I used this book when I taught classical mechanics in the seventies. I found it to be very readable and with a far better coverage of Lie algebras and groups than Hamermesh (who defines scalars and invariants in the right way). The book contains typo errors, too bad that a second edition never came out. I'd like to get a copy, but not at any price! Dover, where are you when we need you?

Translation: nonsense. Anyone who proclaims that reductionism is dead is woefully ignorant of the enormous breakthroughts, by standard 'reductionist' methods, in cell biology, including cancer research. See R. Weinberg's "One Renegade Cell: How Cancer Begins", as an antidote to the anti-scientific philosophy propagated in this book.

First, there are no known laws of "self-organization". The only known laws of nature are the laws of physics and consequences deduced from the laws, namely, chemistry and cell biology. Complex adaptable models and other efforts to mathematize Darwinism are so far not falsifiable, hence are not yet science and may never be. Second, no one has yet defined 'emergence' in any meaningful (i.e., falsifiable) way. Worse, every mathematical model that can be written down is a form of 'reductionism', including so-called complex adaptable ones. Let us think clearly and be try to be precise: Quantum theory reduces phenomena to (explains phenomena via) atoms and molecules. All of chemistry is about that. Cell biology attempts to reduce observed phenomena to DNA, proteins, and cells. Believers in self-organized criticality try to reduce the important features of nature to the equivalent of sandpiles via the hope for a not yet found universality principle. Network enthusiasts hope to reduce phenomena to nodes and links, and also wish for a universality principle. In order to try to isolate cause and effect, there is no escape from reductionism of one form or another. Holism is an empty illusion: holism cannot even be mathematized or falsified. Holism is religion, not science, and should not be advertised as if it would be science.

See Schrödinger's "What is Life" for a clear explanation why we should not expect to discover macroscopic (statistical) laws of biological evolution, the only way to understand evolution being mutation by mutation at the level of DNA. Following Mendel, who was a reductionist in the Galilean spirit of physics, two of those who followed Schrödinger's line of thought discovered the structure of DNA, and the genetic code. Genes and the genetic code are excellent examples of emergent objects that can be studied systematically. The genetic code is the source of the most important complexity in nature: life.

Show me one, single, holist contribution to science or medicine, and I'll eat my words (without Schmarrn...)!

Gene Autry sometimes shot from the hip, but he at least occasionally hit something!

Set in the last days of the Trujillo dictatorship in the Dominican Republic, the book describes the brutality of the dictatorship and the failed attempts to overthrow it. The description is as seen through the eyes and experiences of a few individuals. Maybe few books have been better written, but the description of torture is hard to read, far worse that that described in "The Kite Runner". Also important: the old aunt's denial near the end that her brother had commited any wrong. Ah, yes, the denial of wrongs committed, and the worse the crime, the more complete the state of denial.

I watched this film after seeing my wife's all time favorite, Les Vacances Monsieur Hulot. Bumbling slapstick, nearly as silent film, is used to parodize the era of the happy middleclass housewife of the fifties with all her new appliances, her husband with all his gadgets, and to throw sarcasm at efficient production at the expense of human relations. I don't know of a film that does a better job of this. the ending is happy, with the absent gadget-focused father finally discovering the joy of having a playful young son.

Albert Barabasi presents the lay reader with a stimulating description of the origins of network theory and recent applications. He describes random networks, small world and scalefree networks. In nonrandom networks the importance of hubs is emphasized. Small world networks are the ones with a well defined averge number of links, and in scalefree ones the density of links scales as a power law. For the many interesting examples discussed, I would like to have seen graphs showing scaling over at least three decades in order to be convinced of scaling. However, in practice, whether a network scales or not may not be so important. I liked best the discussions of terrorism, AIDS, and biology. If one could locate the hubs, then a small world network could be destroyed, but as the author points out there is no systematic method for locating the hubs. Also, destroyed hubs in a terror network might be replaced rather fast, whereas airline hubs could not be replaced so quickly. The book might be seen as indicating a starting point to try to develop a branch of mathematical sociology. For example, the maintainance of ethnic identity outside the Heimat is discussed in terms of networking. Now for a little criticism.

