The Rage to Know Horace Freeland Judson (1980) Para.1:Certain moments of the mind have a special quality of well-being.A mathematician friend of mine remarked the other day that his daughter,aged eight,had just stumbled without his teaching onto the fact that some numbers are prime numbers-those,like 11 or 19 or 83 or 1023,that cannot be divided by any other integer (except,trivially,by 1)."She called them 'unfair'numbers,"he said."And when I asked her why they were unfair,she told me,'Because there's no way to share them out evenly.""What delighted him most was not her charming turn of phrase nor her equitable turn of mind(seventeen peppermints to give to her friends?)but-as a mathematician-the knowledge that the child had experienced a moment of pure scientific perception.She had discovered for herself something of the way things are. Para.2:The satisfaction of such a moment at its most intense-and this is what ought to be meant, after all,by the tarnished phrase "the moment of truth"-is not easy to describe.It partakes at once of exhilaration and tranquility.It is luminously clear.It is beautiful.The clarity of the moment of discovery, the beauty of what in that moment is seen to be true about the world,is the fundamental attraction that draws scientists on. Para.3:Science is enormously disparate-easily the most varied and diverse of human pursuits.The scientific endeavor ranges from the study of animal behavior all the way to particle physics,and from the purest of mathematics back again to the most practical problems of shelter and hunger,sickness and war. Nobody has succeeded in catching all this in one net.And yet the conviction persists-scientists themselves believe,at heart-that behind the diversity lies a unity.In those luminous moments of discovery,in the various approaches and the painful tension require to arrive at them,and then in the community of science, organized worldwide to doubt and criticize,test and exploit discoveries-somewhere in that constellation, to begin with,there are surely constants.Deeper is the lure that in the bewildering variety of the world as it is there may be found some astonishing simplicities. Para.4:Philosophers,and some of the greatest among them,have offered descriptions of what they claim is the method of science.These make most scientists acutely uncomfortable.The descriptions don't seem to fit what goes on in the doing of science.They seem at once too abstract and too limited.Scientists don't believe that they think in ways that are wildly different from the way most people think at least in some areas of their lives."We'd be in real trouble-we could get nowhere-if ordinary methods of inference did not apply,"Philip Morrison said in a conversation a while ago.(Morrison is a theoretical physicist at the Massachusetts Institute of Technology.)The wild difference,he went on to say,is that scientists apply these everyday methods to areas that most people never think about seriously and carefully. The philosophers'descriptions don't prepare one for either this ordinariness or this extreme diversity of the scientific enterprise-the variety of things to think about,the variety of obstacles and traps to understanding,the variety of approaches to solutions.They hardly acknowledge the fact that a scientist ought often to find himself stretching to the tiptoe of available technique and apparatus,out beyond the frontier of the art,attempting to do something whose difficulty is measured most significantly by the fact that it has never been done before.Science is carried on-this,too,is obvious-in the field,in the observatory,in the laboratory.But historians leave out the arts of the chef and the watchmaker,the development at the bench of a new procedure or a new instrument."And making it work,"Morrison said
The Rage to Know Horace Freeland Judson (1980) Para. 1: Certain moments of the mind have a special quality of well-being. A mathematician friend of mine remarked the other day that his daughter, aged eight, had just stumbled without his teaching onto the fact that some numbers are prime numbers—those, like 11 or 19 or 83 or 1023, that cannot be divided by any other integer (except, trivially, by 1). “She called them ‘unfair’ numbers,” he said. “And when I asked her why they were unfair, she told me, ‘Because there’s no way to share them out evenly.’” What delighted him most was not her charming turn of phrase nor her equitable turn of mind (seventeen peppermints to give to her friends?) but—as a mathematician—the knowledge that the child had experienced a moment of pure scientific perception. She had discovered for herself something of the way things are. Para. 2: The satisfaction of such a moment at its most intense—and this is what ought to be meant, after all, by the tarnished phrase “the moment of truth”—is not easy to describe. It partakes at once of exhilaration and tranquility. It is luminously clear. It is beautiful. The clarity of the moment of discovery, the beauty of what in that moment is seen to be true about the world, is the fundamental attraction that draws scientists on. Para. 3: Science is enormously disparate—easily the most varied and diverse of human pursuits. The scientific endeavor ranges from the study of animal behavior all the way to particle physics, and from the purest of mathematics back again to the most practical problems of shelter and hunger, sickness and war. Nobody has succeeded in catching all this in one net. And yet the