Here’s a piece I wrote for the Prospect blog on the physics Nobel. For my Prospect article on the renaissance of interest in the foundations of quantum theory, see here.
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There’s never been a better time to be a quantum physicist. The foundations of quantum theory were laid about a hundred years ago, but the subject is currently enjoying a renaissance as modern experimental techniques make it possible to probe fundamental questions that were left hanging by the subject’s originators, such as Albert Einstein, Niels Bohr, Erwin Schrödinger and Werner Heisenberg. We are now not only getting to grapple with the alleged weirdness of the quantum world, but also putting its paradoxical principles to practical use.
This is reflected in the fact that three physics Nobel prizes have been awarded since 1997 in the field of quantum optics, the most recent going this year to Serge Haroche of the Collège de France in Paris and David Wineland of the National Institute of Standards and Technology in Boulder, Colorado. It’s ‘quantum’ because the work of these two scientists is concerned with examining the way atoms and other small particles are governed by quantum rules. And it’s ‘optics’ because they use light to do it. Indeed, light is itself described by quantum physics, being composed (as Einstein’s Nobel-winning work of 1905 showed) of packets of energy called photons. The word ‘quantum’ was coined by Max Planck in 1900 to describe this discrete ‘graininess’ of the world at the scale of atoms.
The basic principle of a quantum particle is that its energy is constrained to certain discrete amounts, rather than being changeable gradually. Whereas a bicycle wheel can spin at any speed (faster speeds corresponding to more energy), a quantum wheel may rotate only at several distinct speeds. And it may jump between them only if supplied with the right amount of energy. Atoms make these ‘quantum jumps’ between energy states when they absorb photons with the right energy – this in turn being determined by the photon’s wavelength (light of different colours has different wavelengths).
Scientists since Planck’s time have been using light to study these quantum states of atoms. The trouble is that this entails changing the state in order to observe it. Haroche and Wineland have pioneered methods of probing quantum states without destroying them. That’s important not just to examine the fundamentals of quantum theory but for some applications of quantum behaviour, such as high-precision atomic clocks (central to GPS systems) and superfast quantum computers.
Wineland uses ‘atom traps’ to capture individual electrically charged atoms (ions) in electric fields. One counter-intuitive conclusion of quantum theory is that atoms can exist in two or more different quantum states simultaneously, called superpositions. These are generally very delicate, and destroyed when we try to look at them. But Wineland had mastered ways to probe superpositions of trapped ions with laser light without unravelling them. Haroche does the opposite: he traps individual photons of light between two mirrors, and fires atoms through the trap that detect the photon’s quantum state without disturbing it.
‘Reading out’ quantum states non-destructively is a trick needed in quantum computers, in which information is encoded in quantum superpositions so that many different states can be examined at once – a property that would allow some problems to be solved extremely fast. Such a ‘quantum information technology’ is steadily becoming reality, and it is doubtless this combination of fundamental insight and practical application that has made quantum optics so popular with Stockholm. Quantum physics might still seem other-worldly, but we’ll all be making ever more use of it.
Sunday, October 14, 2012
Friday, October 12, 2012
Don't take it too hard
This one appeared yesterday on Nature news.
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A study of scientific papers’ histories from submission to publication unearths some unexpected patterns
Just had your paper rejected? Don’t worry – that might boost its eventual citation tally. An excavation of the usually hidden trajectories of scientific papers from journal to journal before publication has found that papers published in a journal after having first been submitted and rejected elsewhere receive significantly more citations on average than ones submitted only to that journal.
This is one of the unexpected insights offered by the study, conducted by Vincent Calcagno of the French Institute for Agricultural Research in Sophia-Antipolis and his colleagues [1]. They have tracked the submission histories of 80,748 scientific articles published among 923 journals between 2006 an 2008, based on the information provided by the papers’ authors.
Using this information, the researchers constructed a network of manuscript flows: a link exists between two journals if a manuscript initially submitted to one of them was rejected and subsequently submitted to the other. The links therefore have a directional character, like flows in a river network.
“The authors should be commended for assembling this previously hidden data”, says physicist Sidney Redner of Boston University, a specialist on networks of scientific citation.
Some of what Calcagno and colleagues found was unsurprising. On the whole, the network was modular, composed of distinct clusters that corresponded to subject categories, such as plant sciences, genetics and developmental biology, and with rather little movement of manuscripts between journals in different categories.
It’s no surprise too that the highest-impact journals, such as Nature and Science, are central to the network. What was less expected is that these journals publish a higher proportion of papers of papers previously submitted elsewhere, relative to more specialized and lower-impact publications.
“We expected the opposite trend, and the result is at first sight paradoxical”, says Calcagno. But Michael Schreiber, an expert in bibliometrics at the Technical University of Chemnitz in Germany, argues that this “is not surprising if you turn it around: it means that lower-impact journals get fewer resubmissions.” For one thing, he says, there are more low-impact journals, so resubmissions are more widely spread. And second, low-impact journals will have a lower threshold for acceptance and so will accept more first-time submissions.
On the whole, however, there are surprisingly few resubmissions. Three-quarters of all published papers appear in the journal to which they are first submitted. This suggests that the scientific community is rather efficient at figuring out where their papers are best suited. Calcagno says he found this surprising: “I expected more resubmissions, in view of the journal acceptance rates I was familiar with.”
Although the papers in this study were all in the biological sciences, the findings show some agreement with a previous study of papers submitted to the leading chemistry journal Angewandte Chemie, which found that most of those rejected ended up being published in journals with a lower impact factor [2].
Whether the same trends will be found for other disciplines remains to be seen, however. “There are clear differences in publication practices of, say, mathematics or economics”, says Calcagno, and he thinks these might alter the proportions of resubmissions.
Perhaps the most surprising finding of the work is that papers published after having been previously submitted to another journal are more highly cited on average than papers in the same journal that haven’t been – regardless of whether the resubmissions moved to journals with higher or lower impact.
Calcagno and colleagues think that this reflects the improving influence of peer review: the input from referees and editors makes papers better, even if they get rejected initially.
It’s a heartening idea. “Given the headaches encountered during refereeing by all parties involved, it is gratifying that there is some benefit, at least by citation counts”, says Redner.
But that interpretation has yet to be verified, and contrasts with previous studies of publication histories which found that very few manuscripts change substantially between initial submission and eventual publication [2].
Nonetheless, there is apparently some reason to be patient with your paper’s critics – they’ll do you good in the end. “These results should help authors endure the frustration associated with long resubmission processes”, say the researchers.
On the other hand, the conclusions that Schreiber draws for journal editors might please authors less: “Reject more, because more rejections improve quality.”
References
1. Calcagno, V. et al., Science Express doi: 10.1126/science.1227833 (2012).
2. Bornmann, L. & Daniel, H.-D. Angew. Chem. Int. Ed. 47, 7173-7178 (2008).
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A study of scientific papers’ histories from submission to publication unearths some unexpected patterns
Just had your paper rejected? Don’t worry – that might boost its eventual citation tally. An excavation of the usually hidden trajectories of scientific papers from journal to journal before publication has found that papers published in a journal after having first been submitted and rejected elsewhere receive significantly more citations on average than ones submitted only to that journal.
This is one of the unexpected insights offered by the study, conducted by Vincent Calcagno of the French Institute for Agricultural Research in Sophia-Antipolis and his colleagues [1]. They have tracked the submission histories of 80,748 scientific articles published among 923 journals between 2006 an 2008, based on the information provided by the papers’ authors.
Using this information, the researchers constructed a network of manuscript flows: a link exists between two journals if a manuscript initially submitted to one of them was rejected and subsequently submitted to the other. The links therefore have a directional character, like flows in a river network.
“The authors should be commended for assembling this previously hidden data”, says physicist Sidney Redner of Boston University, a specialist on networks of scientific citation.
Some of what Calcagno and colleagues found was unsurprising. On the whole, the network was modular, composed of distinct clusters that corresponded to subject categories, such as plant sciences, genetics and developmental biology, and with rather little movement of manuscripts between journals in different categories.
It’s no surprise too that the highest-impact journals, such as Nature and Science, are central to the network. What was less expected is that these journals publish a higher proportion of papers of papers previously submitted elsewhere, relative to more specialized and lower-impact publications.
“We expected the opposite trend, and the result is at first sight paradoxical”, says Calcagno. But Michael Schreiber, an expert in bibliometrics at the Technical University of Chemnitz in Germany, argues that this “is not surprising if you turn it around: it means that lower-impact journals get fewer resubmissions.” For one thing, he says, there are more low-impact journals, so resubmissions are more widely spread. And second, low-impact journals will have a lower threshold for acceptance and so will accept more first-time submissions.
On the whole, however, there are surprisingly few resubmissions. Three-quarters of all published papers appear in the journal to which they are first submitted. This suggests that the scientific community is rather efficient at figuring out where their papers are best suited. Calcagno says he found this surprising: “I expected more resubmissions, in view of the journal acceptance rates I was familiar with.”
Although the papers in this study were all in the biological sciences, the findings show some agreement with a previous study of papers submitted to the leading chemistry journal Angewandte Chemie, which found that most of those rejected ended up being published in journals with a lower impact factor [2].
Whether the same trends will be found for other disciplines remains to be seen, however. “There are clear differences in publication practices of, say, mathematics or economics”, says Calcagno, and he thinks these might alter the proportions of resubmissions.
Perhaps the most surprising finding of the work is that papers published after having been previously submitted to another journal are more highly cited on average than papers in the same journal that haven’t been – regardless of whether the resubmissions moved to journals with higher or lower impact.
Calcagno and colleagues think that this reflects the improving influence of peer review: the input from referees and editors makes papers better, even if they get rejected initially.
It’s a heartening idea. “Given the headaches encountered during refereeing by all parties involved, it is gratifying that there is some benefit, at least by citation counts”, says Redner.
But that interpretation has yet to be verified, and contrasts with previous studies of publication histories which found that very few manuscripts change substantially between initial submission and eventual publication [2].
Nonetheless, there is apparently some reason to be patient with your paper’s critics – they’ll do you good in the end. “These results should help authors endure the frustration associated with long resubmission processes”, say the researchers.
On the other hand, the conclusions that Schreiber draws for journal editors might please authors less: “Reject more, because more rejections improve quality.”
References
1. Calcagno, V. et al., Science Express doi: 10.1126/science.1227833 (2012).
2. Bornmann, L. & Daniel, H.-D. Angew. Chem. Int. Ed. 47, 7173-7178 (2008).
The lightning seeds
Here’s my previous piece for BBC Future. A new one just went up – will add that soon. This Center for Lightning Research in Florida looks fairly awesome, as this picture shows – that’s what I call an experiment!
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It seems hard to believe that we still don’t understand what causes lightning during thunderstorms – but that’s a fact. One idea is that they are triggered by particles streaming into the atmosphere from space, which release showers of electrons that seed the strike. A new study interrogates that notion and finds that, if there’s anything in it, it’s probably not quite in the way we thought.
Famously, Benjamin Franklin was one of the first people to investigate how lightning is triggered. He was right enough to conclude that lightning is a natural electrical discharge – those were the early days of harnessing electricity – but it’s not clear that his celebrated kite-and-key experiment ever went beyond a mere idea, not least because the kite was depicted, in Franklin’s account, as being flown – impossibly – out of a window.
In some ways we’ve not got much further since Franklin. It’s not yet agreed, for example, how a thundercloud gets charged up in the first place. Somehow the motions of air, cloud droplets, and precipitation (at that altitude, ice particles) conspire to separate positive from negative charge at the scale of individual molecules. It seems that ice particles acquire electrical charge as they collide, rather as rubbing can induce static electricity, and that somehow smaller ice particles tend to become positively charged while larger ones become negatively charged. As the small particles are carried upwards by convection currents, the larger ones sink under gravity, and so their opposite charges get separated, creating an electrical field. A lightning strike discharges this field – it is basically a gigantic spark jumping between the ‘live wire’ and the ‘earth’ of an electrical circuit, in which the former is the charged cloud and the latter is literally the earth.
While many details of this process aren’t at all clear, one of the biggest mysteries is how the spark gets triggered. For the electrical fields measured in thunderclouds don’t seem nearly big enough to induce the so-called ‘electrical breakdown’ needed for a lightning strike, in which air along the lightning path becomes ionized (its molecules losing or gaining electrons to become electrically charged.) It’s rather as if a spark were to leap spontaneously out of a plug socket and hit you – the electric field just isn’t sufficient for that to happen.
Something is therefore needed to ‘seed’ the lightning discharge. In 1997 Russian scientist Alexander Gurevich and his coworkers in Moscow suggested that perhaps the seed is a cosmic ray: a particle streaming into the atmosphere from outer space at high energy. These particles – mostly protons and electrons – pervade the universe, being produced in awesomely energetic astrophysical processes, and they are constantly raining down on Earth. If a cosmic ray collides with an air molecule, this can kick out a spray of fundamental particles and fragments of nuclei. Those in turn interact with other molecules, ionizing them and generating a shower of electrons.
In the electric field of a thundercloud, these electrons are accelerated, much as particles are in a particle accelerator, creating yet more energetic collisions in a ‘runaway’ process that builds into a lightning strike. This process is also expected to produce X-rays and gamma-rays, which are spawned by ‘relativistic’ electrons that have speeds approaching the speed of light. Since bursts of these rays have been detected by satellites during thunderstorms, Gurevich’s idea of cosmic-ray-induced lightning seemed plausible.
If it’s right, the avalanche of electrons should also generate radio waves, which would be detectable from the ground. Three years ago Joseph Dwyer of the Florida Institute of Technology began trying to detect such radio signals from thunderstorms, as well as using arrays of particle detectors to look for the showers of particles predicted from cosmic-ray collisions. These and other studies by Dwyer and other groups are still being conducted (literally) at the International Center for Lightning Research and Testing at the US Army base of Camp Blanding in Florida.
But meanwhile, Dwyer has teamed up with Leonid Babich and his colleagues at the Russian Federal Nuclear Center in Sarov to delve further into the theory of Gurevich’s idea. (The Russian pre-eminence in this field of the electrical physics of the atmosphere dates from the cold-war Soviet era.) They have asked whether the flux of high-energy cosmic-rays, with their accompanying runaway electron avalanches, is sufficient to boost the conductivity of air and cause a lightning strike.
To do that, the researchers have worked through the equations describing the chances of cosmic-ray collisions, the rate of electron production and the electric fields this induces. The equations are too complicated to be solved by hand, but a computer can crunch through the numbers. And the results don’t look good for Gurevich’s hypothesis: runaway electron avalanches produced by cosmic-ray showers just don’t seem capable of producing electrical breakdown of air and lightning discharge.
However, all is not lost. As well as the particle cascades caused by collisions of high-energy cosmic rays, the atmosphere can also be electrified by the effects of cosmic rays with lower energy, which are more plentiful. When these collide with air molecules, the result is nothing like as catastrophic: they simply ionize the molecules. But a gradual build-up of such ionized particles within a thundercloud could, according to these calculations, eventually produce a strong enough electrical field to permit a lightning discharge. That possibility has yet to be investigated in detail, but Dwyer and colleagues think that it leaves an avenue still open for cosmic rays to lie at the origin of thunderbolts.
Paper: L. P. Babich, E. I. Bochkov, J. R. Dwyer & I. M. Kutsyk, Journal of Geophysical Research 117, A09316 (2012).
Monday, October 08, 2012
Chemists get the blues
Just got back from judging the Chemistry World science writing competition. Makes me feel old, or perhaps just reminds me that I am. Anyway, many congratulations to the winner Chris Sinclair, whose article I believe will appear soon in Chemistry World. Meanwhile, here is my last Crucible column.
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“Ultramarine blue is a colour illustrious, beautiful, and most perfect, beyond all other colours”, wrote the Italian artist Cennino Cennini in the late fourteenth century. He and his contemporaries adored this mineral pigment for its rich, deep lustre. But they didn’t use it much, at least not unless they had a particularly rich client, because it was so costly. As the name implies, it came from ‘over the seas’ – all the way from what is now Afghanistan, where mines in the remote region of Badakhshan were the only known source of the parent mineral, lapis lazuli, for centuries. Not only was ultramarine expensive to import, but it was laborious to make from the raw material, in a process of grinding and repeated washing that separated the blue colorant from impurities. So ultramarine could cost more than its weight in gold, and painters reserved it for the most precious parts of their altarpieces, especially the robes of the Virgin Mary.
Blue has always been a problem for artists. One of the first synthetic pigments, Egyptian blue (calcium copper silicate), was pale. The best mineral alternative to ultramarine, called azurite (hydrous copper carbonate), was more readily accessible but greenish rather than having ultramarine’s glorious purple-reddish tinge. Around 1704 a misconceived alchemical experiment yielded Prussian blue (iron ferrocyanate), which is blackish, prone to discolour, and decomposes to hydrogen cyanide under mildly acidic conditions. The discovery of cobalt blue (cobalt aluminate) in 1802, followed by a synthetic route to ultramarine in 1826, seemed to solve these problems of hue, stability and cost, but even these ‘artificial’ blues have drawbacks: cobalt is rather toxic, and ultramarine is sensitive to heat, light and acid, which limits its use in some commercial applications.
