The Collapse Of Chaos

Written by Ian Stewart and Jack Cohen, The Collapse Of Chaos is a critique on the direction science is heading. They contrast the pros and cons of reductionism and wholism, and then present a new paradigm: contextualism. In reductionism, things are understood by breaking them into fundamental units. Too much reductionism makes the prediction of emergent phenomena prohibitively complicated. In wholism, things are understood as a unique whole. Too much wholism makes every instance of a phenomenon unique, preventing any deeper understanding to make predictions with. In contextualism, things are understood by how they relate to other things.

​Another theme running through the book is that nobody really knows how to measure complexity and simplicity. Newton’s equation of the gravitational force may be simpler than Kepler’s set of data describing the orbits of the planets, which in turn may be simpler than Ptolemy’s circles, but Newton’s equation (F=Gm1m2/d^2) is only an approximation. Multiple gravitating bodies, friction, air resistance, relativistic effects, and quantum effects all conspire against it. The underlying phenomena that give rise to the behaviors described by Newton are actually very complicated (the quantum wave function of every particle interacting with the quantum wave function of every other particle in the universe, including exotic virtual particles), even though they may in turn be explained by even simpler laws on a more fundamental level. This is the essence of chaos theory. Simple equations, given enough iterations, can yield immensely complex and even fractal results, while immensely complex equations can yield rather simple and boring results. Below is an excerpt from page 8 illustrating how bad humans are at determining true complexity.
 
“The ordinary city-dweller finds the jungle complex and incomprehensible but is entirely comfortable when surrounded by the ordered simplicities of New York, such as department stores, subways, taxicabs, drug-dealers, and muggers. The jungle-dweller is baffled by New York but is entirely at home with the snakes and the spiders in the nice, simple jungle…An apparent complexity that might actually be simple is the fact that most holly bushes have spiky leaves only near the bottom…Now, isn’t it clever of the trees to save on the cost of making spikes and concentrate their efforts at the bottom, where animals might eat the leaves? How incredibly complex nature is! Except, of course, that we don’t know whether it does cost the plant anything to make spikes. It may be harder to make all the leaves the same than it is to make them different, just as it’s harder to make a flat piece of ground (all at the same level) than a sloping one…”
 
Other topics of interest in The Collapse Of Chaos include interesting takes on entropy, the anthropic principle, the selfish gene principle, and the possibility that for some mathematical truths, the shortest possible proof is billions of times longer than the final statement. This book could very well turn your worldview inside out.