Complexity Books

Anyone who has observed the behavior of real networks understands fully the tradeoffs that are involved in performance versus cost. What is typically not understood in real business contexts is that such tradeoffs can be analyzed quantitatively using various tools from mathematics. Network managers frequently shy away from using these tools, usually viewing them as esoteric or too complicated to be practical. They instead rely on intuition or some vague notion of commonsense to guide their decisions on bandwidth assignments, load balancing, and so on.

That the latter approach can sometimes lead to trouble is exemplified by the results of this book. Throughout its pages, the author gives simple examples and straightforward mathematical theory to illustrate the issues that can arise in network traffic management. It is readily apparent when reading it, especially the discussion of Braess's Paradox, that a simple, commonsense belief, such as the belief that adding a link to a network will relieve congestion, should be viewed with caution.

What the author wants to study in the book is more general, as he is interested in finding out to what extent networks can be left to the users, and not managed centrally, in order to have the most optimal performance. When users of a network decide for themselves what paths to take in the network, and if their decisions are made without considering the effects on other users, this is called `selfish routing.' Will selfish routing result in the best distribution of traffic flow in a particular network? If not, what is the worst possible loss of social welfare that can result from selfish routing? What the author asks, is the `price of anarchy'?

To motivate his answers to these questions, the author begins with two examples. One of these examples, called `Pigou's example, deals with a simple source-sink network with two links, one of which has a fixed cost and the other a linear one. This example illustrates the fact that selfish behavior does not necessarily optimize social welfare. The second example is called Braess's Paradox, and illustrates the fact that making network improvements can actually adversely affect network performance.

Readers are expected of course to have the necessary mathematical background in order to gain anything from this book. Network design engineers typically have this background, but network managers typically do not. The book therefore will not get the attention it needs from the latter class of people. This is unfortunate since it is the network manager who typically needs to understand the issues and results discussed in this book. They are rigorous results from a mathematical perspective, but there are plenty of historical and empirical data that support them. Very important throughout the book is the notion of a network flow at Nash equilibrium and of an optimal flow. The price of anarchy is defined to be the worst possible ratio between the costs of these two flows.

The reader will find that it is the collection of cost functions that are most important to the calculation of the price of anarchy. He calculates the price of anarchy with cost functions that are linear, quadratic, cubic, p-th order polynomials, and certain functions used in queuing theory. An interesting construction he uses in his analysis is the `anarchy value' of a collection C of cost functions, which he shows gives an upper bound for the price of anarchy of every instance of the network with cost functions in C. This upper bound is independent of the complexity of the network and the number of commodities that are using it. Optimal and Nash flows are shown to be identical, but with different cost functions. One very interesting calculation that the author performs, and one that is very important for network managers, involves comparing the cost of a flow at Nash equilibrium to that of an optimal flow that must route additional traffic. He shows that this comparison is equivalent to comparing a Nash flow in a better network to an optimal flow in the original network. The conclusion of this analysis is that the benefit of central control is exceeded by the benefit of improvements in link technology. For the queuing cost functions (M/M/1 queues to be exact), one needs to double the capacity of every link in order to beat optimal routing.

Since Braess's Paradox is a real issue, it is important to design networks that do not exhibit it. The author approaches this design problem by finding a subgraph of the original network that minimizes the common cost of all traffic in a Nash flow for this subgraph. Because the number of subgraphs is exponential in the size of the instance the author has to resort to approximate algorithms. He calls these approximations `C-approximation' algorithms since they give a solution that is bounded above by C times the optimal solution, where C is a positive real number and is called the `approximation ratio' or `performance guarantee' of the algorithm. The author realizes that such approximations may not exist for NP-hard problems, the author tries to find upper and lower bounds on C. This allows him to find upper and lower bounds on the severity of Braess's paradox for the worst possible case. These bounds of course depend on the cost functions, and the author studies four versions of cost functions, namely where they are arbitrary, linear, polynomial, and "incline." All of these bounds are proven with the assumption that P is not equal to NP. For linear cost functions, he proves that for every e > 0 there is no (4/3 - e)-approximation algorithm and there is no ([n/2] - e)-approximation algorithm for arbitrary cost functions. In addition, he proves that there is no o(p/lnp)-approximation algorithm for polynomial cost functions of order p. For general cost functions and large networks, the conclusion reached is that Braess's Paradox can be arbitrarily severe.

Besides containing original results from the author's own PHD thesis, the book has complied results and concepts that can not only jump start a new comer in the field, but also give practical tools for network designers. Starting from the very simple description of Pigou's example, Braess's Paradox, the chapter 2 on preliminary [describing Nash equilibrium, optimal flow], and the most interesting author's note [at the end of each chapter] are very well articulated. Author is very careful about introducing any new term/concept so that he does not lose the reader's attention.


Chapter 3 describes the "worst possible" [the upper bound of the price of anarchy] ratio between the cost of a flow at Nash equilibrium and that of a socially optimal outcome. Author considers cost functions that are linear, quadratic, cubic, polynomial, and M/M/1 delay function.

