The world in a grain of sand?

Physicists through the ages have tried to come up with theories that seek to unify disparate views of nature: unfortunately their attempts in this direction have attracted the somewhat ironical label of "theories of everything" due perhaps to the innate scepticism for which their community is known. Undaunted by this, many have gone ahead with their endeavours, which usually involve the linking of theories of elementary particles and gravitation.

Per Bak's book strikes new ground in that it has very ambitious aims while employing ideas of a childlike simplicity. In this book, Bak claims that the theory of self-organised criticality (SOC) explains, as stated in the title, "how nature works". The chosen paradigm for this theory (put forward originally in 1987 by Per Bak, Chao Tang and Kurt Wiesenfeld) is a sand pile: the addition of sand builds up the pile until a critical angle is reached and maintained. Beyond this, the sand pile "organises itself" so that any further addition of sand causes avalanches to flow, till the pile is once more at the critical angle.

This state of affairs is said to be characteristic of a self-organised and critical state, at which avalanches of all lengths and durations are possible. Since it is argued that all microscopic details such as the size of sand grains or the friction between them are irrelevant to this end state, there are no privileged avalanches that tell us what makes a particular sand pile distinct from any other. Bak argues further in this book that all of nature is characterised by this evolution to an SOC state where events on all time and length scales occur, independent of the details of the system chosen.

In his book, Bak gives many examples of such systems, including traffic flow, the evolution of life and the brain, and argues in each case for the existence of a terminal SOC state. In the case of the brain, for example, this is the state at which information is just barely able to propagate; operating at a state much lower than this would cause information not to propagate as the relevant areas of the brain would be disjointed, while operating at a state much higher would cause sensory overload in response to even the simplest information as a consequence of internal chaos in the brain.

The simplicity of such a model is possibly its most appealing aspect: the idea that diverse systems naturally evolve to their most challenging ("minimally stable") state, abjuring simple equilibrium (the "flat" state of the sand pile) and complete chaos (the overly steep state of the sand pile when the avalanches are numerous and have very complex dynamics) on the other, has an inherent appeal for theoretical physicists who would wish there to be such simplifying, unifying assumptions for some of the intricate phenomena that nature burdens us with. In addition there are compelling philosophical arguments that Bak puts forward for a turning away from reductionism, favoured by scientists thus far, towards an acceptance that stripping a system down to its individual components may not always be the best way of analysing complex behaviour.

There are, however, many stringent requirements that such an all-embracing theory has to face. There is the lurking danger of a hypothesis too far, as there is no compelling reason to be convinced that every system in nature organises itself into a dynamical state that is independent of its history or structure; in fact eliminating any dependence on such details can also be construed as being severely reductionist. To imagine that the movement of tectonic plates and transactions within the stock market could be explained in their essence by the same theory would be optimistic. Even if one accepts this, it is an additional leap of the imagination to construct a situation whereby the end state in all these examples has no time scales characteristic of any of them: to imagine that there is no characteristic time between earthquakes at a fault, or for financial transactions in the City, is not part of one's everyday intuition. Accepting even this, one has to ask what such a theory really explains, whether it is indeed sufficiently comprehensive to illuminate the important properties of even one of its paradigms.

And, of course, the real hard-core scientist would demand even more: that such a theory, if is to mean anything at all, must predict something of interest. What, for instance, is the use of saying that earthquakes are symptomatic of SOC, if we can ultimately make no specific predictions about the next likely one? Bak's attitude, especially to the latter question, is that predictions in and of themselves serve no particular purpose, that it is enough to accept that earthquakes of all sizes are equally likely on some cosmic time scale. Apart from the fact that such an attitude is almost karmic in its acceptance of what Bak terms "catastrophism", the idea that physicists are happy not to look for causality in such things is the kind of idea that would make physics rather unpopular with the average earthquake survivor.

The book does not provide ready answers to any of these questions. They are admittedly difficult, some of them demanding a level of theoretical development that has, despite the massive industry in physics presently devoted to SOC, simply not had time to evolve. This is perhaps why the book feels as though it has been written before its time, by contrast with other popular science books that focus on the core ideas underlying a body of research, that are the distilled essence of decades of rigorous work. In the present case, there is a sense of unease that what is being conveyed about SOC is pretty close to what exists at a rigorous level (or indeed at all); that theoretical or experimental verification of the original idea is still under development. While there is nothing wrong with this in principle, that the book's degree of assertiveness (as exemplified by its all-embracing title) is at odds with the spirit of such tentative exploration. A contributing factor to one's sense of unease is that despite the fact that the field is rapidly evolving little room has been made by Bak for opposing points of view; had he done so, the sense of excitement intrinsic to such a dynamic state of affairs would have been conveyed more directly.

A case in point is the sand pile, Bak's chosen paradigm of SOC. There is important theoretical and experimental evidence, notably from Sidney Nagel and his group at the University of Chicago, which suggests that there are lengths and times that are characteristic of a pile of sand - so that contrary to Bak's picture of avalanches of every size being equally likely, some avalanches are more equal than others. The deep origin of this is the fascinating fact that sand piles have "memory", which is why words can be, and often are, written in sand. These "special" avalanches are related to the history of the sand pile, in much the same way as our births and our lives as humans also condition the way we die. But little space is given to this point of view; rather, when space is made for it, one is given the impression that better experiments would prove that sand piles are indeed "explained" by SOC, that the only good theories around are ones which support this stand-point. In the end, such an omission makes the book vulnerable to charges of being based on ideology rather than logic, and damages the credibility of the very view that Bak seeks to project.

All of this, however, is not to downgrade a very worthwhile endeavour: the attempt to make universal many features in nature without getting bogged down in details is a laudable one, and worthy of encouragement. The book is an easy read - Bak's style of writing is informal, almost conversational, although at times too anecdotal to interest readers unfamiliar with the scientists whom he mentions. Once again the timing of the book gets in the way of one's full participation in such informality, because such a style is more enjoyable when applied to the quirks of scientists distinguished enough to be of interest to the lay reader.

Perhaps, in the end, the book's greatest strength is also its greatest weakness. The generality and diversity that Bak's ideas embody also reflect a lack of specificity, emphasised by the lack of an obvious paradigm. Until this is found, it will be hard to overcome the scepticism in the hard sciences surrounding ideas that are not set in the dual stones of proof and observation. The time-honoured traditions of scientific inquiry will always demand that statements about how nature works be preceded by long and persuasive arguments that explain why it works that particular way.

Anita Mehta is reader in physics, S. N. Bose National Centre for Basic Sciences, Calcutta, India.