The World within the World - A rewarding journey to the limits of space and time -	Cat: SCI Pub: 1988 #1622b
	John D. Barrow	16y21u/18227r

Title	The World within the World	世界の中の世界
Index	Preface: Prologue: Time past: Unseen worlds: Inner space and outer space: Why are the laws of Nature mathematical?: Are there any laws of Nature?: Selection effects:	序: 緒論: 過ぎ去った時間: 見えない世界: 内側の空間と外側の空間: 自然の法はなぜ数学的なのか: 自然の法はあるのか: 観測選択効果:

Original resume

Remarks

>Top 0. Preface: This book is to pick up the traditional unspoken assumptions to which we owe all these abstract and pragmatic developments: that the Universe is ordered, that it is logical, that it is mathematical, that it is predictable, that it is governed by something outside ourselves which is the same everywhere and everywhen, but which has a deep resonance with the workings of our own minds; to explore something of the origin and possible meanings of the idea that there exist 'laws of Nature' and some of the unsuspected realms that such an idea had led us. It has become fashionable to believe that the laws of Nature are both necessary and sufficient to explain what we see in the Universe and that hence some grand 'theory of everything' will provide us with the answers to all our cosmological questions.

0. 序: everywhen: of all times, past and present collectively; resonance: the reinforcement or prolongation of sound by reflection from a surface or by the synchronous vibration of a neighbouring object; 回响 huíxiǎng anticipate: regard as probable; expect or predict; 预见 yùjiàn

>Top 1. Prologue: Thomas Melville: O nature, and O soul of Man! how far beyond all utterance are your linked analogies! not the smallest atom stirs or lives in matter, but has its cunning duplicate in mind. Heinrich Hertz: The urge to predict and control: The most direct, and in a sense the most important, problem which our conscious knowledge of Nature should enable us to solve is the anticipation of future events. Nicholas Rashevsky: The paradox of predictability Given a written language, how large in terms of the total number of words must a book printed in that language be in order to contain complete information to manufacture the book? Our ability to predict successfully appears to demonstrate that there is an aspect of Nature that lies outside our control; a part that is external to human influence. Karl Poper: The external world If the physical laws of this world are autonomous, we are not free; if we are free, then the physical laws are not autonomous. Cicero: Pros and cons There is nothing so absurd that it has not been said by philosophers. Shakespeare: Labels What's in a name? that which we call a rose. By any other name would smell as sweet. Gerald Holton: Accidental, legal, and statistical laws: Being built on concepts, hypotheses, and experiments, laws are no more accurate or trustworthy than the wording of the definitions and the accuracy and extent of the supporting experiments.

1. 緒論: utterance: a spoken word, statement, or vocal sound; 言论 yánlùn cunning: having or showing skill in achieving one's ends by deceit or evasion; 狡猾的 jiǎohuá de

>Top 2. Time past Samuel Butler: IT ha been said that though God cannot alter the past, historians can; it is perhaps because they can be useful to him in this respect that He tolerates their existence. At first, like the beasts, primitive Man could learn only the hard way, by the consequences of experience. Gradually, as he noticed daily and seasonal regularities, he was able to recognize those appearances which seem always to follow from others. He discovered that events do not all arise in an unconnected and arbitrary manner, but exhibit a degree of predictability that could be exploited for advantage. Joseph Neddham; Chinese science There is no confidence taht the code of Natures's laws could ever be unveiled and read, because there was no assurance that a divine being, even more rational than ourselves, had ever formulated such a code capable of being read. A.N. Whitehead: The Greeks The real importance of the Greeks for the progress of the world is that they discovered the almost incredible secret that the speculative Reason was itself subject to orderly methods. Marcel Proust: Plato Beauty is a sequence of hypotheses which ugliness cut short when it bars the way that we could already see opening into the unknown. Aristotle: We are all inclined to direct our inquiry not by the matter itself, but by the views of our opponents; and, even when interrogating oneself, one pushes the inquirely only to the point at which one can no longer find objections. Aristotle: Laws of motion A give weight moves a given distance in a given time; a weight which is heavier moves the same distance in less time, the time being inversely proportional to the weights. Voltaire: The Aristotelian legacy: It would be very singular that all Nature, all the planets, should obey eternal laws, and that there should be a little animal, five feet high, who, in contempt of these laws, could act as he pleased, solely according to his caprice. Voltailre: Newtonianism Very few people read Newton, because it is necessary to be learned to understand him. But everybody talks about him. Ludwig Wittgenstein: The rationality of the world The fact that we can describe the motions of the world using Newtonian mechanics tell us nothing about the world. The fact that we do, doe tell us something about the world. R.A. Fisher: Darwinian laws: Natural selection is a mechanism for generating an exceedingly high degree of improbability. a

