Epidemics, tipping points and phase transitions
I just came across this comment in the FT about the kind of social dynamics I discussed in my book Critical Mass.
It’s nicely put, though the spread of ideas/disease/information in epidemiological models can in fact also be described in terms of phase transitions: they’re a far more general concept than is implied by citing just the freezing transition. I also agree that sociologists have important, indeed crucial, things to offer in this area. But Duncan Watts trained as a physicist.
Tuesday, October 21, 2008
Thursday, October 16, 2008
Fractal calligraphy
Everyone got very excited several years ago when some guys claimed that Jackson Pollock’s drip paintings were fractals (R. P. Taylor et al., Nature 399, 422; 1999). That claim has come under scrutiny, but now it seems in any case that, as with everything else in the world, the Chinese were there first long ago. Yuelin Li of Argonne National Laboratory has found evidence of fractality in the calligraphy of Chinese artists dating back many hundreds of years (paper here). In particular, he describes the fractal analysis of a calligraphic letter by Huai Su, one of the legendary figures of Chinese calligraphy (Li calls him a ‘maniac Buddhist monk’, an image I rather enjoyed). Huai Su’s scroll, which hangs in the Shanghai Museum, says “Bitter bamboo shoots and tea? Excellent! Just rush them [over]. Presented by Huai Su.” (See image above: you’ve got to admit, it beats a text message.)
So what, you might be tempted to say? Isn’t this just a chance consequence of the fragmented nature of brush strokes? Apparently not. Li points out that Su seems to have drawn explicit inspiration from natural fractal objects. A conversation with the calligrapher Yan Zhenqing, recorded in 722 CE, goes as follows:
Zhenqing asked: ‘Do you have your own inspiration? Su answered: ‘I often marvel at the spectacular summer clouds and imitate it… I also find the cracks in a wall very natural.’ Zhenqing asked: ‘How about water stains of a leaking house?’ Su rose, grabbed Yan’s hands, and exclaimed: ‘I get it!’
‘This conversation’, says Li, ‘has virtually defined the aesthetic standard of Chinese calligraphy thereafter, and ‘house leaking stains’ and ‘wall cracks’ became a gold measure of the skill of a calligrapher and the quality of his work.’
Monday, October 06, 2008
The drip, drip, drip of environmental change
[You know how I like to give you added value here, which is to say, the full-blown (who said over-blown?) versions of what I write for Nature before the editors judiciously wield their scalpels. In that spirit, here is my latest Muse column.]
Your starter for ten: which of the following can alter the Earth’s climate?
(1) rain in Tibet
(2) sunspots
(3) the Earth’s magnetic field
(4) iron filings
(5) cosmic rays
(6) insects
The answers? They depend on how big an argument you want to have. All have been proposed as agents of climate change. Some of them now look fairly well established as such; others remain controversial; some have been largely discounted.
The point is that it is awfully hard to say. In every case, the perturbations that the phenomena pose to the global environment look minuscule by themselves, but the problem is that when they act over the entire planet, or over geological timescales, or both, the effects can add up. Or they might not.
This issue goes to the heart of the debate over climate change. It’s not hard to imagine that a 10-km meteorite hitting the planet at a speed of several kilometres per second, as one seems to have done at the end of the Cretaceous period 65 million years ago, might have consequences of global significance. But tiny influences in the geo-, bio-, hydro- and atmospheres that trigger dramatic environmental shifts [see Box] – the dripping taps that eventually flood the building – are not only hard for the general public to grasp. They’re also tough for scientists to evaluate, or even to spot in the first place.
Even now one can find climate sceptics ridiculing the notion that a harmless, invisible gas at a concentration of a few hundred parts per million in the atmosphere can bring about potentially catastrophic changes in climate. It just seems to defy intuitive notions of cause and effect.
Two recent papers now propose new ‘trickle effects’ connected with climate change that are subtle, far from obvious, and hard to assess. Both bear on atmospheric levels of the greenhouse gas carbon dioxide: one suggests that these may shift with changes in the strength of the Earth’s magnetic field [1], the other that they may alter the ambient noisiness of the oceans [2].
