“化学当作文学教（Teaching Chemistry as a Liberal Art）”，这不但要有学识、渊识、高识，还要有激情和勇气。哈佛大学教授Dudley Herschbach（Yuan Tseh Lee的博士后导师, 1986年获Nobel化学奖）给一年级大学生开普通化学，一开就是几十年；化学当作文学教，每年吸引三四百人来听课；他真教神了，哈佛大学把这称为“化学谈禅”(Chem Zen)。何谓禅，禅是中土佛教的重要组成部分，也是中国文化的重要组成部分。禅是一种灭苦的生活之道，顿悟的理想玄妙，修持的方法也玄妙，难以言传。但想了解又必须以言传。Dudley Herschbach就是这样一个人，应该说，他给自己揽了一项最大的挑战！ Teaching Chemistry as a Liberal Art Painting, Poetry, and Safaris interact to form potent concoction By Dudley Herschbach For the past 16 years I have taught general chemistry in various versions to large classes of up to 350 students, chiefly freshmen. It has been a challenging and satisfying experience. Students have nicknamed this course "Chem Zen." Perhaps naively, I like to think that endorses its key underlying theme: science as a liberal art. Although the course includes plenty of technical material, my approach emphasizes the human adventure, replete with foibles as well as feats, in exploring a fabulous molecular world. As in the course, I will try to convey aspects of this "liberal science" theme by means of some whimsical metaphors. I will also describe specific efforts to implement the theme in the major components of the course: lectures, homework problems, lab, and exams. I conclude with a plea pertaining to science literacy. Impressionistic epistemology A liberal education aims above all to instill the habit of self-generated questioning and thinking. This habit is essential for science, but too often it is not fostered in introductory courses. Any chemist can attest to the usual reaction on being introduced to someone at a social occasion. Almost always they turn pale or wince, then refer to a mystifying college or high school course. My reaction is sympathetic, since I recall my puzzlement when I first met chemistry as a high-school junior; only after many weeks did I begin to "get the hang of it." Now I think the root problem, confusing for students and teachers alike, resides not in the quirks of atoms and molecules, but simply in how we think and talk about them. My favorite way to explain this to my students invokes a metaphor: chemistry is like an impressionistic painting. If we view it from too close, all we see is bewildering detail in myriad dabs of paint. If we look from too far away, all we see is a shimmering blur. At the right distance, wondrous and lovely things appear. The metaphor emphasizes that, of necessity, chemical descriptions and concepts call on a wide variety of levels of abstraction or approximation. These differ markedly in rigor or sophistication. Until the neophyte develops the knack of picking up clues that specify the appropriate level, most everything will be out-of-focus. Even professional scientists often have the same trouble with chemistry. Physicists always want to reduce things to first principles; they tend to stand too close. Biologists usually want to resolve only the broad features; they tend to stand too far back. Either way, the chemical ideas disappear. There is much more to the painting than the paint. . . . . Empowerment by language Another apt metaphor depicts science as a language. In introductory science textbooks, the number of new or ordinary words used with special meaning is comparable to the vocabulary of a typical language text. Likewise, the array of interlocking concepts met in a science course functions much like grammatical rules. I tell my students about a study conducted by Richard Light, based on interviews with 800 Harvard seniors or freshly minted alumni. When asked what academic classes they felt had been the most valuable, most said it was a language course. Anyone who learns to read or speak a foreign language -- including science, mathematics, or music -- is empowered by gaining access to exhilarating new cultural domains. This metaphor is useful in advising students how to approach the study of science. An aspect emphasized by a language metaphor is the kinship of neophyte students with research scientists. Nature speaks to us in many tongues. They are all alien. In frontier research, the scientist is trying to discover something of the grammar and vocabulary of at least one of these dialects. To the extent the scientist succeeds, we gain the ability to decipher many messages that Nature has left for