10 Books You Should Read ASAP

(Or six important books that will make you realize that everything you thought you knew is wrong, as they say in other clickbaits.)

First published in 1944, Horkheimer & Adorno's The Dialectic of Enlightenment still echoes in debates about rationality and a scientific progress aiming at control over nature while it also alienates us from it. Adorno and Horkheimer's witty and erudite analyses about the entertainment industry, or totalitarian regimes and the naïve press and pundits who cannot foresee their rise to power, remain insightful today.

Humanity with its powerful brain capacity is not a deviation from the natural history, they write; with our machines, chemicals and organizational powers extending our physiology we are able to promote our own species at the cost of eradicating other species. In the bigger perspective, ideas about freedom and justice, religions and political persuasions are relevant only insofar as they increase or diminish our species' prospects of survival on Earth or in the universe.

As Adorno and Horkheimer presciently write:

The human capacity for destruction promises to become so great that―once this species has exhausted itself―a tabula rasa will have been created. Either the human species will tear itself to pieces or it will take all the earth's  fauna and flora down with it, and if the earth is still young enough, the whole procedure―to vary a  famous dictum―will have to start again on a much lower level.

The Sixth Extinction by Elizabeth Kolbert fills in the details about this on-going destruction. It begins with some history of science from a time when it was not even known or accepted that species could go extinct. Even as fossils of long extinct species were being displayed in curiosity cabinets, Carl von Linné "made no distinction between the living and the dead [species] because, in his view, none was required", Kolbert writes. By the late 18th century, the discovery of the mastodon with its bones and teeth that did not quite match those of any known animal led Cuvier to the idea of an animal still larger than the elephant. If such enormous animals were still around they surely would have been spotted somewhere, but since none had been seen, Cuvier concluded that they must have gone extinct.

Kolbert's book offers many glimpses into the process of establishing scientific theories, as popular science books should try to do. Habitat loss, the introduction of invasive species, climate change and various forms of pollution are some of the threats to the survival of many species. Building roads through rainforests is one way the habitat shrinks by trapping highly specialized species in small regions where they become more vulnerable to forest fires, hunting, diseases or other threats. Species are introduced on purpose, as we have done with some plants, or inadvertently, as with rats and snails. If no local predators feed on the introduced species, they may spread very efficiently and replace indigenous species. There is no single mechanism behind all this biodiversity loss, but there is no doubt that it is closely related to the growth of the human population and our exploitation of natural resources.

Although modern civilization has accelerated the threats to biodiversity,
there are many species (such as flightless birds) that were just too easy to hunt, which went extinct at various times when humans began to colonize the continents. The megafauna that existed reproduced very slowly and had no natural enemies. As prehistoric humans occasionally managed to hunt these animals, their population declined too gradually for anyone to notice, until there were none left.

Kolbert does not moralize, and although it is clear that humans are to blame for the current mass extinction, there are also many touching stories in the book about wildlife conservationists who go to exceptional measures trying to save endangered species. In fact, some species would not exist today were it not for the sustained efforts to keep them alive, as is the case with some frogs that have to be kept in "frog hotels" because they would not survive fungus infections in the wild.

And as the ecosystems break apart, eventually humans too will be at risk. One of the researchers Kolbert met while writing the book speculates that rats will be the most advanced species to remain.


The threat that biodiversity loss poses to humans is one of many complementary perspectives one needs to keep in mind when reading a book such as Nick Bostrom's Superintelligence. Bostrom argues that an artificial intelligence explosion is possible; it would happen when an AI discovers how to improve its own intelligence. At that point it will improve itself at an exponentially increasing rate, attaining an incomprehensible level of intelligence by far surpassing that of the most intelligent humans in the course of days or seconds. Once a superintelligence exists, the further fate of humanity would depend on it.

That part of Bostrom's argument is impeccable, but there are some serious omissions and weak spots in this very detailed book. First, there is not much of a discussion of what constitutes intelligence in humans, and what would qualify as intelligence in a machine. For example, it is not clear whether intelligence must be accompanied by consciousness or not, although Bostrom seems to think so. However, he suggests that a superintelligence is likely to take such an unfamiliar form that we might not even recognize it.