Noise? What can a trace gas have to do with that? Peter Brewer and his colleagues at Monterey Bay Aquarium Research Center in Moss Landing, California, point out [2] that the transmission of low-frequency sound in seawater has been shown to be dependent on the water’s pH: at around 1 kHz (a little above a soprano’s range), greater acidity reduces sound absorption. And as atmospheric CO2 increases, more is absorbed in the oceans and seawater gets more acid through the formation of carbonic acid.
This effect of acidity on sound seems bizarre at first encounter. But it seems unlikely to have anything to do with water per se. Rather, chemical equilibria involving dissolved borate, carbonate and bicarbonate ions are apparently involved: certain groups of these ions appear to have vibrations at acoustic frequencies, causing resonant absorption.
If this sounds vague, sadly that’s how it is. Such ‘explanations’ as exist so far seem almost scandalously sketchy. But the effect itself is well documented, including the pH-dependence that follows from the way acids or alkalis tip the balance of these acid-base processes. Brewer and colleagues use these earlier measurements to calculate how current and future changes in absorbed CO2 in the oceans will alter the sound absorption at different depths. They say that this has probably decreased by more than 12 percent already relative to pre-industrial levels, and that low-frequency sound might travel up to 70 percent further by 2050.
And indeed, low-frequency ambient noise has been found to be 9 dB higher off the Californian coast than it was in the 1960s, not all of which can be explained by increased human activity. How such changes might affect marine mammals that use long-distance acoustic communication is the question left hanging.
Uptake of atmospheric carbon dioxide by the oceans is also central to the proposal by Alexander Pazur and Michael Winklhofer of the University of Munich [1] that changes in the Earth’s magnetic field could affect climate. They claim that in a magnetic field 40 percent that of the current geomagnetic value, the solubility of carbon dioxide is 30 percent lower.
They use this to estimate that a mere 1 percent reduction in geomagnetic field strength can release ten times more CO2 than all currently emitted from subsea volcanism. Admittedly, they say, this effect is tiny compared with present inputs from human activities; but it would change the concentration by 1 part per million per decade, and could add up to a non-negligible effect over long enough times.
This isn’t the first suggested link between climate and geomagnetism. It has been proposed, for example, that growing or shrinking ice sheets could alter the Earth’s rotation rate and thus trigger changes in core circulation that drives the geodynamo. And the geomagnetic field also affects the influx of cosmic rays at the magnetic poles, whose collisions ionize molecules in the atmosphere which can then seed the formation of airborne particles. These in turn might nucleate cloud droplets, changing the Earth’s albedo.
Indeed, once you start to think about it, possible links and interactions of this sort seem endless. How to know which are worth pursuing? The effect claimed by Pazur and Winklhofer does seem a trifle hard to credit, although mercifully they are not suggesting any mysterious magnetically induced changes of ‘water structure’ – a favourite fantasy of those who insist on the powers of magnets to heal bodies or soften water. Rather, they offer the plausible hypothesis that the influence acts via ions adsorbed on the surfaces of tiny bubbles of dissolved gas. But there are good arguments why such effects seem unlikely to be significant at such weak field strengths [3]. Moreover, the researchers measure the solubility changes indirectly, via the effect of tiny bubbles on light scattering – but bubble size and coalescence is itself sensitive to dissolved salt in complicated ways [4]. In any event, the effect vanishes in pure water.
So the idea needs much more thorough study before one can say much about its validity. But the broader issue is that it is distressingly hard to anticipate these effects – merely to think of them in the first place, let alone to estimate their importance. Climate scientists have been saying pretty much that for decades: feedbacks in the biogeochemical cycles that influence climate are a devil to discern and probe, which is why the job of forecasting future change is so fraught with uncertainty.
And of course every well-motivated proposal of some subtle modifier of global change – such as cosmic rays – tends to be commandeered to spread doubt about whether global warming is caused by humans, or is happening at all, or whether scientists have the slightest notion of what is going on (and therefore whether we can trust their ‘consensus’).
