Monday, April 29, 2013

Just allow me this little rant, then normal service will resume

I strongly suspect that bête noirs area sign that one needs to get out more. All the same I have mine, among which one of the chief ones is the idea that Giordano Bruno was a martyr to science, being burnt at the stake for his Copernican views. This is a myth. Rather, he was condemned for all manner of religious heresies. Mentioned among them at his trial was the idea of a plurality of worlds, which is of course not explicitly Copernican. Evidently Bruno did have Copernican sympathies, although it isn’t clear how well he understood Copernicus’s arguments. But there is no reason to think that the Church would have burnt him for those.

The myth has doubtless arisen because of the proximity of Bruno’s execution to Galileo’s persecution. But there is no real relation between them, and after all Galileo himself was initially granted considerable tolerance for his own Copernicanism. Now, none of this excuses the Church one whit for a barbaric and dogmatic act. But it is frustrating to see his canard trotted out as some kind of evidence in the “battle” between science and religion, especially when it comes from such an otherwise erudite individual as A. C. Grayling, who, in the April issue of Prospect, castigates Frans de Waal for being so tolerant of religion. (One could doubtless make merry play with Grayling’s remark that the Copernican cosmology was ‘geocentric’, but no one can seriously doubt that Grayling knows very well that Copernicus put the sun, not the earth, at the centre of the universe – such a blunder simply reminds me of how horribly easy it is to commit howlers to print with a slip of the pen.)

Grayling’s attack rehearses all the familiar ‘new atheist’ condemnations of religion, including (I should really have thought this beneath him) references to fairies. Much of what he says is entirely fair, such as how deplorable are the religious fundamentalist attacks on science, women, homosexuality and civil freedoms in general. What I find so endlessly frustrating is the childish conviction among the new atheists that such things will evaporate if religion is ‘vanquished’ – a refusal, in other words, to see these things as expressions of power and prejudice for which various religions provide convenient justification. (I have just seen Richard Dawkins flogging on his website a T-shirt saying “Religion: Together We Can Find the Cure”, and I’m afraid my opinion of him fell several notches.)

The idea that they are putting the cart before the horse is not simply one they reject; it seems to infuriate them. It certainly infuriated Sam Harris, who said this in response to my own remarks to that effect:

“Who does Ball imagine the Taliban would be if they weren’t “Muslim extremists”? They are, after all, Homo sapiens like the rest of us. Let’s change them by one increment: wave a magic wand and make them all Muslim moderates… Now how does the world look? Do members of the Taliban still kill people for adultery? Do they still throw acid in the faces of little girls for attempting to go to school? No. The specific character of their religious ideology—and its direct and unambiguous link to their behavior—is the most salient thing about the Taliban. In fact, it is the most salient thing about them from their own point of view. All they talk about is their religion and what it obliges them to do.”

This is so characteristic of the new atheists in its implication that if one could (hey, literally!) wave a magic wand to wish away the ills of religion, all would be well. (And you know what the magic wand is? Reason! Because reason and religion cannot coexist in a single mind!) It’s a tragically naïve tautology: “if we could make these awful people nicer, they would be nicer.” What is particularly astonishing here is that Sam seems not to have realised that his nice Taliban are… still Muslims! In other words, presumably it was not religion per se that was making them this way, but something that was inducing them to interpret their religion in a punitive, intolerant and murderous way. Whatever that thing was, it was presumably not prescribed by the Quran, since as Sam admits, it is possible to interpret the Quran in a far more moderate way.

Now, I share what I perceive to be Sam’s frustration that religious texts, notoriously the Bible, are so contradictory that one can find in them justification for whatever views one prefers, whether as a Quaker pacifist or a member of the National Rifle Association. But this is the whole point: that one’s interpretation is therefore surely shaped by other factors, related to culture and history and doubtless also individual personality and upbringing. If religion is magicked away (and oh, it will have to be powerful magic), those factors are not going to vanish – as countless secular oppressive regimes show. But addressing predilections instilled by culture and history (for which, I freely admit, religion often functions as a brainwashing tool) is hard. Arguing that religion is a tissue of unsupportable beliefs about the nature of the physical universe is so, so much easier.

Many reviews of Grayling’s latest book The God Argument have implied that this debate has got very tired, and that the argument has moved on. I agree.

Beneath the surface

Next up, a review published in Nature of the latest book by Douglas Hofstadter. Interesting, but God it’s long.


Surfaces and Essences
Douglas Hofstadter & Emmanuel Sander
Basic Books, 2013
608 pages
ISBN 978-0-465-01847-5

I finished this review and stored the file in the 'Nature' folder on my desktop, then emailed it to the editor. Or did I? A file, after all, was once a sheaf of papers, and a folder a cardboard sleeve for holding them. A desktop was wooden, and mail needed a stamp (no, it needed a little piece of adhesive paper). But all I did was use an interfacing device (named for the most superficial resemblance to a rodent) to rearrange the settings of some microprocessor circuits. To see that almost everything we say and do refers by analogy to other things we or others have once said or done – which is the main point of Surfaces and Essences – there is no better illustration than the way we have constructed our computer software as a conceptual and visual simulacrum of the offices our grandparents knew.

On the one hand this is kind of obvious. Why (science fiction writers take note) would we invent new categories and labels for things when we can aid comprehension by borrowing old ones, even if the physical resemblance is negligible? What cognitive scientists Douglas Hofstadter Hofstadter and Emmanuel Sander set out to show, however, is that this sort of elision is not merely a convenience: all our thinking depends on it, from the half-truths of everyday speech ("that always happens to me too!") to the most abstruse of mathematical reasoning. I was convinced, and the ramifications are often thought-provoking. But when you have had authors telling you the same thing again and again for 500 pages, perhaps you’ll believe it whether it's true or not. I’ll come back to that.

Hofstadter is famous for his earlier, Pulitzer-prize-winning treatise on how we think, Gödel, Escher, Bach (1979). Fans of that dazzling performance might find this book surprisingly sober, but it is also lucid and, page for page, a delight to read. Whether there is any conceptual continuity between that and this vision of how we think is debatable, except perhaps that GEB’s delight in puns here becomes an assertion that pretty much all our cognition depends on punning elevated to analogy.

The claim that drawing parallels between one thing and another central in our thinking seems obvious in art: analogies are the bread and butter (there we go again) of the visual, literary and theatrical arts. (Of these, the authors seem curiously unconcerned about anything except poetry.) Yet Hofstadter and Sander are really inverting that usual picture: it is precisely because the brain seems to be an analogy machine that art is possible and meaningful.