us, blithely or coyly. No matter how much effort we might devote to solve a practical problem in science or technology, failure is inevitable unless we can read the answers that Nature is willing to give us. That is why basic research is an essential and practical investment, and why its most important yield is ideas and understanding. In delivering this sermonette, I like to add that the beginning student and the veteran research scientist are very much alike in an important respect: much of the time both are quite confused! That makes many students uneasy or even distraught. However, puzzlement is welcomed by the scientist, who realizes it's usually prerequisite for any exciting new insight. The veteran researcher is also aware of a tremendous advantage enjoyed by science: the goal, call it truth or understanding, waits patiently to be discovered. That is why marvelous advances can be achieved by ordinary human talent, given sustained effort and freedom in the pursuit. . . . . Parables and paradigms Most students taking freshman chemistry have already had a high school course. Thus, they have encountered many standard topics, such as the gas laws, acids and bases, covalent bonding, etc. However, rarely do students have any notion of how such prototypical concepts emerged, how widely applicable they are, or how they affected other developments. In view of this, in my lectures I now introduce each major topic with a story, usually having the character of a parable. By presenting science in a more humanistic mode, these parables can disarm fears, reveal a much broader context for nominally familiar concepts, and even induce students to relate the tales to others. Many of the parables deal with historical episodes or current research discoveries; some are fanciful. Often the stories emphasize the role of analogy and guesswork, or show how error and failure are prevalent in science but can foster progress if "wrong in an interesting way." The introductory story for my lecture on gas laws is titled "How Aristotle and Galileo Were Stumped by the Water Pump." After illustrating how such a suction pump works, because few student have seen one nowadays, I note that Aristotle "explained" it by his famous dictum that "Nature abhors a vacuum." Then I raise the question why the pump will not lift water above a height of 34 feet. This empirical fact was known in Aristotle's day, as evident from artwork that depicts a series of pumps lifting water from a deep river gorge, with human figures providing the scale. Curiously, Aristotle said nothing about why a tall drink seems to quench Nature's abhorrence. Two thousand years later, Galileo specifically considered that question. He suggested that the pump ceases to function because a taller column of water would break of its own weight. That answer is also quite wrong; when asked for contrary examples, students quickly point to waterfalls and fire hoses. The right idea was proposed by Torricelli, one of Galileo's students. (I enjoy pointing out that some of today's students are likewise destined to solve problems that have long stumped their professors.) Galileo knew that air had weight and had devised a means of weighing it, but he did not connect this with the operation of a water pump. Torricelli realized that the weight of the air would force water to rise in the pump barrel. This concept implied that the observed limit of 34 feet represented the weight of water that the pressure of the air on the earth's surface could maintain. To test his idea, Torricelli tried an experiment. For convenience, he used mercury, a liquid about 14 times heavier than water. If he was right, the atmospheric pressure should support a column of mercury only about one-fourteenth as high as that of water, or about 30 inches. His apparatus was simply a glass tube about three feet long, with one end sealed. He filled it with mercury, then inverted the tube in a bowl of mercury open to the atmosphere. In repeating this experiment for my classes, I'm always elated to see the mercury column in the tube drop to a height of about thirty inches above the level in the bowl. From weather reports, everyone knows about variations in atmospheric pressure, but few are aware that it is still monitored