conviction persists—scientists themselves believe, at heart—that behind the diversity lies a unity. In those luminous moments of discovery, in the various approaches and the painful tension require to arrive at them, and then in the community of science, organized worldwide to doubt and criticize, test and exploit discoveries—somewhere in that constellation, to begin with, there are surely constants. Deeper is the lure that in the bewildering variety of the world as it is there may be found some astonishing simplicities. Para. 4: Philosophers, and some of the greatest among them, have offered descriptions of what they claim is the method of science. These make most scientists acutely uncomfortable. The descriptions don’t seem to fit what goes on in the doing of science. They seem at once too abstract and too limited. Scientists don’t believe that they think in ways that are wildly different from the way most people think at least in some areas of their lives. “We’d be in real trouble—we could get nowhere—if ordinary methods of inference did not apply,” Philip Morrison said in a conversation a while ago. (Morrison is a theoretical physicist at the Massachusetts Institute of Technology.) The wild difference, he went on to say, is that scientists apply these everyday methods to areas that most people never think about seriously and carefully. The philosophers’ descriptions don’t prepare one for either this ordinariness or this extreme diversity of the scientific enterprise—the variety of things to think about, the variety of obstacles and traps to understanding, the variety of approaches to solutions. They hardly acknowledge the fact that a scientist ought often to find himself stretching to the tiptoe of available technique and apparatus, out beyond the frontier of the art, attempting to do something whose difficulty is measured most significantly by the fact that it has never been done before. Science is carried on—this, too, is obvious—in the field, in the observatory, in the laboratory. But historians leave out the arts of the chef and the watchmaker, the development at the bench of a new procedure or a new instrument. “And making it work,” Morrison said
"This is terribly important."Indeed,biochemists talk about "the cook-book."Many a Nobel Prize has been awarded,not for a discovery,as such,but for a new technique or a new tool that opened up a whole field of discovery."I am a theoretician,"Morrison said."And yet the most important problem for me is to be in touch with the people who are making new instruments or finding new ways of observing,and to try to get them to do the right experiments."And then,in a burst of annoyance,"I feel very reluctant to give any support to descriptions of'scientific method.'The scientific enterprise is very difficult to model.You have to look at what scientists of all kinds actually do." Para.5:It's true that by contrast philosophers and historians seem book-bound-or paper-blindered, depending chiefly on what has been published as scientific research for their understanding of the process of discovery.In this century,anyway,published papers are no guide to the way scientists get the results they report.We have testimony of the highest authenticity for that.Sir Peter Medawar has both done fine science and written well about how it is done:he won his Nobel Prize for investigations of immunological tolerance,which explained,among other things,why foreign tissue,like a kidney or a heart,is rejected by the body into which it is transplanted,and he has described the methods of science in essays of grace and distinction.A while ago,Medawar wrote,"What scientists do has never been the subject of a scientific... inquiry.It is no use looking to scientific 'papers,'for they not merely conceal but actively misrepresent the reasoning that goes into the work they describe."The observation has become famous,its truth acknowledged by other scientists.Medawar wrote further,"Scientists are building explanatory structures, telling stories which are scrupulously tested to see if they are stories about real life." Para.6:Scientists do science for a variety of reasons,of course,and most of them are familiar to the sculptor,or to the surgeon or the athlete or the builder of bridges:the professional's pride in skill:the swelling gratification that comes with recognition accorded by colleagues and peers;perhaps the competitor's fierce appetite;perhaps ambition for a kind of fame more durable than most.At the beginning is curiosity,and with curiosity the delight in mastery-the joy of figuring it out that is the birthright of every child.I once asked Murray Gell-Mann,a theoretical physicist,how he got started in science.His answer was to point to the summer sky:"When I was a boy,I used to ask all sorts of simple question-like, 'What holds the clouds up?""Rosalind Franklin,the crystallographer whose early death deprived her of a share in the Nobel Prize for the discovery of the structure of DNA,one day was helping a young collaborator draft an application for research money,when she looked up at him and said,"What we can't tell them is that it's so much fun!"He still remembers her glint of mischief.The play of the mind,in an almost childlike innocence,is a pleasure that appears again and again in scientists'reflection on their work. The geneticist Barbara McClintock,as a woman in American science in the 1930s,had no chance at the academic posts open to her male colleagues,but that hardly mattered to her."I did it because it was fin!" she said forty years later."I couldn't wait to get up in the morning!I never thought of it as 'science'." Para.7:The exuberant innocence can be poignant.Francois Jacob2,who won his share of a Nobel Prize as one of the small group of molecular biologists in the fifties who brought sense and order into the interactions by which bacteria regulate their life processes,recently read an account I had written of that work,and said to me with surprise and an evident pang of regret,"We were like children playing!"He meant the fun of it-but also the simplicity of the problems they had encountered and the innocence of mind they had brought to them.Two hundred and fifty years before-although Jacob did not consciously intend the parallel-Isaac Newton',shortly before his dead,said:
“This is terribly important.” Indeed, biochemists talk about “the cook-book.” Many a Nobel Prize has been awarded, not for a discovery, as such, but for a new technique or a new tool that opened up a whole field of discovery. “I am a theoretician,” Morrison said. “And yet the most important problem for me is to be in touch with the people who are making new instruments or finding new ways of observing, and to try to get them to do the right experiments.” And then, in a burst of annoyance, “I feel very reluctant to give any support to descriptions of ‘scientific method.’ The scientific enterprise is very difficult to model. You have to look at what scientists of all kinds actually do.” Para. 5: It’s true that by contrast philosophers and historians seem book-bound—or paper-blindered, depending chiefly on what has been published as scientific research for their understanding of the process of discovery. In this century, anyway, published papers are no guide to the way scientists get the results they report. We have testimony of the highest authenticity for that. Sir Peter Medawar has both done fine science and written well about how it is done: he won his Nobel Prize for investigations of immunological tolerance, which explained, among other things, why foreign tissue, like a kidney or a heart, is rejected by the body into which it is transplanted, and he has described the methods of science in essays of grace and distinction. A while ago, Medawar wrote, “What scientists do has never been the subject of a scientific … inquiry. It is no use looking to scientific ‘papers,’ for they not merely conceal but actively misrepresent the reasoning that goes into the work they describe.” The observation has become famous, its truth acknowledged by other scientists. Medawar wrote further, “Scientists are building explanatory structures, telling stories which are scrupulously tested to see if they are stories about real life.” Para. 6: Scientists do science for a variety of reasons, of course, and most of them are familiar to the sculptor, or to the surgeon or the athlete or the builder of bridges: the professional’s pride in skill: the swelling gratification that comes with recognition accorded by colleagues and peers; perhaps the competitor’s fierce appetite; perhaps ambition for a kind of fame more durable than most. At the beginning is curiosity, and with curiosity the delight in mastery—the joy of figuring it out that is the birthright of every child. I once asked Murray Gell-Mann, a theoretical physicist, how he got started in science. His answer was to point to the summer sky: “When I was a boy, I used to ask all sorts of simple question—like, ‘What holds the clouds up?’” Rosalind Franklin, the crystallographer whose early death deprived her of a share in the Nobel Prize for the discovery of the structure of DNA1 , one day was helping a young collaborator draft an application for research money, when she looked up at him and said, “What we can’t tell them is that it’s so much fun!” He still remembers her glint of mischief. The play of the mind, in an almost childlike innocence, is a pleasure that appears again and again in scientists’ reflection on their work. The geneticist Barbara McClintock, as a woman in American science in the 1930s, had no chance at the academic posts open to her male colleagues, but that hardly mattered to her. “I did it because it was fun!” she said forty years later. “I couldn’t wait to get up in the morning! I never thought of it as ‘science’.” Para. 7: The exuberant innocence can be poignant. Francois Jacob 2 , who won his share of a Nobel Prize as one of the small group of molecular biologists in the fifties who brought sense and order into the interactions by which bacteria regulate their life processes, recently read an account I had written of that work, and said to me with surprise and an evident pang of regret, “We were like children playing!” He meant the fun of it—but also the simplicity of the problems they had encountered and the innocence of mind they had brought to them. Two hundred and fifty years before—although Jacob did not consciously intend the parallel—Isaac Newton 3 , shortly before his dead, said:
I do not know what I may appear to the world,but to myself I seem to have been only like a boy playing on the sea shore,and diverting myself in no and then finding a smoother pebble or a prettier shell than ordinary,whilst the great ocean of truth lay all undiscovered before me. Para.8:For some curiosity and the delight of putting the world together deepen into a life's passion. Sheldon Glashow,a fundamental-particle physicist at Harvard,also got started in science by asking simple questions."In eighth grade,we were learning about how the earth goes around the sun,and the moon around the earth,and so on,"he said."And I thought about that,and realized that the Man in the Moon is always looking at us"-that the moon as it circles always turns the same face to the earth.And I asked the teacher,'Why is the Man in the Moon always looking at us?'She was pleased with the question-but said it was hard to answer.And it turns out that it's not until you're in college-level physics courses that one really learns the answers,"Glashow said."But the difference is that most people would look at the moon and wonder for a moment and say,That's interesting'-and then forget it.But some people can't let go." Para.9:Curiosity is not enough.The word is too mild by far,a word for infants.Passion is indispensable for creation.no less in the sciences than in the arts.Medawar once described it in a talk addressed to young scientists."You must feel in yourself an exploratory impulsion-an acute discomfort at incomprehension."This is the rage to know.The other side of the fun of science,as of art,is pain.A problem worth solving will surely require weeks and months of lack of progress,whipsawed between hope and the blackest sense of despair.The marathon runner or the young swimmer who would be a champion knows at least that the pain may be a symptom of progress.But here the artist and the scientist part company with the athlete-to join the mystic for a while.The pain of creation,though not of the body,is in one way worse.It must be not only endured but reflected back on itself to increase the agility,variety, inventiveness of the play of the mind.Some problems in science have demanded such devotion,such willingness to bear repeated rebuffs,not just for years but for decades.There are times in the practice of the arts,we're told,of abysmal self-doubt.There are like passages in the doing of science. Para.10:Albert Einstein took eleven years of unremitting concentration to produce the general theory of relativity;long afterward,he wrote,"In the light of knowledge attained,the happy achievement seems almost a matter of course,and any intelligent student can grasp it without too much trouble.But the years of anxious searching in the dark,with their intense longing,their alternations of confidence and exhaustion,and the final emergence into the light-only those who have experienced it can understand it." Einstein confronting Einstein's problems:the achievement,to be sure,is matched only by Newton's and perhaps Darwin's-but the experience is not rare.It is all but inseparable from high accomplishment.In the black cave of unknowing,when one is groping for the contours of the rock and the slope of the floor, tossing a pebble and listening for its fall,brushing away false clues as insistent as cobwebs,a touch of fresh air on the cheek can make hope leap up,and unexpected scurrying whisper can induce the mood of the brink of terror."Afterward it can be told-trivialized-like a roman policier,a detective story,"Francois Jacob once said."While you're there,it is the sound and the fury."But it was the poet and adept of mysticism St.John of the Cross who gave to this passionate wrestling with bafflement the name by which, ever since,it has been known:"the dark night of the soul." Para.11:Enlightenment may not appear,or not in time;the mystic at least need not fear forestalling. Enlightenment may dawn in ways as varied as the individual approaches of scientists at work-and,in defiance of stereotypes,the sciences far outrun the arts in variety of personal styles and in the crucial
I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea shore, and diverting myself in no and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me. Para. 8: For some curiosity and the delight of putting the world together deepen into a life’s passion. Sheldon Glashow, a fundamental-particle physicist at Harvard, also got started in science by asking simple questions. “In eighth grade, we were learning about how the earth goes around the sun, and the moon around the earth, and so on,” he said. “And I thought about that, and realized that the Man in the Moon is always looking at us”—that the moon as it circles always turns the same face to the earth. And I asked the teacher, ‘Why is the Man in the Moon always looking at us?’ She was pleased with the question—but said it was hard to answer. And it turns out that it’s not until you’re in college-level physics courses that one really learns the answers,” Glashow said. “But the dif erence is that most people would look at the moon and wonder for a moment and say, ‘That’s interesting’—and then forget it. But some people can’t let go.” Para. 9: Curiosity is not enough. The word is too mild by far, a word for infants. Passion is indispensable for creation, no less in the sciences than in the arts. Medawar once described it in a talk addressed to young scientists. “You must feel in yourself an exploratory impulsion—an acute discomfort at incomprehension.” This is the rage to know. The other side of the fun of science, as of art, is pain. A problem worth solving will surely require weeks and months of lack of progress, whipsawed between hope and the blackest sense of despair. The marathon runner or the young swimmer who would be a champion knows at least that the pain may be a symptom of progress. But here the artist and the scientist part company with the athlete—to join the mystic for a