2. 過ぎ去った時間: beauty: a combination of qualities, such as shape, colour, or form, that pleases the aesthetic senses, especially the sight hypothesis: a supposition or proposed explanation made on the basis of limited evidence as a starting point for further investigation; 假设 jiǎshè ugliness: the quality of being unpleasant or repulsive in appearance; 丑陋 chǒulòu   caprice: a sudden and unaccountable change of mood or behaviour; 变化无常 biànhuà contempt: the offence of being disobedient to or disrespectful of a court of law and its officers:

>Top 3. Unseen worlds: Paul Dirac: I has become increasingly evident, however, that Nature works on a different plan. Her fundamental laws do not govern the world as it appears in our picture in any direct way, but instead they control a substratum of which we cannot form a mental picture without introducing irrelevancies. Heinrich Hertz: Mechanism without a mechanism: Scientific concepts are inner pictures. Albert Einstein: Force fields According to Newton's system, physical reality is characterized by the concepts of space, time, materia point and force ... After Maxwell they conceived physical reality as represented by continuous fields, not mechanically explicable, which are subject to partial differential equations. this change in the conception of reality is the most profound and fruitful one that has come to physics since Newton. Isaac Newton: Preface to Principia: I wish we could derive the rest of the phenomena of nature by the same kind of reasoning from mechanical principles; for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some cause hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other. James Clerk Maxwell: Electricity and magnetism: Faraday, in his mind's eye, saw lines of force traversing all space, where the mathematicians saw centers of force attracting at a distance; Faraday saw a medium where they saw nothing but distance; Faraday sought the seat of the phenomena in real actions going on in the medium, they were satisfied that they had found it in a power of action at a distance impressed on the electric fluids. Humphrey Davy: 'What am I to do? Here's a letter from a young man named Faraday; he has been attending y lectures and wants me to give him employment at the Royal Institution - what can I do?' (Do? Put him to work washing bottles; if he is good for anything he will do it directly, of not, he will refuse.' 'No, no we must try him with something better than that.' Faraday was appointed in 1813 as a laboratory assistant to Davy, working for a menial wage. The true nature of this interrelationship was laid bare in 1865 when the young Scot, Japes Clerk Maxwell, produced a system of four equations which encapsulated the symbiotic relationship of the electric and magnetic fields, and successfully predicted new phenomena. to a considerable extent our modern technological society rest upon what these equations tell us about the intertwined behaviour of electricity and magnetism. Henceforth they would be known as different manifestations of a single entity; the electromagnetic field. Heinrich Hertz: The end of visualization?: Maxwell's theory consists of Maxwell's equations. Michel Faraday: The Sandemanian world-view: There is no philosophy in my religion. Joseph J. Thomson: Mathematical modelling: There is a school of mathematical physicists which objects to the introduction of ideas which do not relate to things which can actually be observed and measured ... I hold that if the introduction of a quantity promotes clearness of thought, then even if at the moment we have no means of determining it with precision, its introduction is not only legitimate but desirable. The immeasurable of today may be the measurable of tomorrow. René Descartes: analogical relations with other areas of science as a necessary condition for a particular explanation to be admissible: I claim that analogies are the most appropriate way available to the human mind for explaining the truth about questions in physics; to such an extent that, if one assumes something about nature which cannot be explained by any analogy, I think that I have conclusively shown that it is false. Albert Einstein: Space and time intertwine: There is a paradox upon which I had already hit at the age of 16. If I pursue a beam of light ... I should observe such a beam of light as a spatially oscillatory electromagnetic field at rest. However, there seems to be no such thing, whether on the basis of experience or according to Maxwell's equations. The speed of light in vacuum will be found the same by any two observers in uniform relative motion. Newtonian mechanics turned out to be but the slow-motion approximation to special relativity. We have