Academics From The United States

"In the face of almost infinite useful knowledge, we have adopted the strategy of "information regeneration rather than information retrieval." ...most importantly, you should be able to generate the result you need even if no one has ever done it before you—you will not be dependent on the past to have done everything you will ever need in mathematics."

"Most mathematics books are filled with finished theorems and polished proofs, and to a surprising extent they ignore the methods used to create mathematics. It is as if you merely walked through a picture gallery and never told how to mix paints, how to compose pictures, or all the other "tricks of the trade.""

"Probability is the mathematics of uncertainty. ...many modern theories have uncertainty built into their foundations. Thus learning to think in terms of probability is essential."

"Probability and statistics are now so obviously necessary tools for understanding many diverse things that we must not ignore them even for the average student."

"Any unwillingness to learn mathematics today can greatly restrict your possibilities tomorrow."

"You live in an age that is dominated by science and engineering. ...Thus if you wish to be effective in the world and to achieve the things that you want, it is necessary to understand both science and engineering (and those require mathematics)."

"The methods of mathematics are the main topic of the course, not a long list of finished mathematical results with such highly polished proofs that the poor student can only marvel at the results, with no hope of understanding how mathematics is actually created by practicing mathematicians."

"Increasingly... the application of mathematics to the real world involves discrete mathematics... the nature of the discrete is often most clearly revealed through the continuous models of both calculus and probability. Without continuous mathematics, the study of discrete mathematics soon becomes trivial and very limited. ...The two topics, discrete and continuous mathematics, are both ill served by being rigidly separated."

"Statistics should be taught early so that the concepts are absorbed by the student's flexible, adaptable mind before it is too late."

"Continuous distributions are basic to the theory of probability and statistics, and the calculus is necessary to handle them with any ease."

"Probability plays a central role in many fields, from quantum mechanics to information theory, and even older fields use probability now that the presence of "noise" is officially admitted. The newer aspects of many fields start with the admission of uncertainty."

"Understanding the methods of calculus is vital to the creative use of mathematics... Without this mastery the average scientist or engineer, or any other user of mathematics, will be perpetually stunted in development, and will at best be able to follow only what the textbooks say; with mastery, new things can be done, even in old, well-established fields."

"The calculus is probably the most useful single branch of mathematics. ...I have found the ability to do simple calculus, easily and reliably, was the most valuable part of mathematics I ever learned."

"Just as there are odors that dogs can smell and we cannot, as well as sounds that dogs can hear and we cannot, so too there are wavelengths of light we cannot see and flavors we cannot taste. Why then, given our brains wired the way they are, does the remark, "Perhaps there are thoughts we cannot think," surprise you?"

"The idea that theorems follow from the postulates does not correspond to simple observation. If the Pythagorean theorem were found to not follow from the postulates, we would again search for a way to alter the postulates until it was true. Euclid's postulates came from the Pythagorean theorem, not the other way around."

"The Postulates of Mathematics Were Not on the Stone Tablets that Moses Brought Down from Mt. Sinai."

"Indeed, one of my major complaints about the computer field is that whereas Newton could say, "If I have seen a little farther than others, it is because I have stood on the shoulders of giants," I am forced to say, "Today we stand on each other's feet." Perhaps the central problem we face in all of computer science is how we are to get to the situation where we build on top of the work of others rather than redoing so much of it in a trivially different way. Science is supposed to be cumulative, not almost endless duplication of the same kind of things."

"Without real experience in using the computer to get useful results the computer science major is apt to know all about the marvelous tool except how to use it. Such a person is a mere technician, skilled in manipulating the tool but with little sense of how and when to use it for its basic purposes."

"The only generally agreed upon definition of mathematics is "Mathematics is what mathematicians do." [...] In the face of this difficulty [of defining "computer science"] many people, including myself at times, feel that we should ignore the discussion and get on with doing it. But as George Forsythe points out so well in a recent article*, it does matter what people in Washington D.C. think computer science is. According to him, they tend to feel that it is a part of applied mathematics and therefore turn to the mathematicians for advice in the granting of funds. And it is not greatly different elsewhere; in both industry and the universities you can often still see traces of where computing first started, whether in electrical engineering, physics, mathematics, or even business. Evidently the picture which people have of a subject can significantly affect its subsequent development. Therefore, although we cannot hope to settle the question definitively, we need frequently to examine and to air our views on what our subject is and should become."