while. The pain of creation, though not of the body, is in one way worse. It must be not only endured but reflected back on itself to increase the agility, variety, inventiveness of the play of the mind. Some problems in science have demanded such devotion, such willingness to bear repeated rebuffs, not just for years but for decades. There are times in the practice of the arts, we’re told, of abysmal self-doubt. There are like passages in the doing of science. Para. 10:Albert Einstein 4 took eleven years of unremitting concentration to produce the general theory of relativity; long afterward, he wrote, “In the light of knowledge attained, the happy achievement seems almost a matter of course, and any intelligent student can grasp it without too much trouble. But the years of anxious searching in the dark, with their intense longing, their alternations of confidence and exhaustion, and the final emergence into the light—only those who have experienced it can understand it.” Einstein confronting Einstein’s problems: the achievement, to be sure, is matched only by Newton’s and perhaps Darwin’s—but the experience is not rare. It is all but inseparable from high accomplishment. In the black cave of unknowing, when one is groping for the contours of the rock and the slope of the floor, tossing a pebble and listening for its fall, brushing away false clues as insistent as cobwebs, a touch of fresh air on the cheek can make hope leap up, and unexpected scurrying whisper can induce the mood of the brink of terror. “Afterward it can be told—trivialized—like a roman policier, a detective story,” Francois Jacob once said. “While you’re there, it is the sound and the fury.” But it was the poet and adept of mysticism St. John of the Cross who gave to this passionate wrestling with bafflement the name by which, ever since, it has been known: “the dark night of the soul.” Para. 11:Enlightenment may not appear, or not in time; the mystic at least need not fear forestalling. Enlightenment may dawn in ways as varied as the individual approaches of scientists at work—and, in defiance of stereotypes, the sciences far outrun the arts in variety of personal styles and in the crucial
influence of style on the creative process.During a conversation with a co-worker-and he just as baffled-a fact quietly sifts from the insignificant background to the foreground;a trivial anomaly becomes a central piece of evidence,the entire pattern swims into focus,and at least one sees."How obvious!We knew it all along!"Or a rival may publish first but yet be wrong-and in the crashing wave of fear that he's got it right,followed and engulfed by the wave of realization that it must be wrong,the whole view of the problem skews,the tension of one's concentration twists abruptly higher,and at last one sees."Not that way, this way!” Para.12:One path to enlightenment,though,has been reported so widely,by writers and artists,by scientists,and especially by mathematicians,that it has become established as a discipline for courting inspiration.The frist stage,the reports agree,is prolonged contemplation of the problem,days of saturation in the data,weeks of incessant struggle-the torment of the unknown.The aim is to set in motion the unconscious processes of the mind,to prepare for the intuitive leap.William Lipscomb,a physical chemist at Harvard who won a Nobel Prize for finding the unexpected structures of some unusual molecules,the boranes,said recently that,for him,"The unconscious mind pieces together random impressions into a continuous story.If I really want to work on a problem,I do a good deal of the work at night-because then I worry about it as I got to sleep."The worry must be about the problem intensely and exclusively.Thought must be free of distraction or competing anxieties.Identification with the problem grows so intimate that the scientist ha the experience of the detective who begins to think like the terrorist,of the hunter who feels, as though directly,the silken ripple of the tiger's instincts.One great physical chemist was credited by his peers,who watched him awestruck,with the ability to think about chemical structures directly in quantum terms-so that if a proposed molecular model was too tightly packed he felt uncomfortable,as though his shoes pinched.Joshua Lederberg,president of the Rockefeller University,who won his Nobel for discoveries that established the genetics of microorganisms,said recently,"One needs the ability to strip to the essential attributes of some actor in a process,the ability to imagine oneself inside a biological situation; I literally had to be able to think,for example,'What would it be like if I were one of the chemical pieces in a bacterial chromosome<生>染色体？'