The word tangle is generally used pejoratively in the English language, as in Walter Scott’s line, Oh what a tangled web we weave, when first we practice to deceive. Or at least disapprovingly, as in tangled mess. Darwin’s usage, in the last passage of The Origin of the Species, is the only famous example I know of where the word is used in an approving way:
“It is interesting to contemplate a tangled bank, clothed with many plants of many kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent upon each other in so complex a manner, have all been produced by laws acting around us.”
The Darwinian notion of a tangle can be understood as a snapshot of a robust, open, evolutionary process, with all the optimality and efficiency properties that entails or doesn’t (I would summarize it as “a mediocre slouching towards continued existence”). Darwin goes on to link his evocative observation directly to his theory of natural selection, but I think the idea of a tangle is more general, and has roots in the fundamental mathematical structure of reality. Take for instance, this picture of various optimal packings from a great thread of many such examples by Daniel Piker (thanks to all who responded to my twitter prompt looking for this sort of thing):
These are very simple examples of a large class of things I define to be proper tangles: complex things that are efficient but not orderly. And you know what these pictures remind me of? Traffic in India.
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