Real-World Probability Books: Science Topics

Ruhla, Charles The Physics of Chance. Oxford University Press, 1992.

Although more mathematical than is appropriate for the readership of these reviews, this book is so good I can't ignore it. It takes a selection of standard topics but treats them in a serious, careful and well written way, via a "horizontal integration" of math theory, its meaning within physics and its experimental verification. Topics include measurement error, the Maxwell velocity distribution for an ideal gas, Boltzmann's statistical physics, deterministic chaos illustrated by a compass needle undergoing forced oscillations, a detailed account of the quantum theory of interference and an "inseparable photons" experiment.

Coles, Peter. From Cosmos to Chaos: The science of unpredictability. Oxford University Press, 2006.

See my review.

Ruelle, David. Chance and Chaos. Princeton University Press, 1991.

A stylistic gem, partly because (as a true mathematician) the author writes only when he has something to say. The core is introductory accounts of topics like sensitivity of deterministic systems to initial conditions, Lorenz attractors, entropy and reversibility, equilibrium statistical mechanics, NP-hard algorithms and Godel's incompleteness theorem. While these have become staple topics of mathematical popularizers, Ruelle manages to pick the essential point and explain in clear words and a few equations. Minor side topics include game theory, information theory and sexual reproduction. Contains anecdotes (unfailingly true to my experience!) about how physics and math research and researchers actually work (note in particular the Physical Review paragraph) and no-nonsense comments about philosophical significance of the math. Unfortunately (for my purposes here) the "probability" component is very secondary; while each topic is somewhat related to probability, the core topics are linked as physics not as probability, and the other topics are hardly linked at all.

Eigen, Manfred and Winkler, Ruthild. Laws of the Game : How the principles of nature govern chance. Princeton University Press, 1993 (original 1975).

See my review.

Morris, S. Brent. Magic Tricks, Card Shuffling and Dynamic Computer memories. Mathematical Association of America, 1998.

The mathematics of card shuffling are related to some magic tricks with cards and to some algorithms in computer science theory. The book contains a lot of sophomore/junior level math, but is clearly written and deals with interesting questions (unfortunately, not "probability" questions). OK, finding this interesting marks me as a math nerd -- and proud of it!

Rastrigin, Leonard. This Chancy, Chancy, Chancy World. Mir, Moscow, 1986.

Written in earnest 1950s popular science style. Covers some of the usual material but emphasizes topics (signal filters, error-correcting codes, learning models, perceptron) relating to the author's professional interest in control engineering and random search algorithms. Having these non-standard topics is a positive feature. But the style tends to oscillate between overstated generalities and too-detailled specifics with block diagrams.

Strevens, Michael. Bigger than Chaos: Understanding complexity through Probability. Harvard University Press, 2003.

See my review.

Puente, Carlos E. Treasures inside the Bell: Hidden order in chance. World Scientific, 2003.

Misleading subtitle. Studies attractors of random dynamical systems where for generic parameters the invariant measure is Gaussian but where for special parameter choices one gets visually elegant deterministic sets. Great pictures, but from a mathematically specialized and artificial model.

Beltrami, Edward. What is Random? Chance and Order in Mathematics and Life. Copernicus, 1999.

A mathematician seeks to give non-technical explanations of topics such as entropy as information/data compression, algorithmic randomness and undecidability, self-organized criticality. This is a bold goal. To my taste the topics are more "philosophy" than "real world", and give a skewed picture of what mathematicians know/work on. For instance the "Janus-faced randomness" discussion (the stationary process $x \to 2x \mod 1$ is deterministic forwards but random backwards) has simpler explanations that don't support the philosophical import the author assigns.

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