This is why the identification of a new inorganic blue pigment in 2009 looked so promising. Mas Subramanian and coworkers at Oregon State University found that trivalent manganese ions produce an intense blue colour, with the prized ‘reddish’ shade of ultramarine, when they occupy a trigonal bipyramidal site in metal oxides [1]. The researchers substituted Mn3+ for some indium ions in yttrium indium oxide (YInO3), forming a solid solution of YInO3 and YMnO3, which has a blue colour even though the two oxides themselves are white and black respectively. The depth of the colour varies from pale to virtually black as the manganese content is increased, although it is significantly blue even for only about 2 percent substitution. The researchers found that inserting manganese into other metal oxides with the same coordination geometry also offers strong blues. Meanwhile, similar substitutions of iron (III) and copper (II) generate bright orange and green pigments [2,3]. Those are traditionally less problematic, however, and while the materials may prove to have useful magnetic properties, it’s the blue that has attracted colour manufacturers.
Producing a commercially viable pigment is much more than a matter of finding a strongly coloured substance. It must be durable, for example. Although ultramarine, made industrially from cheap ingredients, is now available in quantities that would have staggered Titian and Michelangelo, it fades in direct sunlight because the sodalite framework is degraded and the sulphur chromophores are released and decompose – a process only recently understood [4]. This rules out many uses for exterior coatings. In contrast, the manganese compound has good thermal, chemical and light stability.
One of the key advantages of the YIn1-xMnxO3 compounds over traditional blues, however, is their strong reflectivity in the near-infrared region. Many other pigments, including cobalt blue and carbon black, have strong absorption bands here. This means that surfaces coated with these pigments heat up when exposed to strong sunlight. Building roofs coloured with such materials become extremely hot and can increase the demand of air conditioning in hot climates; instrument panels and steering wheels of cars may become almost too hot to touch. That’s why there is a big industrial demand for so-called ‘cool’ pigments, which retain their absorbance in the visible region but have low absorbance in the infrared. These can feel noticeably cooler when exposed to sunlight.
This aspect in particular has motivated the Ohio-based pigment company Shepherd Color to start exploring the commercial potential of the new blue pigment. One significant obstacle is the price of the indium oxide (In2O3) used as a starting material. This is high, because it is produced (mostly in China) primarily for the manufacture of the transparent conductive oxide indium titanium oxide for electronic displays and other optoelectronic applications. Those uses demand that the material be made with extremely high purity (around 99.999 percent), which drives up the cost. In principle, the low-purity In2O3 that would suffice for making Yin1-xMnxO3 could be considerably cheaper, but is not currently made at all as there is no market demand.
That’s why Subramanian and colleagues are now trying to find a way of eliminating the indium from their manganese compounds – to find a cheaper host that can place the metal atoms in the same coordination environment. If they succeed, it’s possible that we’ll see yet another revolution in the chemistry of the blues.
1. A. E. Smith et al., J. Am. Chem. Soc. 131, 17084-17086 (2009).
2. A. E. Smith, A. W. Sleight & M. A. Subramanian, Mater. Res. Bull. 46, 1-5 (2011). 1. A. E. Smith et al., J. Am. Chem. Soc. 131, 17084-17086 (2009).
3. P. Jiang, J. Li, A. W. Sleight & M. A. Subramanian, Inorg. Chem. 50, 5858-5860 (2011).
4. E. Del Federico et al., Inorg. Chem. 45, 1270-1276 (2006).
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“Ultramarine blue is a colour illustrious, beautiful, and most perfect, beyond all other colours”, wrote the Italian artist Cennino Cennini in the late fourteenth century. He and his contemporaries adored this mineral pigment for its rich, deep lustre. But they didn’t use it much, at least not unless they had a particularly rich client, because it was so costly. As the name implies, it came from ‘over the seas’ – all the way from what is now Afghanistan, where mines in the remote region of Badakhshan were the only known source of the parent mineral, lapis lazuli, for centuries. Not only was ultramarine expensive to import, but it was laborious to make from the raw material, in a process of grinding and repeated washing that separated the blue colorant from impurities. So ultramarine could cost more than its weight in gold, and painters reserved it for the most precious parts of their altarpieces, especially the robes of the Virgin Mary.
Blue has always been a problem for artists. One of the first synthetic pigments, Egyptian blue (calcium copper silicate), was pale. The best mineral alternative to ultramarine, called azurite (hydrous copper carbonate), was more readily accessible but greenish rather than having ultramarine’s glorious purple-reddish tinge. Around 1704 a misconceived alchemical experiment yielded Prussian blue (iron ferrocyanate), which is blackish, prone to discolour, and decomposes to hydrogen cyanide under mildly acidic conditions. The discovery of cobalt blue (cobalt aluminate) in 1802, followed by a synthetic route to ultramarine in 1826, seemed to solve these problems of hue, stability and cost, but even these ‘artificial’ blues have drawbacks: cobalt is rather toxic, and ultramarine is sensitive to heat, light and acid, which limits its use in some commercial applications.
This is why the identification of a new inorganic blue pigment in 2009 looked so promising. Mas Subramanian and coworkers at Oregon State University found that trivalent manganese ions produce an intense blue colour, with the prized ‘reddish’ shade of ultramarine, when they occupy a trigonal bipyramidal site in metal oxides [1]. The researchers substituted Mn3+ for some indium ions in yttrium indium oxide (YInO3), forming a solid solution of YInO3 and YMnO3, which has a blue colour even though the two oxides themselves are white and black respectively. The depth of the colour varies from pale to virtually black as the manganese content is increased, although it is significantly blue even for only about 2 percent substitution. The researchers found that inserting manganese into other metal oxides with the same coordination geometry also offers strong blues. Meanwhile, similar substitutions of iron (III) and copper (II) generate bright orange and green pigments [2,3]. Those are traditionally less problematic, however, and while the materials may prove to have useful magnetic properties, it’s the blue that has attracted colour manufacturers.
Producing a commercially viable pigment is much more than a matter of finding a strongly coloured substance. It must be durable, for example. Although ultramarine, made industrially from cheap ingredients, is now available in quantities that would have staggered Titian and Michelangelo, it fades in direct sunlight because the sodalite framework is degraded and the sulphur chromophores are released and decompose – a process only recently understood [4]. This rules out many uses for exterior coatings. In contrast, the manganese compound has good thermal, chemical and light stability.
One of the key advantages of the YIn1-xMnxO3 compounds over traditional blues, however, is their strong reflectivity in the near-infrared region. Many other pigments, including cobalt blue and carbon black, have strong absorption bands here. This means that surfaces coated with these pigments heat up when exposed to strong sunlight. Building roofs coloured with such materials become extremely hot and can increase the demand of air conditioning in hot climates; instrument panels and steering wheels of cars may become almost too hot to touch. That’s why there is a big industrial demand for so-called ‘cool’ pigments, which retain their absorbance in the visible region but have low absorbance in the infrared. These can feel noticeably cooler when exposed to sunlight.
This aspect in particular has motivated the Ohio-based pigment company Shepherd Color to start exploring the commercial potential of the new blue pigment. One significant obstacle is the price of the indium oxide (In2O3) used as a starting material. This is high, because it is produced (mostly in China) primarily for the manufacture of the transparent conductive oxide indium titanium oxide for electronic displays and other optoelectronic applications. Those uses demand that the material be made with extremely high purity (around 99.999 percent), which drives up the cost. In principle, the low-purity In2O3 that would suffice for making Yin1-xMnxO3 could be considerably cheaper, but is not currently made at all as there is no market demand.
That’s why Subramanian and colleagues are now trying to find a way of eliminating the indium from their manganese compounds – to find a cheaper host that can place the metal atoms in the same coordination environment. If they succeed, it’s possible that we’ll see yet another revolution in the chemistry of the blues.
1. A. E. Smith et al., J. Am. Chem. Soc. 131, 17084-17086 (2009).
2. A. E. Smith, A. W. Sleight & M. A. Subramanian, Mater. Res. Bull. 46, 1-5 (2011). 1. A. E. Smith et al., J. Am. Chem. Soc. 131, 17084-17086 (2009).
3. P. Jiang, J. Li, A. W. Sleight & M. A. Subramanian, Inorg. Chem. 50, 5858-5860 (2011).
4. E. Del Federico et al., Inorg. Chem. 45, 1270-1276 (2006).
Thursday, October 04, 2012
The cost of useless information
This was a damned difficult story to write for Nature news, and the published version is a fair bit different to this original text. I can’t say which works best – perhaps it’s just one of those stories for which it’s helpful to have more than one telling. Part of the difficulty is that, to be honest, the real interest is fundamental, not in terms of what this idea can do in any applied sense. Anyway, I’m going to append to this some comments from coauthor David Sivak of the Lawrence Berkeley National Laboratory, which help to explain the slightly counter-intuitive notion of proteins being predictive machines with memories.
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Machines are efficient only if they collect information that helps them predict the future
The most efficient machines remember what’s happened to them, and use that memory to predict what the future holds. This conclusion of a new study by Susanne Still of the University of Hawaii at Manoa and her coworkers [1] should apply equally to ‘machines’ ranging from molecular enzymes to computers and even scientific models. It not only offers a new way to think about processes in molecular biology but might ultimately lead to improved computer model-building.
“[This idea] that predictive capacity can be quantitatively connected to thermodynamic efficiency is particularly striking”, says chemist Christopher Jarzynski of the University of Maryland.
The notion of constructing a model of the environment and using it for prediction might feel perfectly familiar for a scientific model – a computer model of weather, say. But it seems peculiar to think of a biomolecule such as a motor protein doing this too.
Yet that’s just what it does, the researchers say. A molecular motor does its job by undergoing changes in the conformation of the proteins that comprise it.
“Which conformation it is in now is correlated with what states the environment passed through previously”, says Still’s coworker Gavin Crooks of the Lawrence Berkeley National Laboratory in California. So the state of the molecule at any instant embodies a memory of its past.
But the environment of a biomolecule is full of random noise, and there’s no gain in the machine ‘remembering’ the fine details of that buffeting. “Some information just isn't useful for making predictions”, says Crooks. “Knowing that the last coin toss came up heads is useless information, since it tells you nothing about the next coin toss.”
If a machine does store such useless information, eventually it has to erase it, since its memory is finite – for a biomolecule, very much so. But according to the theory of computation, erasing information costs energy - it results in heat being dissipated, which makes the machine inefficient.
On the other hand, information that has predictive value is valuable, since it enables the machine to ‘prepare’ – to adapt to future circumstances, and thus to work optimally. “My thinking is inspired by dance, and sports in general, where if I want to move more efficiently then I need to predict well”, says Still.
Alternatively, think of a vehicle fitted with a smart driver-assistance system that uses sensors to anticipate its imminent environment and react accordingly – to brake in an optimal manner, and so maximize fuel efficiency.
That sort of predictive function costs only a tiny amount of processing energy compared with the total energy consumption of a car. But for a biomolecule it can be very costly to store information, so there’s a finely balanced tradeoff between the energetic cost of information processing against the inefficiencies caused by poor anticipation.
“If biochemical motors and pumps are efficient, they must be doing something clever”, says Still. “Something in fact tied to the cognitive ability we pride ourselves with: the capacity to construct concise representations of the world we have encountered, which allow us to say something about things yet to come.”
This balance, and the search for concision, is precisely what scientific models have to negotiate too. Suppose you are trying to devise a computer model of a complex system, such as how people vote. It might need to take into account the demographics of the population concerned, and networks of friendship and contact by which people influence each other. Might it also need a representation of mass media influences? Of individuals’ socioeconomic status? Their neural circuitry?
In principle, there’s no end to the information the model might incorporate. But then you have an almost one-to-one mapping of the real world onto the model: it’s not really a model at all, but just a mass of data, much of which might end up being irrelevant to prediction.
So again the challenge is to achieve good predictive power without remembering everything. “This is the same as saying that a model should not be overly complicated – that is, Occam's Razor”, says Still. She hopes this new connection between prediction and memory might guide intuition in improving algorithms that minimize the complexity of a model for a specific desired predictive power, used for example to study phenomena such as climate change.
References
1. Still, S., Sivak, D. A., Bell, A. J. & Crooks, G. E. Phys. Rev. Lett. 109, 120604 (2012).
David Sivak’s comments:
On the level of a single biomolecule, the basic idea is that a given protein under given environmental conditions (temperature, pH, ionic concentrations, bound/unbound small molecules, conformation of protein binding partners, etc.) will have a particular equilibrium probability distribution over different conformations. Different protein sequences will have different equilibrium distributions for given environmental conditions. For example, an evolved protein sequence is more likely to adopt a folded globular structure at ambient temperature, as compare to a random polypeptide. If you look over the distribution of possible environmental conditions, different protein sequences will differ in the correlations between their conformational state and particular environmental variables, i.e., the information their conformational state stores about the particular environmental variables.
When the environmental conditions change, that equilibrium distribution changes, but the actual distribution of the protein shifts to the new equilibrium distribution gradually. In particular, the dynamics of interconversion between different protein conformations dictates how long it takes for particular correlations with past environmental variables to die out, i.e., for memory of particular aspects of the environment to persist. Thus the conformational preferences (as a function of environmental conditions) and the interconversion dynamics determine the memory of particular protein sequences for various aspects of their environmental history.
One complication is that this memory, this correlation with past environmental states, may be a subtle phenomenon, distributed over many detailed aspects of the protein conformation, rather than something relatively simple like the binding of a specific ion. So, we like to stress that the model is implicit. But it certainly is the case that an enzyme mutated at its active site could differ from the wild-type protein in its binding affinity for a metal ion, and could also have a different rate of ion dissociation. Since the presence or absence of this bound metal ion embodies a memory of past ion concentrations, the mutant and wild-type enzymes would differ in their memory.
For a molecular motor, there are lots of fluctuating quantities in the environment, but only some of these fluctuations will be predictive of things the motor needs for its function. An efficient motor should not, for example, retain memory of every water molecule that collides with it, even if it could, because that will provide negligible information of use in predicting future fluctuations of those quantities that are relevant for the motor's functioning.
In vivo, the rotary F0F1-ATP synthase is driven by protonmotive flow across the mitochondrial membrane. The motor could retain conformational correlations with many aspects of its past history, but this analysis says that the motor will behave efficiently if it remembers molecular events predictive of when the next proton will flow down its channel, and loses memory of other molecular events irrelevant to its function. In order to efficiently couple that flow to the functional role of the motor, synthesizing ATP, the motor should retain information about the past that is predictive of such protonmotive flow, but lose any correlation with irrelevant molecular events, such as incidental collisions by water molecules.
But we are hesitant to commit to any particular example. We are all thinking about good concrete instantiations of these concepts for future extensions of this work. Right now, the danger of very specific examples like the F0F1 motor is that people who know much more about the particular system than we do might get bogged down in arguing the details, such as what exactly drives the motor, whether that driving involves conformational selection or induced fit, how concerted the mechanism is, etc., when the main point is that this framework applies regardless of the exact manner in which the system and environment are instantiated. Not to mention the fact that some subtle solvent rearrangements at the mouth of the channel may in fact be very predictive of future proton flow.
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Machines are efficient only if they collect information that helps them predict the future
The most efficient machines remember what’s happened to them, and use that memory to predict what the future holds. This conclusion of a new study by Susanne Still of the University of Hawaii at Manoa and her coworkers [1] should apply equally to ‘machines’ ranging from molecular enzymes to computers and even scientific models. It not only offers a new way to think about processes in molecular biology but might ultimately lead to improved computer model-building.
“[This idea] that predictive capacity can be quantitatively connected to thermodynamic efficiency is particularly striking”, says chemist Christopher Jarzynski of the University of Maryland.
The notion of constructing a model of the environment and using it for prediction might feel perfectly familiar for a scientific model – a computer model of weather, say. But it seems peculiar to think of a biomolecule such as a motor protein doing this too.
Yet that’s just what it does, the researchers say. A molecular motor does its job by undergoing changes in the conformation of the proteins that comprise it.
“Which conformation it is in now is correlated with what states the environment passed through previously”, says Still’s coworker Gavin Crooks of the Lawrence Berkeley National Laboratory in California. So the state of the molecule at any instant embodies a memory of its past.
But the environment of a biomolecule is full of random noise, and there’s no gain in the machine ‘remembering’ the fine details of that buffeting. “Some information just isn't useful for making predictions”, says Crooks. “Knowing that the last coin toss came up heads is useless information, since it tells you nothing about the next coin toss.”
If a machine does store such useless information, eventually it has to erase it, since its memory is finite – for a biomolecule, very much so. But according to the theory of computation, erasing information costs energy - it results in heat being dissipated, which makes the machine inefficient.
On the other hand, information that has predictive value is valuable, since it enables the machine to ‘prepare’ – to adapt to future circumstances, and thus to work optimally. “My thinking is inspired by dance, and sports in general, where if I want to move more efficiently then I need to predict well”, says Still.
Alternatively, think of a vehicle fitted with a smart driver-assistance system that uses sensors to anticipate its imminent environment and react accordingly – to brake in an optimal manner, and so maximize fuel efficiency.
That sort of predictive function costs only a tiny amount of processing energy compared with the total energy consumption of a car. But for a biomolecule it can be very costly to store information, so there’s a finely balanced tradeoff between the energetic cost of information processing against the inefficiencies caused by poor anticipation.
“If biochemical motors and pumps are efficient, they must be doing something clever”, says Still. “Something in fact tied to the cognitive ability we pride ourselves with: the capacity to construct concise representations of the world we have encountered, which allow us to say something about things yet to come.”
This balance, and the search for concision, is precisely what scientific models have to negotiate too. Suppose you are trying to devise a computer model of a complex system, such as how people vote. It might need to take into account the demographics of the population concerned, and networks of friendship and contact by which people influence each other. Might it also need a representation of mass media influences? Of individuals’ socioeconomic status? Their neural circuitry?
In principle, there’s no end to the information the model might incorporate. But then you have an almost one-to-one mapping of the real world onto the model: it’s not really a model at all, but just a mass of data, much of which might end up being irrelevant to prediction.