also lost the notion of a universal concept of space and time that is independent of the observer. Instead, each observer determines the nature of those entities relative to the determined by other observers in motion relative to him. the special relativity principles also signal a trend for laws of Nature to be framed in terms of prohibitions on what is possible, rather than direct statements of the effects of certain causes. The principles of special relativity are statements of invariances in Nature. Samuel McChord Crothers: Symmetry: The trouble with facts is that there are so many of them. Erwin Schrödinger: The laws of chance: Research in physics has shown beyond the shadow of a doubt that in the overwhelming majority of phenomena whose regularity and invariability have led to the formulation of the postulate of causality, the common element underlying the consistency observed is chance. A. S. Eddington: Thermodynamics: The law that entropy increase hold the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse fro Maxwell's equations. If it is found to be contradicted by observation - well, these experimentalists do bungle things sometimes. But if your theory is found to be against the Second Law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. The total energy in a closed system cannot be changed Load Kelvin: Untidy desks: If the motion of every particle of matter in the universe were precisely reversed at any instant, the course of nature would be simply reversed for ever after. the bursting bubble of foam at the foot of a waterfall would reunite and descend into the water; the thermal motions would reconcentrate their energy, and throw the mass up the fall in drops reforming in a close column of ascending water ... living creatures would grow backwards, with conscious knowledge of the future, but no memory of the past, and would become again unborn. Maxwell's Demon: For we have seen that the molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected is almost exactly uniform. Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the slower ones to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics. G.B. Shaw: Demons at work: The Devil can quote Shakespeare for his own purpose. Henri Poincaré: The eternal return To see heat pass from a cold body to a warm one, it will not be necessary to have the acute vision, the intelligence, and the dexterity of Maxwell's demon; it will suffice to have a little patience. The Poincaré recurrence time for a system is fantastically large - $10^{10^{80}}$ - compared with 4-18 billion years for the oldest objects we have found in the Universe. Richard Feynman: Nature East of Eden: Only 12 men understood the theory of relativity. There might have been a time when only on man did, because he was the only guy who caught on, before he wrote his paper. But after people read the paper a lot of people understood the theory of relativity in some way or other, certainly more than twelve. On the other hand, I think I can safely say that nobody understands quantum mechanics. G.K. Chesterton; Schizophrenic matter: The poet only asks to get this head into the heaven. It is the logician who seeks to get the heavens into his head. And it is his head that splits. Banesh Hoffmann: Intrinsi uncertainty: The physicists could but make the best of it, and went around with woebegone faces sadly complaining that on Mondays, Wednesdays and Fridays they must look on light as a wave; on Tuesdays, Thursdays and Saturdays, as a particle. On Sundays they simply prayed. Bertrand Russell: The nature of quantum reality: Naïve realism leads to physics, and physics, if true, shows that naïve realism is false. Therefore naïve realism, it true, is false; there it is false. Montaigne: Quantum ailurophobia: When I play with my cat, who knows whether she is not amusing herself with me more than I with her? Paul Dirac: How many worlds do we need? I think that it is quite likely that at some future time we may get an improved quantum mechanics in which there will be a return to determinism and which will therefore justify the Einstein view. But such a return to determinism could only be mad at the expense of giving up some other basic idea which we now assume without question. F. J. Belinfante: The quantum legislature: If I get the impression that Nature itself makes the decisive choice what possibility to realize, where quantum theory says that more than one outcome is possible, then I am ascribing personality to Nature, that is to something that is always everywhere. Omnipresent eternal personality which is omnipotent in taking the decisions that are left undermined by physical law is exactly that in the language of religion is called God.