by Torricelli's barometer, in essentially the same form he devised 350 years ago. I go on to demonstrate how vacuum pumps, evolved from the barometer, enabled measurements that established the gas laws. The story offers several morals. It illustrates well how a maverick idea, tested by experiment, can overthrow long-accepted doctrines. The vacuum left between the top of the mercury column and the sealed end of the glass tube refuted Aristotle's dictum. His venerable authority did not yield quietly. Many scholarly papers in Torricelli's day tried in vain to save the old view by postulating such things as invisible threads holding up the mercury. The story also shows how a new conceptual paradigm gives rise to experimental techniques that further extend its scope. Above all, it exemplifies how profound insights may lurk in seemingly mundane observations. . . . Poetry for Chemists An introductory science course too often comes across to students as a frozen body of dogma. The questions and problems seem to have only one right answer, to be found by some canonical procedure. The student who does not easily grasp the "right" way, or finds it uncongenial, is likely to become alienated. There seems to be very little scope for a personal, innovative experience. Nothing could be further from what actual frontier science is like. At the outset, nobody knows the "right" answer, often not even the right question or approach. So the focus is on asking an interesting question or casting the familiar in a new light. Concern about this syndrome led me years ago to ask my students, at two or three points in the term, to write poems about major themes or concepts: wave-particle duality, entropy, or a host of others. That is more like doing real science than the usual textbook exercises. In fact, I find that most students have never tried to write a poem before and have no idea how to go about it. That, too, is like real science, where we grope along, run into dead ends, try again, and slowly find a way. A selection of the class poems, judged best by the teaching fellows and me, is posted in the science center library. Also, I award the authors a charming little book of verse by Robert W. Wood, a pioneer molecular spectroscopist, also celebrated for his practical jokes. In 1917 he published a book entitled How To Tell the Birds from the Flowers, a collection of 50 woodcuts, each illustrating a poem. Here is a stanza from one of my favorite poems by a student, Kerry Bron, titled Quantumland: Do you know a special secret place Filling much of invisible space Where frogs can only jump so far And the range of an ordinary bike or car Can be only ten or twenty miles And every person has only half or whole smiles Where dogs bark at specific levels of pitch And people can only be a certain amount rich? Qualitative problem solving Introductory courses in physical science typically put much emphasis on solving numerical problems. Students certainly need to develop competence and confidence in solving such problems. But just as with other skillful arts, like music, dance, and sports, practice routines do not automatically produce happy results. Exercises overdone or poorly done often induce dullness or bad habits. The usual textbook problems should bear a warning label: Too much exposure to this stuff is dangerous to your mental health! Typically, the danger is manifested in three ways: 1. The plug-and-chug syndrome. Many students seek to minimize exposure. This is done by flipping rapidly through the textbook to find formulas in which to insert the data supplied in the problem. Authors and editors take great pains to make this process easy, but that is not always obvious to a hasty, drowsy student. 2 The just-the-right-data syndrome. Almost never does a patient tell a physician exactly, nothing less and nothing more, what the doctor needs to know for a diagnosis. Yet, by long-established custom, that is what is done in textbook problems. This deprives the student of the opportunity to practice two key aspects of genuine problem solving: asking "what do I need to know?" and discerning what is significant information. 