In 1264 Pope Clement IV wrote to Roger Bacon asking for his help on an issue so grave he had to refer to it in the vaguest of terms in secret letters “concerning the things you recently indicated”. His circumspection was understandable: the problem was the Antichrist and how to deal with him. Unfortunately, as Robert Bartlett explains in The Natural and the Supernatural in the Middle Ages, Bacon hadn’t actually written the book describing the new remote-controlled weapons of mass destruction Clement was pinning his hopes on after hearing the savant boasting about it a few years earlier.
The Magic Monk, however, rose magnificently to the occasion, producing within a year the Opus Maius, the Opus minus (a guide and supplement to the quarter of a million words of the Opus Maius) and the Opus tertium, a 300-page summary of the other two. He set out a theory of the universe in which every point emits radiation and is bombarded by it (his weapons would have used optics among other things). In this, he anticipates theories of modern electromagnetic radiation, but he was also using an idea developed by the 9th century Muslim scientist al-Kindi. Al-Kindi also helped Bacon calculate the precise date for the coming of the Antichrist (1294, which turned out to be the year of Bacon’s death) based on the common assumption that this would happen when Islam ceased to exist. It seems astonishing to us today, but al-Kindi and another great Arab thinker Abulmazar had actually calculated when their religion would end, using a combination of astronomical data and astrology. Anyway, Clement was pleased to get the books, and presumably even more pleased not to get the Antichrist.
It’s to Clement’s credit that faced with the end of his world, he looked for a practical solution first, whereas most of us tend to shift from science to superstition as the situation grows more desperate. Of course there was a long history of scientific advice to rulers on risk, stretching back thousands of years to the hydrologists who advised the Pharaohs on the likely severity of the Nile’s floods and the outlook for future crop yields based on the alluvia in upstream waters. It would be nice to think that as scientific knowledge has grown, our rulers have come to appreciate and apply it to the business of government. They haven’t. That’s not to say that science is ignored – many governments have a science ministry or sub-ministry as well as scientific advisors and committees to consult on specific issues.
But widespread understanding of what science is, how it works, and what it can and cannot do is far more rare in government circles than is knowledge of other professions. Writing in Prospect magazine, Mark Henderson pointed out that only one of the 650 Members of the UK parliament for instance is a professional research scientist, while there are 158 business people and 86 lawyers. Henderson argues that politicians’ indifference to science “means that not only is their stewardship of science poor, but so is their use of it in policy making”.
That’s not the case in Britain alone, and the OECD’s Global Science Forum (GSF) is trying to change things. A recent symposium to mark the GSF’s 20th anniversary looked at “New Science-Based Tools for Anticipating and Responding to Global Crises”. The biggest science headlines recently have been inspired by the infinitely small – the confirmation of the Higgs boson (that we discussed here) but as the symposium summary says, researchers have been making significant progress at the other end of the scale, tackling large systems of interest to all of us, such as ecosystems, pandemics, financial markets, energy generation and distribution, and what influences weather and climate, as well as societal phenomena such as urbanisation and migration.
Such systems are open (they exchange energy and information with their surroundings); dynamic (they contain numerous internal couplings and feedback loops – often nonlinear ones, operating on multiple spatial and temporal scales); and they are far from equilibrium (they continually transition between states that, individually, are inherently unstable). A pile of sand is a simple example of the type of phenomenon in question. It’s a “self-organising critical system”, keeping its basic cone shape even as more sand is added, provoking little landslides and other local instabilities. If you only look at the big picture, the sand pile may seem stable, whereas if you look at a particular area closely, you’ll see grains tumbling down the slope in avalanches of sand: lots of small ones, fewer intermediate-size ones and, much less frequently, major events where a significant fraction of the whole cone collapses. One of the great advances of science in recent years was to discover that the probabilities of occurrence of avalanches of various sizes is not random, but is in fact governed by a strict mathematical “power law”.
Ever-cheaper, more powerful computing allows us to look at different scales and levels of interaction and study problems that more traditional approaches can’t cope with. In economics, this enables us to go beyond models depending on equilibrium and a certain definition of rationality to examine complex systems in a constant state of flux such as financial markets, and even devise ways to predict and prevent crashes in markets where the nanosecond is a useful division of time.
