SYNOPSIS: Finds Krugman's premise interesting but his thesis to lack depth and broadness.

Paul Krugman cannot be accused of lacking good opening lines:

Is an economic slump like a hurricane, or is it more like an earthquake? Is a growing city like an embryo, or is it more like a meteorite?
Obviously some explaining needs to be done here.

The term ``self-organization'' seems to have entered the language in a 1954 paper in the Proceedings of the Institute of Radio Engineers on machine learning, though related ideas are considerably older. It has, of course, become a buzzword, indeed an indispensable element in modern techno-cant --- your humble narrator was once on a mailing list where some people proposed to write a ``self-organizing'' novel --- but a lot of real science carries on under the label, in some remarkably different fields:

[W]hat links the study of embryos and hurricanes, of magnetic materials and collections of neurons, is that they are all self-organizing systems: systems that, even when they start from an almost homogeneous or almost random state, spontaneously form large-scale patterns. One day the air over a particular patch of tropical ocean is no different in behavior from the air over any other patch; maybe the pressure is a bit lower, but the difference is nothing dramatic. Over the course of the next few days, however, that slight dip in pressure becomes magnified through a process of self-reinforcement: rising air pulls water up to an altitude at which it condenses, releasing heat that reduces the pressure further and makes more air rise, until that particular piece of the atmosphere has become a huge, spinning vortex. Early in the process of growth an embryo is a collection of nearly identical cells, but (or at least so many biologists believe) these cells communicate with each other through subtle chemical signals that reinforce and inhibit each other, leading to the ``decision'' of some cells to become parts of a wing, others parts of a leg. [pp. 3--4]
This is vague, for which I am grateful, since sharpening the notion of self-organization into something quantifiable is the subject of my thesis. But let us draw a veil over this and press on.

There's a sense in which economists have been studying little but the ``spontaneous formation of large-scale patterns'' ever since Adam Smith and the creation of self-regulating markets, but Krugman is not interested in convincing his profession that it has been speaking prose all its life; it would, in his words, ``be entitled to change the channel.'' Rather he wants to look at the way economies organize themselves in space and over time, which they do in a most conspicuous way. (There is, however, a brief discussion of technological lock-in in chapter six.) Krugman picks out three examples in particular: the way cities differentiate themselves into specialized districts; the power-law distribution of city sizes; and business cycles.

That cities --- even Los Angeles --- are not homogenous lumps, with everything mixed together, seems to have been true from earliest times. Some of this is simply because different locations have different advantages --- dockyards go by the water, fortresses on heights, and brothels and bars near fortresses. Some of it is due to zoning boards, planning commissions, real-estate magnates and red-lining, to say nothing of the police and cross-burning --- whether such forces contribute to urban self-organization is a delicate question, and in any case Krugman is silent about them. Still, this leaves a lot of differentiation which seems to be due to nothing but self-reinforcement, which (unlike zoning boards and red-lining) has actually been studied in economic theory, especially by economic geographers, for some time. (Krugman is at pains to point out that self-organization was not unknown to economists before the arrival of missionaries from Santa Fe.) He begins his discussion of this with so-called ``edge cities,'' and then passes on to a marvelously elegant illustration from Thomas Schelling's marvelously elegant book, Micromotives and Macrobehavior, which suggests how the former (requiring that at least 37% of your neighbors be like yourself) can lead to the latter (massive segregation). He then dives into a discussion of ``urban morphogenesis'' directly inspired by Turing's classic work on embryological morphogenesis. He assumes his city is one-dimensional and either infinite or circular, but claims no more value for it than that of qualitative illustration; I can think of physicists who should be so modest. Self-organization happens here because the initial random noise contains components which correspond to many different patterns in nucleo, and the dynamics are such that some of these get magnified faster than others. The pattern which grows fastest ultimately dominates the system, which is called ``pattern selection'' in traditional reaction-diffusion systems. [Note containing the words ``Fourier decomposition.'']