Second, since the superintelligence would develop on computers (on a single computer or a cluster), it would be enlightening to discuss the physical requirements for such an intelligence explosion. There must be physical constraints in terms of material and energy consumption. If the physical computing resources are limited any increase in an AI's capacities must come from software improvements, which must saturate at some point. Given the enormous data centers devoted to scientific number crunching, internet storage or mass surveillance, the computer resources needed for an artificial intelligence takeoff may already be there, waiting to be filled with the appropriate algorithms.

The belief in accelerating scientific and technological progress which Bostrom seems to share is far from the unfettered techno-optimism celebrated by transhumanists, but Bostrom still fails to consider the complexity of the current situation from all the relevant angles.

Although Elon Musk and Stephen Hawking have seconded his concerns for an AI takeover, many have warned about a more immediate cause of concern which is the effects of automation on the labour market. To be fair, Bostrom briefly mentions how the horse population dwindled as automobiles took over the work they performed, noting that a similar course of events could make a large part of the human labour force superfluous. And of course this is already happening. Some of the jobs perhaps could be replaced by more skilled workers, but jobs will be lost faster than they are replaced.

Bostrom is probably right about our inability to grasp the nature of superintelligence and our over-estimation of our intellectual capacities:

Far from being the smartest possible biological species, we are probably better thought of as the stupidest possible biological species capable of starting a technological civilization―a niche we filled because we got there first, not because we are in any sense optimally adapted to it.

But with some effort, we are able to discover our cognitive biases, many of which are discussed in Daniel Kahneman's Thinking, Fast and Slow. According to Kahneman and some other psychologists we have two cognitive systems. One is fast and intuitive. Relying on intuition and stereotypes it usually gets things right, but it checks no facts and does not stop to think critically, so occasionally it gets things really wrong. The slow system is used for hard problems, such as the mental multiplication of 18x23, checking the validity of a logical argument, or anything that demands prolonged attention.

A large part of Kahneman's book is devoted to behavioural economics and effects such as loss aversion. Experiments have shown that most people are reluctant to make an investment if there is a certain chance of a net loss even though the expected gain would be positive. We are not always as rational as we would like to believe, but at least we are able to demonstrate our own cognitive impediments through scientific experiments.

Behavioural economics is limited to the personal perspective, that is, to microeconomics. It prides itself on proving neoclassical theories of the rational agent wrong, but has nothing to say about the role of economics at the level of a society or among nations. Piketty shed light on the history of economic inequality during the last two centuries in Le capital au XXIe siècle (discussed elsewhere). In short, the rich get richer for various reasons, notably because at a certain level, the return on capital investment is greater than the economic growth rate. Wealth therefore accumulates among those who own stock or real estate. Technological inventions and automation also tend to increase inequality by increasing demand for well paid high-skilled workers as well as for low-skilled workers while the middle segment gets hollowed out.


Wilkinson & Pickett's The Spirit Dimension demonstrates the effects of economic inequality on societies and on individuals. They show how more equal countries fare better in several respects, including drug abuse, violence, health, literacy, imprisonment and social mobility. The Scandinavian countries and Japan range among the most equal, whereas USA and Great Britain are two of the most unequal of those considered. As a choice of method, Wilkinson & Pickett have restricted their study to developed countries in order to demonstrate the effects of economic equality separately from the general level of wealth in a country. Comparing the American states, they find the same pattern at that level.

Although the point of The Spirit Dimension is to display the negative consequences of inequality on health, social mobility and so on, each of the problem fields the book touches on has its own set of causes. For example, the high imprisonment rate in USA have other causes beside inequality, notably that prisons have become an industry run for profit.

Moreover, although several pieces of evidence point in the same direction―that inequality is causing the adverse effects in all the domains they describe―it would be unwarranted to rule out an opposite direction of causation in some cases, such as high imprisonment rates and illiteracy leading to increasing inequality. The findings of Wilkinson & Pickett have been questioned, but they have posted rebuttals of the points raised by their critics.