"Typing is no substitute for thinking."

"As a practicing computer veteran, this reviewer has the habit of looking at the hypothesis of a theorem and asking:"

"The purpose of computing is insight, not numbers."

"Your information is based on the meagre translations of our immense literature, if not on the unreliable anecdotes of passing travellers. It is rarely that the chivalrous pen of a Lafcadio Hearn or that of the author of "The Web of Indian Life" enlivens the Oriental darkness with the torch of our own sentiments."

"He is the writer in our language who can best be compared with Hans Christian Andersen and the brothers Grimm."

"To denounce Hearn is the same thing as a denunciation of Japan. Lafcadio Hearn was as Japanese as haiku."

"Mr Hearn began really to count as a writer only when his Hellenic qualities of mind, stunted at first by the conditions of life in North America, were at last developed among a people distinguished by somewhat of that instinctive feeling for beauty which formed an incomparable element in the genius of ancient Greece. His æsthetic sense luxuriated in a land where fineness of taste is still a common characteristic. Through the gate of their art he entered, not only into the ways of life of the Japanese, but into their moods and their religion."

"But what is after all the happiness of mere power? There is a greater happiness possible than to be lord of heaven and earth; that is the happiness of being truly loved."

"The time of illusion, then, is the beautiful moment of passion; it represents the artistic zone in which the poet or romance writer ought to be free to do the very best that he can."

"Any idealism is a proper subject for art."

"It may remain for us to learn … that our task is only beginning; and that there will never be given to us even the ghost of any help, save the help of unutterable unthinkable Time. We may have to learn that the infinite whirl of death and birth, out of which we cannot escape, is of our own creation, of our own seeking;—that the forces integrating worlds are the errors of the Past;—that the eternal sorrow is but the eternal hunger of insatiable desire;—and that the burnt-out suns are rekindled only by the inextinguishable passions of vanished lives."

"The religion of the Jesuits could never have adapted itself to the social conditions of Japan; and by the fact of this incapacity the fate of the missions was really decided in advance. The intolerance, the intrigues, the savage persecutions carried on,~-all the treacheries and cruelties of the Jesuits may simply be considered as the manifestations of such incapacity; while the repressive measures taken by Iyéyasu and his successors signify sociologically no more than the national perception of supreme danger. It was recognized that the triumph of the foreign religion would involve the total disintegration of society, and the subjection of the empire to foreign domination. Neither the artist nor the sociologist, at least, can regret the failure of the missions. Their extirpation, which enabled Japanese society to evolve to its type-limit, preserved for modem eyes the marvellous world of Japanese art, and the yet more marvellous world of its traditions, beliefs, and customs. Roman Catholicism, triumphant, would have swept all this out of existence. The natural antagonism of the artist to the missionary may be found in the fact that the latter is always, and must be, an unsparing destroyer. Everywhere the developments of art are associated in some sort with religion; and by so much as the art of a people reflects their beliefs, that art will be hateful to the enemies of those beliefs. Japanese art, of Buddhist origin, is especially an art of religious suggestion,—not merely as regards painting and sculpture, but likewise as regards decoration, and almost every product of aesthetic taste. There is something of religious feeling associated even with the Japanese delight in trees and flowers, the charm of gardens, the love of nature and of nature's voices,—-with all the poetry of existence, in short. Most)assuredly the Jesuits and their allies would have ended all this, every detail of it, without the slightest qualm. Even could they have understood and felt the meaning of that world of strange beauty.—result of a race-experience never to be repeated or replaced,—-they would not have hesitated a moment in the work of obliteration and effacement. To-day, indeed, that wonderful art-world is being surely and irretrievably destroyed by Western industrialism. But industrial influence, though pitiless, is not fanatic; and the destruction is not being carried on with such ferocious rapidity but that the fading story of beauty can be recorded for the future benefit of human civilization."

