82
" Unfortunately, our minds are bad at grasping these kinds of problems. We’re accustomed to thinking in terms of centralized control, clear chains of command, the straightforward logic of cause and effect. But in huge, interconnected systems, where every player ultimately affects every other, our standard ways of thinking fall apart. Simple pictures and verbal arguments are too feeble, too myopic. That’s what plagues us in economics when we try to anticipate the effect of a tax cut or a change in interest rates, or in ecology, when a new pesticide backfires and produces dire, unintended consequences that propagate through the food chain. "
― Steven H. Strogatz , Sync: The Emerging Science of Spontaneous Order
90
" There, staring us in the face, was the Kuramoto model—an enigma like the monolith in 2001: A Space Odyssey, buried under the soil, waiting for us apes to find it, beckoning, the key to sync. Until now, the Kuramoto model had been thought to be nothing more than a convenient abstraction, the simplest way to understand how groups of dissimilar oscillators could spontaneously synchronize, and under what circumstances. It was born out of pure imagination, concocted as a caricature of biological oscillators: crickets, fireflies, cardiac pacemaker cells. Now here it was, unearthed, in the dynamics of superconducting Josephson junctions. It reminded me of that wonderful feeling that Einstein talked about, the recognition of hidden unity. Soon "
― Steven H. Strogatz , Sync: The Emerging Science of Spontaneous Order
93
" Sophie Germain had taught herself calculus at a young age. The daughter of a wealthy family, she had become entranced by mathematics after reading a book about Archimedes in her father’s library. When her parents found out that she loved mathematics and was staying up late at night to work on it, they took away her candles, left her fire unlit, and confiscated her nightgowns. Sophie persisted. She wrapped herself in quilts and worked by the light of stolen candles. Eventually her family relented and gave her their blessing. Germain, like all women of her era, was not permitted to attend university, so she continued to teach herself, in some cases by obtaining lecture notes from the courses at the nearby École Polytechnique using the name Monsieur Antoine-August Le Blanc, a student who had left the school. Unaware of his departure, academy administrators continued to print lecture notes and problem sets for him. She submitted work under his name until one of the school’s teachers, the great Lagrange, noticed the remarkable improvement in Monsieur Le Blanc’s previously abysmal performance. Lagrange requested a meeting with Le Blanc and was delighted and astonished to discover her true identity. "
― Steven H. Strogatz , Infinite Powers: How Calculus Reveals the Secrets of the Universe
98
" In many ways, this chemical medium behaves like the human sexual response. Sexual arousal and recovery depend on the properties of nerve tissue, which, like Zhabotinsky soup, belongs to a general class of systems called excitable media. A neuron has three states: quiescent, excited, and refractory. Normally a neuron is quiescent. With inadequate stimulation, it shows little response and returns to rest. But a sufficiently provocative stimulus will excite the neuron and cause it to fire. Next it becomes refractory (incapable of being excited for a while) and finally returns to quiescence. The parallels with chemical waves extend to action potentials, the electrical waves that propagate along nerve axons. They too travel without attenuation, and when two of them collide, they annihilate each other. In fact, all of these statements are equally true of electrical waves in another excitable medium: the heart. That’s the beauty of this abstraction—the qualitative properties of one excitable medium hold for them all. They can all be studied in one stroke. "
― Steven H. Strogatz , Sync: The Emerging Science of Spontaneous Order