Chapter 4 extends the results/ bounds from the previous chapters for more general and complicated situations like generalized selfish routing beyond networks [Nonatomic Congestion Games], approximate equilibrium [approximate Nash Flows], selfish routing with explicit edge capacities, and with finite number of network users each controlling a non-negligible amount of flow [that may or may not split]. Example 4.6.1 and the subsequent results shows that the "worst- case inefficiency (or the upper bounds of price of anarchy) of selfish routing should be achieved by only a particular finite range of traffic rates"

Chapter 5 & 6 addresses the interesting design aspects with practical implications, answering the questions how to use a modest degree of centralized control so that selfish routing results in a socially desirable outcome. General network design with arbitrary cost functions, linear network design with linear cost function, Polynomial and Incline network design are considered with and without taxes. In chapter 6, Stackelberg games/routing is studied to see how much central authority can reduce the price of anarchy in a network used by both selfish individuals and some authority. Even though, the strategy reduces the price of anarchy to a constant, the computation complexity is NP hard. However, author stated that there is a fully polynomial-time approximation can be used under certain conditions.

The book started with Pigou's example to show that "selfish behavior need not produce a socially optimal outcome", and Braess's Paradox -"with selfish routing, network improvements can degrade network performance". These statements can seem to be too strong if you ignore the caveats at the section 1.3.4, and the differences with the more general game theory issues beyond networks. Also some readers can correlate this "selfish behavior" with the power of individual dreams/greed that is driving the free market. The "selfish behavior" in this book is different than the one we see in the free market economy which is a closed loop system with feedback to promote sustainable win/win selfish behavior in the long run among the participants. On the other hand the author has considered "centralized optimization" as a separate entity from the selfish participants in the game resembling more like a centralized socialistic government. In an "ideal" free democratic society, "centralized optimization" is by the participants, for the participants.

In building models there is always a question about what is better, a complex model with many parameters or a simple model with few parameters. If one uses all the data to fit models the ordinary measures of goodness of fit willfavor the most complex models. But sometimes these models overfit by trying to explain variation that is simply noise. In such cases these best fitting models are not good models for prediction. This has long been recognized and in regression modeling adjusted R square amd Mallows Cp statistic are used to help with the tradeoff between complexity of the model and the usrfulness of the model to predict new cases. In very general terms there are penalty functions that are used to penalize the method for using lots of parameters, Akaike's information criterion and Schwarz's Bayesian information criterion are two forms of penalized likelihood methods.

Rissanen in a famous paper produced another information theory type criteria called the minimum descrptive length and based on this measure for determines the best model for prediction. This method has proven to be very useful and led Rissanen to write this book as well as several other latter ones.

The book is well written and may someday become a classic.

This book presents the notion of model complexity with the point of view of information theory. It deals with stochastic complexity and its implications on the information theoretical complexity of models. It shows that any modelling approach is a volontary act that has inherent limitations due to its scope. The beginning of the book is devoted to more or less philosophical aspects of modelling while the rest of the book is devoted to formal aspects of the choice of an information theoretical model. Even if the word stochastic is used extensively in the book, by no means is the content dealing with the issues of modelling data from measurements. This is really a pure information theory book which emphasis is on the coding part of models. This is why i give it four stars : the title mentions "statistical inquiry" while the book is devoted mainly to "stochastic complexity". This title is hence somewhat misleading since it is closer to the book by Salomon Kullback than a practical book. On the other hand the content is really good at an information theory point of view...so it deserves its five stars without the drawback of the misleading title...

If any book is being worshipped for it's content on Algorithms in Academia, then it is this book. I have used this book both in my undergraduate and my Masters and definitely the best in the field.

But, I personally think the topics covered are complex to begin with. So, it takes this book and couple of books for reference to understand the topics completely. If you want to develop new efficient algorithms, then this is the book to begin with. Over all a very good book. Would definitely recommend it.

This book is must have for any software programmer. It is one of the best book I had ever had. It has many mathematical concepts and ppl who are mathematical geeks with software skills will love this book even more like me. This was the first book i bought from Used book section and I am extremely satisfied with the condition. I was quite skeptical when I was buying the book, but the sellers are really good with the what they promised. I am totally impressed and i really appreciate it.
Thanks Guys.

I used this book for a graduate level Algorithms course, and I really liked it. It is packed full of content on a wide range of topics. While this book does provide some high-level implementations of algorithms in pseudo-code, you will not find any examples of how to program algorithms in this book. That's really not what this book is meant for anyways.

I found the reading to be easier than Knuth on similar topics, but you still need to have sufficient mathematical background in order to keep up (statistics, discrete math, some calculus). Also, unlike many technical books I've read recently, I did not find any mistakes, not even a typo.

Some people are not aware that the MIT Open Courseware website has some excellent free video course lectures that use this book. I highly recommend at least viewing the first three or four of those lectures if you are new to this topic because they compliment this book very well. Make sure you understand the first four chapters of this book before moving on to other topics.

Also, since it had been a while since I had the math as an undergraduate, I was relieved to learn that this book had several appendices that provided a review of the math topics required by the book.

The only negative about the book is that it does not provide answers to any of the exercises at the end of the chapters, so you really need to use this book in conjunction with a course in order to be able to check your progress and how well you are learning the information. If you're not using this book with a course, check the MIT Open Courseware website that I mentioned previously. It has some sample assignments you can use.