One of the most urgent questions now is how to reduce the impact of economic activity on the environment. The viable solution, according to Wilkinson and Pickett, is a steady-state economy which, instead of growing, adapts to changing demands. Such an economy will have its best chances in an equal society where consumerism is obsoleted in favour of community building.



The astute reader will have found that this list of urgent reading does not add up to ten titles. The reason is that the reviewer has yet to read four of those important books.

Capital in the 21st century: book review

Thomas Piketty: 

Le capital au XXI^e siècle. Seuil 2013

Economic inequality concerns everyone, we all have an opinion about what is fair. On the other hand, equity has not been a primary concern for most economists in recent times, at least not until the publication of Piketty's work. This review is based on the original French edition, although the book has already been translated to several languages.

Piketty's approach is historical, beginning with an overview of capital and revenues in the rich countries from the 18th century to the present. While it turns out to be true that inequalities have increased since the mid 20th century, it is perhaps surprising to learn that there were once even greater inequalities, peaking in the decades before the first world war. Social mobility was low and the best way to ensure a comfortable living standard for someone who was not born into a wealthy family was to marry rich rather than try to get a well paid job. When the gaps between the rich and the poor shrank in the 20th century, at least until the 1970s, Piketty argues that this happened mainly as a consequence of the two world wars. Governments appropriated private capital and introduced heavy marginal taxes that gradually led to a redistribution of wealth and the emergence of a middle class.

Le capital is written for a broad audience with no prior knowledge of economic theory. Central concepts are clearly explained in an accessible way. Mathematical formulas beyond plain arithmetic are avoided, even when their use could have simplified the exposition. However, Piketty stresses that economics is not the exact science it is often believed to be, and he is rightly sceptical about the exaggerated use of fancy mathematical theories with little grounding in empirical facts.

Although Piketty tries to avoid the pitfalls of speculative theories, he still makes some unrealistic thought experiments, not least concerning population growth and its bearings on economic growth. Population growth has two important effects: to increase economic growth and to contribute to a gradual diffusion of wealth. When each person on average has more than one child who inherits equal parts of their parents' patrimony, the wealth gradually becomes more equally distributed. Now, it does not require much imagination to realise that population growth cannot go on for much longer on this finite planet, and large scale space migration is not a likely option any time soon.

Piketty is at his best in polemics against other economists or explaining methodological issues such as how to compare purchasing power across the decades. Some products become cheaper to produce, so being able to buy more of them does not necessarily imply that the purchasing power has risen. Entirely new kinds of products such as computers or mobile phones enter the market, which also makes direct comparisons complicated.

Human capital is often supposed to be one of the most valuable resources there are, but Piketty seems uneasy about the whole concept. Indeed, when discussing the American economy in the 19th century, a conspicuous form of human capital enters the balance sheets in the form of slaves with their market value. The wealth in the Southern states of America before abolition looks very different depending on whether you think it is possible to own other human beings or not.

Top incomes in the United States have seen a spectacular rise in the last decades. An argument often advanced in favour of exceptionally high salaries is that productive people should be rewarded in proportion to their merits. The concept of marginal productivity describes the increase in productivity as a job is done by a person with better qualifications. However, there is no reliable way to measure the marginal productivity, at least not among top leaders. In practice, as Piketty argues, there is a tendency to "pay for luck" and not for merit as such; if the company happens to experience success, then its CEO can be compensated. The modern society's meritocracy, Piketty writes, is more unfair to its losers than the Victorian society where nobody pretended that the economic differences were deserved. At that time, a wealthy minority earned 30-50 times as much as the average income from revenues of their capital alone.

Cette vision de l'inégalité a au moins le mérite de ne pas se décrire comme méritocratique. On choisit d'une certaine façon une minorité pour vivre au nom de tous les autres, mais personne ne cherche à prétendre que cette minorité est plus méritante ou plus vertueuse que le reste de la population. [...] La société méritocratique moderne [...] est beaucoup plus dure pour les perdants (pp. 661-2).