3. 見えない世界: selection effect: Selection bias is the selection of individuals, groups or data for analysis in such a way that proper randomization is not achieved, thereby ensuring that the sample obtained is not representative of the population intended to be analyzed. substratum: an underlying layer or substance; 底层 dǐcéng; 基層･下層     explicable: able to be accounted for or understood; 可解释的 kě jiěshì de; 説明可能   impel: drive, force, or urge to do something; drive forward, propel; 驱使 qūshǐ; 駆り立てる     impress: apply an electric curet from an external source; the total impressed voltage; 铭记 míngjì; 感動させる   menia: not requiring much skill; 技术含量低的 jìshù hánliàng dī de; 単純労働     intertwine: twist or twine together; 使缠绕在一起 shǐ chánrào zài yīqǐ; 絡み合う         legitimate: able to be defended with logic or justification, valid; 合理的 hélǐ de; 道理に合った     admissible: acceptable or valid;可进入的 kě jìnrù de; 正当な･資格がある; conclusively: in a decisive way that has the effect of proving a case; in a way that is achieved easily;不容置疑地 bù róng zhìyí de; 最終的に paradox: a statement that is seemingly contradictory or opposed to common sense and yet is perhaps true; 悖论 bèilùn; 逆説 postulate: a thing suggested or assumed as true as the basis for reasoning, discussion, or belief.; assumption used as a basis for mathematical reasoning; 假设 jiǎshè; 仮定 causality: relationship between cause and effect; 因果性 yīnguǒxìng bungle: carry out a task clumsily or incompetently; 失策; 失误 shīwù untidy: not arranged neatly and in order, messy; 凌乱的 língluàn de   demon: 恶魔 èmó         dexterity: skill in performing tasks, with hands; 灵巧 língqiǎo 灵(靈) suffice: be enough or adequate; 足够 zúgòu; 十分である   schizophrenia: mental disorder, a long-term mental disorder of a type involving a breakdown in the relation between thought, emotion, and behaviour.   woebegone: sad or miserable in appearance; 悲伤的 bēishāng de; 悲嘆 ailurophobia: extreme or irrational fear of cats   determinism: the doctrine that all events, including human action, are ultimately determined by causes regarded as external to the will; 决定论 juédìnglùn; 決定論 undermine: lessen the effectiveness, power, or ability of, especially gradually or insidiously; 侵蚀 qīnshí; 蝕む