This book is (in my opinion) an essential resource of common computer science algorithms. It covers a broad range of different algorithm topics and I found the explanations by the authors extremely helpful and simple to understand (both with simple and advanced topics). It does attempt to cover as many algorithm topics as possible, so some topics may not be covered in fine detail (it does not spend as much time on runtime analysis as other books, or spend much time on NP problems). It is perfect for someone taking an algorithms class (grad or undergrad), or someone looking to broaden their algorithm knowledge. I only wish there was some form of solutions guide to help verify answers to review questions.

There are three versions of the second edition, only one of which has the CD:

The first one is published by the MIT Press, with the title "Introduction to Algorithms". This one has no CD. This is the one Amazon currently carries, so if you buy from Amazon, you get no CD.

The second one is published by McGraw-Hill, also with the title "Introduction to Algorithms". This one also has no CD.

The third one is published by McGraw-Hill too, but has the title "Introduction to Algorithms and Java CD-ROM". This is the one with the CD. It's much more expensive than the other two.

The CD in the third version contains implementations of the algorithms in Java.

To find someone that carries the CD version, search for this ISBN-13 number: 9780072970548 , or for "Introduction to Algorithms and Java CD-ROM" .

Note: Some listings that come up for the ISBN number will not be the correct version. Look carefully for "and Java CD-ROM" before buying.

Chaos by James Gleick is a must read if you like keeping up with science or just like reading things that broaden the perspectives of your thinking. Gleick does a masterful job of simplifying the science of Chaos to a level any bright kid can understand while not diminishing any of its importance or ignoring any of the details. If you're curious about what a Klein bottle actually is or a Lorenzo's butterflies, this is the book for you. The illustrations of the Mandlbrot sets are truly amazing and worth the cost of the book just to look at. With his clear, concise style Gleick leads the reader through the history of Chaos science while building a strong foundation for the understanding of it. You don't need to know how to use a slide rule to read this book and it would be a memorable gift for any adult or child interested in science.

Nutshell review - a good book, written well and very entertaining. A good introduction to chaos and complexity science for us lay-people.

A popular science type of book (the popular part you can see from the numbers), where Gleick takes a look at the science of Chaos theory.

Not in a rigorous mathematical way, but more in a history of and introduction and overview of the subject, with of course examples of what he is talking about throughout.


3.5 out of 5

Okay, so it was a bestseller. That doesn't mean you didn't miss it. It doesn't mean you shouldn't read it again. Order in chaos and vice versa, the butterfly that creates a typhoon, fractal geometry, wildlife populations and dripping faucets (about which, more in a future Soupletter) - a book about ideas formerly on the scientific fringe that are now considered on a par with Relativity Theory (which, you will remember, made a considerable bang). ContempIating this review, I picked up CHAOS at the library (three or four years had elapsed since my first read) and was sucked in afresh. Meet a scientist who experimented with 26 hour days, another who found an operational definition of free will. Fascinatin' Rythms, Smooth Noodle Maps, Ice Ages and heartbeats. This is physics where the rubber meets the road. You don't need to follow the math (I don't, I just roll on by ...) to appreciate the ride. "Beautifully lucid," according to the San Francisco Chronicle which one notes, is published beside a once lucidly beautiful bay.

James Gleick changed my view on the scientific world forever in his book Chaos. I feel that I've removed my old, Euclidean perception of the world and have replaced it with a more complex, organic, and dynamic view. This book is a great introduction to chaos and is not meant to describe the applications of this theory. The applied sciences of chaos, complexity, or systems theories are readily available in journals and other pubs, just do a little research.

This well-written, easy book is a good way to start learning about network theory. It discusses the history, some basics, and the broad application (or presence?) of networks in the world around us.
However, it skims only the surface of what the research is all about, and leaves one thirsty for more, making it a good introduction to further studying (in my case, neural networks).

The writing style is close to story-telling at times, and this got a bit on my nerves. Apart from that I really cannot say anything bad about this book, I am glad I purchased it.

Reminds of "The World is Flat". It covers lots of ground really quickly. It was an interesting subject, something I've speculated a lot on my own and it was reinforcing to have a professional discuss lots of patterns (biology, physics, society, information networks) in a short-form context. It inspired me to write some graphics code based on the diagrams in the book and for that it was worth reading.

This is the first book I've ever read tackling this subject. I've had some science, but physics wasn't my strong suit. This was a great intro, and it made me want to dig deeper.

Before reading this book, I didn't know that Networks theories are with us since serveral decades. I'm almost finishing it, but I couldn't wait to write something about the book; specially to recommend you to buy it!
Barabasi work is really great. His redaction skills are as good that people without mathematics or science knowledge can understand and deeply learn Networks theory.

Excellent read. I'm a systems engineer by trade and although the book is by no means technical, it really drove the "connectedness" topic home for me as the author showed how objects naturally connect and grow in both real and abstract terms. If this sounds interesting- you will enjoy it too.

If you liked Gleick's Chaos, you'll love this book! Though it isn't a book directly concerning Complexity Theory, it definitely gives the reader a great understanding concerning the developments of Complexity Theory and its differences from Chaos Theory. It will definitely make you rethink even what you have just read.