The level of marginal taxes and progressive taxation appear to be decisive for top incomes. Lowering taxes actually makes it easier for top leaders to argue in favour of increased salaries, whereas high marginal taxes mean that most of the increase will be lost in taxation anyway. On the other hand, there is the problem of tax havens or fiscal competition between countries that is not easily solved. In addition to that, lobbyists spend quite some money on trying to convince politicians to keep taxes low, as a new study from Oxfam has shown.

The relative proportions of capital and revenue in the rich countries as it varies over time is studied in detail. The amount of capital is usually equivalent of a few years of revenue. However, the curve of capital over time as measured in years of revenue is found to be U-shaped, with a dip during the two world wars. This relative balance of capital and revenue actually sheds light on the structure of wealth distribution. Most capital is private and consists of real estate and stocks. There are mechanisms that make capital grow, effortlessly as it seems: "L'argent tend parfois à se reproduire tout seul."

Here the interesting principle of capital-dependent growth comes to play. As it happens, the more capital you have to begin with, the faster you can make it grow. This is the case even in bank accounts where the interest rate on savings is usually higher above a certain threshold. However, those interest rates are usually not higher than barely to compensate for the effects of inflation, and for small amounts of savings they are usually lower. On the other hand, capital in the form of real estate or stocks may grow faster than wages. One reason for the level-dependent growth of wealth is that it is easier to take financial risks and to be patient and await the right moment with a larger initial amount of capital, but the most important explanation, according to Piketty, is that the richest investors have more options to engage expert advisors when making their placements so they can seek out less obvious investments with high capital revenues.

Inheritance, rather than well paid work, was the way to wealth in the 19th century. To what extent are we about to return to that economic structure today? Indeed, there are worrisome indications that today's society risks a return of the rentiers, or persons of private means. Piketty's solution to the wealth distribution problem is, roughly, to increase the transparency of banks and to impose a progressive tax on capital in addition to revenue taxation.

Shortcomings

Capital has become a bestseller and has already had a significant impact on the public debate (e.g. a recent report from citi GPS on the future of innovation and employment). Piketty leaves the old quarrels between communism and free market capitalism behind and proposes solutions based on evidence rather than wishful thinking or elegant theories with little grounding in reality. However, the last word in this debate has not been said. Free market proponents will have their familiar criticism, but it seems more appropriate to point out the shortcomings and the limited perspective of Piketty's account from an entirely different point of view. This is still some flavour of classical economic theory that does not seriously consider the role of energy consumption for the economy, nor is it sufficiently concerned with the finite resources of minerals including fossil fuels that are being depleted or the problems of pollution, global warming and ecological collapse that will soon have tremendous impacts on the economy. Piketty is probably fully aware of these problems and yet, with the exception of a brief mention of the Stern Review he neglects to make them a part of the narrative which therefore becomes one-sided. Perhaps this is an unfair criticism since the aim of the book is to demonstrate the mechanisms driving the increasing inequality in a historical perspective, but nonetheless important facets are missing.

Although no background knowledge of economics is assumed and many concepts are lucidly explained to the general audience, the book is not trying to be an introductory text book on economic theory.  Fortunately there are many resources to read up on the basic mechanisms of economy that include the environment and energy resources as part of the equation. Gail Tverberg's introduction is a good place to start. Many interesting articles appear at resilience.org. Ugo Bardi's blog resource crisis is worth a visit for further reading. The interwoven problems of debt, peak oil and climate change have been discussed at length by Richard Heinberg, and also in a previous post here. The new keyword that will shape our understanding of the economic system is degrowth.

The theoretical minimum of physics

The theoretical minimum.