It’s a long way away from worries about the Antichrist, but the medieval scholars were in many respects more sophisticated than us, thinking holistically in terms of a cosmology in which agents and actions at different levels and scales interacted with and influenced each other. And we could probably still learn from their insights about another crucial aspect of the emerging sciences discussed at the OECD symposium: you and me. As the summary notes, the utility of many results “is only as good as the validity of the representations of human behaviour that are incorporated into the models”, going on to recall drily that “This behaviour is, of course, only partially understood by scientists who, moreover, are known to disagree on many essential points”.
So we’ve still got a lot to learn before we find scientific explanations for many of the great questions facing us, but as St Augustine said almost a thousand years before Bacon’s time, “Miracles are not contrary to nature. They are contrary to what we know about nature”. Let’s keep looking.
When relations with the Muslim world are so crucial, it’s a disgrace that so few diplomats are trained in Arabic, according to Roger Bacon. Robert Bartlett also tells us that Bacon was critical of Western education’s neglect of science and mathematics, as well as of foreign languages. Nothing much seems to have changed over the centuries, and the OECD is still trying to encourage student interest in science and convince us of the benefits of learning languages in a globalised world.
This month marks the centennial of the birth of mathematician Alan Turing, the “father” of modern computing and artificial intelligence. To celebrate the occasion, we’ll be publishing a series of articles on modelling and economics. The series starts with a contribution from Professor K. Vela Velupillai of the Algorithmic Social Sciences Research Unit at Trento University’s Economics Department, and Elected Member of the Turing Centenary Advisory Committee.
The “Five Turing Classics” – On Computable Numbers, Systems of Logic, Computing Machinery and Intelligence, The Chemical Basis of Morphogenesis, and Solvable and Unsolvable Problems– should be read together to understand why there can be something called Turing’s Economics. Herbert Simon, one of the founding fathers of computational cognitive science, was deeply indebted to Turing in the way he tried to fashion what I have called “computable economics”, acknowledging that “If we hurry, we can catch up to Turing on the path he pointed out to us so many years ago.”
Simon was on that path, for almost the whole of his research life. It has been my mission, first to learn to take this “path”, and then to teach others the excitement and fertility for economic research of taking it too.
A comparison of Turing’s classic formulation of Solvable and Unsolvable Problems in his last published paper in 1954 and Simon’s variation on that theme, as Human Problem Solving, would show that the human problem solver in the world of Simon needs to be defined – as Simon did – in the same way Turing’s approach was built on the foundations he had established in 1936-37. At a deeper epistemological level, I have come to characterize the distinction between orthodox economic theory and Turing’s Economics in terms of the last sentence of Turing’s paper (italics added): “These, and some other results of mathematical logic may be regarded as going some way towards a demonstration, within mathematics itself, of the inadequacy of ‘reason’ unsupported by common sense.”
We – at ASSRU – characterize every kind of orthodox economic theory, including orthodox behavioural economics, advocating the adequacy of “reason” unsupported by common sense; contrariwise, in Turing’s economics we take seriously what we now refer to as Turing’s Precept: ‘the inadequacy of reason unsupported by common sense’.
At another frontier of research in many of what are fashionably referred to as “the sciences of complexity”, some references to Turing’s The Chemical Basis of Morphogenesis is becoming routine, even in varieties of computational economics exercises, especially when concepts such as “emergence” are invoked. It is now increasingly realized that the notion of “emergence” originates in the works of the British Emergentists, from John Stuart Mill to C. Lloyd Morgan, in the half-century straddling the last quarter of the 19th and the first quarter of the 20th century.
A premature obituary of British Emergentism was proclaimed on the basis of a rare, rash, claim by Dirac (italics added): “The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.”
Contrast this with Turing’s wonderfully laconic, yet eminently sensible precept in his 1954 paper (italics added): “No mathematical method can be useful for any problem if it involves much calculation.”
Turing’s remarkably original work on The Chemical Basis of Morphogenesis was neither inspired by, nor influenced any later allegiance to the British Emergentist’s tradition – such as the neurological and neurophilosophical work of Nobel Laureate, Roger Sperry. On the other hand, the structure of the experimental framework Turing chose to construct was uncannily similar to the one devised by Fermi, Pasta and Ulam in 1955, although with different purposes in mind.
Turing’s aim was to devise a mechanism by which a spatially homogeneous distribution of chemicals – i.e., formless or patternless structure – could give rise to form or patterns via what has come to be called a Turing Bifurcation, the basic bifurcation that lies at the heart of almost all mathematical models for patterning in biology and chemistry, a reaction-diffusion mechanism formalised as a (linear) dynamical system and subject to what I refer to as the linear mouse theory of self-organisation, for reasons you can discover here.