So again the challenge is to achieve good predictive power without remembering everything. “This is the same as saying that a model should not be overly complicated – that is, Occam's Razor”, says Still. She hopes this new connection between prediction and memory might guide intuition in improving algorithms that minimize the complexity of a model for a specific desired predictive power, used for example to study phenomena such as climate change.
References
1. Still, S., Sivak, D. A., Bell, A. J. & Crooks, G. E. Phys. Rev. Lett. 109, 120604 (2012).
David Sivak’s comments:
On the level of a single biomolecule, the basic idea is that a given protein under given environmental conditions (temperature, pH, ionic concentrations, bound/unbound small molecules, conformation of protein binding partners, etc.) will have a particular equilibrium probability distribution over different conformations. Different protein sequences will have different equilibrium distributions for given environmental conditions. For example, an evolved protein sequence is more likely to adopt a folded globular structure at ambient temperature, as compare to a random polypeptide. If you look over the distribution of possible environmental conditions, different protein sequences will differ in the correlations between their conformational state and particular environmental variables, i.e., the information their conformational state stores about the particular environmental variables.
When the environmental conditions change, that equilibrium distribution changes, but the actual distribution of the protein shifts to the new equilibrium distribution gradually. In particular, the dynamics of interconversion between different protein conformations dictates how long it takes for particular correlations with past environmental variables to die out, i.e., for memory of particular aspects of the environment to persist. Thus the conformational preferences (as a function of environmental conditions) and the interconversion dynamics determine the memory of particular protein sequences for various aspects of their environmental history.
One complication is that this memory, this correlation with past environmental states, may be a subtle phenomenon, distributed over many detailed aspects of the protein conformation, rather than something relatively simple like the binding of a specific ion. So, we like to stress that the model is implicit. But it certainly is the case that an enzyme mutated at its active site could differ from the wild-type protein in its binding affinity for a metal ion, and could also have a different rate of ion dissociation. Since the presence or absence of this bound metal ion embodies a memory of past ion concentrations, the mutant and wild-type enzymes would differ in their memory.
For a molecular motor, there are lots of fluctuating quantities in the environment, but only some of these fluctuations will be predictive of things the motor needs for its function. An efficient motor should not, for example, retain memory of every water molecule that collides with it, even if it could, because that will provide negligible information of use in predicting future fluctuations of those quantities that are relevant for the motor's functioning.
In vivo, the rotary F0F1-ATP synthase is driven by protonmotive flow across the mitochondrial membrane. The motor could retain conformational correlations with many aspects of its past history, but this analysis says that the motor will behave efficiently if it remembers molecular events predictive of when the next proton will flow down its channel, and loses memory of other molecular events irrelevant to its function. In order to efficiently couple that flow to the functional role of the motor, synthesizing ATP, the motor should retain information about the past that is predictive of such protonmotive flow, but lose any correlation with irrelevant molecular events, such as incidental collisions by water molecules.
But we are hesitant to commit to any particular example. We are all thinking about good concrete instantiations of these concepts for future extensions of this work. Right now, the danger of very specific examples like the F0F1 motor is that people who know much more about the particular system than we do might get bogged down in arguing the details, such as what exactly drives the motor, whether that driving involves conformational selection or induced fit, how concerted the mechanism is, etc., when the main point is that this framework applies regardless of the exact manner in which the system and environment are instantiated. Not to mention the fact that some subtle solvent rearrangements at the mouth of the channel may in fact be very predictive of future proton flow.
Friday, September 21, 2012
How to copy faster
Yes, there’s more tonight. It's Friday. Here’s my latest news story for Nature. This one was tough, but hopefully worth it. Possibly I ended up with a better explanation on the Nature site than here of why reversibility is linked to the minimum heat output. But it’s a tricky matter, so no harm in having two bites of the cherry.
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Bacteria replicate close to the physical limit of efficiency, says a new study – but might we make them better still?
Bacteria such as E. coli typically take about 20 minutes to replicate. Can they do it any faster? A little, but not much, says biological physicist Jeremy England of the Massachusetts Institute of Technology. In a preprint [1], he estimates that bacteria are impressively close to – within a factor of 2-3 of – the limiting efficiency of replication set by the laws of physics.
“It is heartening to learn this”, says Gerald Joyce, a chemist at the Scripps Research Institute in La Jolla, California, who work includes the development of synthetic replicating molecules based on RNA. “I suppose I should take some comfort that our primitive RNA-based self-replicator apparently operates even closer to the thermodynamic lower bound”, he adds.
At the root of England’s work is a question that has puzzled many scientists: how do living systems seem to defy the Second Law of Thermodynamics by sustaining order instead of falling apart into entropic chaos? In his 1944 book What is Life?, physicist Erwin Schrödinger asserted that life feeds on ‘negative entropy’ – which was really not much more than restating the problem.
Life doesn’t really defy the Second Law because it produces entropy to compensate for its own orderliness – that is why we are warmer than our usual surroundings. England set out to make this picture rigorous by estimating the amount of heat that must unavoidably be produced when a living organism replicates – one of the key defining characteristics of life. In other words, how efficient can replication be while still respecting the Second Law?
To attack this problem, England uses the concepts of statistical mechanics, the microscopic basis of classical thermodynamics. Statistical mechanics relates different arrangements of a set of basic constituents, such as atoms or molecules, to the probabilities of their occurring. The Second Law – the inexorable increase of entropy or, loosely speaking, disorder – is generally considered to follow from the fact that there are many more disorderly arrangements of such constituents than orderly ones, so that these are far more likely to be the outcome of the particles’ movements and interactions.
The question is: what is the cheapest way, in terms of how much energy (technically free energy, which takes into account both the energy needed to make and break chemical bonds and the associated entropy changes) is involved, of going from one bacterium to two? That turns out to be a matter of how easily one can reverse the process.
For the analogous question of the minimal cost of doing a computation – combining two bits of information in a logic operation – the answer depends on how much energy it costs to reset a bit and ‘undo’ the computation. This quantity places a fundamental limit on how low the power consumption of a computer can be.
“The probability that the reverse transition from two cells to one could happen is the quantity that tells us how irreversible the replication process is”, says England. “Whatever this quantity is, it need not be dominated by the trajectories that would just look like the movie playing backwards: there are many ways of starting with two cells and ending up with one. I’m asking what class of paths should dominate that process.”
The problem is precisely those “many ways”. “You can drive yourself nuts trying to think of everything”, England says. But he considered the most general reversal route: if, by chance, the atoms in the replicated bacteria happen to move such that all its molecules disintegrate. That is, of course, immensely unlikely. But by figuring out exactly how unlikely, England can place a rough limit on how reversible replication is, and thus on its minimum energy cost.
By plugging some numbers into the equations describing the likelihood of a replication being reversed – how long on average the chemical bonds holding proteins together will last, say, and how many such bonds there are in a bacterium – England estimates that the minimal amount of heat a bacterium must generate to replicate is a little more than a third of the amount a real E. coli cell generates. That’s impressive: if the cells were only twice as efficient, they’d be approaching the maximum efficiency physically possible.
“The weakest point in my argument is the assumption that we know what the ‘most likely very unlikely path’ for spontaneous disintegration of a bacterium is”, England admits. “We’re talking about things that simply never happen, so we can’t have much intuition about them.” As a result, he says that his treatment “certainly shouldn't be thought of us a proof as much as a plausibility argument.”
It’s precisely this that troubles Joyce, who compares the calculation with the joke about a physicist trying to solve a problem in dairy farming. “As an experimentalist, it is hard for me relate to this ‘spherical cow’ treatment of a self-replicating system”, Joyce says. “Here E. coli seems to be nothing more than the equivalent of its dry weight in proteins.”
England says that we can hardly expect bacteria to do much better than they do given that they have to cope with many different environments and so can’t be optimized for any particular one. But if we want to engineer a bacterium for a highly specialized task using synthetic biology, he says, then there is room for improvement: such a modified E. coli could be at least twice as efficient at replicating, which means that a colony could grow twice as fast. That could be useful in biotechnology. “We may be able to build self-replicators that grow much more rapidly than the ones we're currently aware of,” he says.
He also concludes that there’s a trade-off between speed of replication and robustness: a replicator that is prone to falling apart produces less heat, and so can replicate faster, than one that is more robust. The findings might therefore have implications for understanding the origin of life. Many researchers, including Joyce, suspect that DNA-based replicators were preceded on the early Earth by those based on RNA, which both encoded genetic information and acted as an enzyme-like catalyst for proto-biological reactions. This fits with England’s hypothesis, because RNA is less chemically stable than DNA, and so would be more fleet and nimble in getting replication started. “Something else than RNA might work even better on a shorter timescale at an earlier stage,” England adds.
References
1. England, J. L. preprint http://www.arxiv.org/abs/1209.1179 (2012).
____________________________________________
Bacteria replicate close to the physical limit of efficiency, says a new study – but might we make them better still?
Bacteria such as E. coli typically take about 20 minutes to replicate. Can they do it any faster? A little, but not much, says biological physicist Jeremy England of the Massachusetts Institute of Technology. In a preprint [1], he estimates that bacteria are impressively close to – within a factor of 2-3 of – the limiting efficiency of replication set by the laws of physics.
“It is heartening to learn this”, says Gerald Joyce, a chemist at the Scripps Research Institute in La Jolla, California, who work includes the development of synthetic replicating molecules based on RNA. “I suppose I should take some comfort that our primitive RNA-based self-replicator apparently operates even closer to the thermodynamic lower bound”, he adds.
At the root of England’s work is a question that has puzzled many scientists: how do living systems seem to defy the Second Law of Thermodynamics by sustaining order instead of falling apart into entropic chaos? In his 1944 book What is Life?, physicist Erwin Schrödinger asserted that life feeds on ‘negative entropy’ – which was really not much more than restating the problem.
Life doesn’t really defy the Second Law because it produces entropy to compensate for its own orderliness – that is why we are warmer than our usual surroundings. England set out to make this picture rigorous by estimating the amount of heat that must unavoidably be produced when a living organism replicates – one of the key defining characteristics of life. In other words, how efficient can replication be while still respecting the Second Law?
To attack this problem, England uses the concepts of statistical mechanics, the microscopic basis of classical thermodynamics. Statistical mechanics relates different arrangements of a set of basic constituents, such as atoms or molecules, to the probabilities of their occurring. The Second Law – the inexorable increase of entropy or, loosely speaking, disorder – is generally considered to follow from the fact that there are many more disorderly arrangements of such constituents than orderly ones, so that these are far more likely to be the outcome of the particles’ movements and interactions.
The question is: what is the cheapest way, in terms of how much energy (technically free energy, which takes into account both the energy needed to make and break chemical bonds and the associated entropy changes) is involved, of going from one bacterium to two? That turns out to be a matter of how easily one can reverse the process.
For the analogous question of the minimal cost of doing a computation – combining two bits of information in a logic operation – the answer depends on how much energy it costs to reset a bit and ‘undo’ the computation. This quantity places a fundamental limit on how low the power consumption of a computer can be.
“The probability that the reverse transition from two cells to one could happen is the quantity that tells us how irreversible the replication process is”, says England. “Whatever this quantity is, it need not be dominated by the trajectories that would just look like the movie playing backwards: there are many ways of starting with two cells and ending up with one. I’m asking what class of paths should dominate that process.”
The problem is precisely those “many ways”. “You can drive yourself nuts trying to think of everything”, England says. But he considered the most general reversal route: if, by chance, the atoms in the replicated bacteria happen to move such that all its molecules disintegrate. That is, of course, immensely unlikely. But by figuring out exactly how unlikely, England can place a rough limit on how reversible replication is, and thus on its minimum energy cost.
By plugging some numbers into the equations describing the likelihood of a replication being reversed – how long on average the chemical bonds holding proteins together will last, say, and how many such bonds there are in a bacterium – England estimates that the minimal amount of heat a bacterium must generate to replicate is a little more than a third of the amount a real E. coli cell generates. That’s impressive: if the cells were only twice as efficient, they’d be approaching the maximum efficiency physically possible.
“The weakest point in my argument is the assumption that we know what the ‘most likely very unlikely path’ for spontaneous disintegration of a bacterium is”, England admits. “We’re talking about things that simply never happen, so we can’t have much intuition about them.” As a result, he says that his treatment “certainly shouldn't be thought of us a proof as much as a plausibility argument.”
It’s precisely this that troubles Joyce, who compares the calculation with the joke about a physicist trying to solve a problem in dairy farming. “As an experimentalist, it is hard for me relate to this ‘spherical cow’ treatment of a self-replicating system”, Joyce says. “Here E. coli seems to be nothing more than the equivalent of its dry weight in proteins.”
England says that we can hardly expect bacteria to do much better than they do given that they have to cope with many different environments and so can’t be optimized for any particular one. But if we want to engineer a bacterium for a highly specialized task using synthetic biology, he says, then there is room for improvement: such a modified E. coli could be at least twice as efficient at replicating, which means that a colony could grow twice as fast. That could be useful in biotechnology. “We may be able to build self-replicators that grow much more rapidly than the ones we're currently aware of,” he says.
He also concludes that there’s a trade-off between speed of replication and robustness: a replicator that is prone to falling apart produces less heat, and so can replicate faster, than one that is more robust. The findings might therefore have implications for understanding the origin of life. Many researchers, including Joyce, suspect that DNA-based replicators were preceded on the early Earth by those based on RNA, which both encoded genetic information and acted as an enzyme-like catalyst for proto-biological reactions. This fits with England’s hypothesis, because RNA is less chemically stable than DNA, and so would be more fleet and nimble in getting replication started. “Something else than RNA might work even better on a shorter timescale at an earlier stage,” England adds.
References
1. England, J. L. preprint http://www.arxiv.org/abs/1209.1179 (2012).
What your snoring says about you
OK, BBC Future again. Who said Zzzzz? [Incidentally, who did decree in kids’ books that sleeping would be denoted by “Zzzzz”? It sounds nothing like sleeping, and drives me crazy. Even Julia Donaldson does it. Listen, this is a big deal with a 3- and 7-year-old.]
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Snoring is no joke for partners, but it’s not much fun for the snorer either. Severe snoring is the sound of a sleeper fighting for breath, as relaxed muscles in the pharynx (the top of the throat) allow the airway to become blocked. Lots of people snore, but the loud and irregular snoring caused by a condition known as obstructive sleep apnea (OSA) can leave a sufferer tired and fuddled during the day, even though he or she is rarely fully awoken by the night-time disruption. It’s difficult to treat – there are currently no effective drugs, and the usual intervention involves a machine that inflates the airway, or in extreme cases surgery. But the first step is to distinguish genuine OSA, which afflicts between 4 and 10 percent of the population, from ordinary snoring.
That kind of diagnosis is costly and laborious too. Often a snorer will need to sleep under observation in a laboratory. But some researchers believe that there is a signature of OSA encoded in the sounds of the snores themselves – which can be easily recorded at home for later analysis. A team in Brazil that brings together medics and physicists has now found a way of analysing snore recordings that is able not only to spot OSA but can distinguish between mild and severe cases.
Diagnosing OSA from snore sounds is not a new idea. The question is how, if at all, the clinical condition is revealed by the noises. Does OSA affect the total number of snores, or their loudness, or their acoustic quality, or their regularity – or several or all of these things? In 2008 a team in Turkey showed that the statistical regularity of snores has the potential to discriminate ordinary sleepers from OSA sufferers. And last year a group in Australia found that a rather complex analysis of the sound characteristics, such as the pitch, of snores might be capable of providing such a diagnosis, at least in cases where the sound is recorded under controlled and otherwise quiet conditions.
Physicist Adriano Alencar of the University of SĂŁo Paulo and his colleagues have now added to this battery of acoustic methods for identifying OSA. They recorded the snoring of patients referred to the university’s Sleep Laboratory because of suspected OSA, and studied the measurements for a fingerprint of OSA in the regularity of snores.
A person who snores but does not suffer from OSA typically does so in synchrony with breathing, with successive snores less than about ten seconds apart. In these cases the obstruction of the airway that triggers snoring comes and goes, so that snoring might stop for perhaps a couple of minutes or more before resuming. So for ‘healthy’ snoring, the spacing between snores tends to be either less than ten seconds or, from time to time, more than about 100 seconds.
OSA patients, meanwhile, have snore intervals that fall within this time window. The snores follow one another in train, but with a spacing dictated by the more serious restriction of airflow rather than the steady in-and-out of breathing. The researchers measured what they call a snore time interval index, which is a measure of how often the time between snores falls between 10 and 100 seconds. They compare this with a standard clinical measure of OSA severity called the apnea-hypopnea index (AHI), which is obtained from complicated monitoring of a sleeping patient’s airflow in a laboratory. (Hypopnea is the milder form of OSA in which the airway becomes only partially blocked.)
Alencar and colleagues find that the higher the value of their snore interval index, the higher the patient’s corresponding AHI is. In other words, the snore index can be used as a pretty reliable proxy for the AHI: you can just record the snores rather than going through the rigmarole of the whole lab procedure.
That’s not all. The researchers could also use a snore recording to figure out how snores are related to each other – whether there is a kind of ‘snore memory’, so that, say, a particular snore is linked to a recent burst of snoring. This memory is measured by a so-called Hurst exponent, which reveals hidden patterns in a series of events that, at first glance, look random and disconnected. An automated computer analysis of the snore series could ‘learn’, based on training with known test cases, to use the Hurst exponent to distinguish moderate from severe cases of OSA, making the correct diagnosis for 16 of 17 patients.
