“The solvable systems are the ones shown in textbooks. They behave. Confronted with a nonlinear system, scientists would have to substitute linear approximations or find some other uncertain backdoor approach. Textbooks showed students only the rare non-linear systems that would give way to such techniques. They did not display sensitive dependence on initial conditions. Nonlinear systems with real chaos were rarely taught and rarely learned. When people stumbled across such things-and people did-all their training argued for dismissing them as aberrations. Only a few were able to remember that the solvable, orderly, linear systems were the aberrations. Only a few, that is, understood how nonlinear nature is in its soul. Enrico Fermi once exclaimed, "It does not say in the Bible that all laws of nature are expressible linearly!" The mathematicians Stanislaw Ulam remarked that to call the study of chaos "nonlinear science" was like calling zoology "the study of nonelephant animals.”
― Chaos: Making a New Science
― Chaos: Making a New Science
“In life, we must first learn to crawl, then stand, then walk, then run, and only then, fly. We cannot crawl into flying.”
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“Nature loves courage. You make the commitment and nature will respond to that commitment by removing impossible obstacles. Dream the impossible dream and the world will not grind you under, it will lift you up. This is the trick. This is what all these teachers and philosophers who really counted, who really touched the alchemical gold, this is what they understood. This is the shamanic dance in the waterfall. This is how magic is done. By hurling yourself into the abyss and discovering it's a feather bed.”
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Jonathan’s 2025 Year in Books
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