Very disappointed in it. More form than substance. Author was too intent on patting CA schools on the back.

If you want to focus on complexity...then go to this book's index and start reading at the first page which mentions Kurt Godel.

As you proceed forward you will then find that this book spends progressively more time actually discussing the mathematical concepts underlying complexity or edge of chaos analysis and less time giving war stories about the founders of the Sante Fe Institute...which studied complexity.

Using this method you will learn about complexity theory which posits that simple algorithms can give rise to complicated outcomes.

Like a program to simulate a flock of birds in flight:

This book says that their flight can be similuated by the application of three simple coeffecients relating to maximum distance between birds, their common rate and distance of movement and finally a coeffecient directed to all birds to encourage them forward to being the center bird and leading the pack.

It doesn't take much creative thought to realize that the rules governing birds in flight must be similar to those governing genetic diversity and ultimately molecular diversity and creation itself.

In this way, ideas "merely" having to do with economics become VERY BIG indeed.

It's not surprising that this book was recommended by Richard Hofstadter (author of Godel Escher Bach) and likened to the (much better) Choas by James Glieck. The point is that the characters that this book introduces are very relevant to the discussions started by Hofstadter and so ably advanced by Glieck.

Read the book...or at least those pages following the first mention of Kurt Godel...and you'll see why.

I found the book disappointing. This is definitely NOT in the league of Chaos.

In particular, the coverage of the material of the subject, complexity, was very thin. Waldrop would bring up a subject, address it with some metaphor, and then move on without providing any details. The vast majority of the book is a series of stories about scientists at the Santa Fe Institute who had their inner-child hurt on their journey to discovering complexity. A better title for the book would have been "The Road to Santa Fe: A Tail of Grief."

The book had two redeeming features, the breadth of the material covered and the bibliography; both provide direction for more fruitful reading. Really, getting the feel for most of the subjects covered in this book could be found by putting 'complexity' into wikipedia and reading for a day, though.

Since it was not a complete waist of my time, I gave it 2 stars.

The main thread of the book is the Santa Fe Institute, a multidisciplinary research and education center founded in 1984 in the US. The institute deals with complex adaptive systems from physical, biological, computational, and social point of view. Complexity can be found in for instance environmental, technological, biological, economic, and political systems. Hence, this research area is highly relevant.

The story was interesting to read. However, being an engineer, I prefer a shorter and more concise style of writing. A deeper mathematical discussion about complexity would also have been appreciated. The book tells an exiting scientific story, but it is more of a well written novel than a technical textbook.

When you are the inspiration for a Jurassic Park character (or at least I think he was), then you immediately capture my attention. I'll buy your book, even if its subject matter is generally outside my interests.

Stuart Kauffman seems to have been at least partially the inspiration for the interesting chaotician character "Ian Malcolm" in Jurassic Park, and I thought his real life ideas would be as interesting as his fictional incarnation's ranting on chaos theory.

Not quite. At Home in the Universe sounds a lot more interesting than it was. It's plodding and full of jargon. And for a bonus, atheist polemic is included at no added charge! Yay! *Cough*

Kauffman also inserts random drivel about nature being sacred despite the falsehood of religion. Not only is that absurd on its face (sacred means set aside for religious veneration), but what the hell does it have to do with his ideas about complexity and emerging order? Spare me the atheo-preaching, please.

Actually the books is an outcome of scientific experiments in a computer lab. Differently from other reviewers, I want to notice that the facts of chaos exist in every where such as in Nature or in A Company.
Writer shows that everything in the world can be reduced to a series of chemical reactions. Chemical reactions can generate a complex system such as life from dead. He argues also the equilibrium of life and dead from the view of the number of kinds of molecules and the number of kinds of outcome from these molecules create or which are already in the system.
He also like many chaos theorist says that small changes in the system make big changes in the whole. (Explaining evalution). By some evidents and using probability, he shows that life on earth is the expected.
The books most important view is explaning everything as chemical reactions. And I believe this is the right thing...At Home in the Universe: The Search for the Laws of Self-Organization and Complexity

In this book, Stuart Koaffman opens new doors to us. Through the theory of the chaos, proportions fractals and their networks boulinas, give an interesting speculation us on the origin of the life, the complex systems and the societies. It is hour to be on the awares and to try to focus to us in new horizons. This book took to him of the hand by these new horizons. It is hour to know our house in the universe...

Stuart Kaufman's At Home in the Universe is a lay redaction his scientific hypotheses from his Origins of Order, a rich, fascinating, sophisticated, and complementary set of hypotheses added to Darwin's theories of evolution. For the moment, at least, they are the promising fruit of speculative or theoretical biological hypotheses (with physics, chemistry, geology, paleontology, mathematics, game theory, and economics thrown in), but they go a long way to filling in many of the gaps that strict Darwinists seem content to ignore. And some of his hypotheses, he readily admits, are heretical.

One of the obvious problems, if not primary one, that Kaufman sets to answer, Is how can natural selection work, culling the fittest to survive, without something to act on? In other words, natural selection operates on the already existent (i.e., regressive engineering), not in the formation of the entity itself. Another problem is that 4 billion years, long as that is, is still not sufficient time for natural selection to have acted through a totally random, step-by-step process in determining today's survivors. Even 100 billion years would not be enough. Another problem is how could so many species have come into existence and failed to survive (99.9%), leaving a mere 100 million for the present, in the span of a mere 4 billion years (mathematically impossible on Darwin's theories alone).