I did not find the discussion of ‚the rich get richer' very helpful because network theory at this stage deals only with static geometry, not with empirically-based dynamics. In fact, the dynamics of financial markets have been described empirically accurately without using any notion of networking. In the text the phrase „economic stability" is used but stability is a dynamic idea, and there is no known empirical evidence from the analysis of real markets for any kind of stability. The absence of dynamics on networks means that complexity is not described at all: there is nothing complex about the geometry of a static network! Suggesting that cell biology can be described by networking is empty so long as dynamics are not deduced from empirics. Nonempirical models of dynamics will probably not be of much use for making advances in understanding or treating cancer, e.g. Everything we know about cell biology and cancer was discovered via reductionism, by isolating cause and effect the way that a good auto mechanic does in order to repair a car.

Unfortunately, the author lets his enthusiasm get the best of him when he proclaims „laws of self-organization" and the need to go beyond reductionism. First, there are no known laws of „self-organization". The only known laws of nature are the laws of physics and consequences deduced from the laws, namely, chemistry and cell biology. Worse, every mathematical model that can be written down is a form of reductionism. Quantum theory reduces phenomena to (explains phenomena via) atoms and molecules. All of chemistry is about that. Cell biology attempts to reduce observed phenomena to DNA, proteins, and cells. Believers in self-organized criticality try to reduce the important features of nature to the equivalent of sandpiles. Network enthusiasts hope to reduce phenomena to nodes and links. In order to try to isolate cause and effect, there is no escape from reductionism of one form or another, holism being an empty illusion. So I did not at all like the assertion on pg. 200 that globalization (via deregulation and privatization) is inevitable, because there is no law that tells us that it is.

Summarizng: there is no complexity without dynamics, there are no known „laws of self-organization", and reductionism is the only hope for doing science. Anyone who disagrees with this is welcome to explain to me and others the alternative (jmccauley@uh.edu).

The book is interesting partly because Mankell suggests that the roots of the present mafia lie in the blackmarket network of the old communist system, and partly because the text was written before the total collapse of the USSR.

It's a powerful book, the scene where the fascist police storm in and kill the opposition is frightening, realistic, and bloodthirsty. So is the difficulty of making contact with Baiba, since both are watched. And the ending: who are the good guys, and who are the bad ones?

But Mankell strains the the will to believe too often. Why should Wallender, with a fake Latvian pass, go so far south and then enter the country illegally on foot? Not very likely that Wallender would have survived the massacre and escaped the building, either. Nor can I believe that Wallender could have found his way through the police headquarters, into the archive, and out again so easily. In the end, Mankell gives away a bit too soon who the bad guys really are.

One thing is puzzeling. Wallender did not connect with Baiba in the end. So, in later novels, is it only in his imagination that Baiba is his distant girlfriend? Mankell, realistically enough, does not present us with a happy life for the Commissar!

This review is based on the German translation "Hunde von Riga".

Very clear, straightforward presentation of GR in the spirit of Einstein and also Schrödinger, easy to read. But also too easy to miss the main points of the physics/geometry (see Misner, Thorne, and Wheeler) while becoming an expert at manipulating tensors in general coordinate systems. Very nice presentation of parallel transport and Weyl's formulation of gauge transformations. Better, more recent treatments using awareness of Lie algebras show the connection of curvature with noncommuting translations/operators, and emphasize the importance of relativistic invariance and local coordinate systems (physics). Einstein wrote of general covariance as if it would be a physical principle (it isn't), and this confusion wasn't cleared up for a long time.

Reading the original papers would be best, but if you don't read German then the Dover collection is the next best thing. In the paper on special relativity, the Lorentz transformations are derived via formulating and solving a first order pde, a treatment that no textbook presents (first order pdes aren't taught in math physics, in spite of the fact that every set of first order autonomous odes generates a first order pde). It took my teaching the subject to advanced undergrads in later years to realize what many others have by now noticed, namely, you don't need two postulates for special relativity. "Galilean invariance" is enough. The constancy of the speed of light follows from the requirement that there is no special reference frame.

Einstein's presentation of GR is unsurpassed for conciseness and clarity, is a model for other researchers to follow when writing papers. Here, he introduces the famous misconception (corrected today in the better texts like Misner, Thorne, and Wheeler) that general covariance is a physical principle. Well, even the greatest minds make mistakes.

Feynman wrote well, but no scientist to date has written better than Einstein.

