danced for him again-but only the larger ones,this time,in long rows,"all twining and twisting in snakelike motion.But look!What was that?One of the sakes had seized hold of its own tale,and the form whirled mockingly before my eyes."The chains and rings that carbon atoms form with each other are indeed the fundamental structures of organic chemistry. Para.14:Several other scientists have told me that the fringes of sleep set the problem-sodden mind free to make uninhibited,bizarre,even random connections that may throw up the unexpected answer.One said that the technical trick that led to one of his most admired discoveries-it was about the fundamental molecular nature of genetic mutations-had sprung to mind while he was lying insomniac at three in the morning.Another said he was startled from a deep sleep one night by the fully worked-out answer to a puzzle that had blocked him for weeks-though at breakfast he was no longer able to remember any detail except the jubilant certainty.So the next night he went to sleep with paper and pencil on the bedside table; and when,once again,he awoke with the answer,he was able to seize it. Para.15:More usually,however,in the classic strategy for achieving enlightenment the weeks of saturation must be followed by a second stage that begins when the problem is deliberately set aside.After several days of silence,the solution wells up.The mathematician Henri Poincare was unusually introspective about the process of discovery.(He also came nearer than anyone else to beating Einstein to the theory of relativity,except that in htat case,though he had the pieces of the problem,inspiration did not strike.)In 1908,Poincare gave a lecture,before the Psychological Society of Paris,about the psychology of mathematical invention,and there he described how he made some of his youthful discoveries.He reassured his audience,few of them mathematical:"I will tell you that I found the proof of a certain theorem in certain circumstances.The theorem will have a barbarous name,which many of you will never have heard of.But that's of no importance,for what is interesting to the psychologist is not the theorem-it's the circumstances." Para.16:The youthful discovery was about a class of mathematical functions which he named in honor of another mathematician,Lazarus Fuchs-but,as he said,the mathematical content is not important here.The young Poincare believed,and for fifteen days he strove to prove,that no functions of the type he was pondering could exist in mathematics.He struggled with the disproof for hours every day.One evening. he happened to drink some black coffee,and couldn't sleep.Like Kekule with the carbon atoms,Poincare found mathematical expressions arising before him in crowds,combining and recombining.By the next morning,he had established a class of the functions that he had begun by denying.Then,a short time later, he left town to go on a geological excursion for several days."The changes of travel made me forget my mathematical word."One day during the excursion,though,he was carrying on a conversation as he was about to board a bus."At the moment when I put my foot on the step,the idea came to me,without anything in my former thoughts seeming to have paved the way for it,that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidian geometry."He did not try to prove the idea,but went right on with his conversation."But I felt a perfect certainty,"he wrote.When he got home,"for conscience's sake I verified the result at my leisure." Para.17:The quality of such moments of the mind has not often been described successfully:Charles P.Snow was a scientist as well as a novelist,and whenever his experience of science comes together with his writer's imagination his witness is authentic.In The Search,a novel about scientists at work,the protagonist makes a discovery for which he had long been striving. Then I was carried beyond pleasure....My own triumph and delight and success were there,but they seemeddanced for him again—but only the larger ones, this time, in long rows, “all twining and twisting in snakelike motion. But look! What was that? One of the sakes had seized hold of its own tale, and the form whirled mockingly before my eyes.” The chains and rings that carbon atoms form with each other are indeed the fundamental structures of organic chemistry. Para. 14:Several other scientists have told me that the fringes of sleep set the problem-sodden mind free to make uninhibited, bizarre, even random connections that may throw up the unexpected answer. One said that the technical trick that led to one of his most admired discoveries—it was about the fundamental molecular nature of genetic mutations—had sprung to mind while he was lying insomniac at three in the morning. Another said he was startled from a deep sleep one night by the fully worked-out answer to a puzzle that had blocked him for weeks—though at breakfast he was no longer able to remember any detail except the jubilant certainty. So the next night he went to sleep with paper and pencil on the bedside table; and when, once again, he awoke with the answer, he was able to seize it. Para. 15:More usually, however, in the classic strategy for achieving enlightenment the weeks of saturation must be followed by a second stage that begins when the problem is deliberately set aside. After several days of silence, the solution wells up. The mathematician Henri Poincare was unusually introspective about the process of discovery. (He also came nearer than anyone else to beating Einstein to the theory of relativity, except that in htat case, though he had the pieces of the problem, inspiration did not strike.) In 1908, Poincare gave a lecture, before the Psychological Society of Paris, about the psychology of mathematical invention, and there he described how he made some of his youthful discoveries. He reassured his audience, few of them mathematical: “I will tell you that I found the proof of a certain theorem in certain circumstances. The theorem will have a barbarous name, which many of you will never have heard of. But that’s of no importance, for what is interesting to the psychologist is not the theorem—it’s the circumstances.” Para. 16:The youthful discovery was about a class of mathematical functions which he named in honor of another mathematician, Lazarus Fuchs—but, as he said, the mathematical content is not important here. The young Poincare believed, and for fifteen days he strove to prove, that no functions of the type he was pondering could exist in mathematics. He struggled with the disproof for hours every day. One evening, he happened to drink some black coffee, and couldn’t sleep. Like Kekule with the carbon atoms, Poincare found mathematical expressions arising before him in crowds, combining and recombining. By the next morning, he had established a class of the functions that he had begun by denying. Then, a short time later, he left town to go on a geological excursion for several days. “The changes of travel made me forget my mathematical word.” One day during the excursion, though, he was carrying on a conversation as he was about to board a bus. “At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidian geometry.” He did not try to prove the idea, but went right on with his conversation. “But I felt a perfect certainty,” he wrote. When he got home, “for conscience’s sake I verified the result at my leisure.” Para. 17:The quality of such moments of the mind has not often been described successfully; Charles P. Snow was a scientist as well as a novelist, and whenever his experience of science comes together with his writer’s imagination his witness is authentic. In The Search, a novel about scientists at work, the protagonist makes a discovery for which he had long been striving. Then I was carried beyond pleasure. … My own triumph and delight and success were there, but they seemed