Perhaps this is a good reason to embrace the metaphor of ‘planetary physiology’ proposed by James Lovelock. We are all used to the idea that minute quantities of chemical agents, or small but persistent outside influences, can produce all kinds of surprising, nonlinear and non-intuitive transformations in our bodies. One doesn’t have to buy into the arid debate about whether or not our planet is ‘alive’; maybe we need only reckon that it might as well be.
References
1. Pazur, A. & Winklhofer, M. Geophys. Res. Lett. 35, L16710 (2008).
2. Hester, K. C. et al. Geophys. Res. Lett. 35, L19601 (2008).
3. Kitazawa, K. et al. Physica B 294, 709-714 (2001).
4. Craig, V. S. J., Ninham, B. W. & Pashley, R. M. Nature 364, 317-319 (1993).
Box: Easy to miss?
Iron fertilization
Oceanographer John Martin suggested in the 1980s that atmospheric CO2 might depend on the amount of iron in the oceans (Martin, J. H. Paleoceanography 5, 1–13; 1990). Iron is an essential nutrient for phytoplankton, which absorb and fix carbon in their tissues as they grow, drawing carbon dioxide out of the atmosphere. Martin’s hypothesis was that plankton growth could be stimulated, reducing CO2 levels, by dumping iron into key parts of the world oceans.
But whether the idea will work as a way of mitigating global warming depends on a host of factors, such as whether plankton growth really is limited by the availability of iron and how quickly the fixed carbon gets recycled through the oceans and atmosphere. In the natural climate system, the iron fertilization hypothesis suggests some complex feedbacks: for example, much oceanic iron comes from windborne dust, which might be more mobilized in a drier world.
Cenozoic uplift of the Himalayas
About 40-50 million years ago, the Indian subcontinent began to collide with Asia, pushing up the crust to form the Himalayan plateau. A period of global cooling began at about the same time. Coincidence? Perhaps not, according to geologists Maureen Raymo and William Ruddiman and their collaborators (Raymo, M. E. & Ruddiman, W. F. Nature 359, 117-122; 1992). The mountain range and high ground may have intensified monsoon rainfall, and the uplift exposed rock to the downpour which underwent ‘chemical weathering’, a process involving the conversion of silicate to carbonate minerals. This consumes carbon dioxide from the atmosphere, cooling the climate.
A proof must negotiate many links in the chain of reasoning. Was weathering really more extensive then? And the monsoon more intense? How might the growth of mountain glaciers affect erosion and weathering? How do changes in dissolved minerals washed into the sea interact with CO2-dependent ocean acidity to affect the relevant biogeochemical cycles? The details are still debated.
Plant growth, carbon dioxide and the hydrological cycle
How changes in atmospheric CO2 levels will affect plant growth has been one of the most contentious issues in climate modelling. Will plants grow faster when they have more carbon dioxide available for photosynthesis, thus providing a negative feedback on climate? That’s still unclear. A separate issue has been explored by Ian Woodward at Cambridge University, who reported that plants have fewer stomata – pores that open and close to let in atmospheric CO2 – in their leaves when CO2 levels are greater (Woodward, F. I. Nature 327, 617-618; 1987). They simply don’t need so many portals when the gas is plentiful. The relationship is robust enough for stomatal density of fossil plants to be used as a proxy for ancient CO2 levels.
But stomata are also the leaks through which water vapour escapes from plants in a process called transpiration. This is a vital part of the hydrological cycle, the movement of water between the atmosphere, oceans and ground. So fewer stomata means that plants take up and evaporate less water from the earth, making the local climate less moist and producing knock-on effects such as greater runoff and increased erosion.
Ozone depletion
They sounded so good, didn’t they? Chlorofluorocarbons are gases that seemed chemically inert and therefore unlikely to harm us or the environment when used as the coolants in refrigerators from the early twentieth century. So what if the occasional whiff of CFCs leaked into the atmosphere when fridges were dumped? – the quantities would be tiny.