What you need to know to start doing physics

by Susskind and Hrabovsky, 2013

This crash course of classical mechanics is targeted at those who “regretted not taking physics at university” or who perhaps did but have forgotten most of it, or anyone who is just curious and wants to learn how to think like a physicist. Since first year university physics courses usually have rather high drop out frequencies, there must be some genuine difficulties to come over. Instead of dwelling on the mind-boggling paradoxes of quantum mechanics and relativity as most popular physics books do, and wrapping it up in fluffy metaphores and allusions to eastern philosophy, the theoretical minimum offers a glimpse of the actual calculations and their theoretical underpinnings in classical mechanics.

This two hundred page book grew out of a series of lectures given by Susskind, but adds a series of mathematical interludes that serve as refreshers on calculus. Although covering almost exactly the same material as the book, the lectures are a good complement. Some explanations may be more clear in the classroom, often prompted by questions from the audience. Although Susskind is accompanied by Hrabovsky as a second author, the text mysteriously addresses the reader in the first person singular.

A typical first semester physics text book may cover less theory than the theoretical minimum in a thousand pages volume, although it would probably cover relativity theory which is not discussed in this book. There are a few well chosen exercises in the theoretical minimum, some quite easy and a few that take some time to solve. “You can be dumb as hell and still solve the problem”, as Susskind puts it in one of the lectures while discussing the Lagrangian formulation of mechanics versus Newton's equations. That quote fits as a description of the exercises too, as many of them can be solved without really gaining a solid understanding of how it all works.

The book begins by introducing the concept of conservation of information and how it applies to deterministic, nonreversible systems (all systems considered in classical mechanics are deterministic and nonreversible). Halfways through the book the first more advanced ideas come into play: the Lagrangian and the principle of least action. In general, one gets an idea of what kinds of questions physicists care about, such as symmetries and conservation laws. Examples of symmetries that are discussed include spatial translation invariance and time shift invariance, and the conservation of energy is a recurrent theme. The trick is simple: take a time derivative of the Lagrangian or the Hamiltonian, and show it to be zero. The principle of least action requires more sophisticated mathematics (functional analysis), although the authors try to explain it in very simple terms. Nonetheless, that part is not very easy to follow.

The writing is concise, yet almost colloquial, with only a few typos. Mathematical rigour is thrown out whenever it would clutter the exposition. Susskind does not care for limits in the formulation of derivaties, but uses a delta or an epsilon that is supposedly infinitesimal in a loosely nonstandard analysis kind of way. Most derivations are easy to follow, using elementary calculus and patiently laid out step by step. Some background in one variable and vector calculus will be necessary to follow the text, although all math that is needed (which is not very much) is summarized in the mathematical interludes.

Why should we need to know about Lagrangians, Hamiltonians and Poisson brackets, a student may ask. Susskind's answer might be that Lagrangians make the solution of certain problems much easier than trying to apply Newton's equations, and that Hamiltonians play an important role in quantum mechanics.

The theoretical minimum is probably the most concise introduction to advanced physics out there, highly suitable for self-study. It provides much of the essential background needed for books reviewed here in previous posts, such as Steeb's Nonlinear Workbook or Haken's Synergetics.

Synergetics, the book

Hermann Haken: Synergetics. Introduction and Advanced Topics. 

[Disclaimer: There are many things in this book that I do not understand, although hopefully I have grasped the big picture.]

Under the term Synergetics, Haken collects a number of approaches that can be useful in a variety of scientific disciplines ranging from physics, chemistry and biology, to economics and even sociology. Synergetics is presented as its own discipline with its characteristic concepts and methods. Yet this discipline draws on related fields such as thermodynamics, statistical dynamics, information theory, dynamic systems, control theory, bifurcations and catastrophe theory. Synergetics proposes to shed light on self-organized phenomena in various areas and to treat them within a unified apparatus. In particular, the slaving principle is the one trick that is used again and again. The slaving principle can be thought of in terms of a dynamic system where some variables change fast and others slowly, but there is also a separation into stable and unstable modes. The stable modes can be eliminated and treated as parameters, resulting in great simplifications.