Back in 1983, if a physicist wanted to teach deterministic chaos then this was the only book available, and it served the purpose well (supplemented by Feigenbaum's and Lorentz's papers, among others). There had been earlier math books, Moser's and Arnol'd's, e.g., but they were too hard for most of us. Like Moser and Arnol'd, Lichtenberg and Lieberman concentrated on Hamiltonian systems. One discovered accidentally, later, that von Neuman and Koopman had also studied chaos in a two-degree of freedom Hamiltonian system in one of their papers on ergodic theory in the thirties. Of course, we were all aware of Poincare's earlier work, although nearly no one had read it. In any case, this book is a time piece. Not really written as a text, it had something for everyone. Even a greenhorn could pick out models like the Fermi accelerator and program them graphically on a VIC 20 in order to impress and inspire the class.

In his first book „The Death of Economics", which I still like very much because I found it useful, Paul Ormerod compared in detail the gross failure of the neo-classical equilibrium model, the standard textbook model, compared with economic data. The book did not waste time on philosophy or ideology but presented a criticism that was and remains valid. „Butterfly Econonomics" takes a different tack. I recommend reading at least the first half of „The Death of Economics" first, followed by this one. One must first know what is the problem before one can appreciate the solution.

In the preface, Paul Ormerod apologizes mildly to neo-classical economists and expresses hope that this new book should be easier for them to stomach. He knows, as we all do by now, that that school of thought does not take kindly to criticism. His expressed aim is to concentrate on complex, biological models instead of mechanical ones. In the Introduction, he announces boldly that he will abandon the idea of fixed preferences, an admiriable task! The ‚butterfly' symbolizes not deterministic chaos (the theme of the second half of his first book) but rather the ability of a biological system to interact, adapt and learn. The author's aim is to understand the two main problems of economics: (1) Why is there economic growth, and (2) why are there business cycles?

Complexity as the edge of chaos is alluded to, but the main point of chapter 1 is to introduce the reader to Alan Kirman's ant model, a variation on Brian Arthur's urn model. Here, the emphasis is on modelling the interaction of agents, or ‚agent-based modelling', and Paul does a fine job of explaining the ant model. One wonders, as one reads the book, why econ texts are not written in such stimulating fashion rather than presenting us with a theory that doesn't work. Neither Kirman nor Ormerod present the ant model as solving any economic problem quantatitively, rather, it is discussed in the spirit of showing what is left out of ‚optimizing behavior'.

In chapter 2, Paul explains why we should give up hope of short term prediction, and criticizes the efficient market hypothesis (EMH) for its failure to allow for adequate volatility. I'll come back to this and some other points below. The third and fourth chapters discuss crime and family values in terms of the personal perferences of interacting agents. Again, this stimulates the reader to imagine how one could write an econ text to make it meaningful.

Chapter 5 mentions Radner, whose work (along with Kirman's) every econophysicist should know. Roy Radner is the theorist who drove all the nails in the neo-classical theory coffin back in 1968. He showed that if uncertainty is introduced into the neo-classical equilibrium model then the agents can't locate equilibrium, so that no trades are made. In other words, uncertainty makes the model's economic eficiency plunge from 100% to zero, which is a more realistic model of the Third World (the equilibrium model is not an empirically realistic model of any real market).

In the sixth chapter, business cycle forecasting is introduced and (pre-EU) the question is raised whether Italy can meet the fiscal requirements necessary to enter the European monetary union. I read about the way that Long Term Capital Management helped Italy to solve this problem via ‚creative financing' in Dunbar's „Inventing Money". Chapter 7 discusses the failure of econometrics to extract fixed rules of behavior (machine-like models, if noise-driven) from the data, and begins the discussion of the failure of the standard model (RBC, or real business cycle theory) to explain the data. Economists are correctly lambasted for ignoring empirical data in discussing the „correctness" of their models, and Paul's interesting new model of the GNP is presented in chapter 8. I found these chapters to be the most stimulating. There may still be something here for econophysicists to work on.

Interacting ants (variable preferences), the theme the entire book, are presented explicitly again in chapter 9. We're informed of the neo-classical idea of a ‚production function'in chapter 11, and economists are again properly taken to task for what I would label as Aristotelian-style philosophic postulations, while roundly ignoring the available empirical data. I find the discussion of the production function to be very useful, because Paul presents it, as he presents everything, in clear, simple language. This saves me the trouble of having to read dense, rambling economics papers to learn about that idea, although another source is Mirowski's „More Heat than Light".