But their very inertness meant that they could accumulate in the air. And when exposed to harsh ultraviolet rays in the upper atmosphere, the molecules could break apart into reactive chlorine free radicals, which react with and destroy the stratospheric ozone that protects the Earth’s surface from the worst of the Sun’s harmful UV rays. This danger wasn’t seen until 1974, when it was pointed out by chemists Mark Molina and Sherwood Rowland (Molina, M. J. & Rowland, F. S. Nature 249, 810-812; 1974).
Even then, when ozone depletion was first observed in the Antarctic atmosphere in the 1980s, it was put down to instrumental error. Not until 1985 did the observations become impossible to ignore: CFCs were destroying the ozone layer (Farman, J. C., Gardiner, B. G. & Shanklin, J. D. Nature 315, 207-209; 1985). The process was confined to the Antarctic (and later the Arctic) because it required the ice particles of polar stratospheric clouds to keep chlorine in an ‘active’, ozone-destroying form.
CFCs are also potent greenhouse gases; and changes in global climate might alter the distribution and formation of the polar atmospheric vortices and stratospheric clouds on which ozone depletion depends. So the feedbacks between ozone depletion and global warming are subtle and hard to untangle.
[You know how I like to give you added value here, which is to say, the full-blown (who said over-blown?) versions of what I write for Nature before the editors judiciously wield their scalpels. In that spirit, here is my latest Muse column.]
Your starter for ten: which of the following can alter the Earth’s climate?
(1) rain in Tibet
(2) sunspots
(3) the Earth’s magnetic field
(4) iron filings
(5) cosmic rays
(6) insects
The answers? They depend on how big an argument you want to have. All have been proposed as agents of climate change. Some of them now look fairly well established as such; others remain controversial; some have been largely discounted.
The point is that it is awfully hard to say. In every case, the perturbations that the phenomena pose to the global environment look minuscule by themselves, but the problem is that when they act over the entire planet, or over geological timescales, or both, the effects can add up. Or they might not.
This issue goes to the heart of the debate over climate change. It’s not hard to imagine that a 10-km meteorite hitting the planet at a speed of several kilometres per second, as one seems to have done at the end of the Cretaceous period 65 million years ago, might have consequences of global significance. But tiny influences in the geo-, bio-, hydro- and atmospheres that trigger dramatic environmental shifts [see Box] – the dripping taps that eventually flood the building – are not only hard for the general public to grasp. They’re also tough for scientists to evaluate, or even to spot in the first place.
Even now one can find climate sceptics ridiculing the notion that a harmless, invisible gas at a concentration of a few hundred parts per million in the atmosphere can bring about potentially catastrophic changes in climate. It just seems to defy intuitive notions of cause and effect.
Two recent papers now propose new ‘trickle effects’ connected with climate change that are subtle, far from obvious, and hard to assess. Both bear on atmospheric levels of the greenhouse gas carbon dioxide: one suggests that these may shift with changes in the strength of the Earth’s magnetic field [1], the other that they may alter the ambient noisiness of the oceans [2].
Noise? What can a trace gas have to do with that? Peter Brewer and his colleagues at Monterey Bay Aquarium Research Center in Moss Landing, California, point out [2] that the transmission of low-frequency sound in seawater has been shown to be dependent on the water’s pH: at around 1 kHz (a little above a soprano’s range), greater acidity reduces sound absorption. And as atmospheric CO2 increases, more is absorbed in the oceans and seawater gets more acid through the formation of carbonic acid.
This effect of acidity on sound seems bizarre at first encounter. But it seems unlikely to have anything to do with water per se. Rather, chemical equilibria involving dissolved borate, carbonate and bicarbonate ions are apparently involved: certain groups of these ions appear to have vibrations at acoustic frequencies, causing resonant absorption.
If this sounds vague, sadly that’s how it is. Such ‘explanations’ as exist so far seem almost scandalously sketchy. But the effect itself is well documented, including the pH-dependence that follows from the way acids or alkalis tip the balance of these acid-base processes. Brewer and colleagues use these earlier measurements to calculate how current and future changes in absorbed CO2 in the oceans will alter the sound absorption at different depths. They say that this has probably decreased by more than 12 percent already relative to pre-industrial levels, and that low-frequency sound might travel up to 70 percent further by 2050.