They focus most on the use of analogy in language. Moving steadily from words to phrases and narratives, they show just how deeply embedded is our tendency to generalize, compare, categorize, and forge links. Individual examples seem trivial until you realise their ubiquity: tables have legs, melodies are hauting, time is discussed in spatial terms, and idioms are invariably analogical, if you get my drift. Thus the lexical precision on which dictionaries seem to insist is illusory – words are always standing in for other words, their boundaries malleable. This flexibility extends to our actions: we see that a spoon can serve as a knife when no knife is available. (Indeed, the spoon then becomes a knife – objects may be fixed, but their labels aren’t.)

These arguments can be carried too far. Is to extrapolate to make an analogy (I expect the future to be like the past)? Is a Freudian slip an analogy, or mere crosstalk of neural circuits? Is convention an analogy (why don’t we write mc2=E?). Can we, in fact, turn any mental process into an analogy, by that very process of analogy? These are not rhetorical questions, for one might at least examine whether the same neural circuitry is involved in each case. But a lack of interest in neuroscientific examination of their idea is another of the book’s odd lacunae.

In fact this intriguing, frustrating book seems to exist almost in an intellectual vacuum. Unless one combs through the bibliography, one could mistakenly imagine that it is the first attempt to explore the notion of analogy and metaphor in linguistics, overlooking the work of Raymond Gibbs, Andrew Ortony, Sam Glucksberg, Esa Itkonen and many others. And one is forced to take an awful lot on trust. Hofstadter and Sander describe, for example, the evolution of the concept of ‘mother’ in the mind of a child as he learns to generalize from experience. It all sounds plausible, but the authors offer no empirical evidence for the developmental pathway they describe.

Neither is there any real explanation of why we think this way. Isn't it perhaps, in part, a way of minimizing the mental resources we need to engage in a situation, to avoid having to start from scratch with every unfamiliar encounter, object or perspective? Is it an adaptive technique for making predictions? Are mirror neurons part of a built-in cognitive apparatus for analogizing ourselves into others’ shoes?

The lack of historical perspective is also a problem – it is as if people always thought like they did now. Analogy was arguably all we once had for navigating experience, for example in the Neoplatonic idea of correspondences: “as above, so below.” This “just as… so…” thinking remains at the root of pseudoscience: the Moon influences the tides, so why not our body fluids? So how do we distinguish between good and bad analogies?

There are gems of insight in here, but again flawed by the authors’ relaxed attitude towards evidence. An analysis of Einstein's thought is splendid, explaining what is missing from conventional accounts of the discoveries of light quanta, relativity and mass-energy equivalence, namely what qualities distinguish Einstein from his peers. These qualities are convincingly shown to be analogical: Einstein was able to take leaps of faith and make connections that postpone rigour and are certainly not self-evidently true. One would usually call this intuition - Einstein's friend and biographer Banesh Hoffmann did just that. But it is shown here to be intuition based on a conviction that different areas of physics were comparable. In other words, his intuition is not left ineffable but is taken apart so that the inner workings – some of them – can be seen. As a result, we see that Einstein's insights were very subtle and not self-evidently true. Analogies, the authors say, left Einstein like J. S. Bach on hearing a theme: "very quickly able to imagine all of its possible consequences." All very fine – but such a detailed account must surely be supported by Einstein’s own words. Almost none are offered; we get only fragments of Hoffmann’s commentary.

Maybe at least some of these questions are merely evidence of the fecundity of the authors’ thesis. But they’d have more excuse for not answering them if they did not fill so much space with endless examples to ram the point home: they never give one when 60 will do, and I’m not exaggerating.

Such things make me wonder whom the book is for. Academic linguists will be irritated by the absence of references to other work. Physical scientists aren’t indulged until page 450. General readers could have been given the basic ideas, with equal conviction, in half the length, and will occasionally get the feeling they have been led along and then dumped. The thesis suggests no obvious mode of further development, no manner of testing and probing. It remains stimulating, but less would certainly have been more.

Happy holidays

Here’s the previous piece for my Under the Radar column on BBC Future – there will be another column up very shortly. Peter Dodds, tells me that he and his colleagues have now created a “hedometer” site at that will “provide a real-time measure of happiness that will be useful for many entities including governments at all scales, journalists, analysts, and citizens.” Peter adds that “initially, we'll be showing an interactive happiness time-series for Twitter but we'll be expanding to geography, social networks, etc., as well as other languages and other emotions.” It sounds rather fabulous, and will be free and open to all users when it goes live tomorrow.


Feeling low? Over-worked, anxious, bored with life? A holiday will do your mood the world of good. Really it will: there’s now scientific proof. A team of researchers at the University of Vermont in the United States has found that tweets contain significantly more happy words the further from home they are sent [1].

This is the latest dispatch from an emerging discipline in which social-networking media are mined to gauge people’s moods and opinions. Twitter is one of the most fertile sources of information for this kind of study, partly because the comments are less guarded and self-conscious than responses to questionnaires (the social scientist’s traditional means of sampling opinion) but also because huge amounts of data are available, with automatically searchable content. What’s more, Twitter feeds sometimes come accompanied with useful information such as the tweeter’s profile and location.

Previous studies in “twitteromics” have, for example, monitored the spread of news, the demographics of different languages, and the correlations between obesity and expressions of hunger in particular populations. Since public mood changes such as brewing social unrest will show up on Twitter and other social media, governments, police forces and security organizations are showing an increasing interest in twitteromics, raising questions about the right balance between privacy and security. Meanwhile, potential insights into the emergence and propagation of trends are a gift to company marketing departments.

The new study of the link between happiness and geographical location by Christopher Danforth and colleagues at Vermont takes advantage of the “garden hose” public-access feed for Twitter, which makes freely available a random 10 percent of all messages posted. This provided the researchers with four billion tweets for the year 2011 to analyse.

Since Danforth and colleagues were interested in how the mood expressed in the messages correlated with the location from which they were sent, they sifted through this immense data set to pick out those tweets that were accompanied by the precise latitude and longitude of the sender’s mobile phone – a facility optionally available for tweets, which uses the Global Positioning System (GPS) to locate the message’s origin within a 10m radius. About 1% of the messages included this information, giving a data set of 37 million messages sent by more than 180,000 individuals from all over the planet.

But identifying where the sender is situated doesn’t in itself reveal what the researchers wanted to know. They were interested in how the message content varied with distance from home. How could they know where ‘home’ was?