The central theme of Kaufman's work is Self-organized Criticality, a scientific twist on the notion of irreducible complexity (from the Discovery Institute's lexicon, no less), where a minimal degree of inherent complexity in a subcritical-supercritical phase transition is what spontaneously orders the animate world and generates and sustains life in accord with other, as yet, unknown, but implicit laws. From the moment that a sufficiently critical diversity of molecules reached the ideal phase transition, life itself was "spontaneously generated" as inevitable, not by accident. Once life appeared, the acts of natural selection, adaptation, coevolution, evolution of coevolution, cellular, morphological, and physiological differentiation, ontogeny, niches, populations, stable cum-chaotic dynamics, etc., could operate, but in addition to forces beyond natural selection. And while speculative, apparently many scientists share Kaufman's intuitions, inferences, and insights.

But the "other" force or forces is not mystical, much less divine, even if they may be truly awesome. Rather, it is in the nature of the universe, and more particularly in our evolving earth, that these implicit laws work in tandem with Darwin's laws. At this point, these laws are posited from the empirical knowledge we do have, but have not yet demonstrated in the scientific manner to make them even hypotheses. But Kaufman's speculative biology is not a whimsical or arbitrary metaphysics, but logical inferences based on laws and facts already in place. Having done the easy work (thinking the notions of what these other general laws of nature must be like), now science must work in earnest to confirm or reject his speculative hypotheses.

The key word and concept throughout this humorous, heady, and exacting exposition is "complexity" and within the manifold complexities of lives, environments, and mutually intersecting dynamics is a spontaneous order that arises "for free" that in turn sustains stable and steady systems just at the subcritical-supercrticial phase transition (e.g., horizon, or "edge of chaos"). Another key word and concept is "dynamic." Steady-state and homeostasis are often thought of as a static plateau, but that is mistaken, as such states are actually in a fluctuating dynamic at the phase transition between equilibrium (death) and disequilibrium (disorder). Indeed, on many different levels, living organisms are born, dwell, and die precisely at this phase transition between the subcritical (stasis, moribund) and supercritical (chaotic, disordered) states. And the key thesis is that order ("for free") is embedded in the delicate balancing act precisely at this phase transition.

Kaufman extrapolates some of these implicit biological laws and applies them to human cultural and technological advancement. The "fit" is remarkably uncanny, helping us to understand some of the dynamics of technological improvements (and diminishing returns), innovation, extinction, and spontaneity of the economy. Perhaps the most salient features are the concepts of "dynamic" and "spontaneous."

Moreover, if an analogy can be drawn from the biosphere and ecology to the social and political realms, the overwhelming preponderance of biological evidence screams complexity, diversity, and interdependence of organisms and their environments, which arise spontaneously and reciprocally to each other, in a constant dynamic that is vibrant, active, and always on the threshold of "chaos," but retains some stability through change. It is only those social and political forms that are "adaptive" that are socially and politically the "fittest," and democracy and market economies are obviously the most adaptive mechanisms to adapt to changing human needs.

Frederick Hayek addressed himself to these very issues over 50 years ago, and called the market economy and democracies "spontaneous" associations, in contradistinction to "planned" economies and governments. The former "adapt" to changing environments and circumstances, while the latter lack flexibility, and thus do not easily yield to adaptive mechanisms. "Planned" economies attempt to calculate rationally human desires, motivations, and needs in either an abstract or a priori fashion, then calculate the mode of production, the degree, and whether to accommodate, as if some "Absolute Human Mind" could anticipate all contingencies and changes by a simple mathematical formula. The problem is that bureaucrats are notoriously theory-laden and too calculating to include, much less advance, diversity (think Medicare Part D for "planned" absurdity). In practice, socialisms impede innovation and stifle ingenuity. With no means of adaptation, there is no "fittest," much less any mechanism to adapt to the actual dynamics of the world.

Communism's planned economy is an extreme case of an irrational calculus asserting what the government will allow, applying the lowest-common denominator as a criterion of sufficiency. We all know of the U.S.S.R.'s food lines, limited products, forced housing, inferior merchandise, and minimal labor investment. But even weaker forms of the rational calculus, such as socialism, does not do much better. At least their democracies allow policies to change, even if it becomes years for government to adapt to the new exigencies. Even the most socialized societies have "capitalist" outlets, to provide some barometer of social wants and meeting them. Social insurance makes sense on many fronts, but social or state "planning" of economics has rotted state and worker. Kaufman's biological analogies explain why.

Postscript: Kaufman's book is a provocative, challenging, and fascinating (sometime heady) read. Even if all of his hypotheses in the abstract are found to be untrue, at least he captures the reader's imagination, and asks the questions that most of us non-dogmatic Darwinians have raised for some time. In a time when the "easy" and "orthodox" are all too convenient for slipping under the rug, Kaufman's questions (and suggested answers) go the the very nexus of the difficulties. His suggested answers are at once perhaps too simple, on the other hand, perhaps too complex. What is refreshing, above all, is that he's not afraid to ask, and even less fearful of suggesting solutions. Thank gawd for the Sante Fe Institute, where brave and curious minds still ask questions.

