliest work in 1950 on the curvature of knots.
But his work on group theory is quite different. Group theory was partly invented by the nineteenth-century Norwegian mathematician Niels Henrik Abel, after whom the award is named. In the formulation developed by Abel, a group can be represented as all non-equivalent combinations (‘words’) of a set of symbols. Milnor and the Czech mathematician Frantisek Wolf clarified how the number of words grows as the number of symbols increases for a wide class of groups called solvable groups.
More recently, Milnor, now 80, has been working in the field of holomorphic dynamics, which concerns the trajectories generated in the plane of real and imaginary numbers by iterating equations: the branch of maths that led to the discovery of fractal patterns such as the Mandelbrot and Julia sets.
Milnor has already won just about every other key prize in mathematics, including the Fields medal (1962) and the Wolf prize (1989). But beyond his skills as a researcher, Milnor has been widely praised as a communicator. His books “have become legendary for their high quality”, according to mathematician Timothy Gowers of the University of Cambridge.
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