It turns out that positional information disclosed by our mobile phones reveals this pretty clearly. In 2008 a team of researchers in the US used the locations of mobile phones – recorded by phone companies whenever calls are made – to track the trajectories of 100,000 (anonymized) individuals [2]. They found that, as we might imagine, we tend to return over and over again to certain places, especially our homes and workplaces, and only rarely venture very far from these locations.

In much the same way, Danforth and colleagues could figure out the most common locations for each individual in their survey, along with an associated number describing how widely the person tended to roam from those places. They found that people generally have two such preferred locations, just a short distance apart, which they attributed to the home and workplace.

How, then, do the messages differ when individuals are at home, at work, or further away? To assess the ‘happiness’ of a tweet, the Vermont team has developed what they call a ‘hedonometer’ [3]: an algorithm that searches the text for words implying a positive or enjoyable context (such as ‘new’, ‘great’, ‘coffee’ and ‘lunch’) or a negative one (‘no’, ‘not’, ‘hate’, ‘damn’, ‘bored’). On this basis the hedonometer assigns each message a happiness score.

The authors report that “we see a general decline in the use of negative words as individuals travel further from their expected [home] location”. More precisely, the average happiness score first declines slightly for distances of around 1 km – the kind of distance expected for a short commute to work – and then rises steadily with increasing distances of up to several thousand kilometres. What’s more, individuals with a larger typical ‘roaming radius’ use happy words more often – a result that probably reflects the higher socioeconomic status of such jet-setting types.

So it seems we’re least happy at work and most happy when we are farthest from home. At least, that’s the case for the roughly 15% of American adults who use Twitter, or to be even more cautious, for the English-speaking subset of those who chose to ‘geotag’ their tweets. One key question is whether this sample is representative of the population as a whole – Twitter is less used among older people, for example. It’s also an open question whether ‘happy words’ are a true indicator of one’s state of mind – are you less likely to tweet about your holiday when the weather is awful and the family is fractious? But such quibbles aside, you might want to consider that costly flight to Bermuda or Kathmandu after all.

1. M. R. Frank, L. Mitchell, P. S. Dodds & C. M. Danforth, preprint (2013).
2. M. C. Gonzalez, C. A. Hidalgo & A. L. Barabasi, Nature 453, 779-782 (2008).
3. P. S. Dodds, K. D. Harris, I. M. Kloumann, C. A. Bliss & C. M. Danforth, PLoS ONE 6(12), e26752 (2011).

Friday, April 26, 2013

Can Google predict the markets?

Here’s another Nature news story. I’ll be interested to see what other media outlets make of it.


Traders reveal their mood in the search terms they use.

Suppose you had a direct line into the minds of stock market traders. Would you be able to predict which investment decisions they will take, and thus anticipate the markets?

A team of researchers in the UK and US now suggests that such a crystal ball might exist, in the form of the search terms recorded and made publicly available by Google Trends. Tobias Preis of the University of Warwick Business School and his colleagues say that their analyses of Google Trends data show “early warning signs” of how the markets will shift – including the financial crash of 2008 [1].

Don’t, however, imagine that this is the way to make a fast buck. It’s one thing to offer a retrospective account of why markets behave as they do – which is what Preis and colleagues have done – and quite another to provide a genuinely predictive tool.

That’s why the work is “interesting but not earth-shattering”, in the view of British economist Paul Ormerod of the consultancy Volterra Partners in London.

Mathematical physicist Didier Sornette of the Swiss Federal Institute of Technology (ETH) in Zürich agrees, pointing out that the predictive power of the strategies the authors deduced from Google Trends data are only slightly better than predictions which assume traders make random decisions. “No investor or hedge-fund would be interested in such a strategy”, he says.

The predictive value of Google Trends has been demonstrated in other areas of social science. Most famously, outbreaks of influenza have been seen emerging in real time by monitoring the numbers of Google searches for terms related to flu prevention and cure [2].

The potential of using such information to study economic behaviour has already been spotted. Preis and coauthor Gene Stanley of Boston University have themselves shown that certain search terms reflect the volume of stock market transactions [3]. Sornette, in collaboration with Japanese economists, has found that the volatility (fluctuations) of financial markets can be correlated with the prevalence of particular topics in business news [4].

But what traders and investors really want is a method not just to assess the current state of markets but to anticipate their future course. In particular, episodes of instability, such as the financial crisis of 2008, are often preceded by periods of concern during which investors avidly seek information to decide whether to buy or sell.

Preis and colleagues figured that such anxieties and moods might be signaled by Google search terms. Just before the onset of the latest crisis, for instance, “debt” might be expected to feature prominently. That’s just what the researchers found.

To test if such correlations could be made predictive, they devised trading strategies in which a decision to buy or sell is linked to the recent prevalence of particular search terms. They simulated how these strategies would have performed between 2004 and 2011 based on real data from the financial markets.

Of the 98 ‘Google Trends’ strategies the researchers explored, that based on “debt” performed best. By 2011 it would have increased the value of a portfolio by more than 300 percent, compared with just 16 percent for a common conventional investment strategy.

Although this sounds impressive, the relevance of a predictive Google search term isn’t always clear. The second-best strategy, for example, was linked to “color”, and the fourth best to “restaurant”.

Even the use of “debt” is not obvious, since its role in the financial crash was apparent only as it happened. “How would they know in advance that they should use ‘debt’?” asks Sornette.

“In retrospect it is always possible to derive what appear to be highly successful trading strategies”, says Ormerod. “But what we want is to be able to do that before the event, not after.”

What’s more, economists acknowledge that any transparently profitable strategy for playing the markets will quickly lead to a change of trader behaviour that cancels it – a principle called Goodhart’s Law, after the British economist Charles Goodhart. “Social systems have the complication that the system may directly react to predictions being made about its behaviour”, coauthor Susannah Moat of University College London agrees.

The researchers suggest, however, that a key outcome of their approach might be to elucidate the psychological mechanisms that guide traders to their decisions, which could be encoded in their information-gathering. “Stock market data themselves tell us little about how traders make decisions”, says Preis.

“We think that the overall pattern we observe may reflect loss aversion”, he adds – the fact that humans are more concerned about losing money than they are about missing an opportunity to gain the same amount.

1. Preis, T., Moat, H. S. & Stanley, H. E. Nat. Sci. Rep. 3, 1684 (2013).
2. Ginsberg, J. et al. Nature 457, 1012–1014 (2009).
3. Preis, T., Reith, D. & Stanley, H. E. Phil. Trans. R. Soc. A 368, 5707–5719 (2010).
4. Hisano, R. et al., preprint (2012).

