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1、精选优质文档-倾情为你奉上科技文选电子教材Unit oneAThe Known, The Unknown and The Unknowable 1. We are all taught what is known, but we rarely learn about what is not known, and we almost never learn about the unknowable. That bias can lead to misconceptions about the world around us. 2. The known is pressed on us from
2、the first. In school we start each course at the beginning of a long book full of things that are known but that we do not yet know. We understand that beyond that book lies another book and that beyond that course lies another course. The frontier of knowledge, where it finally borders on the unkno
3、wn, seems far away and irrelevant, separated from us by an apparently endless expanse of the known. We don not see that we may be proceeding down a narrow path of knowledge and that if we look slightly left or right we will be staring directly at the unknown. 3. Even when we are right on the edge of
4、 the unknown, we may not be aware of it. Those of us who learned the history of the Persian Wars in school did not know that the events so vividly described are all based on the writings of the one source who survivedHerodotus. If you want to know almost anything that happened in the Greece of that
5、time and it was not recorded by Herodotus, it is unknown and in all probability can never be known. But we did not think of his accounts as fragments of knowledge on the edge of the unknown; it was just more stuff from the huge pile of facts we had to learn about the history of Greece.4. Because of
6、such lessons, we grow up thinking more is known than actually is. If we had a better description of the limits of present knowledge, that description could be a part of what we are taught. Such insight would give us a better perspective on what is known and what is currently unknown.5. In time, many
7、 things now unknown will become known. We will learn more about what lies below the surface of the earth, and we may learn how neurons interact to let us perceive and think. The accumulating pile of data can be misleading, however. Beyond the currently unknown are the things that are inherently unkn
8、owable.6. Few unknowable are consciously recognized as such. The outcome of a spinning roulette wheel and the local weather three months from now belong to that small class. Every day, however, we bump into phenomena that may well be unknowable but that we do not recognize as such. Some of these unk
9、nowable form the bases of respected professions. Brokers make a living anticipating the fluctuations of stock prices. Presidents run for office based on claims of what they will do for a vast and poorly understood economy composed of many unpredictably interacting sectors. We do not even know if we
10、are dealing here with the partly known, the mainly unknown or the unknowable.7. Nevertheless, we unconsciously recognize that the unknowable surrounds us. Nobody thinks about or pretends to know who will run for president 20 years from now. now do people try to predict the automobile accidents they
11、will be involved in. to know that we will be struck by a car next year, we would have to know, with impossible accuracy, the particulars of the life of the driver, his habits, his timing, his way of pressing the accelerator and so forthall the facts that are needed to bring him with perfect precisio
12、n to that unpleasant encounter. It is clear that all these details are unknown, and we do not try very hard to learn about them because we instinctively realize they are also unknowable.8. In distinguishing the known or the unknown from the unknowable, the level of detail can be decisive. The level
13、of detail is what separates the delusion of the gambler from the wealth of the casino owner. The gambler attempts to predict the individual and unpredictable spins of the roulette wheel; the owner concerns himself with the quite predictable average outcome.9 The prediction process is aided by the fa
14、ct that the artificial is generally simpler than the natural. The roll of a bowling ball down an alley, for instance, is easier to predict than the motion of an irregular stone tumbling down a rough hillside. It is likely that the artificial will increasingly save us from the unpredictable. It may b
15、e easier to move gradually toward a completely enclosed earth whose climate could be artificially controlled than to learn to predict the natural weather.10 It is in creating the artificial and controllable that science excels. Science and engineering have made it possible to construct the partially
16、 artificial surroundings we live in today, replete with huge bridges trucks, airplanes, antibiotics and genetically altered species. We are likely to build an increasingly artificial, and hence increasingly knowable, world.11 Two limitations may constrain the march of predictability. First, as the a
17、rtifacts of science and engineering grow ever larger and more complex, they may themselves become unpredictable. Large pieces of software, as they are expanded and amended, can develop a degree of complexity reminiscent of natural objects, and they can and do behave in disturbing and unpredictable w
18、ays. And second, embedded within our increasingly artificial world will be large numbers of complex and thoroughly idiosyncratic humans. BThe Wests debt to China1 One of the greatest untold secrets of history is that the modern world in which we live is a unique synthesis of Chinese and Western ingr
19、edients. Possibly more than half of the basic inventions and discoveries upon which the modern world rests come from china. And yet few people know this. Why?2 The Chinese themselves are as ignorant of this fact as Westerners. From the seventeenth century onwards, the Chinese became increasingly daz
20、zled by European technological expertise, having experienced a period of amnesia regarding their own achievements. When the Chinese were shown a mechanical clock by Jesuit missionaries, they were awestruck. They had forgotten that it was they who had invented mechanical clocks in the first place!3 I