And indeed, low-frequency ambient noise has been found to be 9 dB higher off the Californian coast than it was in the 1960s, not all of which can be explained by increased human activity. How such changes might affect marine mammals that use long-distance acoustic communication is the question left hanging.
Uptake of atmospheric carbon dioxide by the oceans is also central to the proposal by Alexander Pazur and Michael Winklhofer of the University of Munich [1] that changes in the Earth’s magnetic field could affect climate. They claim that in a magnetic field 40 percent that of the current geomagnetic value, the solubility of carbon dioxide is 30 percent lower.
They use this to estimate that a mere 1 percent reduction in geomagnetic field strength can release ten times more CO2 than all currently emitted from subsea volcanism. Admittedly, they say, this effect is tiny compared with present inputs from human activities; but it would change the concentration by 1 part per million per decade, and could add up to a non-negligible effect over long enough times.
This isn’t the first suggested link between climate and geomagnetism. It has been proposed, for example, that growing or shrinking ice sheets could alter the Earth’s rotation rate and thus trigger changes in core circulation that drives the geodynamo. And the geomagnetic field also affects the influx of cosmic rays at the magnetic poles, whose collisions ionize molecules in the atmosphere which can then seed the formation of airborne particles. These in turn might nucleate cloud droplets, changing the Earth’s albedo.
Indeed, once you start to think about it, possible links and interactions of this sort seem endless. How to know which are worth pursuing? The effect claimed by Pazur and Winklhofer does seem a trifle hard to credit, although mercifully they are not suggesting any mysterious magnetically induced changes of ‘water structure’ – a favourite fantasy of those who insist on the powers of magnets to heal bodies or soften water. Rather, they offer the plausible hypothesis that the influence acts via ions adsorbed on the surfaces of tiny bubbles of dissolved gas. But there are good arguments why such effects seem unlikely to be significant at such weak field strengths [3]. Moreover, the researchers measure the solubility changes indirectly, via the effect of tiny bubbles on light scattering – but bubble size and coalescence is itself sensitive to dissolved salt in complicated ways [4]. In any event, the effect vanishes in pure water.
So the idea needs much more thorough study before one can say much about its validity. But the broader issue is that it is distressingly hard to anticipate these effects – merely to think of them in the first place, let alone to estimate their importance. Climate scientists have been saying pretty much that for decades: feedbacks in the biogeochemical cycles that influence climate are a devil to discern and probe, which is why the job of forecasting future change is so fraught with uncertainty.
And of course every well-motivated proposal of some subtle modifier of global change – such as cosmic rays – tends to be commandeered to spread doubt about whether global warming is caused by humans, or is happening at all, or whether scientists have the slightest notion of what is going on (and therefore whether we can trust their ‘consensus’).
Perhaps this is a good reason to embrace the metaphor of ‘planetary physiology’ proposed by James Lovelock. We are all used to the idea that minute quantities of chemical agents, or small but persistent outside influences, can produce all kinds of surprising, nonlinear and non-intuitive transformations in our bodies. One doesn’t have to buy into the arid debate about whether or not our planet is ‘alive’; maybe we need only reckon that it might as well be.
References
1. Pazur, A. & Winklhofer, M. Geophys. Res. Lett. 35, L16710 (2008).
2. Hester, K. C. et al. Geophys. Res. Lett. 35, L19601 (2008).
3. Kitazawa, K. et al. Physica B 294, 709-714 (2001).
4. Craig, V. S. J., Ninham, B. W. & Pashley, R. M. Nature 364, 317-319 (1993).
Box: Easy to miss?
Iron fertilization
Oceanographer John Martin suggested in the 1980s that atmospheric CO2 might depend on the amount of iron in the oceans (Martin, J. H. Paleoceanography 5, 1–13; 1990). Iron is an essential nutrient for phytoplankton, which absorb and fix carbon in their tissues as they grow, drawing carbon dioxide out of the atmosphere. Martin’s hypothesis was that plankton growth could be stimulated, reducing CO2 levels, by dumping iron into key parts of the world oceans.