>Top 4. Inner space and outer space: Rudolf Carnap: Setting the scene: Physics originally began as a descriptive macrophysics, containing an enormous number of empirical laws with no apparent connections In the beginning of a science, scientists may be very proud to have discovered hundreds of laws. But, as the laws proliferate, they become unhappy with this state of affairs; they begin to search fro underlying principles. Niels Bohr: Dissecting the atom: We now know, it is true, that the often expressed skepticism with regard to the reality of atoms was exaggerated; for, indeed, the wonderful development of the art of experimentation has enables us to study the effects of individual atoms. Benjamin Lee Whorf: Brave new world: An explicit scientific world view may arise by a higher specialization of the same basic grammatical patterns that fathered the naïve and implicit view. Thus the world view of modern science arises by higher specialization of the basic. Albert Michelson (in 1894): No conceivable thing left to be invented: The more important fundamental laws and facts of physical science have all been discovered, and these are now s firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote ... Our future discoveries must be looked for in the sixth place of decimals. Jonathan Swift: Incestuous matter? So, Naturalists observe, a Flea hath smaller Fleas that on him prey, and these have smaller Fleas to bite 'em and so proceed ad infinitum. Steven Weinberg: Quantum fields: The laws of Nature give a fundamental role to certain entities. We are not really sure what they are, but at the present level of understanding they seem to be the elementary quantum fields. Karl Popper: The fundamental legislation of inner space: I am inclined to think that scientific discovery is impossible without faith in ideas which are of a purely speculative kind and sometimes quite hazy; a faith which is quite unwarranted from the scientific point of view. Modern prejudices and expectations: Are there simple principles which dictate what forces and particles exist in Nature and how they interact with one another? Is there a single unified law of Nature; a 'theory of everything'? Why do the forces of Nature have the strengths they do? What at the ultimate constituents of matter - the most elementary of elementary particles? What are the ultimate principles which we should employ to discern laws of Nature? Freeman Dyson: Unification Physics is littered with the corpses of dead unified field theories. Inner space and outer space: A New Dimension (D): What determines the total number of dimensions of space? What are three of them large and observable by us, while all the others remain curled-up to an infinitesimal extent? Albert Einstein: A new dimension The idea of achieving a unified field theory by means of a 5D cylinder world never dawned on me ... I like your idea enormously. A. S. Eddington: Why are there 3D of space? In 2D any two lines are almost bound to meed sooner or later; but in 3D, and still more in 4D, two lines can and usually do miss one another altogether, and the observation that they do meet is a genuine addition to knowledge. Oscar Mandel: The inner space credo: No, no! You have merely painted what is! Anyone can paint what is; the real secret is to paint what isn't! Pierre Laplace: The goals of theory: If the present state of the universe was exactly similar to the anterior state which has produced it, it would give birth in its turn to a similar state: the success of these states would then be eternal. Herman Bondi: The legacy of the steady statesmen: We have already learnt that geography does not matter. The steady state theory teaches us that history does not matter either. Immanuel Kant: Chaotic cosmology: God has put a secret art into the forces of Nature so as to enable it to fashion itself out of chaos into a perfect world system. David Everett: Large streams from little fountains flow, tall oaks from little acorns grow. Antoine de Saint-Exupéry: The inflationary paradigm: Truth is not that which is demonstrable, but that which is ineluctable. Arthur Bloc: The future: The universe is simmering down, like a giant stew left to cook for 4B years. Sooner or later we won't be able to tell the carrots from the onions.