Stuart brings the science of complexity and complex adaptive systems to a broad range of topics from evolution to business to learning curves. The book is masterly written to allow you to skim over the formulas without lossing the excitement or to dig into the technology to understand its broad application.

1. Strategic thinking has two major components: insight about the present and foresight about the future.

2. What we thought would change almost never did, yet change was constant and often unexpected.

3. In a world of sameness, the only possibilities are somehow something might change.

4. One way to look at history is a collection of campfires of thought - dotting social, cultural, and political fields of time.

5. By listening to the historical voices we will learn how we gained our preferences for linear, mechanistic thinking and the assumptions upon which we live and begin to understand the limitations of this worldview.

6. Myths account for the mundane as well as the extraordinary giving form to the formless.

7. Writing allowed ideas and information to be stored, transferred, compared, supplemented, and critiqued.

8. Together, philosophy and science represented the cultivation of knowledge through reasoning, experimentation, critique, and proof.

9. The Greeks believed that all things work or change according to their basic natures. The results of philosophy and science eliminated myth as the probable cause of natural phenomena. The Greeks developed a formal system of scientific inquiry.

10. Plato envisioned two realms: a superior changeless realm of ideas and forms and an ever-changing material world. Plate believed that the truth existed only in the realm of ideas and forms. The world we see and experience through our senses is but a shadow of the true reality. The senses were in opposition to reality.

11. Plato believed various noninterfering gods ensured stability and order in the universe.

12. Aristole believed that natural objects behave in certain ways according to their natures.

13. Aristole believed form and matter were inseparable. Qualities do not exist without matter, and matter is differentiated by its qualities. Form follows function - favoring observation and description over experimentation.

14. Aristole believed the universe was eternal; no beginning, no end. He believed the earth was round and the center of the Universe, with the sun, moons, stars, and planets revolving around it in perfect circular orbits. The celestial realm was made of a perfect and unchanging fifth element called the aether following unchanging cycles. Aristole believed that the motion in the celestial realm was not forced but inspired by the perfection of a supreme and changeless diety whom he called the Prime Mover.

15. The Artistotelian-Ptolemaic cosmos was based more on conceptualization than on observation and experimentation.

16. From its center in Rome, the Roman Church worked to resolve doctrinal disputes among local churches by developing a unified doctrine and a disciplined organization. The Roman Catholic faith assumed three roles: keeper of the faith, translator of important written works, and indoctrinator to the masses. Formal education remained a privilege for the upper class.

17. During the dark ages (500-1000 Ad) some monastic traditions allowed an encourage monks to continue annotating, transcribing, and translating ancient texts while at the same time building libraries. The libraries were safe havens for classic works to survive.

18. Learning began to the spread from the monastries into society during the Renissance (1000-1450 AD). During this time period Latin and Greek texts were recovered primarily from Islamic texts used in their Universities.

19. The Roman Church wanted to be viewed as the center of society and adopted the doctrine of the earth being the center of the Universe. The church institutionalized the earth centered worldview. To question the church was heresy.

20. The Protestant Reformation spread across Europe in the 1500s and lead to the French revolution. The Protestant Reformation promoted freedom of religion and religious tolerance.

21. The inquisition was used to force conformity and unify through fear and power. Individual engages in any type of activity that threatened to undermine the Church's authority, including thoses exploring new scientific ideas, were subject to tortures.

22. Great leaders anticipate where change is going and make sure their organization gets there first.

23. There exists a type of self-organizing pattern, shape, or structure that becomes obvious when the behavior of the system is seen as a whole. There is order hidden beneath the disorder. the pattern arises because the variables in the system are attracted to and interact with each other in a unique way.

24. While it may not be possible to solve or predict the future of a nonlinear system, it is possible to provide a qualitative description of of its characteristics and behavior as a whole.

25. Chaos theory is a type of mathematics used to explain complex behavior of nonlinear systems. Nonlinear dynamic systems are systems that, like weather, move, grow, or change. It's difficult to predict the outcome of future state of a nonlinear system, because the variables are interacting and changing constantly in response to each other. Most of the world is made up of nonlinear systems.

26. A predictable attractor is the end state into which a system settles. For example a handful of marbles thrown into a bowl settle at the bottom, the attractor.

27. A chaotic system that never settles into a predictable or steady state are said to be strange attractors. A tornado is an example of an energy system held together by a strange attractor. No external container or funnel gives a tornado its unique form.

28. The strange attractor coalesces the energy and creates the system boundaries, while at the same time allowing dynamic activity within its boundaries. Strange attractors have an unique shape and form.

29. A nonlinear system responds to changes in itself through a type of feedback loop, set in motion by the butterfly effect. Through this process, small changes can produce complex results.

30. Complex adaptive systems are characterized as non knowing the initial conditions at any point in time and their existence depends on the steady flow of information and are constantly processing/changing and incorporating new information. Complex adaptive system sit on the boundaries of chaos and order.

I can honestly say that this was one of the poorest strategic planning books that I have ever read. The substance of it could have been boiled down to 10 or 20 pages. There is substantial interesting historical information at the front end, which was enlightening, but utterly unrelated to the book's topic. Save your money...