But whether the idea will work as a way of mitigating global warming depends on a host of factors, such as whether plankton growth really is limited by the availability of iron and how quickly the fixed carbon gets recycled through the oceans and atmosphere. In the natural climate system, the iron fertilization hypothesis suggests some complex feedbacks: for example, much oceanic iron comes from windborne dust, which might be more mobilized in a drier world.
Cenozoic uplift of the Himalayas
About 40-50 million years ago, the Indian subcontinent began to collide with Asia, pushing up the crust to form the Himalayan plateau. A period of global cooling began at about the same time. Coincidence? Perhaps not, according to geologists Maureen Raymo and William Ruddiman and their collaborators (Raymo, M. E. & Ruddiman, W. F. Nature 359, 117-122; 1992). The mountain range and high ground may have intensified monsoon rainfall, and the uplift exposed rock to the downpour which underwent ‘chemical weathering’, a process involving the conversion of silicate to carbonate minerals. This consumes carbon dioxide from the atmosphere, cooling the climate.
A proof must negotiate many links in the chain of reasoning. Was weathering really more extensive then? And the monsoon more intense? How might the growth of mountain glaciers affect erosion and weathering? How do changes in dissolved minerals washed into the sea interact with CO2-dependent ocean acidity to affect the relevant biogeochemical cycles? The details are still debated.
Plant growth, carbon dioxide and the hydrological cycle
How changes in atmospheric CO2 levels will affect plant growth has been one of the most contentious issues in climate modelling. Will plants grow faster when they have more carbon dioxide available for photosynthesis, thus providing a negative feedback on climate? That’s still unclear. A separate issue has been explored by Ian Woodward at Cambridge University, who reported that plants have fewer stomata – pores that open and close to let in atmospheric CO2 – in their leaves when CO2 levels are greater (Woodward, F. I. Nature 327, 617-618; 1987). They simply don’t need so many portals when the gas is plentiful. The relationship is robust enough for stomatal density of fossil plants to be used as a proxy for ancient CO2 levels.
But stomata are also the leaks through which water vapour escapes from plants in a process called transpiration. This is a vital part of the hydrological cycle, the movement of water between the atmosphere, oceans and ground. So fewer stomata means that plants take up and evaporate less water from the earth, making the local climate less moist and producing knock-on effects such as greater runoff and increased erosion.
Ozone depletion
They sounded so good, didn’t they? Chlorofluorocarbons are gases that seemed chemically inert and therefore unlikely to harm us or the environment when used as the coolants in refrigerators from the early twentieth century. So what if the occasional whiff of CFCs leaked into the atmosphere when fridges were dumped? – the quantities would be tiny.
But their very inertness meant that they could accumulate in the air. And when exposed to harsh ultraviolet rays in the upper atmosphere, the molecules could break apart into reactive chlorine free radicals, which react with and destroy the stratospheric ozone that protects the Earth’s surface from the worst of the Sun’s harmful UV rays. This danger wasn’t seen until 1974, when it was pointed out by chemists Mark Molina and Sherwood Rowland (Molina, M. J. & Rowland, F. S. Nature 249, 810-812; 1974).
Even then, when ozone depletion was first observed in the Antarctic atmosphere in the 1980s, it was put down to instrumental error. Not until 1985 did the observations become impossible to ignore: CFCs were destroying the ozone layer (Farman, J. C., Gardiner, B. G. & Shanklin, J. D. Nature 315, 207-209; 1985). The process was confined to the Antarctic (and later the Arctic) because it required the ice particles of polar stratospheric clouds to keep chlorine in an ‘active’, ozone-destroying form.
CFCs are also potent greenhouse gases; and changes in global climate might alter the distribution and formation of the polar atmospheric vortices and stratospheric clouds on which ozone depletion depends. So the feedbacks between ozone depletion and global warming are subtle and hard to untangle.
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