A power law distribution means that the number of objects whose size is at least S is proportional to S^a, for some (hopefully negative) constant a. It happens that the size of cities obeys a power law known as Zipf's law, which is usually stated thus: the size of a city is inversely proportional to its rank order so that, for example, the 100th largest city is a tenth the size of the 10th largest city. This rule is almost exactly true of the sizes of American cities (it corresponds to a value of a of -2), and has been for at least a century. Physicists have liked power laws ever since Galileo, and recently we've developed a taste for power law distributions; Prof. Per Bak and his disciples sometimes seem to want to claim everything obeying a power law distribution for ``self-organized criticality.'' Krugman explains the power law distribution as an outcome of growth processes where the expected rate of growth is independent of the size already attained. Such processes do, in fact, generate power laws, and have been known to for some time --- Herbert Simon proposed one, ``in a completely impenetrable exposition,'' in 1955. Alas, none of them are as regular as the empirical data!

At this point Krugman tells us that what we have just seen are order from instability (``When a system is so constituted that a flat or disordered structure is unstable, order spontaneously emerges.'' --- p. 99) and order from random growth (``[O]bjects are formed by a growth process in which the expected rate of growth is approximately independent of scale, but the actual rate of growth is random.'' --- p. 100). He declines, thankfully, to call these universal laws of self-organization, but he does suggest they are ``principles,'' or rather common ways of self-organizing.

Temporal self-organization in the economy is more familiarly known as business cycles, or yet more familiarly as booms and crashes (err, depressions; err, recessions; err, slumps; err, slow-downs). Since Keynes (at least) the idea that these are in some way self-reinforcing has been common, and Krugman resurrects a body of Keynesian theory from the '50s, ``non-linear business cycle theory.'' This is of the order-from-instability type, and so predicts a characteristic size to business cycles, which, on a comparison of 1933 with the recent unpleasantness, or even the early 1980s, is less than plausible. Krugman also presents an order-from-random-growth theory --- really percolation theory in wolf's clothing --- which avoids that problem at the cost of ``[making] less contact with what seems to happen during a boom or slump,'' and predicting a power law distribution for business fluctuations, which is not observed. Charitably, Krugman chooses to ``regard them both more as illustrations as how one might approach self-organization in time than as finished statements of how one actually ought to do it.'' Some such theory will be necessary if we are not to continue treating shifts in aggregate demand as external shocks --- administered, perhaps, by the vengeful specter of Karl Marx.

If this were a formal and comprehensive treatise, I would be disappointed by the passing over of evolutionary and institutional economics; the cavalier starting of models from tabulæ rasæ rather than already-differentiated settings; the fact that most of the models are what in physics would be called ``phenomenological,'' i.e. they don't try to connect to the underlying mechanisms, such as markets; the absence of even qualitative comparisons with empirical data; and the indifference to exogenous forces, natural , social or political, which in practice are very important in all of the topics Krugman discusses. But this is not a formal and comprehensive work; that will have to wait for a good many years. It is a self-described ``discourse'' of exactly a hundred pages, a very brief introduction and an appeal for further development, for the work which will make the treatise possible. As befits such a book, Krugman's writing is clear, informal and concise (but then, it usually is). His attitude towards the mathematics is that it should be used and not seen; accordingly we get the hypotheses once as stories (``I do not want to dignify them by calling them models''); a second time with a bit of calculus; and a third time in an appendix for those who want the nitty-gritty. (Even there he draws the line at Fourier decomposition and linear stability analysis; phase space and attractors are explained verbally, and well, in the body of the text.) The economics should be accessible to anyone who's taken Econ. 1, and probably many (such as your humble narrator) who haven't. The book will be of particular interest to those crossing the bridge from economics to self-organization and dynamics in either direction, but most educated readers should find it informative and engaging.

vi + 122 pp. (including appendix), minimal bibliography, index
Economics / Self-Organization, Complexity, etc.
Currently in print as a hardback, ISBN 1-55786-698-8, and a paperback, ISBN 1-55786-699-6, LoC HB199.K75. The list price for the latter is $19.95; while I would never advocate copyright piracy, 20 cents a page is asking for it.
16 March 1996, minor corrections 29 January 1997