21、t is just as much a surprise for the Chinese as for Westerners to realize that modern agriculture, modern shipping, the modern oil industry, modern astronomical observatories, modern music, decimal mathematics, paper money, umbrellas, fishing reels, wheelbarrows multi-state rockets, guns, underwater
22、 mines, poison gas parachutes, hot-air balloons, manned flight, brandy, whisky the game of chess, printing, and even the essential design of the steam engine, all came from China.4 Without the importation from china of nautical and navigational improvements such as ships rudders, the compass and mul
23、tiple masts, the great European Voyages of Discovery could never have been undertaken. Columbus would not have sailed to America, and Europeans would never have established colonial empires.5 Without the importation from china of the stirrup, to enable them to stay on horseback, knights of old would
24、 never have ridden in their shining armor to aid damsels in distress; there would have been no Age of Chivalry. And without the importation from china of guns and gunpowder, the knights would not have been knocked from their horses by bullets which pierced the armor, bringing the Age of Chivalry to
25、an end.6 Without the importation from china of paper and printing, Europe would have continued for much longer to copy books by hand. Literacy would not have become so widespread.7 Johann Gutenberg did not invent movable type. It was invented in china. William Garvey did not discover the circulation
26、 of the blood in the body. It was discoveredor rather, always assumedin china. Isaac Newton was not the first to discover his First Law of Motion. It was discovered in china.8 These myths and many others are shattered by our discovery of the true Chinese origins of many of the things, all around us,
27、 which we take for granted. Some of our greatest achievements turn out to have been not achievements at all, but simple borrowings. Yet there is no reason for us to feel inferior or downcast at the realization that much of the genius of mankinds advance was Chinese rather than European. For it is ex
28、citing to realize that the East and the West are not as far apart in apirit or in fact as most of us have been led, by appearances, to believe, and that the East and the West are already combined in a synthesis so powerful and so profound that it is allpervading. Within this synthesis we live our da
29、ily lives, and from it there is no escape. The modern world is a combination of Eastern and Western ingredients which are inextricable fused. The fact that we are largely unaware of it is perhaps one of the greatest cases of historical blindness in the existence of the human race.9 Why are we ignora
30、nt of this gigantic, obvious truth? The main reason is surely that the Chinese themselves lost sight of it . if the very originators of the inventions and discoveries no longer claim them, and if even their memory of them has faded, why should their inheritors trouble to resurrect their lost claims?
31、 Until our own time, it is questionable whether many Westerners even wanted to know the truth. It is always more satisfying to the ego to think that we have reached our present position alone and unaided, that we are the proud masters of all abilities and all crafts.10 The discovery of the truth is
32、a result of incidents in the life of the distinguished scholar Dr Joseph Needham, author of the great work Science and Civilization in China. In 1937, aged 37, Needham was one of the youngest Fellows of the Royal Society and a biochemist of considerable distinction at Cambridge. He had already publi
33、shed many books, including the definitive history of embryology. One day he met and befriended some Chinese students, in particular a young woman from Nanking named Lu Gweidjen, whose father had passed on to her his unusually profound knowledge of the history of Chinese science. Needham began to hea
34、r tales of how the Chinese had been the true discoverers of this and that important thing, and at first he could not believe it. But as he looked further into it, evidence began to come to light from Chinese texts, hastily translated by his new friends for his benefit.11 Needham became obsessed with
35、 this subject, as he freely admits. Not knowing a word of Chinese, he set about learning the language. In 1942 he was sent to china for several years as scientific Counsellor to the British Embassy in Chungking. He was able to travel all over china, learn the language thoroughly, meet men of science
36、 everywhere he went, and accumulate vast quantities of priceless ancient Chinese books on science. These were flown back to Britain by the Royal Air Force and today form the basis of the finest library, outside china, on the history of Chinese science, technology and medicine, at the Needham Researc
37、h Institute in Cambridge. After the War, Needham was among those who put the s into Unesco, having persuaded that organization to concern itself with science as well as education and culture. He became Unescos first Assistant Director General for the natural sciences.12 In july 1946 Needham stated i
38、n a lecture to the china Society in London that:What is really very badly needed is a proper book on the history of science and technology in china, especially with reference to the social and economic background of Chinese life. Such a book would be by no means academic, but would have a wide beari
39、ng on the general history of thought and ideas.13 Needham, now back in Cambridge, went ahead and wroteand is still writingthe very work which he envisaged, except for the fact that it is, indeed, very academic. Few general readers embark on even one of the thirteen volumes of science and civilizatio
40、n in china so far published. It is in fact much easier to read than it looks, but of course is very expensive, and even many libraries cannot afford it. Needham, however, has never lost his early vision of a work which was by no means academic: he was always wanted to make his work more accessible i