Crowdsourcing in manhunts can work

So much to post right now… but I will start with the easy stuff. Here is a news story for Nature on a preprint that seemed almost too topical to be true.


Despite mistakes over the Boston bombers, social media can help to find people quickly.

The social news website Reddit was left red-faced after mis-identifying the suspects for the Boston marathon bombings last week, raising questions about whether crowd-sourcing to gather information might do more harm than good in such situations.

But work by a team of scientists from the United Arab Emirates and coworkers in the US and UK offers a more upbeat message about the potential of social media to assist in crime investigations and societal searches. Last year they enlisted communities on networks such as Twitter and Facebook to look for five people in different cities around the world, and were able to find three of them within the 12-hour deadline imposed [1].

In a new preprint, the researchers now analyse the behaviour that made this possible. They say that participants responded to the urgency of the search not by sending out messages to their contacts in an indiscriminate, blind panic, but by becoming even more focused and directed about whom they contacted [2].

The experiment, by computer scientist Iyad Rahwan at the Masdar Institute of Science and Technology in Abu Dhabi and his colleagues, constituted the team’s entry in the Tag Challenge staged by the US State Department in March 2012. The Tag Challenge required teams to find individuals (posing as jewel thieves) in New York City, Washington DC, London, Stockholm and Bratislava within 12 hours. Participants were given only a ‘mug shot’ of each target wearing a T-shirt bearing the competition logo, released on the morning when the competition started.

Rahwan’s team used crowd-sourcing to find the targets, offering cash incentives to individuals for uploading photos of suspects to web and cell phone apps and for recruiting more searchers. Although they failed to locate the targets in London and Stockholm, the team out-performed all others and won the competition [1].

The results showed that “among this noisy stream of tweeting and retweeting, of news articles and messages being fired off to acquaintances around the globe, people are able to efficiently guide a message towards a target in a particular city”, says Rahwan’s colleague Alex Rutherford at the Masdar Institute.

The new analysis of the information provided by participants shows that communications such as tweets became more specific and targeted as the day of the competition approached, being increasingly directed towards other users in the target cities. “Despite increasing time pressure, and its associated cognitive load, people actually became more selective in their recruitment of others, making sure information is directed in an intelligent manner”, says Rahwan.

“This makes good sense to me, and it's what I would have expected”, says Peter Sheridan Dodds of the University of Vermont. In 2003 Dodds and coworkers conducted a social-search experiment [3] to route emails to a few target people worldwide – an electronic version of the famous ‘small-world’ experiment by psychologist Stanley Milgram in 1967, in which he asked random people to forward letters to addressees identified only by name, profession and city [4]. “In our small-world experiment we found that successful searches were much more focused than unsuccessful ones and less likely to involve scattershot, connect-to-everyone attempts,” Dodds says.

Defence and security organizations have a growing interest in these outcomes. In 2009 the US defence research agency DARPA staged the Red Balloon Challenge, in which competitors were challenged to locate ten red weather balloons tethered at random locations all over the US. That challenge was won by a team at the Massachusetts Institute of Technology led by Manuel Cebrian, who collaborated with Rahwan and colleagues for the Tag Challenge. The MIT team found the red balloons in 9 hours by harnessing social-networking media [5,6].

How does all this reflect on the search for the Boston bombers? Last week, Reddit users, acting on photographs of suspects posted by the FBI, collectively pointed the finger at several individuals who had nothing to do with the bombings, including an innocent student from Brown University. The eventual arrest of Dzhokhar Tsarnaev, who previously escaped with wounds after a shootout with police, came after a neighbour spotted blood on the tarpaulin covering the boat in which he was hiding.

“The Boston manhunt is an example of how things can go wrong”, says Rahwan. “It appears that information was very much misdirected. This may be, in part, due to the high profile of the event, which led everyone to want to help even if they were incapable or misinformed.”

“There may be a tradeoff between mass mobilization and effective mobilization of a more specialized group of reliable and well-informed individuals”, he adds. “Having too many people involved might actually make things worse.” He and his colleagues have begun to explore schemes for supporting the checking and verification of crowd-sourced reporting [7].

Even President Barack Obama has commented on the hazards of search efforts like those on Reddit. “Crowd-sourcing via social media can be incredibly powerful in mobilizing people”, says Rahwan, “but it is not a silver bullet.”

“I think the web-enhanced ‘collective detective’ is potentially very powerful and is here to stay”, agrees Dodds. “But we have to ensure that the distributed social search is always used for good, meaning for example that ‘bad’ actors cannot corrupt the search, and that good, well-intentioned actors are prevented from collectively generating errors leading to witch hunts.”

“There's a lot of wisdom in the crowd when people are actually aggregating independent pieces of information”, says David Liben-Nowell of Carleton College in Northfield, Minnesota, a specialist on the searching of social networks. “But when purported information is amplified and echoed by people without truly independent information being collected, as seemed to happen in the Reddit case, then we may end up with the folly of the mob instead.”

In situations like that, says Dodds, “unofficial efforts are very important, but the onus is now on governments to create and maintain distributed social search sites that allow the public to aid in finding people. A system should already be in place that is transparent and sophisticated, and that allows for the public to provide analysis, not just photos.”

“It's not just for finding bad guys”, he adds. “Missing children are an obvious example.”

“With any kind of task like this one, we have to accept that there's a tradeoff between the risk of a false negative and a false positive”, says Liben-Nowell. “As a society, we have to think carefully about where we want to be in that spectrum.”

1. Rahwan, I. et al., IEEE Computer April, 68-75 (2013).
2. Rutherford, A. et al., preprint
3. Dodds, P. S., Muhamad, R. & Watts, D. J. Science 301, 827-829 (2003).
4. Milgram, S. Psychology Today 61, 60-67 (1967).
5. Tang, J. et al., Commun. ACM 54, 78-85 (2011).
6. Rutherford, A. et al., Proc. Natl Acad. Sci. USA 110, 6281-6286 (2013).
7. Naroditskiy, V., Rahwan, I., Cebrian, M. & Jennings, N. R. PLoS ONE 7, e45924 (2012).

Wednesday, April 24, 2013


Here’s a piece I wrote for BBC Future this week, before discovering that the blighters on their science news desk were covering the work already. So there will be something else from me on Under the Radar later this week…


Attempts to measure and define intelligence are always controversial and open to interpretation. But none, perhaps, is quite as recondite as that now proposed by two mathematical physicists. They say that there’s a kind of rudimentary intelligence that comes from acting in a way that maximizes your future options.