The work of Alencar and colleagues hasn’t yet been peer-reviewed. But in the light of the earlier studies of OSA signatures in snore sounds, it adds to the promise of an easy and cheap way of spotting snorers who have a clinical condition that needs treatment. What’s more, it supports a growing belief that the human body generates several subtle but readily measured indicators of health and disease, revealed by statistical regularities in apparently random signals. For example, sensitive measurement of the crackling sounds generated when our airways open as we breathe in can tell us about the condition of our lungs, perhaps revealing respiratory problems, while ‘buried’ statistical regularities in heartbeat intervals or muscle movements encode information about cardiac health or sleep states. Our bodies tell us a lot about ourselves, if only we know how to listen.
Reference: A. M. Alencar et al., preprint http://www.arxiv.org/abs/1208.2242.
______________________________________________________
Snoring is no joke for partners, but it’s not much fun for the snorer either. Severe snoring is the sound of a sleeper fighting for breath, as relaxed muscles in the pharynx (the top of the throat) allow the airway to become blocked. Lots of people snore, but the loud and irregular snoring caused by a condition known as obstructive sleep apnea (OSA) can leave a sufferer tired and fuddled during the day, even though he or she is rarely fully awoken by the night-time disruption. It’s difficult to treat – there are currently no effective drugs, and the usual intervention involves a machine that inflates the airway, or in extreme cases surgery. But the first step is to distinguish genuine OSA, which afflicts between 4 and 10 percent of the population, from ordinary snoring.
That kind of diagnosis is costly and laborious too. Often a snorer will need to sleep under observation in a laboratory. But some researchers believe that there is a signature of OSA encoded in the sounds of the snores themselves – which can be easily recorded at home for later analysis. A team in Brazil that brings together medics and physicists has now found a way of analysing snore recordings that is able not only to spot OSA but can distinguish between mild and severe cases.
Diagnosing OSA from snore sounds is not a new idea. The question is how, if at all, the clinical condition is revealed by the noises. Does OSA affect the total number of snores, or their loudness, or their acoustic quality, or their regularity – or several or all of these things? In 2008 a team in Turkey showed that the statistical regularity of snores has the potential to discriminate ordinary sleepers from OSA sufferers. And last year a group in Australia found that a rather complex analysis of the sound characteristics, such as the pitch, of snores might be capable of providing such a diagnosis, at least in cases where the sound is recorded under controlled and otherwise quiet conditions.
Physicist Adriano Alencar of the University of SĂŁo Paulo and his colleagues have now added to this battery of acoustic methods for identifying OSA. They recorded the snoring of patients referred to the university’s Sleep Laboratory because of suspected OSA, and studied the measurements for a fingerprint of OSA in the regularity of snores.
A person who snores but does not suffer from OSA typically does so in synchrony with breathing, with successive snores less than about ten seconds apart. In these cases the obstruction of the airway that triggers snoring comes and goes, so that snoring might stop for perhaps a couple of minutes or more before resuming. So for ‘healthy’ snoring, the spacing between snores tends to be either less than ten seconds or, from time to time, more than about 100 seconds.
OSA patients, meanwhile, have snore intervals that fall within this time window. The snores follow one another in train, but with a spacing dictated by the more serious restriction of airflow rather than the steady in-and-out of breathing. The researchers measured what they call a snore time interval index, which is a measure of how often the time between snores falls between 10 and 100 seconds. They compare this with a standard clinical measure of OSA severity called the apnea-hypopnea index (AHI), which is obtained from complicated monitoring of a sleeping patient’s airflow in a laboratory. (Hypopnea is the milder form of OSA in which the airway becomes only partially blocked.)
Alencar and colleagues find that the higher the value of their snore interval index, the higher the patient’s corresponding AHI is. In other words, the snore index can be used as a pretty reliable proxy for the AHI: you can just record the snores rather than going through the rigmarole of the whole lab procedure.
That’s not all. The researchers could also use a snore recording to figure out how snores are related to each other – whether there is a kind of ‘snore memory’, so that, say, a particular snore is linked to a recent burst of snoring. This memory is measured by a so-called Hurst exponent, which reveals hidden patterns in a series of events that, at first glance, look random and disconnected. An automated computer analysis of the snore series could ‘learn’, based on training with known test cases, to use the Hurst exponent to distinguish moderate from severe cases of OSA, making the correct diagnosis for 16 of 17 patients.
The work of Alencar and colleagues hasn’t yet been peer-reviewed. But in the light of the earlier studies of OSA signatures in snore sounds, it adds to the promise of an easy and cheap way of spotting snorers who have a clinical condition that needs treatment. What’s more, it supports a growing belief that the human body generates several subtle but readily measured indicators of health and disease, revealed by statistical regularities in apparently random signals. For example, sensitive measurement of the crackling sounds generated when our airways open as we breathe in can tell us about the condition of our lungs, perhaps revealing respiratory problems, while ‘buried’ statistical regularities in heartbeat intervals or muscle movements encode information about cardiac health or sleep states. Our bodies tell us a lot about ourselves, if only we know how to listen.
Reference: A. M. Alencar et al., preprint http://www.arxiv.org/abs/1208.2242.
The silk laser
Here is my latest piece for BBC Future (which you can’t see in the UK). I have at least one other piece from this column yet to put up here – that will follow.
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Electronic waste from obsolete phones, cameras, computers and other mobile devices is one of the scourges of the age of information. The circuitry and packaging is not only non-biodegradable but is laced with toxic substances such as heavy metals. Imagine, then, a computer that can be disposed of by simply letting soil bacteria eat it – or even, should the fancy take you, by eating it yourself. Biodegradable information technology is now closer to appearing on the menu following the announcement by Fiorenzo Omenetto of Tufts University in Medford, Massachusetts, and coworkers of a laser made from silk.
In collaboration with David Kaplan, a specialist in the biochemistry of silk at Tufts, Omenetto has been exploring the uses of silk for several years. He is convinced that it can offer us much more than glamorous clothing. It is immensely strong – more so than steel – and can be used to make tough fibres and ropes. In the Far East silk was once used to pad armour, and in pre-revolutionary Russia a form of primitive bullet-proof clothing was made from it. It can be moulded like plastic, yet is biodegradable: silk cups can be thrown away to quickly break down in the environment. It is also biocompatible, and so could be used to make medical implants such as screws to hold together mending bones, or artificial blood vessels. You can even eat it safely, although it doesn’t taste good.
What’s more, all of this comes from sustainable and environmentally friendly processing. Spiders and silkworms make silk in water at ordinary body temperature, spinning the threads from a solution of the silk protein. Harvesting natural silk is one option, but the genes that encode the protein can be transferred to other species, so that it can be produced by bacteria in fermentation vats, or even expressed in the milk of transgenic goats. Turning this raw silk protein into strong fibres is not easy – it’s hard to reproduce the delicate thread-spinning apparatus of spiders – but if you just want to cast films of silk as if it were a plastic then this isn’t an issue.
Perhaps some of the most remarkable potential uses for this ancient material are in high-tech optical technology, like that which forms the basis of optical storage and telecommunications. Using moulds patterned on the microscopic scale, silk can be shaped into structures that reflect and diffract light, like those on DVDs – it will support holograms, for instance. Its transparency commends it for optical fibres, and Omenetto and colleagues have previously shaped silk films into so-called waveguides, rather like very thin optical fibres laid down directly on a solid surface such as a silicon chip. But rather than just using silk to passively guide and direct light, they wanted to generate light from it too. This is what the silk laser enables.
In a laser, a light-emitting substance – the lasing medium – is sandwiched between mirrors which allow the light to bounce back and forth. The medium is placed in a light-emitting state by pumping in energy, typically using either another light source or an electrical current. When light is emitted, its trapping by the mirrors means that it triggers still more emission as it bounces to and fro, so that all the light is released in an avalanche. This puts all the light waves in step with one another, which is what gives laser light its intensity and narrowly focused beam. The beam eventually escapes through one of the mirrors, which is designed to be only partially reflective.
Because of their brightness, focus and rapid on-off switching, lasers are used in telecommunications to transmit information as a stream of light pulses that encode the binary digital information of computers and microprocessors: a pulse corresponds to “1”, say, and a gap in the pulse stream to a “0”. In this way, information can be fed over long distances down optical fibres. Increasingly, computer and electrical engineers are now aiming to move and process information directly on microchips in the form of light. Then there’s no cumbersome light-to-electrical conversion of data at each end of the transmission, and light-based information processing could potentially be faster and carry more signal, since different data streams can be conveyed simultaneously in light of different colours. These so-called photonic chips could transform information technology, and Omenetto believes that with silk it should be possible to create ‘biophotonic’ circuits. That demands not just channelling light but generating it – in a laser.
Silk doesn’t absorb or emit light at the visible and infrared frequencies used in conventional telecommunications and optical information technology. So to make it into a laser medium, one needs to add substances that do. Organic dyes (carbon-based molecules) are already widely used, dispersed in a liquid solvent or in some solid matrix, to make dye lasers. The researchers figured they could mix such a dye into silk. They used one called stilbene, which is water-soluble and closely related to chemical compounds found in plants and used as textile brighteners.
Working with Stefano Toffanin and colleagues at the Institute for the Study of Nanostructured Materials in Bologna, Italy, Omenetto and his coworkers patterned a thin layer of silica (silicon dioxide) on the surface of a slice of silicon into a series of grooves about a quarter of a micrometre wide, which act as a mirror for the bluish-purple light that stilbene emits. They then covered this with a layer of silk spiced with the dye, and found that when they pumped this structure with ultraviolet light, it emitted light with the characteristic signature of laser light: an intense beam with a very narrow spread in frequency.
Making the device on silicon means that it could potentially be controlled electronically and merged with conventional chip circuitry. But that’s not essential – silk-based light circuits and devices could be laid down on other materials, perhaps on cheap, flexible and degradable plastics.
This isn’t the first time that biological materials have been used to make lasers. For example, in 2002 a team in Japan made one using films of DNA infused with organic dyes. And last year, two researchers in the US and Korea made lasers from living cells that were engineered to produce a fluorescent protein found naturally in a species of jellyfish. But the attraction of silk is that it is cheap, easy to process, biodegradable and already used to make a range of other light-based devices.
There might be even more dramatic possibilities. Recently, Omenetto and colleagues showed that silk is a good support for growing neurons, the cells that communicate nerve signals in the nervous system and the brain. This leads them to speculate that silk might mediate between optical and electronic technology and our nervous system, for example by bringing light sources intimately close to nerve cells for imaging them, or perhaps even developing circuitry that can transmit signals across damaged nerves.
Reference: S. Toffanin et al., Applied Physics Letters 101, 091110 (2012)
______________________________________________________________
Electronic waste from obsolete phones, cameras, computers and other mobile devices is one of the scourges of the age of information. The circuitry and packaging is not only non-biodegradable but is laced with toxic substances such as heavy metals. Imagine, then, a computer that can be disposed of by simply letting soil bacteria eat it – or even, should the fancy take you, by eating it yourself. Biodegradable information technology is now closer to appearing on the menu following the announcement by Fiorenzo Omenetto of Tufts University in Medford, Massachusetts, and coworkers of a laser made from silk.
In collaboration with David Kaplan, a specialist in the biochemistry of silk at Tufts, Omenetto has been exploring the uses of silk for several years. He is convinced that it can offer us much more than glamorous clothing. It is immensely strong – more so than steel – and can be used to make tough fibres and ropes. In the Far East silk was once used to pad armour, and in pre-revolutionary Russia a form of primitive bullet-proof clothing was made from it. It can be moulded like plastic, yet is biodegradable: silk cups can be thrown away to quickly break down in the environment. It is also biocompatible, and so could be used to make medical implants such as screws to hold together mending bones, or artificial blood vessels. You can even eat it safely, although it doesn’t taste good.
What’s more, all of this comes from sustainable and environmentally friendly processing. Spiders and silkworms make silk in water at ordinary body temperature, spinning the threads from a solution of the silk protein. Harvesting natural silk is one option, but the genes that encode the protein can be transferred to other species, so that it can be produced by bacteria in fermentation vats, or even expressed in the milk of transgenic goats. Turning this raw silk protein into strong fibres is not easy – it’s hard to reproduce the delicate thread-spinning apparatus of spiders – but if you just want to cast films of silk as if it were a plastic then this isn’t an issue.
Perhaps some of the most remarkable potential uses for this ancient material are in high-tech optical technology, like that which forms the basis of optical storage and telecommunications. Using moulds patterned on the microscopic scale, silk can be shaped into structures that reflect and diffract light, like those on DVDs – it will support holograms, for instance. Its transparency commends it for optical fibres, and Omenetto and colleagues have previously shaped silk films into so-called waveguides, rather like very thin optical fibres laid down directly on a solid surface such as a silicon chip. But rather than just using silk to passively guide and direct light, they wanted to generate light from it too. This is what the silk laser enables.
In a laser, a light-emitting substance – the lasing medium – is sandwiched between mirrors which allow the light to bounce back and forth. The medium is placed in a light-emitting state by pumping in energy, typically using either another light source or an electrical current. When light is emitted, its trapping by the mirrors means that it triggers still more emission as it bounces to and fro, so that all the light is released in an avalanche. This puts all the light waves in step with one another, which is what gives laser light its intensity and narrowly focused beam. The beam eventually escapes through one of the mirrors, which is designed to be only partially reflective.
Because of their brightness, focus and rapid on-off switching, lasers are used in telecommunications to transmit information as a stream of light pulses that encode the binary digital information of computers and microprocessors: a pulse corresponds to “1”, say, and a gap in the pulse stream to a “0”. In this way, information can be fed over long distances down optical fibres. Increasingly, computer and electrical engineers are now aiming to move and process information directly on microchips in the form of light. Then there’s no cumbersome light-to-electrical conversion of data at each end of the transmission, and light-based information processing could potentially be faster and carry more signal, since different data streams can be conveyed simultaneously in light of different colours. These so-called photonic chips could transform information technology, and Omenetto believes that with silk it should be possible to create ‘biophotonic’ circuits. That demands not just channelling light but generating it – in a laser.
Silk doesn’t absorb or emit light at the visible and infrared frequencies used in conventional telecommunications and optical information technology. So to make it into a laser medium, one needs to add substances that do. Organic dyes (carbon-based molecules) are already widely used, dispersed in a liquid solvent or in some solid matrix, to make dye lasers. The researchers figured they could mix such a dye into silk. They used one called stilbene, which is water-soluble and closely related to chemical compounds found in plants and used as textile brighteners.
Working with Stefano Toffanin and colleagues at the Institute for the Study of Nanostructured Materials in Bologna, Italy, Omenetto and his coworkers patterned a thin layer of silica (silicon dioxide) on the surface of a slice of silicon into a series of grooves about a quarter of a micrometre wide, which act as a mirror for the bluish-purple light that stilbene emits. They then covered this with a layer of silk spiced with the dye, and found that when they pumped this structure with ultraviolet light, it emitted light with the characteristic signature of laser light: an intense beam with a very narrow spread in frequency.
Making the device on silicon means that it could potentially be controlled electronically and merged with conventional chip circuitry. But that’s not essential – silk-based light circuits and devices could be laid down on other materials, perhaps on cheap, flexible and degradable plastics.
This isn’t the first time that biological materials have been used to make lasers. For example, in 2002 a team in Japan made one using films of DNA infused with organic dyes. And last year, two researchers in the US and Korea made lasers from living cells that were engineered to produce a fluorescent protein found naturally in a species of jellyfish. But the attraction of silk is that it is cheap, easy to process, biodegradable and already used to make a range of other light-based devices.
There might be even more dramatic possibilities. Recently, Omenetto and colleagues showed that silk is a good support for growing neurons, the cells that communicate nerve signals in the nervous system and the brain. This leads them to speculate that silk might mediate between optical and electronic technology and our nervous system, for example by bringing light sources intimately close to nerve cells for imaging them, or perhaps even developing circuitry that can transmit signals across damaged nerves.
Reference: S. Toffanin et al., Applied Physics Letters 101, 091110 (2012)
Tuesday, September 11, 2012
As easy as ABC?
Here’s my latest news story for Nature. There’s a lot of superscripts in here, for which I’ll use the x**n notation. Every time I encounter mathematicians, I’m reminded what a very different world they live in.
_____________________________________________________________________________
If it’s true, a Japanese mathematician’s solution to a conjecture about whole numbers would be an ‘astounding achievement’
The recondite world of mathematics is abuzz with a claim that one of the most important problems in number theory has been solved.
Japanese mathematician Shinichi Mochizuki of Kyoto University has released a 500-page proof of the ABC conjecture, which describes a purported relationship between whole numbers – a so-called Diophantine problem.
The ABC conjecture might not be as familiar to the wider world as Fermat’s Last Theorem, but in some ways it is more significant. “The ABC conjecture, if proved true, at one stroke solves many famous Diophantine problems, including Fermat's Last Theorem”, says Dorian Goldfeld, a mathematician at Columbia University in New York.
“If Mochizuki’s proof is correct, it will be one of the most astounding achievements of mathematics of the 21st century”, he adds.
Like Fermat’s theorem, the ABC conjecture is a postulate about equations of the deceptively simple form A+B=C that relate three whole numbers A, B and C. It involves the concept of a square-free number: one that can’t be divided by the square of any number. 15 and 17 are square free-numbers, but 16 and 18 – divisible by 4**2 and 3**2 respectively – are not.
The “square-free” part of a number n, denoted sqp(n), is the largest square-free number that can be formed by multiplying prime factors of n. For instance, sqp(18) = 2×3 = 6.