41、n every possible way. Therefore, when I approached him in 1984 with the suggestion that I write a popular book for the general reader based upon his half-centurys labors, he agreed more readily than at that time I could understand. It is now clear that this was a project which he had long envisaged,
42、 and which he felt he could no longer hope to accomplish himself. At the age of 86, he is still fully occupied seven days a week in the task of completing his main work, aided by and army of collaborators and buoyed up by his Institute and its staff. Since I regard his as the greatest scholar of the
43、 twentieth century, I consider it an honor to be associated with him.Unit twoATopology1 Topology is the geometry of distortion. It deals with fundamental geometric properties that are unaffected when we stretch, twist or otherwise change and objects size and shape. It studies linear figures, surface
44、s or solids; anything from pretzels and knots to networks and maps. Another name for topology is analysis of position. Unlike the geometries of Euclid, Lobachevsky, Riemann and others, which measure lengths and angles and are therefore called metric, topology is a nonmetric or nonquantitative geomet
45、ry. Its propositions hold as well for objects made of rubber as for the rigid figures encountered in metric geometry.2 Topology seems a queer subject; it delves into strange implausible shapes and its proposition are either childishly obvious(that is, until you try to prove them) or so difficult and
46、 abstract that not even a topologist can explain their intuitive meaning. But topology is no queerer than the physical world as we now interpret it. A world made up entirely of erratic electrical gyrations in curved space requires a bizarre mathematics to do it justice. Euclidian geometry, despite i
47、ts familiar appearance, is a little too bizarre for this world; it is concerned with wholly fictitious objectsperfectly rigid figures and bodies which suffer no change when moved about. Topology starts from the sound premise that there are no rigid objects, that everything is the world is a little a
48、skew, and is further deformed when its position is altered. The aim is to find the elements of order in this disorder, the permanence in this impermanence.3 Mathematicians use the word transformation to describe changes of position, size or shape, and the word invariant to describe the properties un
49、affected by these changes. In ordinary geometry metric properties are said to be invariant under the transformation of motion. Motion is assumed to have no distorting effect; my pen retains its dimensions as it moves over the paper, this book neither shrinks nor expands as the reader turns its paper
50、s. In topology the problem is to find the geometric properties invariant under distorting transformations. If a triangle is stretched into a circle, which of its geometric properties are retained? Is the holeinside or outside the doughnut. How can the hole be removed? What is a knot? Can a surface b
51、e constructed which has only one side? Can a cylinder with a hole through it be squeezed into a sphere? Is it possible to make a bottle with no edges, no inside and no outside? These are examples of topological questions.4 The origins of topology go back to major discoveries made by Descartes and Eu
52、ler. Both had observed (Descartes in 1640, Euler in 1752) a fundamental relationship between the vertices, edges and faces of a simple polyhedron. Euler expressed this important geometric fact in a famous formula V-E+F=2, where V stand for vertices, E for edges, F for faces. He also solved the celeb
53、rated problem of the seven bridges in a memoir which must be regarded as one of the foundation stones of topology. Two famous problems of topology5 The Seven Bridges of Koenigsber( Leonhard Euler) The problem, which I understand is quite well known, is stated as follows: in the town Koenigsberg in P
54、russia there is an island A, called “Kneiphor”, with the two branches of the river(Pregel) flowing around it, as shown in Figure I. There are seven bridges, a, b, c, d, e, f and g, crossing the two branches. The question is whether a person can plan a walk in such a way that he will cross each of th
55、ese bridges once but not more than once.6 I was told that while some denied the possibility of doing this and others were in doubt, there were none who maintained that it was actually possible. On the basis of the above I formulated the following very general problem for myself: given any configurat
56、ion of the river and the branches into which it may divide, as well as any number of bridges, determine whether or not it is possible to cross each bridge exactly once.7 The four color problem In coloring a geographical map it is customary to give different colors to any two countries that have a po
57、tion of their boundary common. It has been found empirically that any map, no matter how many countries it contains nor how they are situated, can be so colored by using only four different colors. It is easy to see that no smaller number of colors will suffice for all cases.8 Fig 2 shows an island
58、in the sea that certainly cannot be properly colored with less than four colors, since it contains four countries, each of which touches the other three. The fact that no map has yet been found whose coloring required more than four colors suggests the following mathematical theorem: forany subdivis
59、ion of the plane into non-overlapping regions, it is always possible to mark the regions with one of the numbers 1, 2, 3, 4 in such a way that no two adjacent regions receive the same number. By adjacent regions we mean regions with a whole segment of boundary in common; two regions which meet at a single point only or at a finite number of points(such as the states of Colorado and Arizona) wi
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