A self-referential biographical history of mathematics and logic in the later 19th and early 20th century, with narrative interludes on ancient GreekA self-referential biographical history of mathematics and logic in the later 19th and early 20th century, with narrative interludes on ancient Greek tragedy. Framed around the life of Bertrand Russell, several contemporary thinkers (Frege, Wittgenstein, Gödel, Schlink, Wallace, von Neumann). Manages to describe incredibly complex concepts in understandable language, and only a few relatively minor errors.

I'd like to see more, if that was possible. One for each of the other thinkers, especially Wittgenstein or Gödel....more

This is a largely reliable and interesting overview of statistical analysis in a variety of fields. Silver has gained popularity in 2008 and last yearThis is a largely reliable and interesting overview of statistical analysis in a variety of fields. Silver has gained popularity in 2008 and last year for his wizardry in aggregating poll numbers and correctly predicting the results of the election. He takes a few jabs at media pundits who are not interested in polls, but insist on manufacturing a narrative which appeals to pre-conceived notions and biases.

Silver's interests are broad and eclectic, ranging from Texas Hold 'Em and the stock market to baseball. His use of statistics here is judicious and well-explained.

Silver also does a reasonable job explaining statistical concepts to a mass audience, where little more than high-school math is necessary. He does overly use the Bayesian method of statistics — that is, where probability cannot be interpreted from the event itself, but also from the hypotheses and predictions which preceded it.

In politics, Silver separates the wheat from the chaff, throwing out bad guesses with ease. However, he is less careful in the studies of climatology. He refers to bad data sets as reasonable priors, and gives an undue focus to biased sets of data, and misinterprets the recent political focus which is given to environmental science. He overemphasizes the role of controversy in these fields, taking data at face value which in all likelihood is flawed or maybe even manufactured.

These omissions are made all the more puzzling due to his reasoned acceptance of other complexities of the field, noting the vast amounts of data to sift through, as well as the non-linear dynamics in meteorology, and noting the difference between climate and weather. One data point does not make or break a broad trend. Because winter is cold, this does not prove or disprove anything on a global scale.

In summary, Silver does a fine job at pointing out the many advantages and pointed flaws of statistical analysis. It can be an invaluable tool for dismissing false 'experts', but it is also important to carefully consider the role of prior analysis and carefully setting up your examples....more

This is one of the most important books on Game Theory, and also, thankfully, one of the more accessible (certainly much more so than von Neumann's anThis is one of the most important books on Game Theory, and also, thankfully, one of the more accessible (certainly much more so than von Neumann's and Morgenstern's book).

His main theses are that not all games are zero-sum. That is, they are 'variable-sum', or dependent upon the strategies used. Not all actors are apparently rational, and some may act on seemingly irrational behavior in order to alter their opponent's responses. On the individual level, this could be the abusive lover threatening to kill themselves in order to keep you obedient to them. On the international level, this could be the North Koreans lobbing more missiles into the ocean to get more food. Decisions are interdependent upon the other's decisions.

Perceptions are also a vital component of decision making. Limiting information available to the opponent, or restricting their choices by other means, is a way to appropriately modify your own action. Strategy is not only a way of dealing with force, but also potential force.

In cooperative games, coordination is necessary. If communication is possible, then it would be best to aim for some point that you know that the other target might think of as being a valuable and important meeting point. These are now referred to as 'focal points', or, more recently, 'Schelling points'.

The idea of 'deterrence' has to have two necessary components: a conflict, and a common interest. Bargaining is a means by which both actors can find ways to benefit, but this becomes more difficult in areas of more open conflict, as the means of communication may become impeded. Therefore, a tacit communication or tacit bargaining - a scale of responses with which one communicates, up to and including armed force.