If you’ve got that, you should get the ABC conjecture. Proposed independently by David Masser and Joseph Oesterle in 1985, it concerns a property of the product of the three integers A×B×C, or ABC – or more specifically, of the square-free part of this product, which involves their distinct prime factors.
The conjecture states that the ratio of sqp(ABC)**r/C always has some minimum value greater than zero for any value of r greater than 1. For example, if A=3 and B=125, so that C=128, sqp(ABC)=30 and sqp(ABC)**2/C = 900/128. In this case, where r=2, sqp(ABC)**r/C is nearly always greater than 1, and always greater than zero.
It turns out that this conjecture encapsulates many other Diophantine problems, including Fermat’s Last Theorem (which states that A**n + B**n = C**n has no integer solutions if n>2). Like many Diophantine problems, it is at root all about the relationships between prime numbers – according to Brian Conrad of Stanford University, “it encodes a deep connection between the prime factors of A, B and A+B”.
“The ABC conjecture is the most important unsolved problem in Diophantine analysis”, says Goldfeld. “To mathematicians it is also a thing of beauty. Seeing so many Diophantine problems unexpectedly encapsulated into a single equation drives home the feeling that all the subdisciplines of mathematics are aspects of a single underlying unity.”
Unsurprisingly, then, many mathematicians have expended a great deal of effort trying to prove the conjecture. In 2007 the French mathematician Lucien Szpiro, whose work in 1978 led to the ABC conjecture in the first place, claimed to have a proof of it, but it was soon found to be flawed.
Like Szpiro, and also like Andrew Wiles who proved Fermat’s Last Theorem in 1994, Mochizuki has attacked the problem using the theory of elliptic curves, which are the smooth curves generated by algebraic relationships of the sort y**2 = x**3 + ax + b.
There, however, the relationship of Mochizuki’s work to previous efforts stops. In the present and earlier papers he has developed entirely new techniques that very few other mathematicians yet fully understand. “His work is extremely novel”, says Conrad. “It uses a huge number of new insights that are going to take a long time to be digested by the community.”
This novelty invokes entirely new mathematical ‘objects’ – abstract entities analogous to more familiar examples such as geometric objects, sets, permutations, topologies and matrices. “At this point he is probably the only one that knows it all”, says Goldfeld.
As a result, Goldfeld says, “if the proof is correct it will take a long time to check all the details.” The proof is spread over four long papers, each of which rests on earlier long papers. “It can require a huge investment of time to understand a long and sophisticated proof, so the willingness by others to do this rests not only on the importance of the announcement but also on the track record of the authors”, Conrad explains.
Mochizuki’s track record certainly makes the effort worthwhile. “He has proved extremely deep theorems in the past, and is very thorough in his writing, so that provides a lot of confidence”, says Conrad. And he adds that the payoff would be more than a matter of simply verifying the claim. “The exciting aspect is not just that the conjecture may have now been solved, but more importantly that the new techniques and insights he must have had to introduce should be very powerful tools for solving future problems in number theory.”
Mochizuki’s papers:
Paper 1
Paper 2
Paper 3
Paper 4
_____________________________________________________________________________
If it’s true, a Japanese mathematician’s solution to a conjecture about whole numbers would be an ‘astounding achievement’
The recondite world of mathematics is abuzz with a claim that one of the most important problems in number theory has been solved.
Japanese mathematician Shinichi Mochizuki of Kyoto University has released a 500-page proof of the ABC conjecture, which describes a purported relationship between whole numbers – a so-called Diophantine problem.
The ABC conjecture might not be as familiar to the wider world as Fermat’s Last Theorem, but in some ways it is more significant. “The ABC conjecture, if proved true, at one stroke solves many famous Diophantine problems, including Fermat's Last Theorem”, says Dorian Goldfeld, a mathematician at Columbia University in New York.
“If Mochizuki’s proof is correct, it will be one of the most astounding achievements of mathematics of the 21st century”, he adds.
Like Fermat’s theorem, the ABC conjecture is a postulate about equations of the deceptively simple form A+B=C that relate three whole numbers A, B and C. It involves the concept of a square-free number: one that can’t be divided by the square of any number. 15 and 17 are square free-numbers, but 16 and 18 – divisible by 4**2 and 3**2 respectively – are not.
The “square-free” part of a number n, denoted sqp(n), is the largest square-free number that can be formed by multiplying prime factors of n. For instance, sqp(18) = 2×3 = 6.
If you’ve got that, you should get the ABC conjecture. Proposed independently by David Masser and Joseph Oesterle in 1985, it concerns a property of the product of the three integers A×B×C, or ABC – or more specifically, of the square-free part of this product, which involves their distinct prime factors.
The conjecture states that the ratio of sqp(ABC)**r/C always has some minimum value greater than zero for any value of r greater than 1. For example, if A=3 and B=125, so that C=128, sqp(ABC)=30 and sqp(ABC)**2/C = 900/128. In this case, where r=2, sqp(ABC)**r/C is nearly always greater than 1, and always greater than zero.
It turns out that this conjecture encapsulates many other Diophantine problems, including Fermat’s Last Theorem (which states that A**n + B**n = C**n has no integer solutions if n>2). Like many Diophantine problems, it is at root all about the relationships between prime numbers – according to Brian Conrad of Stanford University, “it encodes a deep connection between the prime factors of A, B and A+B”.
“The ABC conjecture is the most important unsolved problem in Diophantine analysis”, says Goldfeld. “To mathematicians it is also a thing of beauty. Seeing so many Diophantine problems unexpectedly encapsulated into a single equation drives home the feeling that all the subdisciplines of mathematics are aspects of a single underlying unity.”
Unsurprisingly, then, many mathematicians have expended a great deal of effort trying to prove the conjecture. In 2007 the French mathematician Lucien Szpiro, whose work in 1978 led to the ABC conjecture in the first place, claimed to have a proof of it, but it was soon found to be flawed.
Like Szpiro, and also like Andrew Wiles who proved Fermat’s Last Theorem in 1994, Mochizuki has attacked the problem using the theory of elliptic curves, which are the smooth curves generated by algebraic relationships of the sort y**2 = x**3 + ax + b.
There, however, the relationship of Mochizuki’s work to previous efforts stops. In the present and earlier papers he has developed entirely new techniques that very few other mathematicians yet fully understand. “His work is extremely novel”, says Conrad. “It uses a huge number of new insights that are going to take a long time to be digested by the community.”
This novelty invokes entirely new mathematical ‘objects’ – abstract entities analogous to more familiar examples such as geometric objects, sets, permutations, topologies and matrices. “At this point he is probably the only one that knows it all”, says Goldfeld.
As a result, Goldfeld says, “if the proof is correct it will take a long time to check all the details.” The proof is spread over four long papers, each of which rests on earlier long papers. “It can require a huge investment of time to understand a long and sophisticated proof, so the willingness by others to do this rests not only on the importance of the announcement but also on the track record of the authors”, Conrad explains.
Mochizuki’s track record certainly makes the effort worthwhile. “He has proved extremely deep theorems in the past, and is very thorough in his writing, so that provides a lot of confidence”, says Conrad. And he adds that the payoff would be more than a matter of simply verifying the claim. “The exciting aspect is not just that the conjecture may have now been solved, but more importantly that the new techniques and insights he must have had to introduce should be very powerful tools for solving future problems in number theory.”
Mochizuki’s papers:
Paper 1
Paper 2
Paper 3
Paper 4
Friday, September 07, 2012
Cold fusion redux
This obituary of Martin Fleischmann appears in a similar form in the latest issue of Nature. No one, of course, wants to seem carping or churlish in an obit, and I hope this achieves some kind of balance. But I have to admit that, looking back now, I couldn’t help but be reminded of how badly Pons and Fleischmann behaved while cold fusion was at its height. In particular, the way they threatened Utah physicist Michael Salamon, who tried to replicate their experiments with their own equipment, was unforgivable. And it was pretty distasteful to see Fleischmann more recently bad-mouthing all his critics, searching for ways to belittle or dismiss Mark Wrighton, Frank Close, Nate Lewis, Gary Taubes and others. As I try to say here, it’s not getting things wrong that should count against you, but how you handle it.
____________________________________________________
OBITUARY
Martin Fleischmann, 1927-2012
Pioneering electrochemist who claimed to have discovered cold fusion
“Whatever one’s opinion about cold fusion, it should not be allowed to dominate our view of a remarkable and outstanding scientist.” This plea appears in the University of Southampton’s obituary of Martin Fleischmann, who carried out much of the work there that made him renowned as an electrochemist. It is not clear that it will be heeded.
Fleischmann died on 3rd August at the age of 85 after illness from Parkinson’s disease, heart disease and diabetes. He made substantial contributions to his discipline, being the first person to observe surface-enhanced Raman emission (now the basis of a widely used technique) and developing the use of ultramicroelectrodes as sensitive electrochemical probes. But he is best known now for his claim in 1989 to have initiated nuclear fusion on a bench top using only the kind of equipment a school lab might possess.
The ‘cold fusion’ debacle provoked bitter disputes, court cases and controversies that reverberate today. Along with polywater and homeopathy, cold fusion is now regarded as one of the most notorious cases of what chemist Irving Langmuir called ‘pathological science’ – as he put it, “the science of things that aren’t so”.
It would be wrong to draw a veil over cold fusion as an aberration in Fleischmann’s otherwise distinguished career. For it was instead an extreme example of the style that characterized his research: a willingness to suggest bold and provocative ideas, to take risks and to make imaginative leaps that could sometimes yield a rich harvest.
Fleischmann was born in Karoly Vary (Karlsbad) in Czechoslovakia in 1927. His father was of Jewish heritage and opposed Hitler’s regime; his family fled just before the German invasion to the Netherlands and then England. Fleischmann studied chemistry at Imperial College in London and, after a PhD in electrochemistry, he moved to the University of Newcastle. In 1967 he was appointed to the Faraday Chair of Chemistry at Southampton, where he explored reactions at electrode surfaces.
In 1974, Fleischmann and his coworkers observed unusually intense Raman emission (scattered light shifted in energy by the interaction with molecular vibrational states) from organic molecules adsorbed on the surface of silver electrodes. They did not immediately recognize that the enhancement was caused by the surface, and indeed the mechanism is still not fully understood – but surface-enhanced Raman spectroscopy (SERS) has become a valuable tool for investigating surface chemistry.
Around 1980 Fleischmann and Mark Wightman independently pioneered the use of ultramicroelectrodes just a few micrometres across to study otherwise-inaccessible electrode processes – for example, at low electrolyte concentrations or with very fast rates of reaction. Such innovations gave Fleischmann international repute. In 1985, two years after his early retirement from Southampton, he was elected a Fellow of the Royal Society.
Fleischmann’s longstanding interest in hydrogen surface chemistry on palladium led to the cold fusion experiments. When hydrogen molecules adsorbed onto palladium dissociate into atoms, these atoms can diffuse into the metal lattice, making the metal a ‘sponge’ able to soak up large amounts of hydrogen. Very high pressures of hydrogen can build up – perhaps, Flesichmann wondered, sufficient to trigger nuclear fusion.
Fleischmann’s retirement in 1983 freed him to conduct self-funded experiments at the University of Utah – a location conducive to Fleischmann, a passionate skier – with his former student Stanley Pons. They electrolysed solutions of lithium deuteroxide, collecting deuterium at the palladium cathode, and claimed to measure more heat output than could be accounted for by the energy fed in – a signature, they said, of deuterium fusion within the electrode. On returning in the morning to one experiment left running overnight, they found that the apparatus had been vaporized and the fume cupboard and part of the floor destroyed. Was this a particularly violent outburst of fusion?
Not until 1989 did Fleischmann, Pons and their student Marvin Hawkins move to publish their data. They discovered they were in competition with a team at Brigham Young University in Utah, led by physicist Steven Jones, which was conducting similar studies. Initially Fleischmann and Pons accused Jones of plagiarizing their ideas, but eventually the groups agreed to coordinate their announcements with a joint submission to Nature on 24th March. Yet Fleischmann and Pons first rushed a (highly uninformative) paper into print with the Journal of Electroanalytical Chemistry, organized a press conference on 23nd March, and faxed their paper to Nature that same day without telling Jones.
The rest, as they say, is history, told for example in Frank Close’s Too Hot To Handle (1991) and Gary Taubes’ Bad Science (1993). The fusion claims shocked the world: physicists had been trying for decades, at great expense but with no success, to harness nuclear fusion for energy generation. Now it appeared that chemists had achieved it at a minuscule fraction of the expense, potentially solving the energy crisis. Jones’ paper was eventually [Nature 338, 737; 1989] published by Nature; that of Pons, Fleischmann and Hawkins was withdrawn when the authors professed to be too busy, in the wake of their astounding announcement, to address the reviewers’ comments. When Pons spoke at the spring meeting of the American Chemical Society on 12th April, the atmosphere was jubilant: it was hailed as a triumph of chemistry over physics. Physicists were more sceptical, and pointed out serious problems with Fleischmann and Pons’ claims to have detected the emission of neutrons diagnostic of deuterium fusion.
Accusations that they had manipulated the neutron data were never substantiated, but what really put paid to cold fusion was the persistent failure of other groups to reliably reproduce the purported excess heat generation and other signatures of potential fusion. More accusations, recriminations and general bad behaviour followed: coercion, intimidation, litigation (Pons’ lawyer threatened Utah physicist Michael Salamon with legal action after he published his negative attempts at replication in Nature), withholding of data (Fleischmann refused outright at one meeting of physicists to discuss crucial control experiments), and suspicions of experimental tampering (were some groups spiking their equipment with tritium, a fingerprint of fusion?). The University of Utah sought aggressively to capitalize, throwing $5m at a ‘National Cold Fusion Institute’ that closed only two years after it opened.
Once cold fusion lost its credibility, Fleischmann and Pons moved to France to continue their work with private funding, but later fell out. Now only a few lone ‘believers’ pursue the work. Fleischmann did not distinguish himself in the aftermath, belittling critical peers in interviews and hinting at paranoid conspiracy theories. But perhaps the biggest casualty of cold fusion was electrochemistry itself, suddenly made to seem a morass of charlatanism and poor technique. That was unfair: some of the most authoritative (negative) attempts to replicate the results were conducted by electrochemists.
Flesichmann’s tragedy was almost Shakespearean, not least because he was himself in many ways a sympathetic character: resourceful, energetic, immensely inventive and remembered warmly by collaborators. As Linus Pauling and Fred Hoyle also exemplified, once you’ve been proved right against the odds, it becomes harder to accept the possibility of error. “Many a time in my life I have been accused of coming up with crazy ideas,” he once said. “Fortunately, I'm able to say that, so far, the critics have had to back off.” But although a final reckoning should not let genuine achievements be overshadowed by errors, the blot that cold fusion left on Fleischmann’s reputation is hard to expunge. To make a mistake or a premature claim, even to fall prey to self-deception, is a risk any scientist runs. The true test is how one deals with it.
____________________________________________________
OBITUARY
Martin Fleischmann, 1927-2012
Pioneering electrochemist who claimed to have discovered cold fusion
“Whatever one’s opinion about cold fusion, it should not be allowed to dominate our view of a remarkable and outstanding scientist.” This plea appears in the University of Southampton’s obituary of Martin Fleischmann, who carried out much of the work there that made him renowned as an electrochemist. It is not clear that it will be heeded.
Fleischmann died on 3rd August at the age of 85 after illness from Parkinson’s disease, heart disease and diabetes. He made substantial contributions to his discipline, being the first person to observe surface-enhanced Raman emission (now the basis of a widely used technique) and developing the use of ultramicroelectrodes as sensitive electrochemical probes. But he is best known now for his claim in 1989 to have initiated nuclear fusion on a bench top using only the kind of equipment a school lab might possess.
The ‘cold fusion’ debacle provoked bitter disputes, court cases and controversies that reverberate today. Along with polywater and homeopathy, cold fusion is now regarded as one of the most notorious cases of what chemist Irving Langmuir called ‘pathological science’ – as he put it, “the science of things that aren’t so”.
It would be wrong to draw a veil over cold fusion as an aberration in Fleischmann’s otherwise distinguished career. For it was instead an extreme example of the style that characterized his research: a willingness to suggest bold and provocative ideas, to take risks and to make imaginative leaps that could sometimes yield a rich harvest.
Fleischmann was born in Karoly Vary (Karlsbad) in Czechoslovakia in 1927. His father was of Jewish heritage and opposed Hitler’s regime; his family fled just before the German invasion to the Netherlands and then England. Fleischmann studied chemistry at Imperial College in London and, after a PhD in electrochemistry, he moved to the University of Newcastle. In 1967 he was appointed to the Faraday Chair of Chemistry at Southampton, where he explored reactions at electrode surfaces.
In 1974, Fleischmann and his coworkers observed unusually intense Raman emission (scattered light shifted in energy by the interaction with molecular vibrational states) from organic molecules adsorbed on the surface of silver electrodes. They did not immediately recognize that the enhancement was caused by the surface, and indeed the mechanism is still not fully understood – but surface-enhanced Raman spectroscopy (SERS) has become a valuable tool for investigating surface chemistry.
Around 1980 Fleischmann and Mark Wightman independently pioneered the use of ultramicroelectrodes just a few micrometres across to study otherwise-inaccessible electrode processes – for example, at low electrolyte concentrations or with very fast rates of reaction. Such innovations gave Fleischmann international repute. In 1985, two years after his early retirement from Southampton, he was elected a Fellow of the Royal Society.