3. The don't-know-how syndrome. Studies in cognitive science show that even quite able students cannot solve problems only slightly different from those they have done before, unless they have a qualitative understanding. The usual textbook problems condition students to rely on a carefully structured context, to follow a safe path to the right answer. Guessing and qualitative reasoning is thereby discouraged. Students too often do not discover how much they can figure out on their own, the most gratifying and essential lesson. The four preceding paragraphs are from my introduction to a book of problems prepared by Dan Brouch, an excellent head teaching fellow for Chem Zen. The book presents one hundred qualitative problems, spanning the whole subject matter of the course. None requires other than trivial arithmetic. Each has a plausible "real-life" or humorous setting. Some even have more than one correct answer, but the wrong ones are nonetheless instructive, as often happens in scientific research. By avoiding the usual syndromes, the book aims to help students nurture latent talent for qualitative reasoning. This is needed as well to handle so-called word problems that require understanding to set up calculations. Safari in the chem lab Too often, laboratory work in general chemistry courses has a ritualistic character. Students follow a carefully specified protocol, enshrined in a laboratory manual and interpreted or reinforced by priestlike figures garbed in white coats -- the teaching fellows. This fosters slavish imitation and timidity rather than the self-reliant, innovative, experimental spirit that is the essence of science. The approach taken in Chem Zen simply emulates the pursuit of actual frontier research in order to encourage students to be adventurous and enterprising. Nothing is done as an exercise for its own sake; rather, everything serves as preparation for projects chosen by and designed by the students. The lab manual, titled Chemistry Safari, was prepared in several successive editions by Paul Ma, another excellent head teaching fellow. The manual offers a user-friendly guide, rather than itemizing a step-by-step path. The journey is enlivened and aided by the company of Jafari, an evangelical and exuberant commentator strikingly like Paul Ma. During the early weeks of the term, students read general descriptions of six to eight feasible projects in a "Chosen Adventure" section at the back of the manual. Literature references allow them to track down pertinent background. Each student selects a general project and starts developing a personal version. In each of the first seven weeks, students carry out a training project acquainting them with basic techniques in a different area of chemistry. These require working out designs in a "Jungle Bootcamp" portion of the manual. The last four weeks of the term are devoted to executing the chosen adventure. A report in the style and format of research article is required. It is submitted, reviewed by teaching fellows, and accepted, rejected, or returned for revision and resubmission in the same way articles are handled by science journals. In recent years, several of the best reports have been published in a Journal of Undergraduate Sciences launched by Paul Ma and alumni/ae of Chem Zen. Exams and grades Student attitudes and morale naturally are greatly influenced by exam and grading policies. Chem Zen has two distinctive precepts: (1) no competition among students is allowed and (2) no points can be "lost" on hour exams. To implement the first, we simply use an absolute grading scale, defining at the outset how many points from exams, homework, and labs are needed to reach each grade level. This enables us to encourage students to help each other and to assign some homework and quizzes as team problems, again emulating how most real science is done. In principle, everyone can get an A, in contrast to the customary, mindless grading on the curve, which guarantees disappointing a fair fraction of the class. I call the second a "resurrection" policy. Any points a student fails to earn on an hour exam are added to the corresponding section of that student's final exam, so the student gets a second shot at earning those points. This reduces anxiety about a subpar performance on an hour exam and helps students to view the exams as trial runs indicating