Those interested in the nonlinear, endogenous, theory of the business cycle know that the Turing Bifurctions are at least as relevant as the Hopf Bifurcation in modeling the “emergence” and persistence of unstable dynamics in aggregative economic dynamics.
Turing’s Economics straddles the micro-macro divide in a way that makes the notion of microfoundations of macroeconomics thoroughly irrelevant; more importantly, it is also a way of circumventing the excessive claims of reductionists in economics, and their obverse! This paradox would have, I conjecture, provided much amusement to the mischievous child that Turing was, all his life.
Pr Velupillai kindly provided this extended version of his article, including notes and comments
Computable Economics (Elgar, 2012) edited by Veupillai, Zambelli and Kinsella brings together the seminal papers of computable economics from the last sixty years and encompass the works of some of the most influential researchers in this area, including Turing
Applications of complexity science for public policy from the OECD Global Science Forum
Algorithmic Social Sciences Research Unit (ASSRU) at the Univesity of Trento
France fought to get the “exception culturelle” recognised by the GATT, the forerunner of the World Trade Organization, in particular to protect its own cinema against Hollywood. So it’s all the weirder that French movie distributors insist on translating titles from English into er, English. Wild Things, for instance, becomes Sex Crimes. It’s even weirder when the original uses a word of French origin in the title. Triage with Colin Farrell becomes, for French audiences, Eyes of War. However, the French are not alone, as I learned on reading this article by Quentin Cooper on the BBC website. Quentin wonders why the latest Aardman film The Pirates! In an Adventure with Scientists has been rebranded as The Pirates! Band of Misfits in the US.
The quick answer is that to many people, the subtitles are synonymous, and this isn’t surprising given the way science and scientists are often presented. You either get a man in a white lab coat staring intelligently at some exotic glassware full of scientific-looking liquid, or a wild-haired eccentric solving mile-long equations but incapable of posting a letter.
Scientific issues are regularly sensationalised, trivialised, or misunderstood by the media, with basically three types of story: breakthrough, silly or scare. Scare stories give a poor image of science, reinforcing the stereotype of the mad scientist whose research is dangerous for human health or the environment, with “Frankenstein” being used to label practically any product of genetic research for instance, even ants.
Breakthrough stories give an image that is positive, but just as inaccurate as scares and trivia, ignoring the way ideas and intuitions emerge, are formulated as hypotheses and then tested, vindicated, revised or rejected over a period of time. Look at any health breakthrough article and if the full story is given, chances are that the researchers have come up with something that will take years to influence treatment, if it ever does.
At the same time, scientists must take their share of the blame too. Ananyo Bhattacharya, chief online editor of Nature argues here that if reporters wrote stories the way some scientists seem to want, few people would read science coverage. Both sides have to make an effort because an understanding of science and technology is necessary not only for those whose career depends on it directly, but also for any citizen who wishes to make informed choices about controversial issues ranging from stem cell research to global warming to genetically modified organisms to teaching the theory of evolution in schools. And new issues are bound to emerge in the years to come.
But could science do more than provide the knowledge needed to understand natural processes? A symposium organised by the Global Science Forum (GSF) at the OECD today explores new science-based tools for anticipating and responding to global crises. The premise is that new types of scientific inquiry, and new modes of science-policy interactions, are emerging based on the ability of researchers to analyse and to make reliable forecasts about policy-relevant phenomena that have, until now, been seen as lying outside the scope of useful scientific analysis.
Typically, these are systems and networks consisting of vast numbers of individual elements that interact in complicated ways, such as ecosystems, financial markets, energy networks, or societal phenomena such as urbanisation and migration.
In one sense, the symposium will simply be trying to bring policy makers up to date with developments since the last time they adopted a new set of scientific tools in the 19th century. The social sciences that now form a natural part of government decision making were only emerging, and borrowed much of their metaphors and terminology from the existing sciences, especially physics.
We still talk about flows, masses, equilibrium and so on (there’s actually something called a “gravity model” of trade, for example). But these terms are rooted in “classical” physics, developed before relativity and quantum theory. The GSF has been working for several years now to show how the new sciences of complexity can provide insights into systems that operate not just as series of actions and reactions, but with feedback, non-linearity, tipping points, singularities and so on.
We’ll report back on tools for anticipating and responding to global crises once the summary of today’s symposium is available. In the meantime, we laugh in the face of danger!
The symposium marks the 20th anniversary of the Global Science Forum and the 100th meeting of the OECD Committee for Scientific and Technological Policy