Mitchell has a talent for explaining difficult material
Reviewed in the United States on 27 January 2020
In “Complexity”, Mitchell utilizes her talent for explaining difficult material. She also seems wise, objective, humble despite her qualifications. Whenever possible she uses simple, concrete examples to get her points across. Ironically, the one subject where the book almost totally failed me was in the explanation of an AI computer program to generate analogies, Mitchell’s Ph.D. thesis subject.
As Mitchell observes, “what we might call modern complex systems science is, like its forebears, still not a unified whole but rather a collection of disparate parts with some overlapping concepts.” A key concept is the complexity that can arise from simple rules. In fractal geometry a simple rule is applied repeatedly. In the behavior of ants, complex, seemingly purposeful behavior arises from each ant following a simple set of rules, but in endeavors like foraging, only probabilistically. This is typical whether it is ants foraging or the immune system combatting infection; many agents are working in parallel, and the most likely paths are followed the most intensively, but with some probability less likely paths or solutions are tried. Genetic algorithms, which are heuristics for solving problems that cannot be solved by mathematical optimization, also work probabilistically, combining what have been the most successful solutions in each iteration with some chance of trying what are likely to be unsuccessful variants, thereby avoiding finding only local optima.
Many subjects, such as neural connections in the brain, can be modelled as networks, embodying common concepts. For example, often many nodes are connected to “nearby” hubs, which then provide longer connections to more distant hubs. The distribution of the number of links to each node can often be approximated by a power law.
Mitchell uses a simple equation to illustrate chaos. For certain values of the equation parameter, successive iterations of the equation are supersensitive to the initial value of the input x, and generate a string of outputs that appear to be random numbers, whereas for other parameter values, the string of outputs converges to a single point, or oscillates between a fixed number of points.
Mitchell often illustrates concepts by using biology. I was surprised to learn that the eyes in many different creatures, humans vs. octopi, may not illustrate convergent evolution, but all start with the same critical gene – if a mouse version is implanted into a fruit fly leg during development, you get a fruit fly eye on the leg. Conversely, not only is there not a single exponent for how metabolic rates vary with animal mass across all animals as Mitchell discusses, but the metric to examine is not resting metabolism, but maximum metabolic rate, for that is what is constrained by blood supply (cf “Power, Sex, Suicide: Mitochondria and the Meaning Of Life” by Nick Lane).
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