It seems that there were two authors, or at least two different books welded together. The first book was an excellent background on complexity theory and how it applies to business. This part was excellent. But the book promised "insight" and "foresight" - the abilities to understand and then the ability to predict.

But the book doesn't deliver on the ability to derive insight or predict. First, the how-to part of the book starts near the end of the book and is presented quickly and without much detail. Second, other than one page of questions to ask yourself when preparing the author's format of a mind map, there was no magic, few detailed procedures, and little methodology to speak of.

I waited for this great epihany of understanding after the big build up on the history of thinking and complexity theory. I followed the author through Plato, Socrates, Aristotle and up through recent thinkers and on to New Mexico's complexity wizards. Then the book shifted down into a simplistic reading style with buzzwords on every page.

I felt that the author may indeed be able to lead groups through her tiny methodology and derive some benefit. But as a text on how to derive insight or create a forecast the book falls short. Buy this book for the interesting background on thinking, philosophy, knowledge, and complexity. Then you'll be happy if the insight/foresight system doesn't delight.

John Dunbar
Sugar Land, TX

Besides being a wonderful strategy resource for any organization, this book provides an absolutely wonderful view into the epistimology of complexity theory. From the presocratics to current day paradigms, Irene Sanders has collected a detailed and readable history of knowledge and its marriage to the complex world. This book is highly recommended for practitioners, academics working on their dissertation (like myself), and those with an eager interest in complexity theory.

Amazon needs to add a Blog spot for authors to respond to reviewers and engage with readers. Because I still do a lot of writing in this subject area, I typically either email and/or call reviewers who write a less-than-favorable review of my book. What I want to know is how my book could have responded more fully to their questions or concerns, and what, from their perspective, would have made my book more useful. Their comments and suggestions are almost always interesting and helpful. Other times, it's clear to me that the reviewer just took an opportunity to take a broadside swing at me and my work, or to get their name on amazon.com. and often in the list of "amazon's top 1000 reviewers," whatever that means. In other words, reviewers often use the amazon site for my book to promote their own name or work. So, my suggestion to Amazon and to all other authors is that we encourage amazon.com to set up a Blog site for authors to respond to reviewers comments and to engage with readers. The reviews have an impact on the sale and credibility of the author's work. So, it only seems fair to ask that "we" the authors have an opportunity to respond publically to critical reviews. It would also be very interesting to engage with readers who have ideas, insights or questions, but choose not to submit a review. Also, because it's an unfortunate fact that publishers use amazon.com sales and rankings as a "key indicator" in terms of future contracts, it only seems reasonable and current with 21st century technolgoy that amazon.com find a way to increase the interactivity between authors, reviewers and other readers.

This book is simply awesome. The book gets straight to the point of why being simple is better. If you need some guidance on keeping the business simple, this is your book. I do personal investments, and have used the principles in the book to simplify my information process. Awesome book!

Give it to them plain and simple as Trout says. They will feel comfortable with following a leader who gets on their level, but will be intimidated a speaker who speaks in tongues...

I lead people to live young and flourish through simple strategies, not kill them with complicated terms and alien metaphors like a wizard guru.

Dr. Garner

Jack Trout's books on marketing and brand positioning (with Al Reis) have a deep resonance with many readers. A big reason is that they are clearly written with a simple message that is readily understood. Trout expands this concept of the importance of simplicity in this book beyond marketing and applies it to business in general. In it, he gives a refreshing, counter-cultural voice opposed to all the laborious guru-hype, endless buzzwords and MBA-babble - that too often only adds complexity without adding value. Trout quotes Jack Welch on this idea: "Insecure managers create complexity. Real leaders have the self-confidence to be clear, precise and to be sure every person in their organization understands what the business is trying to achieve."

In an entertaining and often-sarcastic tone, Trout goes after many deeply-ingrained business practices to expose their unhelpful complexity: LONG-TERM PLANNING (mere wishful thinking), GOALS (sound nice but can hinder emerging opportunities), GROWTH (those mandated 15% projections can lead to terrible long-term consequences) and those cumbersome MISSION STATEMENTS (add needless confusion). What may be most comforting for those who value a common-sense approach is how Trout stands up for the simple, obvious idea. But, in our high-tech, over-analyzed age, such simplicity can sound ... well, too simple. As such people in business often fear speaking up and being viewed as "an unsophisticated simpleton" lacking the latest analytical models. But, Trout encourages businesses not to fear that which is simple, but to embrace its wisdom and guiding light. His many relevant examples of success and failure help paint an effective picture. In all, Jack Trout is a refreshing voice of reason in a world beset by budensome complexity. Practitioners of gut instincts and old-fashioned common-sense should love this book. 4.5 stars.

Most young Engineers and MBAs are more into hype and complexity than into solving engineering/business problems in a simplistic manner.

How many of us in our universities have been influenced, inspired by complexities of business and engineering ? Many of them even took the path of making their job seem complex and continued on their career - totally deviating from the basic objectives of why their jobs existed in the first place.

After 10 years in Software and consulting, when I read this book, it feels very much like reaffirming the basics of any work and business objectives.