Fleischmann’s longstanding interest in hydrogen surface chemistry on palladium led to the cold fusion experiments. When hydrogen molecules adsorbed onto palladium dissociate into atoms, these atoms can diffuse into the metal lattice, making the metal a ‘sponge’ able to soak up large amounts of hydrogen. Very high pressures of hydrogen can build up – perhaps, Flesichmann wondered, sufficient to trigger nuclear fusion.
Fleischmann’s retirement in 1983 freed him to conduct self-funded experiments at the University of Utah – a location conducive to Fleischmann, a passionate skier – with his former student Stanley Pons. They electrolysed solutions of lithium deuteroxide, collecting deuterium at the palladium cathode, and claimed to measure more heat output than could be accounted for by the energy fed in – a signature, they said, of deuterium fusion within the electrode. On returning in the morning to one experiment left running overnight, they found that the apparatus had been vaporized and the fume cupboard and part of the floor destroyed. Was this a particularly violent outburst of fusion?
Not until 1989 did Fleischmann, Pons and their student Marvin Hawkins move to publish their data. They discovered they were in competition with a team at Brigham Young University in Utah, led by physicist Steven Jones, which was conducting similar studies. Initially Fleischmann and Pons accused Jones of plagiarizing their ideas, but eventually the groups agreed to coordinate their announcements with a joint submission to Nature on 24th March. Yet Fleischmann and Pons first rushed a (highly uninformative) paper into print with the Journal of Electroanalytical Chemistry, organized a press conference on 23nd March, and faxed their paper to Nature that same day without telling Jones.
The rest, as they say, is history, told for example in Frank Close’s Too Hot To Handle (1991) and Gary Taubes’ Bad Science (1993). The fusion claims shocked the world: physicists had been trying for decades, at great expense but with no success, to harness nuclear fusion for energy generation. Now it appeared that chemists had achieved it at a minuscule fraction of the expense, potentially solving the energy crisis. Jones’ paper was eventually [Nature 338, 737; 1989] published by Nature; that of Pons, Fleischmann and Hawkins was withdrawn when the authors professed to be too busy, in the wake of their astounding announcement, to address the reviewers’ comments. When Pons spoke at the spring meeting of the American Chemical Society on 12th April, the atmosphere was jubilant: it was hailed as a triumph of chemistry over physics. Physicists were more sceptical, and pointed out serious problems with Fleischmann and Pons’ claims to have detected the emission of neutrons diagnostic of deuterium fusion.
Accusations that they had manipulated the neutron data were never substantiated, but what really put paid to cold fusion was the persistent failure of other groups to reliably reproduce the purported excess heat generation and other signatures of potential fusion. More accusations, recriminations and general bad behaviour followed: coercion, intimidation, litigation (Pons’ lawyer threatened Utah physicist Michael Salamon with legal action after he published his negative attempts at replication in Nature), withholding of data (Fleischmann refused outright at one meeting of physicists to discuss crucial control experiments), and suspicions of experimental tampering (were some groups spiking their equipment with tritium, a fingerprint of fusion?). The University of Utah sought aggressively to capitalize, throwing $5m at a ‘National Cold Fusion Institute’ that closed only two years after it opened.
Once cold fusion lost its credibility, Fleischmann and Pons moved to France to continue their work with private funding, but later fell out. Now only a few lone ‘believers’ pursue the work. Fleischmann did not distinguish himself in the aftermath, belittling critical peers in interviews and hinting at paranoid conspiracy theories. But perhaps the biggest casualty of cold fusion was electrochemistry itself, suddenly made to seem a morass of charlatanism and poor technique. That was unfair: some of the most authoritative (negative) attempts to replicate the results were conducted by electrochemists.
Flesichmann’s tragedy was almost Shakespearean, not least because he was himself in many ways a sympathetic character: resourceful, energetic, immensely inventive and remembered warmly by collaborators. As Linus Pauling and Fred Hoyle also exemplified, once you’ve been proved right against the odds, it becomes harder to accept the possibility of error. “Many a time in my life I have been accused of coming up with crazy ideas,” he once said. “Fortunately, I'm able to say that, so far, the critics have had to back off.” But although a final reckoning should not let genuine achievements be overshadowed by errors, the blot that cold fusion left on Fleischmann’s reputation is hard to expunge. To make a mistake or a premature claim, even to fall prey to self-deception, is a risk any scientist runs. The true test is how one deals with it.
Friday, August 31, 2012
The chemical brain
Here’s my latest Crucible column for Chemistry World. A techie one, but no harm in that. I also have a feature on nanobubbles in this (September) issue, and will try to stick that up, in extended form, on my website soon.
___________________________________________________________________
Bartosz Grzybowski of Northwestern University in Illinois, who has already established himself as one of the most inventive current practitioners of the chemical art, has unveiled a ‘chemo-informatic’ scheme called Chematica that can stake a reasonable claim to being paradigm-changing. He and his colleagues have spent years assembling the transformations linking chemical species into a vast network that codifies and organizing the known pathways through chemical space. Each node of the network is either a molecule or element, or a chemical reaction. Links connect reactants and products via the nexus of a known reaction. The full network contains around 7 million compound nodes and about the same number of reaction nodes. Grzybowski calls it a “collective chemical brain.”
I predict a mixed reaction from chemists. On the one hand the potential value of such a tool for discovering improved or entirely new synthetic pathways to drugs, materials and other useful products is tremendous, and has already been illustrated by Grzybowski’s team. On the other hand, Chematica seems to imply that chemistry is indeed, as the old jibe puts it, just cookery, and is something now better orchestrated by computer than by chemists.
I’ll come back to that. First let’s look at what Chematica is. Grzybowski first described the network in 2005 [1], when he was mostly concerned with its topological properties rather than with chemical insights. Like the Internet or some social networks, the chemical network has ‘scale-free’ connectivity, meaning that the distribution of nodes with different degrees of connectivity n is a power law: the number of nodes with n links is proportional to n(exp-α), where α is a constant. This means that a few very highly connected nodes are the hubs that bind the network together and provide shortcuts. The same structure is also found in the reaction network of compounds in metabolic pathways.
In a trio of new papers the researchers have now started to put the network to use. In the first, they perform an automated trawl for new one-pot reactions that can replace existing multi-step syntheses [2]. The advantages of single-step processes are obvious: no laborious separation and purification of products after each step, with consequent reductions in yield. Identifying potential one-pot processes linking molecular nodes that hitherto lacked a direct connection here means subjecting the relevant reactions to several filtering steps that check for compatibility – for example, checking that a water-solvated synthesis will not unintentionally hydrolyse functional groups. This filtering is painstaking in principle, but very quick once automated.
It is one thing to demonstrate that such one-pot syntheses are possible in principle, but Grzybowski and colleagues have ensured that at least some of those identified work in practice. Specifically, they looked for syntheses of quinoline-based molecules – common components of drugs and dyes – and thiophenes, which have useful electronic and optical properties. Many of the new pathways worked with high yields, in some cases demonstrably higher than those of alternative multi-step syntheses. Some false positives arise from errors in the literature used to build the network.
Another use of Chematica is to optimize existing syntheses – something previously reliant on manual or inexhaustive semi-automated searches. Looking for improved – basically, cheaper – routes to a given target is a matter of stepping progressively backwards from that molecule to preceding intermediates [3]. An algorithm can calculate the costs of all such steps in the network, working recursively backwards to a specified ‘depth’ (maximum number of synthetic steps) and finding the cheapest option. Applied to syntheses conducted by Grzybowski’s company ProChimia, Chematica offered potential savings of up to 45 percent if instituted for 51 of the company’s targets. The greatest the number of targets, the greater the savings because of the economies of shared ingredients and intermediates.
Finally, and perhaps most controversially, the researchers show how Chematica can be used to identify threats of chemical-weapons manufacture by terrorists [4]. The network can be searched for routes to harmful substances such as nerve agents using unregulated ingredients. Of course, it can also disclose such routes, but as with viral genomic data [5], open access to such data should be the best antidote to the risks they inherently pose.
Does all this, then, mean that synthetic organic chemists are about to be automated? The usual response is to insist that computers will never match human creativity. But that defence is looking increasingly under threat in, say, chess, maths and perhaps even music and visual art. In some ways chemical synthesis is as rule-bound as music if not chess, and thus ripe for an algorithmic approach. Perhaps at least some of the beauty rightly attributed to classic syntheses should be seen as illustrating human ingenuity in the face of tasks for which no better solution then existed. Synthetic schemes designed by humans surely won’t become obsolete any time soon – but there seems no harm in acknowledging that the time may come when the art and creativity of chemistry resides more solidly in our decisions of what to make, and why, than in how we make it.
References
1. M. Fialkowski, K. J. M. Bishop, V. A. Chubukov, C. J. Campbell & B. A. Grzybowski, Angew. Chem. Int. Ed. 44, 7263 (2005).
2. C. M. Gothard et al., Angew. Chem. Int. Ed. online publication 10.1002/anie.201202155 (2012).
3. M. Kowalik et al., Angew. Chem. Int. Ed. online publication 10.1002/anie.201202209 (2012).
4. P. E. Fuller, C. M. Gothard, N. A. Gothard, A. Wieckiewicz & B. A. Grzybowski, Angew. Chem. Int. Ed. online publication 10.1002/anie.201202210 (2012).
5. M. Imai et al., Nature 10.1038/nature10831 (2012).
___________________________________________________________________
Bartosz Grzybowski of Northwestern University in Illinois, who has already established himself as one of the most inventive current practitioners of the chemical art, has unveiled a ‘chemo-informatic’ scheme called Chematica that can stake a reasonable claim to being paradigm-changing. He and his colleagues have spent years assembling the transformations linking chemical species into a vast network that codifies and organizing the known pathways through chemical space. Each node of the network is either a molecule or element, or a chemical reaction. Links connect reactants and products via the nexus of a known reaction. The full network contains around 7 million compound nodes and about the same number of reaction nodes. Grzybowski calls it a “collective chemical brain.”
I predict a mixed reaction from chemists. On the one hand the potential value of such a tool for discovering improved or entirely new synthetic pathways to drugs, materials and other useful products is tremendous, and has already been illustrated by Grzybowski’s team. On the other hand, Chematica seems to imply that chemistry is indeed, as the old jibe puts it, just cookery, and is something now better orchestrated by computer than by chemists.
I’ll come back to that. First let’s look at what Chematica is. Grzybowski first described the network in 2005 [1], when he was mostly concerned with its topological properties rather than with chemical insights. Like the Internet or some social networks, the chemical network has ‘scale-free’ connectivity, meaning that the distribution of nodes with different degrees of connectivity n is a power law: the number of nodes with n links is proportional to n(exp-α), where α is a constant. This means that a few very highly connected nodes are the hubs that bind the network together and provide shortcuts. The same structure is also found in the reaction network of compounds in metabolic pathways.
In a trio of new papers the researchers have now started to put the network to use. In the first, they perform an automated trawl for new one-pot reactions that can replace existing multi-step syntheses [2]. The advantages of single-step processes are obvious: no laborious separation and purification of products after each step, with consequent reductions in yield. Identifying potential one-pot processes linking molecular nodes that hitherto lacked a direct connection here means subjecting the relevant reactions to several filtering steps that check for compatibility – for example, checking that a water-solvated synthesis will not unintentionally hydrolyse functional groups. This filtering is painstaking in principle, but very quick once automated.
It is one thing to demonstrate that such one-pot syntheses are possible in principle, but Grzybowski and colleagues have ensured that at least some of those identified work in practice. Specifically, they looked for syntheses of quinoline-based molecules – common components of drugs and dyes – and thiophenes, which have useful electronic and optical properties. Many of the new pathways worked with high yields, in some cases demonstrably higher than those of alternative multi-step syntheses. Some false positives arise from errors in the literature used to build the network.
Another use of Chematica is to optimize existing syntheses – something previously reliant on manual or inexhaustive semi-automated searches. Looking for improved – basically, cheaper – routes to a given target is a matter of stepping progressively backwards from that molecule to preceding intermediates [3]. An algorithm can calculate the costs of all such steps in the network, working recursively backwards to a specified ‘depth’ (maximum number of synthetic steps) and finding the cheapest option. Applied to syntheses conducted by Grzybowski’s company ProChimia, Chematica offered potential savings of up to 45 percent if instituted for 51 of the company’s targets. The greatest the number of targets, the greater the savings because of the economies of shared ingredients and intermediates.
Finally, and perhaps most controversially, the researchers show how Chematica can be used to identify threats of chemical-weapons manufacture by terrorists [4]. The network can be searched for routes to harmful substances such as nerve agents using unregulated ingredients. Of course, it can also disclose such routes, but as with viral genomic data [5], open access to such data should be the best antidote to the risks they inherently pose.
Does all this, then, mean that synthetic organic chemists are about to be automated? The usual response is to insist that computers will never match human creativity. But that defence is looking increasingly under threat in, say, chess, maths and perhaps even music and visual art. In some ways chemical synthesis is as rule-bound as music if not chess, and thus ripe for an algorithmic approach. Perhaps at least some of the beauty rightly attributed to classic syntheses should be seen as illustrating human ingenuity in the face of tasks for which no better solution then existed. Synthetic schemes designed by humans surely won’t become obsolete any time soon – but there seems no harm in acknowledging that the time may come when the art and creativity of chemistry resides more solidly in our decisions of what to make, and why, than in how we make it.
References
1. M. Fialkowski, K. J. M. Bishop, V. A. Chubukov, C. J. Campbell & B. A. Grzybowski, Angew. Chem. Int. Ed. 44, 7263 (2005).
2. C. M. Gothard et al., Angew. Chem. Int. Ed. online publication 10.1002/anie.201202155 (2012).
3. M. Kowalik et al., Angew. Chem. Int. Ed. online publication 10.1002/anie.201202209 (2012).
4. P. E. Fuller, C. M. Gothard, N. A. Gothard, A. Wieckiewicz & B. A. Grzybowski, Angew. Chem. Int. Ed. online publication 10.1002/anie.201202210 (2012).
5. M. Imai et al., Nature 10.1038/nature10831 (2012).
Friday, August 24, 2012
Computers get emotional
Here’s more on Iamus, the computer programme that writes music you might actually want to listen to. It is published in Nature this week, although there are more references in this version. The CD of Iamus’ music is released in mid-September (not the 1st, as the Nature piece says), and is simply called Iamus (Melomics Records). I’m looking forward to that.
________________________________________________________________
If a computer can produce something that moves us, would this take artificial intelligence beyond an important threshold? That’s one of the questions seemingly raised by an algorithm called Iamus, developed by Francisco Vico and colleagues at the University of Malaga, which composes music from scratch.
There’s nothing new about computers making music. They have been used by composers since the early days of computer technology in the 1960s, most notably by the experimental Greek composer Iannis Xenakis. Neither is there anything mysterious about an algorithmic approach to composition: most music is highly rule-bound, even formulaic, and so lends itself to that. An early attempt at computer music in the 1980s, the programme called CHORAL devised by computer scientist Kemal Ebcioglu to harmonise chorales in the style of J. S. Bach [1], drew on well formulated principles of harmony and melody that were observed by Bach himself [2].
But it’s one thing to slavishly follow the rules, quite another to come up with original melodies and harmonic progressions that will captivate and even move the listener – especially if the composing is being performed without any human input. Computer scientists have been quite successful in making programmes that can learn from human examples. Early improvisational algorithms such as the jazz-inflected GenJam [3], devised by computer scientist John Biles, and GenBebop, a system created by cognitive scientists Lee Spector and Adam Alpern to produce solos in the style of Charlie Parker [4], gave indifferent results even by their creators’ admission. But Continuator, a programme devised by François Pachet at Sony’s Computer Science Laboratory in Paris, is much more convincing [5]. In a kind of ‘Turing test’ where Continuator alternated with an improvising human pianist and elaborated on his suggestions, expert listeners had trouble telling man and machine apart.
Contrary to common perception, however, improvising is fairly rule-bound too, so it’s not hard to see how human-derived musical material can be plausibly mutated and elaborated in an automated way. Coming up with the raw musical ideas is a much harder task for a computer. Before now, efforts to achieve this have been distinctly underwhelming, sounding like bland pastiche all too evidently shaped by clichĂ©d harmonic progressions and melodic structures.
This is where Iamus’ creators claim to have something new. The algorithm, named after the legendary son of Apollo who could understand the language of birds, is inspired by Darwinian evolution. The computer generates very simple ‘musical genomes’ , rather like little motifs, which are then evolved, mutated and elaborated until they acquire genuine musical content and interest [6]. Genetic and evolutionary algorithms for making music are also not new (see, for example, ref. 7), but Iamus seems capable of dramatic invention: the music is far more than just a succession of transparent variations. Vico and colleagues, in collaboration with composer and pianist Gustavo DĂaz-Jerez of the Conservatory of the Basque Country in San Sebastian, recently recorded some of Iamus’s scores with leading musicians, including two orchestral pieces played by the London Symphony Orchestra, for release in September. They broadcast a live performance of two of these pieces from the University of Malaga in July to commemorate the 100th anniversary of Alan Turing’s birth.
The recorded compositions are all in a modernist classical style – full of dissonance, but with hints of harmony and rich textures that might put a listener in mind of composers such as Gyorgy Ligeti and Krzysztof Penderecki. But the same approach can be used for other idioms too, and Vico and colleagues say that it might supply a cheap, convenient way of generating music for commercial purposes.
The willingness of professionals to perform the works marks out Iamus as unique. The LSO’s chairman Lennox Mackenzie was impressed with what it had achieved but felt that the music still fell short of that by good human composers. It struck him as “going nowhere” – a complaint often made of other modernist works – yet ultimately achieving an “epic” quality. Many of the other musicians were pleasantly surprised by the material, and found some of it genuinely expressive.
