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As an electronics engineer, I'm an "armchair scientist" -- using that term without any disrespect. In my context it means I love studying math, physics, chemistry, etc. even though my field is harmonics, and much narrower than scientists like Sole who grasp wonderful big as well as small pictures. Recently, a number of outstanding books have come out on complexity theory and dynamical systems-- most notably the p vs. np series that includes Fortnow's excellent book: The Golden Ticket: P, NP, and the Search for the Impossible.
You know the old saying that publishers who allow even a few math symbols in a text, let alone a sigma or derivative, are condemning the book to an exponential decay in sales. It thus takes a courageous or detached author to insist on not removing the "meat" of the math. Sole is such an author! While phase transitions (and boundary value problems in general) are at the heart of most field and phase work at the cutting edge of complexity theory and dynamical systems research today, very few books have been written that are accessible to the educated but non professional mathematician reader. Where the few exist, they cover only one of two applications of the research (sometimes unfortunately to "make a point") like ecology or sociology.
What about physics, cancer, human language development, computer networks, ant behavior, economics, day trading, genetics, monte carlo, decision theory, neurons... ok, we can see why only ONE book (this one) attempts to survey the entire field with sufficient depth to elicit deep enjoyment and further curiosity without being $190 and 600 pages!
The author is extremely intellectually honest in admitting that keeping the calculus (and dynamic systems, even in Neurology, for example, is filled with partial differential equations) at a basic undergrad level oversimplifies the picture. He tells us right up front that he will be focusing on mean field theory and leaving out fluctuations and local "tipping point" interactions that require a LOT of postgrad math, including advanced topology.
This concession is ostensibly to allow undergrads to survey the field with a career eye, and advanced researchers to see enough depth to decide on focus for further research. Sole also gives a HUGE bank of recent references, online, articles and books, so it is quite easy to "drill down" into deeper math if you like. I'd like to break that pattern and suggest that the book is now equally appropriate for non complexity specialists to get a grasp of possibly the most important area of complexity research going on today.
You will be richly rewarded by this book. Our lives, from the tiniest quantum micro fields and phases, to our own deepest relationships, are continually undergoing phase transitions, and we're often the victims of forces just outside our grasp! We, literally, ARE a dynamical system living in other networks of dynamical systems. The author points out that the "big bang" events like meteors and wars "seem" to precipitate sea change, but far less "rare" events can have the same effect! Citing (not exactly the butterfly wing) gradual temperature change in the lush Sahara "rainforest" Sole describes the shockingly quick change to a desert at the tipping point that required no meteor at all!
A twitter message that causes a revolution, an underground nuke test, a certain debt/equity ratio in GDP... and... revolution! I'm not a big global warming type, so was truly thankful that the author stayed scientific and didn't stray into a bunch of political warnings, but between the lines... a LOT of wisdom and insight that causes against the odds rethinking of our future as a social species. The biomass of ants here is a great reminder... like the biomass of neurons voting in our moment by moment phase decisions! Highly recommended, and certainly not only for complexity theorists or dynamical systems/ chaos/ fractal lovers, though they are warmly welcomed by this author too. If you're into finding hidden gems like I am, this one is a must.
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