This tome contains two classic volumes in one. Volume one (Introduction) begins gently with tutorial chapters on basic probability theory, ordinary differential equations, and their combination in stochastic differential equations. After the theoretical background has been presented, there is a chapter on self-organization followed by several chapters devoted to applications in various domains. First, the chapter on physics deals mainly with lasers. Then, as the chapters turn to chemistry, biology and economics in turn, the treatment becomes more and more accessible to the non-specialist. However, at the same time the models seem to become increasingly simplistic. Already the examples from biology and population dynamics are sketchy, and the discussion of applications to economics and sociology do not introduce many useful ideas. Nonetheless, one should remember that Haken was among the pioneers who brought a physicist's tool kit to these fields. In particular,

[...] synergetics has established links between dynamic systems theory and statistical physics. Undoubtedly, the marriage between these two disciplines has started. (p. 364 of the double volume) 

Further, regarding the connections of physics, chemistry, biology and even softer sciences:

It thus appears that we are presently from two different sides digging a tunnel under a big mountain which has so far separated different disciplines, in particular the “soft” from the “hard” sciences. (p. 364-5) 

We see the results of this excavation in numerous papers today, where physicists have begun to address such problems as the motion of crowds at concerts or the opinion formation before elections. However, there are obvious dangers involved in attacking problems that lie far beyond one's sphere of specialization. In the words of Buckminster Fuller (who also wrote a two volume book called Synergetics, otherwise bearing little resemblance to Haken's):

The word generalization in literature usually means covering too much territory too thinly to be persuasive, let alone convincing. In science, however, a generalization means a principle that has been found to hold true in every special case.

Apparently both kinds of generalization are involved in Hakens work; the applicability seems to decrease the further away from physics one gets, till it begins to look suspicious when applied to the social sciences. Meanwhile, the single finding that unites all chapters, the slaving principle, exemplifies the kind of generalization that holds true in several special cases, if not in all conceivable scenarios. It is the method of finding solutions that survives generalizations, not necessarily so with the modelling of systems in different fields.

Volume two (Advanced Topics) starts over with a long expository chapter on the application domains followed by the introduction of the theory. There are short sections on deterministic chaos, but Haken is not the best source on this. Quasi-periodicity is treated extensively. Although the exposition is clear to begin with, soon enough matters get complicated. If you ever wondered what makes a system of differential equations with quasi-periodic coefficients stable or unstable, this is the text to read.

Matters of style

The first chapters of each volume are tutorial in character and cover material that most readers probably already know. The manner of exposition changes as Haken begins to introduce his own findings—one can sense a shifting of gears when his enthusiasm sets in. Unfortunately, these parts involve solutions that stretch over sections or entire chapters, sometimes using idiosyncratic notation. It is often hard to tell whether a variable is supposed to be real, complex, or a vector, even though one may be able to figure it out from the context.

The writing has the appearance of a stream of consciousness layed out at the blackboard, rather than elaborated at the typing machine. Throughout the book, variable substitutions are profusely employed; so much, in fact, that one almost inevitably loses track of the variables' meaning. The derivations are decidedly informal, with almost no theorems and proofs. (There are a handful of theorems that rely on a long list of assumptions with long, unwieldy proofs.) Instead there are long chains of “simplifications” or “abbreviations”, often resulting in expressions that are longer than the one they replace, truncations of higher order terms in series expansions and other sorts of approximations. All these tricks are of course what physicists are usually good at, but for readers without the proper background, they may appear as incomprehensible as pulling rabbits out of a hat.

If synergetics has to do with self-organization of complex systems, it must be said that Haken is quite terse on the topic of self-organization as such. This is where some conceptual analysis is lacking. On the other hand, the cyberneticians have already contributed much hand-waving philosophizing on self-organization, without necessarily having contributed much to its understanding. Here, at least, one has a class of problems and an approach to their solution, but there is more to self-organization than what is covered in this book.

Editorial neglect

The Nonlinear Workbook 

by Willi-Hans Steeb. 

World Scientific 2011, 5th edition.