Some of these points may seem obvious now, fifty years later, but they seem even more important only because of how often they are overlooked. Schelling is important not entirely because of his mathematical analysis, but because how he also encompasses the human element in decision-making. The Cuban Missile Crisis, the ultimate 'game' of brinksmanship, coordination, and negotiation, only occurred two years after this book was published. Valuable reading for economists, politicians, and anybody who wants more than a passing knowledge of these games we play....more

A history of the early computer and what miracles were done with it. The computer, says the author, is one of the great creative forces of the 20th ceA history of the early computer and what miracles were done with it. The computer, says the author, is one of the great creative forces of the 20th century, compared to the great destructive force of the atom bomb - and certain instrumental figures worked on both.

The title appears to be misleading, as Mr. Turing himself only appears some 200 pages in. His contributions, although not immediately evident, are still quite important. The majority of the early part of the book concerns Princeton's Institute for Advanced Study - originally intended as a refuge from the bureaucracy and 'old-boys-club' mentality of American universities, which became one of the greatest accumulations of mathematical talent anywhere in human history.

One of the central figures here is a certain John von Neumann, who can be truthfully described as a genius, responsible for the foundations of everything from game theory, to nuclear physics. There are too many others in the book to list here, but you get the idea of their sort of caliber.

With the earliest and most primitive of computers, the scientists here were able to work on weather prediction, statistical analysis, and basically the foundations for almost every computer since - all with the processing power reserved for single cursors today.

Even with this bare minimum of processing power, the ideas which these thinkers discussed are still used today - advanced climate modelling is still a topic of various supercomputers. von Neumann's and Turing's theories on 'self-replicating autonoma' can be used in both biological mathematics applications and possibly a description of computer viruses. It would be futile to attempt to list it all, but Dyson gives a very solid overview.

The tragedy is that some of the greatest architects of our new age never lived to see it. Turing's tragedy is well known, and computer scientists and the LGBT community see him as a martyr. John von Neumann died in his 50s from cancer, possibly from all of his atomic bomb observations. Both for those others who survived, and many of the great ones did, they bore witness to a new age in discovery, the greatest shift in human knowledge seen since the printing press and the Renaissance....more

DeLillo has always been more of a novelist of ideas more than the basic linear event-event-event-conclusion linear plot style.

Here he experiments withDeLillo has always been more of a novelist of ideas more than the basic linear event-event-event-conclusion linear plot style.

Here he experiments with mathematics, logic, and the meanings of language, and language as a means to shape the world. This is no bullshit and repetition of terminology - he's obviously done his homework - I see discussions of Higgs theory, the origins of language, and the intersection between the pursuit of science and the almost mystical devotions of mathematics/language. This is dense reading, but DeLillo's fantastic prose style still illuminates.

As an aside, I wonder how many contemporary authors have some sort of training in math/science? DFW did work on modal logic and Wittgenstein, and Cormac McCarthy edits physics books in his spare time at the Santa Fe institute. ...more

A readable and witty introduction to chaos theory, which is only too misunderstood. This book focuses on the implications which chaos has in mathematiA readable and witty introduction to chaos theory, which is only too misunderstood. This book focuses on the implications which chaos has in mathematics, with an emphasis on maps, fractals, and other such phenomenon. A solid layman introduction....more

Not a bad little book, detailing briefly the history of transfinite numbers, the lives of Cantor and Gödel, and their theories. Delved a little bit toNot a bad little book, detailing briefly the history of transfinite numbers, the lives of Cantor and Gödel, and their theories. Delved a little bit too deeply into religious speculation, and not too much at all in the mathematical implications of the work produced. Recommended, but only as a primer and with additional research. ...more

Dear FSM, what a rambling mess of a book. This review is going to be longer than usual for me, as I have a lot of bile to get out of my system.

As I reDear FSM, what a rambling mess of a book. This review is going to be longer than usual for me, as I have a lot of bile to get out of my system.

As I read through the first several pages, I was bemused by the author's arrogant and lofty tone. I was willing to give him a bit of credit, if he had any logical backup behind it.

Finished the introduction. The book makes clear its intentions: to analyze and reduce complex phenomenon to simple mathematical representations. Not bad, but hardly revolutionary. This had been done in various forms since Newton, perhaps even earlier, if you play fast and loose with my terms. Simple rules can produce complex results. Every CompSci student now knows this.