4. 内側の空間と外側の空間: empirical: based on, concerned with, or verifiable by observation or experience rather than theory or pure logic; 以经验为依据的 yǐ jīngyàn wéi yījù de; 経験に基づいた dissect: methodically cut up (a body or plant) in order to study its internal parts; 解剖 jiěpōu experimentation: the process of performing a scientific procedure, especially in a laboratory, to determine something; 实验 shíyàn brave: endure or face (unpleasant conditions or behaviour) without showing fear incestuous: excessively close and resistant to outside influence     speculative: engaged in, expressing, or based on conjecture rather than knowledge; 推测的 tuīcè de conjecture: an opinion or conclusion formed on the basis of incomplete information; 推测 tuīcè unwarranted: not justified or authorized; 不合理的 bù hélǐ de   constituent: being a part of a whole; 成分 chéngfèn discern: distinguish (someone or something) with difficulty by sight or with the other senses; 分辨出 fēnbiàn chū   Inner space and outer space:       dimension: a measureable extent of a particular kind, such as length, breadth, depth, or height.; a mode of linear extension which corresponds to one of a set of coordinates specifying the position of a point; (二)维 (èr)wé     ineluctable: unable to be resisted or avoided; inescapable; 不可避免的 bù kě bìmiǎn de simmer: (of water or food) stay just below boiling point while bubbling gently; 煨炖 wēidùn; とろ火で煮る

>Top 5. Why are the laws of Nature mathematical? Galileo Galilei: A puzzle: Philosophy is written in that great book which ever lies before our eyes, I mean the universe, but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. this book is written in the mathematical language, and the symbols are triangles, circles, and other geometrical figures, without whose help it is humanly impossible to comprehend a singe word of it. Johann Wolfgang von Gothe: What is mathematics? Mathematicians are a species of Frenchman: if you say something to them they translate it into their own language and presto! it is something entirely different. What is mathematics? Whereas science is like a long text that is constantly being redrafted, updated, and edited, mathematics is entirely cumulative. Contemporary science is going to be proven wrong but mathematics is not. The mechanics of Aristotle is wrong, but the geometry of Euclid is, was, and always will be correct. Right and wrong mean different things in science and mathematics. In the former, right means correspondence with reality; in mathematics it means logical consistency. Conceptualism: complete antithesis of Platonism, and is popular with sociologists rather than mathematicians and scientists. It maintains that we create an array of mathematical structures, symmetries, and patterns, and then force the world into this mould because we find it so compelling. Ultimately, the choice of what mathematics we construct is culturally derived. We invent mathematics, we do not discover it. Mathematics is entirely a product of the human mind. Conceptualists would not expect to be able to communicate with the Andromedans by using our mathematical concepts. Formalism: Logicians had uncovered a number of embarrassing logical paradoxes. John Conway's board game 'Life', but which cannot be reached from some starting state in a finite number of moves. These logical entities arouse as a consequence of properties of infinite collections of objects. Intuitionism: Infinite sets share the obvious properties possessed by finite ones, it was proposed that only quantities that can be constructed from the natural numbers 1,2,3, ... in a finite number of logical steps should be regarded as proven true. Intuitionism reflects the idea that only the simplest intuitive ideas could be used. Anything outside our experience must be constructed from the simplest ingredients by a sequence of intuitively familiar steps. Whenever you tell me that mathematics is just a human invention like the game of chess ....But why does the mathematics we have discovered in the past so often turn out to describe the workings of the Universe? Surely this cannot be an accident? André Weil: A shock for the formalists: God exists since mathematics is consistent, and the Devil exists since we cannot prove it. Albert Einstein: Consequences for physical science: As far as the laws of mathematics refer to reality they are not certain; and as far as they are certain, they do not refer to reality. Mathematical (or logical) system: Some formula, call it F, in terms of the symbols defined in the system, then one of four things can be true of F: F can be proved true in the system. F can be proved false in the system. F can be proved both true and false in the system. F can be proved neither true nor false in the system. The options (1) and (2) are obvious possibilities. The result (3) would show our logical system to be inconsistent; if (3) holds, then that system is meaningless because it can be used to show that any statement made in the language of the system is true. The possibility (4), that the system is incomplete; This situation that Kurt Gödel established could occur in mathematical systems. Adding new axioms to an incomplete system never cures the problem. While this may allow previously undecidable statements to be decided (just add them as new axioms for example), it always generates some new undecidable propositions. The story of Bertrand Russell being asked by McTaggart to show 'If twice 2 is 5, how can you show that I am the Pope?' Russel replied at once: If twice 2 is t, then 4 is 5, subtract 3; then 1=2. But McTaggart and the Pope are 2; therefore McTaggart and the Pope are one!' Or, alternatively find the flaw in the following proof that every statement must be either consistent or inconsistent; therefore either they all are or at least one is not. In the latter case the system must be consistent with any statement at all, including the one that it is consistent! Logical contradiction Barber Paradox by Bertrand Russell: A barber shaves all those individuals who do not shave themselves. Who shaves the barber. Paradox of Epimenides. All Cretans are liars. One of their own poets has said so. Tomaso Toffoli; Computability: Computation - whether by man or by machine - is a physical activity. If we want to computer more, faster better, more efficiently, and more intelligently, we will have to learn more about nature. In a sense nature has been continually computing the next state of the universe for billions of years; all we have to do, actually all we can do is hitch a ride on this huge ongoing computation, and try to discover which parts of it happen to go near to where we want. Stephen Wolfram: Inherently difficult problems: Many physical systems are computationally irreducible, so that their own evolution is effectively the most efficient procedure for determining their future. It may be disappointing to learn that there are problems which computers cannot solve, so let us return to those which they can. There may exist functions which are uncomputable when all possible inputs are considered, but perfectly computable for some particular sub-collection of inputs which are of interest in practice. Bertrand Russell: Equations: Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover. Differential equations: To solve the differential equation means to find an expression which tells us what all the future states ensuing from any starting state could be, and when and where thy will arise. The algorithmic structure; that is, how one determines the future state from the present. The starting state, or initial conditions as they are usually called. Various constant quantities which are unchanged by the application of the algorithm. these are the quantities that we call constants of Nature.