what to focus on most diligently in preparing for the final. By extension, this policy also offers a paradigm for later life. Science literacy A liberal arts education must aim to integrate science into our general culture. Many admirable efforts have been made, but at present science literacy, by any sensible definition, remains remarkably low even among college graduates. It seems to me unlikely that much will be accomplished if we continue to confine science to separate courses. Even a "physics for poets" course reinforces the prevalent view that science belongs solely to its professionals. My experience with Chem Zen, reinforced by conversations with many students who have avoided science, convinces me that it would be feasible and worthwhile to include scientific parables in many other subjects: history, economics, even literature. This is affirmed by students in such fields, not in my course, who attend lectures or come to office hours in order to pursue a parable they have heard about. I urge science teachers to become unabashedly evangelical by suggesting suitable parables to receptive faculty colleagues. Liberal science can foster an educational alchemy that seeks to make the whole greatly exceed the sum of its parts. Dudley Herschbach, Frank B. Baird Jr. Professor of Science, received the Nobel Prize in Chemistry in 1986. This piece is excerpted with permission from Liberal Education, Volume 82, No. 4. Copyright is held by the Association of American Colleges and Universities.
数学史家 Eves 搜罗了一些文学作品里的“数学描述”，挺有意思—— @ “总之，女人是个问题，自打布鲁克先生对它无可奈何，它几乎比不规则固体的旋转还要复杂。”（ George Eliot, Middlemarch ） @ “在乳白色粉墙的另一边，木工店的圆锯唧唧呀呀响不停，在尖利而可怕的啸声中锯下一块块木头。他解决了十道三角题。他解开缠绕在头脑里的结，把它们从联系平面几何与立体几何的长长问题中一个个分离出来，得到答案。” ( John Updike ， Pigeon Feathers ) @ “他内心的恐惧经过那场严峻的考验已经孤立了，现在却无言能表达孤立与伙伴之间的深渊。也许可以向数学家承认二加二等于四，但二不等于一加一；二是一的两千倍。就因为这一点，纵然有千般不好，世界最终还是要回到一夫一妻制。”（ Gilbert Keith Chesterton, The Man Who Was Thursday ） @ 他的脸有点儿方，他的下巴也是方的，他的肩膀还是方的，就连他的外套都是方的。实际上，在当时流行的野派漫画里，比尔博姆（ Max Beerbohm ）先生就把自己画成欧几里得《原本》第四卷的一个命题。（ Chesterton, The Wisdom of Father Brown ）【欧几里得《原本》第四卷命题 6 ， 7 ， 8 ， 9 都是关于正方形作图的。】 @ “他知道有一个联系时间和距离的数学公式。还没人为两者之比给一个名称或符号，而时间与罪行的关系也是错综复杂的。距离一个案件写进书里的时间越久，正义的力量也就显得越小，二者是成反比的。”（ Catherine Aird, Harm’s Way ） @ “我想你是在回避这个问题，”海多克说，“而我可以隐约看见那是一个可怕的概率练习：六个人戴白帽子，六个人戴黑帽子，你得靠数学来回答，这些帽子有多大可能混淆起来，比例是多少。如果你开始考虑这样的事情，你也就要疯了。还是让我来替你算吧！” (Agatha Christie, The Mirror Crack’d )
“右旋星系之战只是加速了干戈，战争从没有停止过，只是形势变得更复杂了。宇宙多国互相牵制，形成脆弱的春秋和平，一旦平衡被打破，宇宙的结局不亚于一场宇宙大爆炸，后果不堪设想。伟大的时代呼唤着天马行空般的人物，你赶快从第一时空的红尘噩梦中醒醒吧！” 我感到我看到妖星美女的眼睛，她刚好往我瞧来，眼神相触，我顿时心生异样的感觉。她的眼神再不是冷冰冰的，而是暗藏悲哀和无奈，虽淡而不浓，却令我感到深沉的复杂。在这一刻，我心中激荡着一种强烈的怀念情绪，周围光线箭一般流逝，好像又记起将来的过去故事，我们在梦幻河边嬉笑的时光， 100 个太阳的巨大光团 。 眼前又是一片金色的混沌，出现的星空变得透亮，整个星空的温度正在陡然上升，越来越热，不知哪来的宇宙热风把我吹得像离线的风筝。 天空变得像开始燃烧着的大幕，巨大的光轮从大幕的后面冒了出来，它的光芒把天空中的群星都赶走了。 我猛然意识到，这是妖星外部时空对内部时空的影响，显然妖星的外面就是正时空，人类赖以生存的时空，燃烧的巨大光轮来自太阳，妖星已经十分接近这颗统领太阳系的炙热恒星了。 “风筝飘啊飘，一直飘到时空口，永恒寻机缘，剑气爱恨愁。” 宇宙热风转急，天旋地转，只觉得，头部一阵昏眩，眼前电光转瞬，接着是云梯连绵，似彩虹桥，桥的尽头就是进来时的入口。 我几乎是毫无意识地走出了那个“时空口”， 思感里还不可遏止地定格在一组组画面上： “星宇渺渺，时光遥遥，山川更替，星系顿逍，聚之成形，散之为息，息中有气，道中奥妙。” 唉，妖星美女，你到底是什么？我陷于无尽的迷茫。 “正负相随，永恒主旋，无垠泪洒，满天星光，绚丽星系，穿梭逍遥 …” 仍然是单调而又夺人心神音频序列信号： “ 轰 --- 哈 --- 轰 --- 哈 ---” 。 "Right-hand Galaxy battle only accelerated war, war never stops, but the situation becomes more complicated. The nations contain each other, forming a vulnerable age of peace, once the balance is broken, the outcome is no less than a big bang, and consequences are unbearable to contemplate. Great period calls with a powerful and unconstrained style figure; please wake up quickly from the nightmares in first time-space!" I feel I see MS girl's eyes, she is just looking me, eyes touch, I suddenly have a strange feeling. Her eyes are no longer cold, but hidden sadness and resignation, though weak and not strong, but make me feel a deep complex. At this moment, my heart arise a kind of intense emotion of Miss arrow, ambient light passes, as of future past story, our playful times in the dream River, a great light group of 100 suns. The present is a golden chaos, the sky become bright, the sky temperature is steep rise, more and hotter, and I do not know where the wind blows me as a kite off line. The sky became like started burning curtain, great glory from the big screen back out, it drives the light of the stars in the sky away. I