Alex Wissner-Gross of Harvard University in Cambridge, Massachusetts, and Cameron Freer of the University of Hawaii at Manoa have figured out a ‘law’ that enables inanimate objects to behave this way, in effect allowing them to glimpse their own future. If they follow this law, they can show behaviour reminiscent of some of the things humans do: for example, cooperating or using ‘tools’ to conduct a task.

The researchers think that their mathematical principle might help to provide a “physics of intelligence”: an explanation of smart actions rooted in the laws of thermodynamics.

Central to their claim is the concept of entropy. Popularly described as a measure of disorder, entropy more properly describes the number of different equivalent states a system can adopt. Think of a box full of gas molecules. There are lots more ways that they can disperse uniformly throughout the available space than there are ways they can all congregate in one corner. The former situation has greater entropy.

In principle, either arrangement could arise purely from the random motions of the molecules. But there are so many more configurations of the uniformly spread gas that it is much more likely, and in practice we never see all the gas shift into one corner. This illustrates the second law of thermodynamics, which states that the total entropy of the universe always increases – simply because that’s more probable than the alternatives.

Some scientists have generalized this idea to propose that all processes of change happen in a way that has the greatest rate of entropy production. Not only do things head for the highest-entropy state, but they do so along a route that produces entropy at the greatest rate. There’s no rigorous proof that all things must happen this way, but the hypothesis of maximum entropy production has been used to account for processes such as the appearance of life, and also to design artificial-intelligence strategies that allow computers to become adept at complex games such as Go.

Wissner-Gross and Freer wondered if this hint at a link between maximal entropy production and intelligence could be made more concrete. They hit on the idea that ‘true’ intelligence is not, as they put it, “just greedily maximizing instantaneous entropy production”, but involves foresight: looking for a path that maximizes its production between now and some distant time horizon. For example, a good computer algorithm for playing Go might seek a strategy that offers the player the greatest number of options at all points into the future, rather than playing itself into a corner.

But how would an inanimate particle find that strategy? The researchers show that it can be defined via a mathematical expression for what they call the ‘causal path entropy’: the entropy production for all possible paths the particle might take. How would a particle behave if governed by the law that it must, at every instant, maximize this casual path entropy – which means, in effect, planning ahead?

Objects whose motions are guided solely by the conventional laws of motion are doomed to a blind, dumb presentism – they just go where the prevailing forces take them. Think again of those gas molecules in a box: each particle wanders aimlessly in a random walk, exploring the confining space without prejudice.

Yet when Wissner-Gross and Freer impose on such a meandering particle the demand that it move in a way that maximizes the casual path entropy, its behaviour is quite different: it tends to hover around in the centre of the box, where it suffers the least constraints on its future motion. They then explored the consequences of their new law for a so-called ‘cart and pole’ – a pendulum attached to a mobile cart, which can be stabilized in an inverted, head-up position by moving the cart back and forth, like balancing a stick on your palm. Early hominids are thought to have mastered such a delicate balancing act when they learnt to stand upright – and it’s a trick achieved by a cart-and-pole obeying the ‘maximum causal entropy’ law.

Weirder things become possible too. Wissner-Gross and Freer looked at a system composed of three disks in a box: a large one (I), a small one (II), and another small one (III) trapped inside a tube too large for I to enter. Suppose now that the movements of disk I are dictated by causal entropic ‘forcing’. In this case, the disk conspires to collide with II so that II can bounce into the tube and eject disk III. Liberating III means that the disks now have more ways to arrange themselves than when it was confined – they have more entropy. But to gain access to that entropy, disk I essentially uses II as a tool.

Similarly, two small disks governed by the causal entropic force showed a kind of social collaboration to collectively drag down a large disk into a space where they could ‘play’ with it, offering more possible states in total – another behaviour that looks strangely ‘intelligent’.

In these cases there is no real reason why the particles should be controlled by the causal entropic force – the researchers just imposed that property. But they suggest that, in a Darwinian evolving system, objects that are able this way to ‘capture’ a greater slice of the future might gain an adaptive advantage, so that such a force might be naturally selected. Not only could this offer clues about the emergence of intelligent, adaptive behaviour in the living world, but the general principle might also be useful for designing artificial intelligent systems and perhaps even for understanding problems in economics and cosmology.

A. D. Wissner-Gross & C. E. Freer, Physical Review Letters 110, 168702 (2013).

Sunday, April 21, 2013

Burning issues

Nice piece in the Observer to day by Will Hutton on the absurdity of valuing fossil-fuel reserves on the assumption that they will all be burned, which will doom us to a probable degree of global warming that you just don’t want to think about.

Shame he trips up here though:
“Galileo had to take on the Catholic church to prove the world was round, today's scientists have to take on the right to prove that climate change is man-made.”
Um, Galileo did what, exactly? Well, y'know, he did something or other really sciency and the church just hit him with the Bible until he said sorry. Sometimes I worry that the popular view of Galileo is going to get ever more mangled until one can suggest without fear of contradiction that he was burned at the stake for proving that the universe began with a Big Bang.

However, it is as depressing as ever to read some of the feedback on the Guardian’s Comment is Free, including remarks like this:
“The planet will do absolutely fine. To think humanity has any influence on climate takes human arrogance to the extreme. The planet was here long before we were, and it will remain long after the human race has destroyed itself by other means.”
It would be tempting just to roll one’s eyes at this kind of head-in-sand, defiant ignorance if it were not so widespread. One can’t help suspecting that some of those oil magnates take this same view.

Wednesday, April 17, 2013

Lest we forget

Before my weekly game of 5-a-side football it was proposed that the team in white would be the Thatcherites and those in black the Scargillites. How fitting, then, that the blacks never looked like winning, but struggled valiantly while constantly undermining their efforts with poor tactics.

I guess I was never going to be so interested in demonstrating at a funeral, though I understand the motives of those who did. I was in the NUJ in the late 1980s and will never forget the contempt and glee that was palpable behind its de-recognition in the publishing industry.

As I stepped off the plane from China last Tuesday, I picked up a copy of the FT and was soon enough spluttering like a retired colonel over the pathetic tributes it ran from the likes of Niall Ferguson. At least the FT has published my letter in response to those pieces. Here is the original – and while I understand the need for shortening, it was her legacy of arms dealing (remember Jonathan Aitken?) that sticks most in my craw.