5. 自然の法はなぜ数学的なのか:   Conceptualism: a philosophical theory that explains universality of particulars as conceptualized frameworks situated within the thinking mind.; Intermediate between nominalism and realism; 概念论 gàiniànlùn Formalism: within mathematics claim that mathematics is no more than the symbols written down by the mathematician, which is based on logic and a few elementary rules alone; 形式主义 xíngshì zhǔyì This is as opposed to non-formalists, within that field, who hold that there are some things inherently true, and are not, necessarily, dependent on the symbols within mathematics so much as a greater truth. Intuitionism: mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality; 直觉 zhíjué           consistent: not containing any logical contradictions; 连贯一致的 liánguàn yīzhì de                 flaw: a mistake or shotcoming in a plan, theory, etc. which cuases it to fail ore reduced its effectivess; 瑕疵 xiácī               irreducible: not able to be reduced or simplifed; 无法简化的 wúfǎ jiǎnhuà de       differential: 微分的 wēifēn de   constant: 常数 chángshù

>Top 6. Are there any laws of Nature?: John a. Wheeler: There is no law except that there is no law. Francis Hackett: Heretical notions: Heresy is but the bridge between two orthodoxies. George Santayana: Between a rock and a hard place: A really naked spirit cannot assume that he world is thoroughly intelligible. There may be surds, there may be hard facts, there may be dark abysses before which intelligence must be silent, for fear of going mad. Lewis Carroll: Too many laws?: 'We actually made a map of the country, on the scale of a mile to a mile!' 'Have you used it much?' I enquired. 'It has never been spread out, yet,' said Mein Herr; 'the farmers objected: they said it would cover the whole country, and shut out the sunlight! So we now use the country itself, as its own map, and I assure you it does nearly as well.' Eden Phillpotts: Spontaneous order: The universe is full of magical things patiently waiting our wits to grow sharper. Werner Heisenberg: The concepts 'soul' or 'life' do not occur in atomic physics, and they could not even indirectly, be derived as complicated consequences of some natural law. Their existence certainly doe not indicate the presence of any fundamental substance other than energy, but it shows only the action of other kinds of forms which we cannot match with the mathematical forms of modern atomic physics ... If we want to describe living or mental processes, we shall have to broaden these structures. It may be that we shall have to introduce yet other concepts. Subrahmanyan Chandrasekhar: Black hole ontogenesis: The black holes of nature are the most perfect macroscopic objects there are in the universe: the only elements in their construction are our concepts of space and time. Stephen Hawking (1974): showed that black holds are, thermodynamically, black bodies. They obey the laws of equilibrium thermodynamics. They have temperatures and entropies given by their gravitational fields and surface areas. when the influence of quantum mechanics upon black holes is considered this analogy becomes a reality. Quantum black holes radiate particles with a temperature and entropy actually determined by the gravity and area of the horizon, and after a finite time this radiation could result in the complete evaporation of the black hole. The end-result of this evaporation process in not yet clear. It may well be a naked singularity. The end-result of the evaporation may well be some new type of object - a superstring remnant, however small, the formation of a singularity will be avoided. Jules-Heinri Poincaré: Suppose that instead of 60 chemical elements there were 60 milliards of them ... uniformly distributed. Then every time we picked up a new pebble there would be a great probability of its being formed of some unknown substance; all that we know of pebbles would be worthless for it. Constants of Nature: The discovery of a new fundamental constant of Nature. A formula showing how the value of one constant of Nature is determined only by the numerical values of others, or, The discovery that a quantity believed to be a constant of Nature is not constant. Isaac Newton: Varying constants?: God could vary the laws of Nature, and make worlds of several sorts in several parts of the universe. Will Rogers: It ain't what you don't know, that counts, it's what you know that ain't so. I am always surprised when a young man tells me he wants to work at cosmology; I think of cosmology as something that happens to one, not something one can choose.

6. 自然の法はあるのか: heresy: belief or opinion contrary to orthodox religious doctorine, <G. hairesis, choice; 异端邪说 yìduān xiéshuō; 異端 intelligible: able to be understood, comprehensible; 可理解的 kě lǐjiě de; わかりやすい surd: irrational             ontogenesis: the development of an individual organism or anatomical or behavioural feature from the earliest stage to maturity.

>Top ７. Selection effects: Francis Bacon: Pattern in the trees: Let every student of nature take this as his rule that whatever the mind seized upon with particular satisfaction is to be held in suspicion. Patterns: Psychologically we find pattern, symmetry, and order appealing. Throughout the arts of ancient cultures we find symmetrical patterns of great sophistication developed for purely decorative purposes. Subsequently, some of these patterns and symmetries have been found to possess sophisticated mathematical properties. Maurits Escher have turned out to exploit very subtle mathematical symmetries. Max Planck: The phantoms of the laboratory: Science cannot solve the ultimate mystery of Nature. and it is because in the last analysis we ourselves are part of the mystery we are trying to solve. Errors: to the scientist the term 'error' means two other things: The first is straightforward; the limiting accuracy to which a quantity can be measures. However, in practice, the measurement errors that limit the accuracy of scientific measurements, even in elementary particle physics, are considerably larger than the irreducible minimum imposed by the quantum theory. The second form of error that besets experimental science i more subtle in its origins, and more serious in its consequences because one can never be certain that it has even been identified, let alone minimized or eradicated. The species of error we call a 'selection effect' or 'systematic error', and its identification requires careful thought and a wide-ranging appreciation of the phenomenon under study. E.M. Forster: The Anthropic Principle: There is no such person as a philosopher; no one is detached; the observe like the observed, is in chains. J.B. Priestley: Coincidences: Although we talk so much about coincidence we do not really believe in it. In our heart of hearts we think better of the universe, we are secretly convinced that it is not such a slipshod, haphazard affair, that everything in it has meaning.

7. 選択の効果: pattern: a repeated decorative design; 式样 shìyàng       error: a measure of the estimated difference between the observed or calculated value of a quantity and its true value; 错误 cuòwù   detached: separate or disconnected, in particular; 单独的 dāndú de   slipshod: characterized by a lack of care, thought, or organizatio; 马虎的 mǎhu de

Comment

In studying science in Japan, most of the famous scientific episodes are expressed and explained in Japanese. It is worth reading them in English, which could transfer more vivid situation what and how the episodes were made.

日本の科学教育では、科学上のエピソードなどは日本語で表現され説明されている。 英語で読めば、そのエピソードが作られた状況がより生き生きと伝わることになる。