一and to try to understand what my environment was,.try to know where I was,and so forth."Total preoccupation to the point of absent-mindedness is no eccentricity-just as the monstrous egoism and contentiousness of some scientists,like that of some artists,are the overflow of the strength and reserves of sureness they must find how they can. Para.13:Sometimes out of that saturation the answer arises,spontaneous and entire,as though of its own volition.In a famous story,Friedrich Kekule,a German chemist of the mid-nineteenth century, described how a series of discoveries came to him in the course of hypnagogic reveries-waking dreams.His account,though far from typical,is charming.Kekule was immersed in one of the most perplexing problems of his day,to find the structural basis of organic chemistry-that is,of the chemistry of compounds that contain carbon atoms.Enormous numbers of such compounds were coming to be known,but their makeup-from atoms of carbon,hydrogen,oxygen,and a few other elements-seemed to follow no rules.Kekule had dwelt on the compounds'behavior so intensely that the atoms on occasion seemed to appear to him and dance.In the dusk of a summer evening,he was going home by horse-drawn omnibus,sitting outside and alone."I fell into a reverie,and lo!The atoms were gamboling before my eyes," he later wrote."I saw how,frequently,two smaller atoms united to form a pair,how a larger one embraced to smaller ones;how still larger ones kept hold of three or even four of the smaller,whilst the whole kept whirling in a giddy dance.I saw how the larger ones formed a chain."He spent hours that night sketching the forms he had envisioned.Another time,when Kekule was nodding in his chair before the fire,the atoms
influence of style on the creative process. During a conversation with a co-worker—and he just as baffled—a fact quietly sifts from the insignificant background to the foreground; a trivial anomaly becomes a central piece of evidence, the entire pattern swims into focus, and at least one sees. “How obvious! We knew it all along!” Or a rival may publish first but yet be wrong—and in the crashing wave of fear that he’s got it right, followed and engulfed by the wave of realization that it must be wrong, the whole view of the problem skews, the tension of one’s concentration twists abruptly higher, and at last one sees. “Not that way, this way!” Para. 12:One path to enlightenment, though, has been reported so widely, by writers and artists, by scientists, and especially by mathematicians, that it has become established as a discipline for courting inspiration. The frist stage, the reports agree, is prolonged contemplation of the problem, days of saturation in the data, weeks of incessant struggle—the torment of the unknown. The aim is to set in motion the unconscious processes of the mind, to prepare for the intuitive leap. William Lipscomb, a physical chemist at Harvard who won a Nobel Prize for finding the unexpected structures of some unusual molecules, the boranes 硼烷, said recently that, for him, “The unconscious mind pieces together random impressions into a continuous story. If I really want to work on a problem, I do a good deal of the work at night—because then I worry about it as I got to sleep.” The worry must be about the problem intensely and exclusively. Thought must be free of distraction or competing anxieties. Identification with the problem grows so intimate that the scientist ha the experience of the detective who begins to think like the terrorist, of the hunter who feels, as though directly, the silken ripple of the tiger’s instincts. One great physical chemist was credited by his peers, who watched him awestruck, with the ability to think about chemical structures directly in quantum terms—so that if a proposed molecular model was too tightly packed he felt uncomfortable, as though his shoes pinched. Joshua Lederberg, president of the Rockefeller University, who won his Nobel for discoveries that established the genetics of microorganisms, said recently, “One needs the ability to strip to the essential attributes of some actor in a process, the ability to imagine oneself inside a biological situation; I literally had to be able to think, for example, ‘What would it be like if I were one of the chemical pieces in a bacterial chromosome <生>染色体?’—and to try to understand what my environment was, try to know where I was, and so forth.” Total preoccupation to the point of absent-mindedness is no eccentricity—just as the monstrous egoism and contentiousness of some scientists, like that of some artists, are the overflow of the strength and reserves of sureness they must find how they can. Para. 13:Sometimes out of that saturation the answer arises, spontaneous and entire, as though of its own volition. In a famous story, Friedrich Kekule, a German chemist of the mid-nineteenth century, described how a series of discoveries came to him in the course of hypnagogic 催眠的 reveries—waking dreams. His account, though far from typical, is charming. Kekule was immersed in one of the most perplexing problems of his day, to find the structural basis of organic chemistry—that is, of the chemistry of compounds that contain carbon atoms. Enormous numbers of such compounds were coming to be known, but their makeup—from atoms of carbon, hydrogen, oxygen, and a few other elements—seemed to follow no rules. Kekule had dwelt on the compounds’ behavior so intensely that the atoms on occasion seemed to appear to him and dance. In the dusk of a summer evening, he was going home by horse-drawn omnibus, sitting outside and alone. “I fell into a reverie, and lo! The atoms were gamboling before my eyes,” he later wrote. “I saw how, frequently, two smaller atoms united to form a pair; how a larger one embraced to smaller ones; how still larger ones kept hold of three or even four of the smaller; whilst the whole kept whirling in a giddy dance. I saw how the larger ones formed a chain.” He spent hours that night sketching the forms he had envisioned. Another time, when Kekule was nodding in his chair before the fire, the atoms
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 seemed
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 seemed