Sir, It is astonishing that none of your fawning tributes to Margaret Thatcher is able to connect the current economic crisis to the deregulatory, venal, credit-buoyed Thatcherite 1980s – unless the remark in your leader that their “impact has been lasting” is supposed to be ironic. (Certainly your remark that “deregulation and liberalisation are no longer in fashion” suggests that you might after all have some satirical intent.) You, Niall Ferguson and Janan Ganesh seem under the impression that Thatcher’s economic nous bequeathed a solid and continued legacy of prosperity. Yet whatever improvement in Britain’s standard of living that manages to survive today’s crisis stems from a trend that has been both steady for at least four decades and common throughout Europe.

Your writers betray the same breed of fantastical thinking that led President Obama to praise a “great champion of freedom” who befriended and defended Augusto Pinochet, called Nelson Mandela a terrorist, brokered lucrative arms deals with some of the most repressive regimes in the world, and severely and sometimes brutally curtailed civil liberties at home.

Ganesh suggests that to call Thatcher divisive is feeble and mealy-mouthed. He can rest assured that many of us who lived through her incumbency will not be so coy.

Friday, April 12, 2013

Mystical atoms

Here is my Crucible column in the latest issue of Chemistry World.


A strong contender for the strangest book about chemistry ever written is Occult Chemistry (1909) by Annie Besant and Charles Leadbeater. It offers an element-by-element account of what atoms really look like, and the answer is that they are astonishingly rich in substructure and detail – some like ornate frozen splashes, others resembling the rose windows of Gothic cathedrals. Far from being unsplittable – this was 8 years before Ernest Rutherford astonished the world by “splitting the atom” – these atoms are composites of more fundamental particles, of which hydrogen is composed of 18 and nitrogen of no fewer than 290.

You’re wondering, no doubt, how on earth the authors knew all this in the days before X-ray diffraction, electron microscopy and high-energy particle physics. The answer is that they saw it for themselves. Besant was President of the Theosophical Society, the Eastern-tinged mystical group founded by the Russian medium Madame Blavatsky, and Leadbeater was a Spiritualist medium. Their occult powers enabled the duo to shrink their perceptive faculties to atomic dimensions, whereupon they could perceive the shapes of atoms directly.

So far, so deluded. But that was a very strange time, and one can’t quite just dismiss Besant and Leadbeater as mad fantasists. They were connected with, and in a wider sense in tune with, several leading scientists of their age, some of whom read the book (with varying degrees of scepticism). Like it or not, Occult Chemistry is a part – a bizarre, even unsettling part – of chemical history.

While Blavatsky was little more than a wily, self-promoting fraud, Besant warrants more consideration. Born in 1847, she was a fearless social campaigner, arguing for women’s rights and birth control, better conditions for workers, free school meals, educational reform, and home rule for India, her spiritual home. Her conversion to Blavatsky’s pseudo-religion in 1889 dismayed many of her progressive friends, including George Bernard Shaw, but it didn’t in itself mark her out as odd in an age when mystical inclinations were shared by many scientists, most notoriously the Spiritualist sympathizers Oliver Lodge and William Crookes.

Crookes, the chemist and entrepreneur who was President of the Royal Society from 1913 to 1915, was himself a member of the Theosophical Society, and was convinced that Spiritualism offered glimpses into an invisible world populated by spirit beings. He was flattered and courted by the Theosophists – Blavatsky referred to his work on an alleged new form of ‘radiant matter’ – and Besant sent him an initial account of her ‘occult chemistry’ published in the Theosophical magazine Lucifer in 1895. Since Crookes had suggested in 1887 that elements might be sub-divided further into a basic ingredient called protyle, he was somewhat sympathetic to Besant and Leadbeater’s assertions, and he seems to have replied politely, telling Besant that the book might encourage chemists to search for the missing elements in Mendeleyev’s periodic table1.

Besant and Leadbeater claimed they had used mediation techniques to gaze on atoms with ‘etheric eyes’. This revealed atoms with elaborate, lobed shapes that fall into distinct classes: ‘spikes’, ‘dumbbells’ and arrangements like the Platonic solids. Closer inspection showed a substructure made up of units they call anu, the Sanskrit word for atoms. The anu are themselves “atoms of ether”, the medium still then considered the matrix of electromagnetic waves, and here identified with Crookes’ protyle. That the ether was a particulate material was not in itself an outrageous suggestion – Mendeleyev believed this too. Some scientists, including Crookes, suspected the ether was a bridge between the physical and spiritual worlds.

Most of Occult Chemistry in taken up with descriptions and diagrams of these elemental substructures. The images are mesmerizing, elaborated in meticulous and often beautiful detail. With their ‘sciency’ appearance, bedded down amidst numerical calculations, it’s easy to see how – especially at a time when the discoveries of X-rays, electrons, radioactivity and atomic structure were making atomic physics a veritable phantasmagoria where anything seemed possible – contemporary readers might have found this stuff impossible to distinguish from real science. But the allure goes deeper, for you can’t look at these images today without experiencing some frisson. The triplets of fundamental particles at the atom’s core must put you in mind of the quark structure of nucleons – and indeed it’s been argued that the revelations of Occult Chemistry bear uncanny resonances with the discoveries of particle physics2. What’s more, the lobes and dumbbells speak immediately to the chemist of the electron orbitals shortly to emerge from quantum chemistry. It’s sheer coincidence – has to be, right? – but it’s eerie all the same.

What most of Crookes’ contemporaries made of all this is unknown. But I bet they were intrigued. J. J. Thomson, the discoverer of the electron, went to séances, as did Pierre Curie. George Johnstone Stoney, who named the electron, was convinced that the universe was an infinite series of worlds within worlds. Francis Aston, the discoverer of isotopes, read the book and borrowed from it the term “meta-neon” to refer to his newly discovered neon-22 (ref. 3).

Occult Chemistry is, then, pretentious and outrageous – but curiously compelling.

1. W. H. Brock, William Crookes (1832-1919) and the Commercialization of Science. Ashgate, Aldershot, 2008.
2. S. M. Phillips, Extra-Sensory Perception of Quarks. Theosophical Publishing House, London, 1980.
3. J. Hughes, Physics World September, 31-35 (2003).

Thursday, April 11, 2013

A demon-haunted theory

Here is a piece I’ve just published in the April issue of Physics World, in pre-edited form (sort of).


James Clerk Maxwell originally devised his demon as a thought experiment to evade the second law of thermodynamics. But some of the physicist’s contemporaries actually believed it was an intelligent being that could bridge hidden worlds and provide a scientific route to immortality of the human soul.