Beginning with chaos and dynamic systems, from one-dimensional maps and fractals to ordinary differential equations, the usual topics are presented succinctly in the first half of the book. Short chapters on chaos control and synchronization are also included. Then, the second half deals with topics that should be more familiar to computer scientists, such as neural networks, genetic algorithms, optimization, wavelets and fuzzy logic. This is a huge span of topics that cannot be covered in depth in a single volume. According to Steeb, most of these disparate fields are interrelated. If so, there is a valid motivation for presenting them in the same book and highlighting their relations. However, many interesting and often difficult fields are only presented in glimpses. The chapter on wavelets is a case in point; that material is not used in the rest of the book so the chapter might as well have been left out.

To be clear, this is not a book for beginners. It serves better as a complement to other literature, and to some extent it offers a different point of view than many other sources.

The book claims to balance a theoretical exposition with practical computer code. Several short stand-alone programs written in C++, Java and Symbolic C++ (the latter being a library developed by the author) form the backbone of the text. There is even a short routine in assembler. The treatment of chaotic systems is different from many other comparable texts in that exact numerical algorithms are used to study the iterations of maps. The SymbolicC++ library is used for this, but unfortunately this code is neither included nor explained in the book despite the many programs relying upon it.

The solution of ODEs is for a large part done with the Lie series technique, which is not very accessibly explained. Another frequently used technique is the Runge-Kutta-Fehlberg method, which makes use of a set of coefficients that are copied and pasted into each code snippet where they are needed. Needless to say, this makes for a lot of redundancy, which could easily have been avoided by placing this part of the code in an include file. In Chapter 11, where the integration techniques for ODEs should presumable be explained, the same mysterious coefficients appear again without any hint as to how they are derived (there is just a reference to the literature). This avoidance of explanations stands in stark contrast to the style of another, excellent source on scientific computation — the Numerical Recipes by Press et al. Although the Nonlinear Workbook is not at all on a par with Numerical Recipes regarding stylistic issues, clarity of presentation, and general usefulness, it does contain much material that cannot be found there (at least not in the third printed edition).

Already in its fifth edition, one would think that the Nonlinear Workbook has all kinds of editorial flaws sorted out by now. Unfortunately, this is not the case. The text suffers from a lack of efforts to organize the material. Skimming through the text, there appears to be no single illustration; in fact there are less than a dozen across its more than six hundred pages, but they are not very visually striking. Most books about chaos theory and matters cognate will include a number of elegant pictures of attractors or fractals; this one does not, except for the one on its cover. Certainly most readers will have already seen an assortment of representative fractals and attractors and do not need them printed in yet another book; better yet, using the code in the book one should be able to generate and experiment with them for oneself. However, a few explanatory diagrams would often make ideas in the text more accessible to the reader. Or how about trying to explain a Poincaré section in words and formulae, with no illustrations? That is surely a recipe for making simple things look hard.

On the whole, the book suffers from editorial neglect. Code examples are often given without any indentation, making nested routines hard to read. The copy-and-paste manner of coding does not make things any better. The prose is awkward in many places, such as the following:

If we want to compare two hidden Markov models then we need a measure for the distance between two hidden Markov models.

There is very little cross-referencing inside the book and the equations are almost never numbered. On the positive side, one never needs to turn the pages to find some equation that was introduced earlier. 

The level of exposition is also a bit uneven. Some sections assume rather much mathematical background, whereas others are quite accessible. Presumably someone who already is at ease with Lie series, exterior products and what not will have little need for the guidance provided by the code examples. Some programs are rather trivial and probably pose no difficulty to a first semester student of computer science. A few programs are far from trivial, however, and the lack of explanatory comments in the code as well as in the main text make them hard to understand. There are almost as little exercises as there are illustrations. Why should a text book have exercises at all, though? The intelligent reader will find his or her own problems to solve, spurred by puzzling remarks in the text or unproven propositions. 

To round up, this workbook provides glimpses into many fascinating topics, albeit presented in a less than ideal way. The text is too tersely written to serve as an introduction to any of the many fields that it covers, but may be valuable to someone who has studied the theory before.

See for yourself, sample chapters are available for free.