Which brings us to the initial question. If Iamus can simulate (and thus stimulate) emotionality, is it not just ‘thinking’ in the limited sense of the Turing test but apparently displaying human characteristics?
Here we should heed studies of music cognition which have shown that emotion in music is not some deeply mysterious process but has its own rules and regularities [8]. For example, certain musical structures, such as ‘false trails’ that create and then confound expectations, or judicious injections of dissonance followed by resolution, can elicit emotion quite reliably [9]. This should be no surprise to anyone whose emotions have been helplessly manipulated by formulaic film scores.
What’s more, the involvement of human performers is vital. Music lovers know very well that the same piece can be performed in a dry, unengaged manner or with heart-rending fervour. Good performers achieve expression with a wide range of ‘tricks’, such as subtle distortions of tempo, intonation and timbre [10].
Iamus’ work might therefore be considered to demonstrate the often neglected role of performer and listener in ‘making music’. The nineteenth-century Romantic tradition has fostered a deep-seated belief in the inherent genius of the composer, as though he or she has imbued the very notes with passion. It’s not to deny the undoubted sensitivity and skill of the greatest composers to say that a composition only becomes music in the mind of the listener, through the interaction of the composer’s and the performer’s choices with the wealth of learning and association that even allegedly ‘unskilled’ listeners possess.
This consideration ought also to diminish an inherent prejudice (evident in the critical responses to Iamus so far) against computer-composed music. Neuroscientists Stefan Koelsch and Nikolaus Steinbeis have shown that part of this prejudice is unconscious: the same piece of music may or may not activate parts of the brain associated with ascribing intention to others, depending on whether listeners have been told that the piece was composed by a human or by computer [11]. It’s possible that human performance of computer-made music might at least partly override this obstacle to emotional engagement. But we should also celebrate the way that Iamus, far from threatening our supposedly unique claim to creativity, can put the audience back in the picture as a participant in the creative act.
References
1. EbcioÄźlu, K. Proc. 1984 Int. Computer Music Conf., 135-144, held in IRCAM, Paris. Computer Music Association, San Francisco, 1985.
2. Rohrmeier, M. & Cross, I. (2008), in Proc. 10th Int. Conf. on Music Percept. Cognit. (ICMPC 2008), Sapporo, Japan.
3. Biles, J. A., in Proc. 1994 Int. Computer Music Conf., 131-137. International Computer Music Association, San Francisco, 1994.
4. Spector, L. & Alpern, A., in Proc. Twelfth Natl Conf. Artificial Intelligence, AAAI-94, 3-8. AAAI Press/MIT Press, Menlo Park CA and Cambridge MA (1994).
5. Pachet, F., J. New Music Res. 32, 333-341 (2003).
6. DĂaz-Jerez, G. Leonardo Music J. 21, 13-14 (2011).
7. MacCallum, R. M., Mauch, M., Burt, A. & Leroi, A. M. Proc. Natl Acad. Sci. USA 10.1073/pnas.1203182109 (2012).
8. Sloboda, J. A. The Musical Mind: The Cognitive Psychology of Music. Clarendon Press, Oxford, 1985.
9. Juslin, P. N. & Sloboda, J. A. (eds). Music and Emotion. Oxford University Press, Oxford, 2001.
10. Meyer, L. B. Emotion and Meaning in Music. University of Chicago Press, Chicago, 1956.
11. Steinbeis, N. & Koelsch, S. Cerebral Cortex 19, 619-623 (2009).
________________________________________________________________
If a computer can produce something that moves us, would this take artificial intelligence beyond an important threshold? That’s one of the questions seemingly raised by an algorithm called Iamus, developed by Francisco Vico and colleagues at the University of Malaga, which composes music from scratch.
There’s nothing new about computers making music. They have been used by composers since the early days of computer technology in the 1960s, most notably by the experimental Greek composer Iannis Xenakis. Neither is there anything mysterious about an algorithmic approach to composition: most music is highly rule-bound, even formulaic, and so lends itself to that. An early attempt at computer music in the 1980s, the programme called CHORAL devised by computer scientist Kemal Ebcioglu to harmonise chorales in the style of J. S. Bach [1], drew on well formulated principles of harmony and melody that were observed by Bach himself [2].
But it’s one thing to slavishly follow the rules, quite another to come up with original melodies and harmonic progressions that will captivate and even move the listener – especially if the composing is being performed without any human input. Computer scientists have been quite successful in making programmes that can learn from human examples. Early improvisational algorithms such as the jazz-inflected GenJam [3], devised by computer scientist John Biles, and GenBebop, a system created by cognitive scientists Lee Spector and Adam Alpern to produce solos in the style of Charlie Parker [4], gave indifferent results even by their creators’ admission. But Continuator, a programme devised by François Pachet at Sony’s Computer Science Laboratory in Paris, is much more convincing [5]. In a kind of ‘Turing test’ where Continuator alternated with an improvising human pianist and elaborated on his suggestions, expert listeners had trouble telling man and machine apart.
Contrary to common perception, however, improvising is fairly rule-bound too, so it’s not hard to see how human-derived musical material can be plausibly mutated and elaborated in an automated way. Coming up with the raw musical ideas is a much harder task for a computer. Before now, efforts to achieve this have been distinctly underwhelming, sounding like bland pastiche all too evidently shaped by clichĂ©d harmonic progressions and melodic structures.
This is where Iamus’ creators claim to have something new. The algorithm, named after the legendary son of Apollo who could understand the language of birds, is inspired by Darwinian evolution. The computer generates very simple ‘musical genomes’ , rather like little motifs, which are then evolved, mutated and elaborated until they acquire genuine musical content and interest [6]. Genetic and evolutionary algorithms for making music are also not new (see, for example, ref. 7), but Iamus seems capable of dramatic invention: the music is far more than just a succession of transparent variations. Vico and colleagues, in collaboration with composer and pianist Gustavo DĂaz-Jerez of the Conservatory of the Basque Country in San Sebastian, recently recorded some of Iamus’s scores with leading musicians, including two orchestral pieces played by the London Symphony Orchestra, for release in September. They broadcast a live performance of two of these pieces from the University of Malaga in July to commemorate the 100th anniversary of Alan Turing’s birth.
The recorded compositions are all in a modernist classical style – full of dissonance, but with hints of harmony and rich textures that might put a listener in mind of composers such as Gyorgy Ligeti and Krzysztof Penderecki. But the same approach can be used for other idioms too, and Vico and colleagues say that it might supply a cheap, convenient way of generating music for commercial purposes.
The willingness of professionals to perform the works marks out Iamus as unique. The LSO’s chairman Lennox Mackenzie was impressed with what it had achieved but felt that the music still fell short of that by good human composers. It struck him as “going nowhere” – a complaint often made of other modernist works – yet ultimately achieving an “epic” quality. Many of the other musicians were pleasantly surprised by the material, and found some of it genuinely expressive.
Which brings us to the initial question. If Iamus can simulate (and thus stimulate) emotionality, is it not just ‘thinking’ in the limited sense of the Turing test but apparently displaying human characteristics?
Here we should heed studies of music cognition which have shown that emotion in music is not some deeply mysterious process but has its own rules and regularities [8]. For example, certain musical structures, such as ‘false trails’ that create and then confound expectations, or judicious injections of dissonance followed by resolution, can elicit emotion quite reliably [9]. This should be no surprise to anyone whose emotions have been helplessly manipulated by formulaic film scores.
What’s more, the involvement of human performers is vital. Music lovers know very well that the same piece can be performed in a dry, unengaged manner or with heart-rending fervour. Good performers achieve expression with a wide range of ‘tricks’, such as subtle distortions of tempo, intonation and timbre [10].
Iamus’ work might therefore be considered to demonstrate the often neglected role of performer and listener in ‘making music’. The nineteenth-century Romantic tradition has fostered a deep-seated belief in the inherent genius of the composer, as though he or she has imbued the very notes with passion. It’s not to deny the undoubted sensitivity and skill of the greatest composers to say that a composition only becomes music in the mind of the listener, through the interaction of the composer’s and the performer’s choices with the wealth of learning and association that even allegedly ‘unskilled’ listeners possess.
This consideration ought also to diminish an inherent prejudice (evident in the critical responses to Iamus so far) against computer-composed music. Neuroscientists Stefan Koelsch and Nikolaus Steinbeis have shown that part of this prejudice is unconscious: the same piece of music may or may not activate parts of the brain associated with ascribing intention to others, depending on whether listeners have been told that the piece was composed by a human or by computer [11]. It’s possible that human performance of computer-made music might at least partly override this obstacle to emotional engagement. But we should also celebrate the way that Iamus, far from threatening our supposedly unique claim to creativity, can put the audience back in the picture as a participant in the creative act.
References
1. EbcioÄźlu, K. Proc. 1984 Int. Computer Music Conf., 135-144, held in IRCAM, Paris. Computer Music Association, San Francisco, 1985.
2. Rohrmeier, M. & Cross, I. (2008), in Proc. 10th Int. Conf. on Music Percept. Cognit. (ICMPC 2008), Sapporo, Japan.
3. Biles, J. A., in Proc. 1994 Int. Computer Music Conf., 131-137. International Computer Music Association, San Francisco, 1994.
4. Spector, L. & Alpern, A., in Proc. Twelfth Natl Conf. Artificial Intelligence, AAAI-94, 3-8. AAAI Press/MIT Press, Menlo Park CA and Cambridge MA (1994).
5. Pachet, F., J. New Music Res. 32, 333-341 (2003).
6. DĂaz-Jerez, G. Leonardo Music J. 21, 13-14 (2011).
7. MacCallum, R. M., Mauch, M., Burt, A. & Leroi, A. M. Proc. Natl Acad. Sci. USA 10.1073/pnas.1203182109 (2012).
8. Sloboda, J. A. The Musical Mind: The Cognitive Psychology of Music. Clarendon Press, Oxford, 1985.
9. Juslin, P. N. & Sloboda, J. A. (eds). Music and Emotion. Oxford University Press, Oxford, 2001.
10. Meyer, L. B. Emotion and Meaning in Music. University of Chicago Press, Chicago, 1956.
11. Steinbeis, N. & Koelsch, S. Cerebral Cortex 19, 619-623 (2009).
Why selfishness still doesn’t pay
Here’s my latest news story for Nature.
____________________________________________________________________
A recent finding that undermines conventional thinking on the evolution of cooperation doesn’t, after all, prevent altruistic behaviour from emerging.
For the past several decades, one of the central results of game theory has seemed to be that self-interest can drive social cooperation, because in the long term selfish behaviour hurts you as much as your competitors. Last May, two leading physicists, William Press of the University of Texas and Freeman Dyson of the Institute of Advanced Study in Princeton, argued otherwise. They showed how, in the classic ‘game’ from which cooperation seems to evolve, called the Prisoner’s Dilemma, it’s possible to be successfully selfish [1].
This apparently revolutionary idea has now been challenged by two evolutionary biologists at Michigan State University in East Lansing. In a preprint [2], Christoph Adami and Arend Hintze say that the strategy proposed by Press and Dyson is “evolutionarily unstable”. In a population of agents all seeking for the best way to play the Prisoner’s Dilemma, those using the new selfish strategy will eventually be bested by more generous players.
The Prisoner’s Dilemma is a simple ‘game’ that captures the fundamental problem faced by a population of organisms competing for limited resources: the temptation to cheat or freeload. You might do better acting together (cooperating) than alone, but the temptation is to let others put in the effort or face the risks while sharing yourself in the rewards.
In the Prisoner’s Dilemma as it was formulated by researchers in the 1950s, two prisoners accused of a crime are questioned. If one helps convict the other by testifying against him, he is offered a lighter sentence. But if both testify against the other, their sentences will be heavier than if both refuse to do so.
In a single ‘round’ of this game, it always makes sense to ‘defect’ – to shop the other guy. That way you’re better off whatever your opponent does. But if the game is played again and again – if you have repeated opportunities to cheat on the other player – you both do better to cooperate. This so-called iterated Prisoner’s Dilemma has been used to show how cooperation could arise in selfish populations: those genetically disposed to cooperate will be more successful than those predisposed to defect.
But what’s the best way to play the iterated game in a population of individuals using many different strategies? In the 1980s, political scientist Robert Axelrod tried to answer that question by staging computerized tournaments, inviting anyone to submit a strategy and then pitching them all against one another in many one-to-one bouts.
The winner was a very simple strategy called Tit-for-Tat (TfT), which merely copies its opponent’s behaviour from the last round. If the opponent defected in the last round, TfT does so in the current one. Against cooperators, TfT always cooperates; against defectors, it always defects. It is, in effect, ‘tough but fair’. The moral message seemed reassuring: it pays to be nice, but nastiness should be punished.
However, in further studies it became clear that TfT might not always dominate in evolutionary games where the most successful strategies are propagated from generation to generation. Slightly more forgiving strategies, which don’t get caught in cycles of mutual recrimination by a single mistaken defection, can do better in the long run. In fact, there is no single best way to play the game – it depends on your opponents. Nonetheless, the iterated Prisoner’s Dilemma seemed to explain how cooperation between unrelated individuals might evolve: why some animals hunt in packs and why we have altruistic instincts.
Press and Dyson seemed to shatter this cosy picture. They showed that there exists a class of strategies, which for technical reasons they call zero-determinant (ZD) strategies, in which one player can force the other to accept a less-than-equal share of the ‘payoff’ in the Prisoner’s Dilemma. In effect, the victim has to either grit his teeth and accept this unfair division, or punish the other player at a greater cost to himself. This turns the game into a different one, known as an Ultimatum game, in which one player is presented with the choice of either accepting an unequal distribution of the payoff or, if he refuses, both players losing out.
It turns out that TfT is just a special case of these ZD strategies in which the payoffs happen to be equal. Like a TfT player, a ZD player bases his next choice of cooperate/defect on what happened in the last round: it is said to be a ‘memory-one’ strategy. But instead of being rigidly deterministic – this previous outcome dictates that choice – it is probabilistic: the choice to cooperate or defect is made with a certain probability for each of the four possible outcomes of the last round. A judicious choice of these probabilities enables one player to control the payoff that the other receives.
According to William Poundstone, author of the 1992 book The Prisoner’s Dilemma, “The Press-Dyson finding directly challenges the two notions at the heart of the Prisoner’s Dilemma – that you can't fool evolution, and that the most successful strategies are fair strategies.” Nonetheless, Press says that “Freeman's and my paper has been warmly received by Prisoner’s Dilemma experts. More than one has expressed regret at not having discovered the ZD strategies previously.”
“The paper did indeed cause quite a stir, because the main result appeared to be completely new, despite intense research in this area for the last 30 years”, says Adami. It wasn’t totally new, however – in 1997 game theorists Karl Sigmund of the University of Vienna and Martin Nowak of Harvard University discovered strategies that similarly allow one player to fix the other’s payoff at a specified level [3]. But they admit that “we didn’t know about the vast and fascinating realm of zero-determinant strategies.” The work of Press and Dyson “opens a new facet in the study of trigger strategies and folk theorems for iterated games, and offers a highly stimulating approach for moral philosophers,” they say.
The ZD strategies are not as dispiriting as perhaps they sound, says Press, because they allow a new balance to be found if both players understand the principles. “Once both players understand ZD, then each has the power to set the other’s score, independent of the other’s actions. This allows them to make an enforceable treaty, not possible using simpler strategies.”
In other words, the ZD strategy forces players to reflect, to think ahead, to consider the opponent’s point of view, and not just try to get the highest possible score. It “allows for a whole range of careful, deliberative negotiations”, Press says. “This is a world in which diplomacy trumps conflict.”
But now Adami and Hintze say that this world might not exist – or not for long. They find that, in an evolutionary iterated Prisoner’s Dilemma game in which the prevalence of particular strategies depends on their success, ZD players are soon out-competed by others using more common strategies, and so they will evolve to become non-ZD players themselves. That’s because ZD players suffer from the same problem as habitual defectors: they do badly against their own kind.
There’s one exception: ZD players can persist if they can figure out whether they are playing another ZD player or not. Then they can exploit the advantages of ZD strategies against non-ZD players, but will switch to a more advantageous non-ZD strategy when faced with their own kind.
That in turn means, however, that non-ZD players could gain the upper hand by using strategies that look like ZD but are not, thus fooling ZD players into abandoning their extortionate strategy. This could lead to the same kind of ‘arms race’ seen in some kinds of biological mimicry, where a harmless species evolves to look like a harmful one, while the harmful one tries to evolve away from its imitator.
Sigmund and Nowak, with colleague Christian Hilbe, have also shown in work not yet published that the ZD strategy is evolutionarily unstable, but can pave the way for the emergence of cooperators from a more selfish community. “ZD strategies do not establish a strong foothold in the population”, says Sigmund.
Game theorist and economist Samuel Bowles at the Santa Fe Institute in New Mexico feels that these results demote the interest of the ZD strategies. “The question of their evolutionary stability is critical, and the paper makes their limitations clear. Because they are not evolutionarily stable, I’d call them merely a curiosity of little interest to evolutionary biology or any of the other biological sciences.”
Adami is not so sure that they won’t be fund in the wild. “We don’t usually have nearly enough information about animal decisions”, he says. “But in my experience, anything that is imaginable has probably evolved somewhere, sometime. To gather conclusive evidence about it is a whole different matter.”
Could they be found in human society too? “It’s not inconceivable”, says Adami, “but we have to keep in mind that humans very rarely make decisions based only on their and their opponent's last move. It is much more likely that this type of strategy is in use in automated trading programs, such as those involved in high-frequency trading of stocks and commodities. However, because these programs are usually secret, we wouldn't know about it.”