Positives of this book:
* Reaffirms that most problems are to be simplistically analyzed and addressed
* Simplify your communication and reduce the clutter and hype

Negatives:
* Being simple does not always take you a long way - maybe in engineering, but definitely not in management. Ever heard of a manager who speaks up simplistically and been very successful ?
* The auther talks about being simplistic in communication, but has totally ignored the fact that communication is always good when it well wrapped and well packaged.
* Is simplicity always good when you are selling stuff ? People like the mystery behind complexity. While complexity itself does not sell, the mystery behind complex words does sell. Would you buy a Washine machine which has 'Fuzzy Logic' or would you buy the one that has 'Automatic Load Detection' ? Obviously the one with Fuzzy Logic - it kind of sounds cool and complex, even though you do not know whats in it.

Several ideas and examples are drawn from the authors' earlier work on positioning, 22 immutable laws of marketing, and bottom-up marketing. There were a few ideas that are worth chewing on. For example, per Trout, success is often riding the right horse. Both hard work and intelligence are long shots, finding fast-growing successful companies is a long-shot; finding a successful product is a medium shot; finding a person with successful career trajectory and hitching your career to theirs is a more reliable way of duplicating success. Others such as avoiding all recent advances in technology may be a little simple-minded and perhaps, unnecessary in the end.

This is a great popular maths book. Which is relatively easy to understand and I think Chaitin is a great narrator in the background.
Loved It.

John

Besides Chaitan's Omega there is only one other fundamental physical known constant that has as great a weight: alpha, the fine structure
constant in physics. Funny since they are near the same
in value:
alpha =0.007297353079644819 ( 10 places known in government standards)
omega=0.0078749969978123844 ( 17 places known in tables: OEIS)
From the definition of Omega given as a sum of inverse powers of two, there is obviously another constant:
Not_Omega= 2-omega=Sum[2^(-n), {n, 0, Infinity}]-Sum[2^(-p), {p_halting, 0, Infinity}]
Not_Omega=Sum[2^(-q), {q_not_halting, 0, Infinity}]
Another equation that the book suggests to me is the elliptic:
w^2=(x+2)*(x-omega)*(x+omega)=x^3+2*x^2-omega^2*x-2*omega^2
I'm not really ready to write this review:
I somehow doubt I will ever be.
This guy Chaitin has discovered a fundamental property or law of nature.
I doubt it will be much better understood in an hundred years,
but more places will have been calculated.
Maybe even a formula for the digits will be derived like that for Pi.
He is a modern Pythagoras or Euclid.

I don't see any boasting, let alone self-boasting in this book. It is a deeply humane and modest book. After all, how modest must we be guessing, as it is, that the universe evolved such that it is able to observe itself via the human mind, that is via a communication that engages our consciousnesses of which we in any case know just one individual case, our own.

We know how the classic (Greek) idea of perfection led to the the modern (French) idea of perfectibility. And we think that the printing press is not without impact in that story, since it had us switch from the one book we always deviantly, to be sure, comment upon to the many books which get better and better but never just hit the mark. Chaitin is able to show that in mathematics the same story went from completeness (Hilbert) to incompleteness (Gödel) and from an all powerful mathesis universalis (Leibniz) to uncomputability (Turing).

But what makes this book so important is that it manages quite (!) perfectly to show the philosophy of mathematical reasoning. It is quite a step to go from mathematics invented as an avenue to find out about God's ideas about the universe (very common, it appears, among both physicists and mathematicians) to mathematics as a means to prove our random singularity or singulary randomness.

Yet randomness, thanks to Thomas Bayes, does not seem to be the last word on that issue of our existence in the universe. There is conditioned probability, too. And we would love to see where those conditions come from. They are immanent, that seems to the fair assumption. They are themselves a product from evolution. So the next step would be to go for an evolutionary mathematics?

I really enjoyed this book. It contains a lot of ideas that I had been thinking about and was really glad to have decided to pick it up. I wish it went into a little more technical detail on some of the ideas, but it was good b/c anyone could read it and grasp the general concepts. The cover looks quite nice and the pages are a good size as well :-)

Rather than writing a full review as I intended to do, I see that other readers have stated very clearly my problem with this book. I wish I had read those reviews prior to ordering... It is very sloppily written, and should have been much better edited. (Or rather, much better edited!! as he would have written it.) In fact it is one of the poorest written popular science books I've read among the dozens I've accumulated over the years. Although his thesis is very convincing, and the concept of omega is very fascinating with regards to incompleteness and noncomputable numbers, etc., the actual informational content is larded with numerous references to how brilliant the writer is, what a genius he was as a child, how important his work is, how well he compares with Turing and Godel (how reasonable is that?), and multiple comments that are just downright weird, as when he talks about the information content of having sex with a woman (in terms of genetic transfer of information, that is). So the earlier reviewer who mentioned that he seems to be hiding low self-esteem with self-aggrandizement seems to me to be right on the mark. Either that, or the author is living on a planet of his own where he doesn't understand how embarassing and unsuitable this sort of heavy-handed arrogance is for this kind of book. Eventually I gave up reading it because of the odd writing style. Another minor drawback is that the content is very repetitive, particularly in comparison with other popular science books which appear dense with information.