After this, the book rapidly goes downhill. What follows are several hundred slogging pages of examples, and after that, faulty hypothetical applications to such disparate fields as evolution, cognitive science, complexity theory, gravity, quantum mechanics, etc. Most of his methods are either demonstrably false, or so reduced in effectiveness as to be useless, or restatements of ideas already discovered - without giving any fair credit. The author frequently downplays the contributions of other scientists, even trying to reduce Turing, Zuse, and Goedel to mere footnotes in his book, and blandly restating simplified or distorted or useless or plagiarized versions of their discoveries.

The author's arrogant tone does nothing to help his case. This book is a damned foolish waste of time, and I expected a hell of a lot better. What a shame. The creator of Mathematica and Wolfram Alpha (both excellent tools) should stick with those....more

Stephen Hawking is famous for both his expertise in the field of modern physics, and for popularizing the most recent discoveries for the lay audienceStephen Hawking is famous for both his expertise in the field of modern physics, and for popularizing the most recent discoveries for the lay audience. He said about his latter books, "For every equation I put in, sales are halved."

This new book is a significant departure from his past design philosophy - he has compiled, edited, and presented some of the great works of mathematical history, with the intent of presenting the lay reader with some of the great and elegant proofs of ages past, from Archimedes to Alan Turing.

There is one glaring flaw - whoever edited the book has made numerous errors - not only typos, but in the actual proofs and formulas and equations themselves! It will be difficult enough for most people to follow these lines of work if they are correct, but some of these mistakes are just nonsensical!

This could be a much better book than it is. I humbly suggest Professor Hawking should switch his Moog synthesizer to a stern voice and give the editors a good dressing down, for mangling the work of his distinguished forebearers....more

A series of extremely interesting and well-written biographies and anecdotes which don't really explain directly what chaos theory really is. No equatA series of extremely interesting and well-written biographies and anecdotes which don't really explain directly what chaos theory really is. No equations and lots of graphs, but that's just to make sure the general public isn't scared away.

Still, Gleick conveys the 'appeal' of chaos theory, or at least what people think it is about. In a complex system, the most minuscule change in initial conditions leads to drastic or unpredictable changes in the output. It is important not just in physics or mathematics, but astronomy, climatology, biology, even economics. Even if we can find a mathematical model behind the behavior of these complex systems, we cannot necessarily predict them. That's chaos theory. ...more

One of the titanic founding works of Game Theory. Requires an extensive background of mathematics to understand, but it is very comprehensive, coverinOne of the titanic founding works of Game Theory. Requires an extensive background of mathematics to understand, but it is very comprehensive, covering many types of games (including a version of poker). Some significant advances have been made in the field after this was published (Nash, etc.) but still something worth reading if you can handle it....more

It would be grossly inaccurate to call this simply a 'scifi novel'. If anything, it's a mathematics-philosophy-science-speculative-adventure fiction,It would be grossly inaccurate to call this simply a 'scifi novel'. If anything, it's a mathematics-philosophy-science-speculative-adventure fiction, but that doesn't abbreviate very well.

This is a nice big chunky piece of brain candy, with a wonderfully rendered setting, a large glossary of invented jargon (refer to the back if you're having trouble), and other neat tricks.

A feast for any physicist, or anyone who wants to learn the depth and beauty of physics, etc. as we know it. Not dumbed down at all. Throws every subjA feast for any physicist, or anyone who wants to learn the depth and beauty of physics, etc. as we know it. Not dumbed down at all. Throws every subject imaginable at you. If you can understand it, this book is truly amazing.

EDIT: I have recently learned in a conversation at uni that there are some controversies with the book and orthodox physics, most notably in the areas of string theory, Penrose's idea of twistors and the idea of more than 4 dimensions. However - considering how much else that he covers and so well, that if the general public still put forth the time and Herculean effort necessary to read the book, the world might be much better off for it. Still 5 stars....more