Maxwell’s demon represents one of the great “thought experiments” of physics. Just like Einstein riding a light wave or Schrödinger’s cat facing quantum extermination, it poses a ‘what if’ question that illuminates a deep property of nature. The Scottish physicist James Clerk Maxwell proposed his little being as a way of picking a hole in the second law of thermodynamics by enabling heat to flow from cold to hot and resisting entropy’s disruptive influence. He had no idea that he was actually posing a riddle for the theory of information, which would lead ultimately to the recent demonstration that information and energy can be interconverted.

But the popularity that Maxwell’s demon has enjoyed thanks to the current burgeoning interest in the thermodynamics of information overlooks the way this little being was regarded by Maxwell and his contemporaries. Placed in its historical context, Maxwell’s demon played a rather different role – one that is surprising and in some respects shocking. For one thing, this wasn’t exactly a thought experiment at all. Some of Maxwell’s contemporaries saw in the demon a link between science and religion, a solution to the problem of free will, a bridge to hidden worlds, even a scientific route to immortality of the human soul. In some ways, Maxwell’s original demon seems more closely linked to ancient demonology than to the future of computing and information science.

Picking holes

Maxwell’s idea was a response to the gloomy prediction of a ‘cosmic heat death’ of the universe. In 1850 the German physicist Rudolph Clausius formulated the first and second laws of thermodynamics: the conservation of energy and the irreversibility of heat flow from hot to cold. A year later William Thomson (later Lord Kelvin) pointed out that the flow of heat involves ‘dissipation’ of mechanical energy: it flows into random motions of molecules and can never be recovered. This process, he said, must eventually create a universe of uniform temperature, from which no useful work can be extracted, and in which nothing really happens.

Maxwell realised that this inexorable slide into an inert state challenged human free will. If, as the second law says, there is only one way for things to happen, we would seem to be locked into rigid determinism, with human freedom just an illusion. As a devout Christian, he could not accept that God would arrange things this way. But how could free will be rescued without violating thermodynamics?

Maxwell’s seminal work on the microscopic theory of gases gave him an escape clause. He was convinced that the second law is simply statistical. Gases contain molecules with a bell-shaped statistical distribution of speeds, the faster ones being in a sense ‘hotter’. Temperature gradients get dissipated because it is far more likely that the faster molecules will mingle with the slower, rather than by chance congregating into a ‘hot’ patch. There’s nothing in the laws of mechanics to forbid the latter; it’s just very unlikely.

But what if we could arrange for that to happen? Then the second law would be undone. We can’t manage it in practice, Maxwell recognized, because we can’t possibly find out about the velocities of all the individual molecules. But what if there were, as Maxwell put it, a “finite being”, small enough to ‘see’ each molecule and able to keep track of it, who could open and shut a trapdoor in a wall dividing a gas-filled vessel? This being could let through fast-moving molecules in one direction so as to congregate the heat in one compartment, separating hot from cold and creating a temperature gradient that could be tapped to do work.

Maxwell laid out this idea in December 1867 in response to a letter from his friend, the physicist Peter Guthrie Tait, who was drafting a book on the history of thermodynamics. Maxwell told Tait that his aim was explicitly to “pick a hole” in the second law – to show that it was “only a statistical certainty”. The thought experiment offered a loophole that might rescue free will.

Exorcising the demon

It took over a century for the problem with Maxwell’s demon to be identified. In 1929 the Hungarian physicist Leo Szilárd believed he saw a flaw: to measure the speed of molecules the demon would have to expend energy, which would dissipate enough heat – produce enough entropy – to compensate for the demon’s manipulations. But in 1961 the German-American physicist Rolf Landauer, drawing on the relationship between information processing and thermodynamics developed by Claude Shannon in the 1940s, pointed out that measurements can in principle be conducted without increasing entropy.

That may be done, however, only by retaining all the information that the demon acquires. But, said Landauer, if he is a ‘finite being’ with a finite memory, this accumulation of data can’t go on forever: eventually some information will have to be erased to make room for more. And Landauer showed that while measurement can be free of an entropic cost, erasing data can’t be. Resetting a binary digit (from 1 to 0, say) must inevitably dissipate energy of at least kTln2, where k is Boltzmann’s constant. So in effect the demon generates entropy by forgetting. Charles Bennett of IBM’s research centre in Yorktown Heights later showed that this act of ‘forgetting’ is unavoidable, since it is equivalent to resetting the measuring equipment ready for the next measurement.

Landauer’s discovery has profound implications for the theory of computation. The digital circuits in today’s computers – which are inevitably reset from one calculation to the next – will always dissipate a certain minimum amount of heat during processing, although at present they still create far more heat than this lower limit because of other sources of dissipation. The existence of this unavoidable heat output in computing was proved experimentally last year by a team at the University of Augsburg in Germany, who were able to measure the amount of energy dissipated when a microscopic silica bead was moved between two optical traps to encode a binary digit. They found that as a cycle of switching and resetting the bead’s position was made ever slower, the amount of energy dissipated fell to a minimum of kTln2: for infinitely slow switching, all of this was due solely to the resetting operation [1].

In effect Landauer’s principle implies an equivalence between information and heat: information itself can be converted to heat. This too has recently been confirmed experimentally. In 2010 a team of physicists at the University of Tokyo led by Shoichi Toyabe moved a nanoscale polystyrene bead in a particular direction, doing useful work, not by using any energy as such but by taking advantage of the information gathered about the bead’s position [2]. They put the bead on a spiral staircase of sorts, on which the bead could hop up or down one step at a time using thermal energy. Left to its own devices, the ball would, on average, move down the staircase. But if a demon knew the position of the ball, it could place a barrier to prevent any downhill motion, so that the ball only moves uphill. In the experiment, the physicists took on the role of the demon: if the bead was measured to have moved uphill by one step, the barrier was moved upwards by one step too. By taking advantage of information gathered about the bead’s position, the physicists – using no energy as such – ensured the bead’s net uphill movement and thereby caused the bead to gain potential energy. This demonstrated experimentally that information can be converted into energy.

These studies reveal that Maxwell’s thought experiment is now accessible to direct experimental probing, and that such efforts are at the forefront of information science and technology. Moreover, even if Landauer’s principle currently represents the standard doctrine, some commentators feel that it may still be too early to be sure that the demon is dead, and that ultimately it will prove to have ramifications for the foundations of quantum information theory [3,4].