References
1. Press, W. H. & Dyson, F. J. Proc. Natl Acad. Sci. USA 10.1073/pnas.1206569109 (2012).
2. Adami, C. & Hintze, A. preprint http://www.arxiv.org/abs/1208.2666 (2012).
3. Nowak, M. A., Boerlijst, M. C. & Sigmund, K., Am. Math. Soc. Monthly 104, 303-307 (1997).
____________________________________________________________________
A recent finding that undermines conventional thinking on the evolution of cooperation doesn’t, after all, prevent altruistic behaviour from emerging.
For the past several decades, one of the central results of game theory has seemed to be that self-interest can drive social cooperation, because in the long term selfish behaviour hurts you as much as your competitors. Last May, two leading physicists, William Press of the University of Texas and Freeman Dyson of the Institute of Advanced Study in Princeton, argued otherwise. They showed how, in the classic ‘game’ from which cooperation seems to evolve, called the Prisoner’s Dilemma, it’s possible to be successfully selfish [1].
This apparently revolutionary idea has now been challenged by two evolutionary biologists at Michigan State University in East Lansing. In a preprint [2], Christoph Adami and Arend Hintze say that the strategy proposed by Press and Dyson is “evolutionarily unstable”. In a population of agents all seeking for the best way to play the Prisoner’s Dilemma, those using the new selfish strategy will eventually be bested by more generous players.
The Prisoner’s Dilemma is a simple ‘game’ that captures the fundamental problem faced by a population of organisms competing for limited resources: the temptation to cheat or freeload. You might do better acting together (cooperating) than alone, but the temptation is to let others put in the effort or face the risks while sharing yourself in the rewards.
In the Prisoner’s Dilemma as it was formulated by researchers in the 1950s, two prisoners accused of a crime are questioned. If one helps convict the other by testifying against him, he is offered a lighter sentence. But if both testify against the other, their sentences will be heavier than if both refuse to do so.
In a single ‘round’ of this game, it always makes sense to ‘defect’ – to shop the other guy. That way you’re better off whatever your opponent does. But if the game is played again and again – if you have repeated opportunities to cheat on the other player – you both do better to cooperate. This so-called iterated Prisoner’s Dilemma has been used to show how cooperation could arise in selfish populations: those genetically disposed to cooperate will be more successful than those predisposed to defect.
But what’s the best way to play the iterated game in a population of individuals using many different strategies? In the 1980s, political scientist Robert Axelrod tried to answer that question by staging computerized tournaments, inviting anyone to submit a strategy and then pitching them all against one another in many one-to-one bouts.
The winner was a very simple strategy called Tit-for-Tat (TfT), which merely copies its opponent’s behaviour from the last round. If the opponent defected in the last round, TfT does so in the current one. Against cooperators, TfT always cooperates; against defectors, it always defects. It is, in effect, ‘tough but fair’. The moral message seemed reassuring: it pays to be nice, but nastiness should be punished.
However, in further studies it became clear that TfT might not always dominate in evolutionary games where the most successful strategies are propagated from generation to generation. Slightly more forgiving strategies, which don’t get caught in cycles of mutual recrimination by a single mistaken defection, can do better in the long run. In fact, there is no single best way to play the game – it depends on your opponents. Nonetheless, the iterated Prisoner’s Dilemma seemed to explain how cooperation between unrelated individuals might evolve: why some animals hunt in packs and why we have altruistic instincts.
Press and Dyson seemed to shatter this cosy picture. They showed that there exists a class of strategies, which for technical reasons they call zero-determinant (ZD) strategies, in which one player can force the other to accept a less-than-equal share of the ‘payoff’ in the Prisoner’s Dilemma. In effect, the victim has to either grit his teeth and accept this unfair division, or punish the other player at a greater cost to himself. This turns the game into a different one, known as an Ultimatum game, in which one player is presented with the choice of either accepting an unequal distribution of the payoff or, if he refuses, both players losing out.
It turns out that TfT is just a special case of these ZD strategies in which the payoffs happen to be equal. Like a TfT player, a ZD player bases his next choice of cooperate/defect on what happened in the last round: it is said to be a ‘memory-one’ strategy. But instead of being rigidly deterministic – this previous outcome dictates that choice – it is probabilistic: the choice to cooperate or defect is made with a certain probability for each of the four possible outcomes of the last round. A judicious choice of these probabilities enables one player to control the payoff that the other receives.
According to William Poundstone, author of the 1992 book The Prisoner’s Dilemma, “The Press-Dyson finding directly challenges the two notions at the heart of the Prisoner’s Dilemma – that you can't fool evolution, and that the most successful strategies are fair strategies.” Nonetheless, Press says that “Freeman's and my paper has been warmly received by Prisoner’s Dilemma experts. More than one has expressed regret at not having discovered the ZD strategies previously.”
“The paper did indeed cause quite a stir, because the main result appeared to be completely new, despite intense research in this area for the last 30 years”, says Adami. It wasn’t totally new, however – in 1997 game theorists Karl Sigmund of the University of Vienna and Martin Nowak of Harvard University discovered strategies that similarly allow one player to fix the other’s payoff at a specified level [3]. But they admit that “we didn’t know about the vast and fascinating realm of zero-determinant strategies.” The work of Press and Dyson “opens a new facet in the study of trigger strategies and folk theorems for iterated games, and offers a highly stimulating approach for moral philosophers,” they say.
The ZD strategies are not as dispiriting as perhaps they sound, says Press, because they allow a new balance to be found if both players understand the principles. “Once both players understand ZD, then each has the power to set the other’s score, independent of the other’s actions. This allows them to make an enforceable treaty, not possible using simpler strategies.”
In other words, the ZD strategy forces players to reflect, to think ahead, to consider the opponent’s point of view, and not just try to get the highest possible score. It “allows for a whole range of careful, deliberative negotiations”, Press says. “This is a world in which diplomacy trumps conflict.”
But now Adami and Hintze say that this world might not exist – or not for long. They find that, in an evolutionary iterated Prisoner’s Dilemma game in which the prevalence of particular strategies depends on their success, ZD players are soon out-competed by others using more common strategies, and so they will evolve to become non-ZD players themselves. That’s because ZD players suffer from the same problem as habitual defectors: they do badly against their own kind.
There’s one exception: ZD players can persist if they can figure out whether they are playing another ZD player or not. Then they can exploit the advantages of ZD strategies against non-ZD players, but will switch to a more advantageous non-ZD strategy when faced with their own kind.
That in turn means, however, that non-ZD players could gain the upper hand by using strategies that look like ZD but are not, thus fooling ZD players into abandoning their extortionate strategy. This could lead to the same kind of ‘arms race’ seen in some kinds of biological mimicry, where a harmless species evolves to look like a harmful one, while the harmful one tries to evolve away from its imitator.
Sigmund and Nowak, with colleague Christian Hilbe, have also shown in work not yet published that the ZD strategy is evolutionarily unstable, but can pave the way for the emergence of cooperators from a more selfish community. “ZD strategies do not establish a strong foothold in the population”, says Sigmund.
Game theorist and economist Samuel Bowles at the Santa Fe Institute in New Mexico feels that these results demote the interest of the ZD strategies. “The question of their evolutionary stability is critical, and the paper makes their limitations clear. Because they are not evolutionarily stable, I’d call them merely a curiosity of little interest to evolutionary biology or any of the other biological sciences.”
Adami is not so sure that they won’t be fund in the wild. “We don’t usually have nearly enough information about animal decisions”, he says. “But in my experience, anything that is imaginable has probably evolved somewhere, sometime. To gather conclusive evidence about it is a whole different matter.”
Could they be found in human society too? “It’s not inconceivable”, says Adami, “but we have to keep in mind that humans very rarely make decisions based only on their and their opponent's last move. It is much more likely that this type of strategy is in use in automated trading programs, such as those involved in high-frequency trading of stocks and commodities. However, because these programs are usually secret, we wouldn't know about it.”
References
1. Press, W. H. & Dyson, F. J. Proc. Natl Acad. Sci. USA 10.1073/pnas.1206569109 (2012).
2. Adami, C. & Hintze, A. preprint http://www.arxiv.org/abs/1208.2666 (2012).
3. Nowak, M. A., Boerlijst, M. C. & Sigmund, K., Am. Math. Soc. Monthly 104, 303-307 (1997).
Thursday, August 23, 2012
Are we not reproducing enough?
Here is my Crucible column from the August issue of Chemistry World. This topic seems to be becoming a big deal, as witnessed for example by the creation of this initiative for replication of results from the PLoS journals – I note that their advisory board includes Brian Nosek, whose work I mention below.
________________________________________________________________
How much of the published literature should you believe? Not much, by some accounts. A 2005 paper by epidemiologist John Ioannidis of the University of Ioannina School of Medicine in Greece had the stark title “Why most published research findings are false” [1]. Ioannidis claimed that “for most study designs and settings, it is more likely for a research claim to be false than true”, and that often published claims simply reflected the prevailing bias of the field. Ioannidis suspected that some “established classics” in the literature wouldn’t stand up to close scrutiny.
His focus was on biomedical research, in particular clinical trials of drugs, where inferences have to be made from complex statistics, perhaps with small sample sizes. Here, not only might the effects being sought be rather marginal but there are also strong biases and prejudices introduced by financial pressures. Reports of drug trials certainly do have a bias towards positive outcomes, prompting valid calls for all drug trials to be registered before the study is undertaken so that negative findings can’t be quietly dropped.
These problems with pharmaceutical research are in themselves troubling for some chemists. But is this mostly an issue for Big Pharma, with its distorting profit motives and its reliance on statistics rather than more reductive, step-by-step experimentation? Probably not, Daniel Sarewitz of the Consortium for Science, Policy and Outcomes at Arizona State University claimed in Nature last May [2]. According to Sarewitz, systematic error due to bias, whether conscious or not, is “is likely to be prevalent in any field that seeks to predict the behaviour of complex systems – economics, ecology, environmental science, epidemiology and so on”. This figures: all these fields tend to depend on statistical inference of often marginal effects operating through mechanisms that may be poorly understood and perhaps nigh impossible to delineate.
But what about the subjects we like to think of as the “hard sciences” – like most of chemistry? Surely you can place more trust in spectra and rate constants and crystal structures than in scatter plots? Perhaps – but ‘trust’ is often what it is. Not many studies are ever repeated verbatim, and it’s generally acknowledged that crystallographic databases are probably full of errors, if only minor. The chance of experiments being replicated is probably proportional to the significance of the results. Maybe the greater good doesn’t suffer much from a literature full of flawed but uninteresting work – but that would offer scant support for science’s supposedly self-correcting nature.
And problems do crop up on close examination. Take, for example, the recent attempt by Darragh Crotty and colleagues at Trinity College Dublin to replicate the claims of Russian biochemist Anatoly Buchachenko and his coworkers, who since 2004 have been documenting (in good journals) the influence of a weak magnetic field on the rate of enzymatic production of ATP [3]. The Russians report that millitesla magnetic fields can more than double the reaction rate when the phosphorylating enzymes contain 25Mg (which is magnetic) rather than the other two stable isotopes 24Mg and 26Mg. Crotty and colleagues set out to test this because it bore on controversial claims of physiological effects from weak electromagnetic fields. They found no difference in reaction rate for all three magnesium isotopes [4]. So far the discrepancy remains puzzling.
If this is indeed a wider problem than is commonly recognized for all sciences, what to do? Sarewitz suggests reducing hype and strengthening ties between fundamental research and real-world testing. Ioannidis implores researchers to be honest with themselves about the ‘pre-study odds’ of their hypothesis being true. This purging of preconception and self-deception is what Francis Bacon called for in the seventeenth century when he argued that natural philosophers seeking truth must free themselves from ‘idols of the mind’. But as Ioannis recognizes, changing mindsets isn’t easy.
Another perspective is offered in a preprint by psychologist Brian Nosek of the University of Virginia and his colleagues [5]. They point out that professional success for scientists relies on publishing, but publication both favours positive results and prefers novelty over replication. What is needed is a way to rescue scientists’ ostensible aim – getting it right – from their short-term, pragmatic aim – getting it published. Among things that won’t work, the authors say, are journals devoted to replications and tougher peer review (which can already display stifling conservatism). Instead we need metrics for evaluating what is worth replicating, journal editorial policies that focus on soundness rather than ‘importance’, less focus on sheer publication productivity for job and tenure applicants, lower barriers to publication (so that it becomes less coveted in itself), and in particular, new ways of releasing results: open access to data, methods, tools and lab books. One can find problems with all of these, but the old ways of science publishing are looking increasingly archaic and flawed. What have we got to hide?
1. J. P. A. Ioannis, PLoS Med. 2, e124 (2005).
2. D. Sarewitz, Nature 485, 149 (2012).
3. A. L. Buchachenko & D. A. Kuznetsov, J. Am. Chem. Soc. 130, 12868-12869 (2008).
4. D. Crotty et al., Proc. Natl Acad. Sci. USA 109, 1437-1442 (2012).
5. B. A. Nosek, J. R. Spies & M. Motyl, preprint http://arxiv.org/abs/1205.4251.
________________________________________________________________
How much of the published literature should you believe? Not much, by some accounts. A 2005 paper by epidemiologist John Ioannidis of the University of Ioannina School of Medicine in Greece had the stark title “Why most published research findings are false” [1]. Ioannidis claimed that “for most study designs and settings, it is more likely for a research claim to be false than true”, and that often published claims simply reflected the prevailing bias of the field. Ioannidis suspected that some “established classics” in the literature wouldn’t stand up to close scrutiny.
His focus was on biomedical research, in particular clinical trials of drugs, where inferences have to be made from complex statistics, perhaps with small sample sizes. Here, not only might the effects being sought be rather marginal but there are also strong biases and prejudices introduced by financial pressures. Reports of drug trials certainly do have a bias towards positive outcomes, prompting valid calls for all drug trials to be registered before the study is undertaken so that negative findings can’t be quietly dropped.
These problems with pharmaceutical research are in themselves troubling for some chemists. But is this mostly an issue for Big Pharma, with its distorting profit motives and its reliance on statistics rather than more reductive, step-by-step experimentation? Probably not, Daniel Sarewitz of the Consortium for Science, Policy and Outcomes at Arizona State University claimed in Nature last May [2]. According to Sarewitz, systematic error due to bias, whether conscious or not, is “is likely to be prevalent in any field that seeks to predict the behaviour of complex systems – economics, ecology, environmental science, epidemiology and so on”. This figures: all these fields tend to depend on statistical inference of often marginal effects operating through mechanisms that may be poorly understood and perhaps nigh impossible to delineate.
But what about the subjects we like to think of as the “hard sciences” – like most of chemistry? Surely you can place more trust in spectra and rate constants and crystal structures than in scatter plots? Perhaps – but ‘trust’ is often what it is. Not many studies are ever repeated verbatim, and it’s generally acknowledged that crystallographic databases are probably full of errors, if only minor. The chance of experiments being replicated is probably proportional to the significance of the results. Maybe the greater good doesn’t suffer much from a literature full of flawed but uninteresting work – but that would offer scant support for science’s supposedly self-correcting nature.
And problems do crop up on close examination. Take, for example, the recent attempt by Darragh Crotty and colleagues at Trinity College Dublin to replicate the claims of Russian biochemist Anatoly Buchachenko and his coworkers, who since 2004 have been documenting (in good journals) the influence of a weak magnetic field on the rate of enzymatic production of ATP [3]. The Russians report that millitesla magnetic fields can more than double the reaction rate when the phosphorylating enzymes contain 25Mg (which is magnetic) rather than the other two stable isotopes 24Mg and 26Mg. Crotty and colleagues set out to test this because it bore on controversial claims of physiological effects from weak electromagnetic fields. They found no difference in reaction rate for all three magnesium isotopes [4]. So far the discrepancy remains puzzling.
If this is indeed a wider problem than is commonly recognized for all sciences, what to do? Sarewitz suggests reducing hype and strengthening ties between fundamental research and real-world testing. Ioannidis implores researchers to be honest with themselves about the ‘pre-study odds’ of their hypothesis being true. This purging of preconception and self-deception is what Francis Bacon called for in the seventeenth century when he argued that natural philosophers seeking truth must free themselves from ‘idols of the mind’. But as Ioannis recognizes, changing mindsets isn’t easy.
Another perspective is offered in a preprint by psychologist Brian Nosek of the University of Virginia and his colleagues [5]. They point out that professional success for scientists relies on publishing, but publication both favours positive results and prefers novelty over replication. What is needed is a way to rescue scientists’ ostensible aim – getting it right – from their short-term, pragmatic aim – getting it published. Among things that won’t work, the authors say, are journals devoted to replications and tougher peer review (which can already display stifling conservatism). Instead we need metrics for evaluating what is worth replicating, journal editorial policies that focus on soundness rather than ‘importance’, less focus on sheer publication productivity for job and tenure applicants, lower barriers to publication (so that it becomes less coveted in itself), and in particular, new ways of releasing results: open access to data, methods, tools and lab books. One can find problems with all of these, but the old ways of science publishing are looking increasingly archaic and flawed. What have we got to hide?
1. J. P. A. Ioannis, PLoS Med. 2, e124 (2005).
2. D. Sarewitz, Nature 485, 149 (2012).
3. A. L. Buchachenko & D. A. Kuznetsov, J. Am. Chem. Soc. 130, 12868-12869 (2008).
4. D. Crotty et al., Proc. Natl Acad. Sci. USA 109, 1437-1442 (2012).
5. B. A. Nosek, J. R. Spies & M. Motyl, preprint http://arxiv.org/abs/1205.4251.
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