suddenly realize, this is outside time-space to affect internal time-space of MS, obviously the outside is a positive time-space, the survival of the human space-time, burning the immense light comes from the sun, MS is very close to this hot star leading the solar system. "Kite is floating and floating, until the entrance of time-space, forever seeking opportunities, sword with love hate and worry." The hot air to rush, dizzy, I feel a fit of dizziness, as eyes see flashing and lightning, then a ladder is continuous, like a rainbow bridge, the end of the bridge is the entrance. I was almost unconsciously walked out of the entrance, think feeling also unstoppable fixed on a group of pictures: "Universe is grand, time is long, landscape is turnover, Galaxy is destroyed, together forming, scattered as information, and information contain qi, which is secret in Tao." Alas, MS beauty, what hell are you? I caught in endless confusion. “The positive with negative, eternal main tune, past endless tears, through star light full sky, tunneling brilliant galaxies, the shuttle is happy ..." Still is a monotonous and audio sequence signal which seizes personal mind: "Hong - Ha –Hong- Ha".
然后我的指挥舰屏幕上出现了她，妖星美女！ 她的目光似深邃的宇宙，异能奇迹出现了， 100 个太阳像被一种不可思议的能量联成一个巨大的右旋光团，然后飞了过来。 轰隆！ 100 个太阳爆炸了，七色能量风暴狂击着百亿 艘智能生物的飞船组成的 巨大长矛，引发起连锁式的超新星似的能量激爆，整个光爆外层的热度攀上太阳内核般的高温，长矛右旋扭曲变形，没有一个分子是稳定的，解体和分裂时刻在发生。 我的思感能几乎瘫痪了，整个时空似乎也在右旋，巨大的右旋漩涡不知把军团带入哪种可怕的状态。 仅有一点思感余能还在全力硬挺著，长矛一层一层的剥落融解，化为粒子残屑，然而太阳光团的右旋的力量还在增加，只剩下四分之一厚度的长矛外壳能量分子陡然彩芒剧盛，就像要熄灭前的灿烂，尽管所有人都藏身于飞舰各自的保护层内，但是巨大辐射穿透而来还是令我们处于 地狱 的边缘 …… 不，这是可怕的故事，这是可怕的右旋时空，我一定在梦中！我睁大眼睛死命的朝巨大的光团撞去。 瞬时周围的光线箭一般地飞逝，前面就像时空隧道，隧道的尽头就是巨大的星空一跃而出。 没有了十三光球，没有了大厅，没有了 满氮气的蓝天、浩瀚无涯的海洋、树木参天的森林，还有那浅红色的巨月， 周围是无穷的星空，繁星点点。 我猛然惊醒过来，已泪流满面，我这是怎么啦？刚才的经历仅仅是时空幻象？ “时空也是一种信息，信息也可外化为时空。基础的时空是 16 重，你刚才经历的是第 9 时空，空间特性：右旋，时间特性：将来时倒流加局部顺流，空间表示：三阳一阴卦。” 啊，妖星美女，一切的幻象是由她控制的。但愿那将来的过去故事是虚幻的，绝不发生，我好像从死亡返回般似的，严重忐忑不安地想道。 Then she appears on the screen in my command ship, MS beautiful girl! Her eyes like the profound universe, miracle energy appeared, 100 suns are connected as a huge right rotation light group by an unbelievable energy, and then fly over distance to come. Rumble! 100 sun exploded, seven-color energy storm swipes with tens of billions of intelligent spacecraft consisting of giant lance, cause a chain type supernova like energy excitation detonation, the smooth blasting of outer heat climbed as high temperature solar core, a right-hand twist deformation, no one molecule is stable, disintegration and split are creating. My thinking wave is almost paralyzed, the whole time-space also appears to rotate rightly, and the huge right whirlpool brings the Legion to which terrible unknown state. Only a little more thinking wave energy still fight hard, a layer of spear peeling melt, as the particle debris, however the sun light group of dextral strength increasing, only 1/4 of the thickness of the lance outer shell energy molecular suddenly color bright wave strongly, like to put out before the bright, although all hide their ship protective shell, but the great penetrating radiation still make us at the edge of the hell... No, this is a terrible story, this is terrible right rotation space and time, I must be dreaming! I stare desperately at the giant light group to hit. Instantaneous light around an arrow flies, the front like a time-space tunnel, at the end of the tunnel is a huge star space leap out. No thirteen balls, not the hall, without full nitrogen blue sky, vast boundless ocean, towering trees of the forest, and the red giant moons, there is surrounded by endless starry space with numerous stars. I suddenly woke up, has been in tears, how I am? Experience is only time and space illusion? "Time-space is a kind of information; information can also be transformed into time and space. Basic time-space is 16; you have just gone through ninth time-space, in which the space characteristics is right rotation, the time characteristics is the future back plus local downstream, the spatial representation is three positive adding one negative divinatory symbols." Ah, the MS evil beauty, all illusions are controlled by her. I hope that the future past story is fictional, will never happen; I seem to return from death like, seriously be very upset.
标签: 文学