Little helpers

Maxwell didn’t intend his creature to be called a demon. That label was applied by Thomson in an 1874 paper in Nature, where he defined it as “an intelligent being endowed with free will, and fine enough tactile and perceptive organization to give him the faculty of observing and influencing individual molecules of matter.” Whether he meant it or not, this seemingly trivial change connected Maxwell’s being to a long genealogy of tiny or invisible spirits acting as agents and familiars with special powers, dating back to the demon that allegedly advised Socrates. Maxwell was not pleased. “Call him no more a demon but a valve”, he grumbled to Tait.

"Who gave them this name? Thomson." Maxwell grumbles to Tait in this letter.

Maxwell’s apparent victory over the second law in the nineteenth century might seem decidedly Pyrrhic, since as he admitted, we can’t possibly do what the demon does anyway. Maxwell presumably could have argued that we might one day have the technological means, but he didn’t seem to hold out much prospect of that. There is, however, another way that his thought experiment could work: the demons might be real. Maxwell seems to have entertained this idea, for he took seriously the possibility that free will depended on it.

The notion of invisible, perhaps demonic, beings that intervene in the world was widely shared among philosophers of the Middle Ages and the Renaissance. But surely such ideas were banished by Victorian times? Not at all. Maxwell himself seems never to have stated whether he regarded his ‘demon’ as a being – his references to a “valve” and a “self-acting” device suggest he may have preferred the image of a machine, as physicists do today – albeit a ‘machine’ with intelligence and autonomy, as he once put it “a doorkeeper, very intelligent and exceedingly quick.” Yet his touchiness about Thomson’s quip seems rather puritanical even for a religious man until one realises that Maxwell might have entertained a belief in evil spirits.

Demons performing useful work for humans in a sixteenth-century illustration.

Several of his contemporaries had little doubt that these ‘demons’ were to be taken literally. Thomson himself took pains to stress that the demon was plausible, calling it “a being with no preternatural qualities, [which] differs from real animals only in extreme smallness and agility.” Tait evidently believed they might exist, and he enlisted them for an extraordinary cause. In 1875 Tait and the Scottish physicist Balfour Stewart, an expert on the theory of heat, published a book called The Unseen Universe in which they attempted to show that “the presumed incompatibility of Science and Religion does not exist.” There must be, they wrote, “an invisible order of things which will remain and possess energy when the present system has passed away.” They believed that this “invisible” or “spiritual” domain must be capable of interacting energetically with the familiar physical world, perhaps bridged by the pervasive ether that was then thought to carry Maxwell’s electromagnetic waves. Thus energy might be transferred from the physical to the invisible realm to sustain our souls after death: through living, we store up immortality.

Tait and Stewart were aware of the apparent conflict between the Christian doctrine of the immortality of the soul and the second law of thermodynamics, which seemed to enforce an eventual universe of insensate stasis. “The dissipation of energy must hold true”, they admitted, “and although the process of decay may be delayed by the storing up of energy in the invisible universe, it cannot be permanently arrested.” Maxwell’s demon gave them a way out. “Clerk-Maxwell’s demons”, they wrote, “could be made to restore energy in the present universe without spending work” – and as a result, “immortality is possible.”

Today these speculations, coming from two highly respected scientists who Maxwell esteemed, look bizarre. But in the late nineteenth century such ideas were widely held. Spiritualism interested many scientists, including William Crookes, Oliver Lodge, J. J. Thomson and Pierre Curie. Even though some, like Tait and Stewart, were sceptical of the claims of mediums, they did not object to the basic concept.

Scientific spirit

Not only did these scientists believe in a spiritual world, but they felt that science was on the threshold of proving its existence. Many regarded the ether as a mediator. Cromwell Varley, a pioneer in transatlantic telegraphy, drew analogies between the use of electromagnetic signals for long-distance communication and the invisible messages that were alleged to pass from spirits to the living. The distinguished English physicist William Barrett wrote in 1917 that “it is not a very incredible thing to suppose that in the luminiferous ether life of some kind exists.” He speculated about “four-dimensional beings” and “human-like intelligences – good or bad daimonia” that might be responsible for events at séances. The Irish physicist Edmund Fournier d’Albe proposed in 1907 that there might exist “infra-men” on the scale of atoms, and drew on the discoveries of radioactivity and the electron to present a “physical theory of immortality.”

Indeed, the discoveries of new ‘invisible rays’, such as X-rays and radioactivity (“Roentgen rays”) bolstered beliefs in unseen universes. William Crookes – one of the most notorious sympathizers of the Spiritualists, mediums and Theosophists of the age – felt that vibrations beyond X-rays might account for telepathy. He too found a striking role for Maxwell’s demon, arguing that it might in effect explain the mystery of radioactive uranium’s seemingly inexhaustible supply of energy. He suggested that uranium atoms might be like demons themselves, mining energy from the surrounding atmosphere by sifting hot gas molecules from cold. “Let uranium or polonium”, he said at the annual meeting of the British Association in 1898, “have a structure that enables them to throw off the slow moving molecules of the atmosphere, while the quick moving molecules, smashing on to the surface, have their energy reduced and that of the target correspondingly increased.” It’s not clear that Crookes thought any intelligent agency was involved here, although he certainly believed in the possibility of invisible beings that have “intelligence, thought, and will, existing without form or matter” – and Maxwell had made clear that intelligence was needed to make the selection among gas molecules.

All this reveals that Maxwell’s demons had a much more ambiguous ontological status than imaginary ‘thought-creatures’. As well as reminding us that even apparently ‘modern’ historical scientists didn’t necessarily see things was we do, it shows how sometimes science doesn’t banish mystical beliefs but offers ‘rational’ justifications for them.

1. A. Bérut et al. Nature 483, 187–189 (2012).
2. S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki & M. Sano, Nat. Phys. 6, 988-992 (2010).
3. J. Earman & J. D. Norton, Stud. Hist. Phil. Mod. Phys. 29, 435-471 (1998) & 30, 1-40 (1999).
4. K. Maruyama, F. Nori & V. Vedral, Rev. Mod. Phys. 81, 1-23 (2009).

Further reading
B. Stewart & P. G. Tait, The Unseen Universe. Macmillan, London, 1875.
R. H. Harman, The Natural Philosophy of James Clerk Maxwell. Cambridge University Press, 1998.
W. H. Brock, William Crookes (1832-1919) and the Commercialization of Science. Ashgate, Aldershot, 2008.
J. Canales & M Krajewski, Interdisciplinary Science Reviews 37, 314-331 (2012).