A very interesting thought is mentioned as a footnote on page 168, and I'll leave it to the reader to ponder that one. In chapter 13, Paul further advises governments against too much regulation, no doubt having in mind his own UK before it was Thatcherized to the opposite limit (the US is presented as a happy counter-example, but since Reagonization we have our own severe unsloved problems). Here, the basis of his recommendation is the impossibility of accurate short-term predictions, something else for econophysicists to think about. It is true that short term prediction is useless in a stochastic system. In a deterministic chaotic or complex system, one sees only regular behavoir at short times (because of local integrability). I guess the point here is that the GNP can be modelled stochastically. But however correct ‚hands off' advice may be in many cases, I would point out that the fixing of the Thai Baht after Thailand's financial collapse seems to provide a good counterexample to a complete ‚hands-off' policy. Also, the failure of Mexico to fix the Peso and refuse to pay international loans ca. 1997 caused nearly total economic collapse for the then-growing middle class there, who held unpayable floating mortgage loans. So there's a lot of grist here for the econophysical mill. Ending this fine little book, Paul Ormerod emphasizes the ant model as an example of „one variant of the overall complex systems approach which (is proposed) in this book". That model is claimed to be only an extension of neo-classical economic theory. Now for some comments, which I hope will prove useful.

First, I see no reason why neo-classical econmists should take any solace from this book (thank goodness!): the ant model doesn't rely on utility maximization, and is in not an extension of their model. It doesn't begin by perturbing the neo-classical equilibrium model (as Per Bak did by adding noise in „Dynamics of Money"), and seems completely unrelated to optimizing behavior. However, the ant model, while interesting and instructive, also is not complex and so references to complexity, or to complexity as living the edge of chaos seem unnecessary. Physicists do not yet agree on a definition of „complexity", but I like Chris Moore's definition, where „surprises at every length scale"are the essence of complexity. This rules out scaling and attractors, and food sources in the ant model are analogous to attractors. Here's what Moore means, I think. Chaotic and „random"/stochastic systems are simple, by this definition, not complex: the statistics of the distant future for specific classes of initial conditions can be known in advance for chaotic or stochastic systems without doing a step by step calculation. For a complex system, in contrast, there are „surprises" that prevent one from knowing any statistical distribution at long times, for a given initial condition, other than by watching the system unfold step by step. In other words, the system cannot be characterized by any statistical distribution because ‚surprises' all the way to infinite time occur (volatility and fat tails are not examples of ‚surprises'). For my taste, mutations of bacteria and viruses to new forms are the essence of complexity, physically. This kind of complexity is presumably found in markets, but where and how? We don't know how to quantify that stuff.

Here's a more serious criticism. The idea of the EMH presented in the text is Shiller's notion, based on dividends discounted infinitely far into the future. This is not a useful definition because it's not falsifiable (Modligliani-Miller even teaches that dividends are irrelevant). The best definition of the EMH, the one used by finance theorists, is represented by the Martingale condition (plus, I would add, with Hurst exponent H=0), which guarantees that there are no patterns in the statistics that can be exploited for unusual profit. Markov proceses fall into this category, and have been used to describe financial market statistics, including option pricing, quite accurately (see my new econophysics book). So the EMH doesn't rule out either fat tails or nonstationary processes, both of which are required to describe the observed ‚volatility' of financial markets.

Finally, the ant model is not really ‚biology' but is instead noise driven mechanics. Why is that? Every mathematical model that can be written down is a mechanical model. As Turing showed, mathematics is a mechanical process, so whatever can be mathematicized classically is classical mechanical, in some sense. Turing's famous typewritter tape is a classical mechanical system. More to the point, financial market statistics are very accurately described by simple noise-driven ‚mechanical' models. The only known way to get away from fixed-machinery models (fixed hardware and fixed software) is to go to a neural net model that can learn from the environment, so that the connections change with time. The neural net may even be deterministic, but interaction with the environment prevents us from knowing the future, even theoretically. Finally, there is a reference to ‚value' in the text. I have described elsewhere why ‚value' is nonunique and therefore is an ill-defined notion.

In context, these are pretty minor criticisms, and to answer them properly (excepting the EMH error) one could not write an elementary book. So I think, in the end, that Paul Ormerod has done a fine job of using the ant model to symbolize what's missing in the standard, boring econ texts. Again, reading this book made me think how an econ text could be written to stimulate the reader to think about solving real, empirically-driven econ problems, and if Paul doesn't do take on that arduous task then someone else eventually will. If you want to read less than the entire book, then I strongly recommend chapters 1, 7, 8, and 12. The RBC and Paul's model of business cycles are presented for the reader's convenience as appendices.