"With the massacre of Shimabara ends the real history of the Portuguese and Spanish missions. After that event, Christianity was slowly, steadily, implacably stamped out of visible existence. It had been tolerated, or half tolerated, for only sixty-five years: the entire history of its propagation and destruction occupies a period of scarcely ninety years. People of nearly every rank, from prince to pauper, suffered for it thousands endured tortures for its sake - tortures so frightful that even three of those Jesuits who sent multitudes to useless martyrdom were forced to deny their faith under the infliction;* and tender women, sentenced to, the stake, carried their little ones with them into the fire, rather than utter the words that would have saved both mother and child. Yet this religion, for which thousands vainly died, had brought to Japan nothing but evil disorders, persecutions, revolts, political troubles, and war. Even those virtues of the people which had been evolved at unutterable cost for the protection and conservation of society, - their self-denial, their faith, their loyalty, their constancy and courage, - were by this black creed distorted, diverted, and transformed into forces directed to the destruction of that society. Could that destruction have been accomplished, and a new Roman Catholic empire have been founded upon the ruins, the forces of that empire would have been used for the further extension of priestly tyranny, the spread of the Inquisition, the perpetual Jesuit warfare against freedom of conscience and human progress. Well may we pity the victims of this pitiless faith, and justly admire their useless courage: yet who can regret that their cause was lost? ... Viewed from another standpoint than that of religious bias, and simply judged by its results, the Jesuit effort to Christianize Japan must be regarded as a crime against humanity, a labour of devastation, a calamity comparable only, - by reason of the misery and destruction which it wrought, - to an earthquake, a tidal-wave, a volcanic eruption."

"After the first recognition even by theology of physical evolution, it was easy to predict that the recognition of psychical evolution could not be indefinitely delayed; for the barrier erected by old dogma to keep men from looking backward had been broken down. And today for the student of scientific psychology the idea of pre-existence passes out of the realm of theory into the realm of fact, proving the Buddhist explanation of the universal mystery quite as plausible as any other. "None but very hasty thinkers," wrote the late Professor Huxley, "will reject it on the ground of inherent absurdity. Like the doctrine of evolution itself, that of transmigration has its roots in the world of reality; and it may claim such support as the great argument from analogy is capable of supplying.”"

"With the acceptance of the doctrine of evolution, old forms of thought crumbled; new ideas everywhere arose to take the place of worn-out dogmas; and we now have the spectacle of a general intellectual movement in directions strangely parallel with Oriental philosophy. The unprecedented rapidity and multiformity of scientific progress during the last fifty years could not have failed to provoke an equally unprecedented intellectual quickening among the non-scientific. That the highest and most complex organisms have been developed from the lowest and simplest; that a single physical basis of life is the substance of the whole living world; that no line of separation can be drawn between the animal and vegetable; that the difference between life and non-life is only a difference of degree, not of kind; that matter is not less incomprehensible than mind, while both are but varying manifestations of one and the same unknown reality – these have already become the commonplaces of the new philosophy."

"They are hideous Golgothas, these old intermural cemeteries of ours. In other cities cemeteries are beautiful with all that the art of the gardener and sculptor can give....There the horror is masked. Here it glares at us with empty sockets. The tombs are fissured, or have caved in, or have crumbled down into shapeless bricks and mortar...[and] crawfish undermine the walls to feast upon what is hidden within."

"Times are not good here. The city is crumbling into ashes. It has been buried under a lava flood of taxes and frauds and maladministrations so that it has become only a study for archaeologists. Its condition is so bad that when I write about it, as I intend to do soon, nobody will believe I am telling the truth. But it is better to live here in sackcloth and ashes than to own the whole state of Ohio."

"My friends are much more dangerous than my enemies. These latter – with infinite subtlety – spin webs to keep me out of places where I hate to go, – and tell stories of me to people whom it would be vanity and vexation to meet; – and they help me so much by their unconscious aid that I almost love them."

"Japanese affection is not uttered in words; it scarcely appears even in the tone of voice; it is chiefly shown in acts of exquisite courtesy and kindness."

"Whatever doubts or vexations one has in Japan, it is only necessary to ask one's self: "Well, who are the best people to live with?""

"How sweet Japanese woman is! All the possibilities of the race for goodness seem to be concentrated in her."

"Clearly, one can obfuscate one's ideas with a compiler language but it's harder. To some extent one is talking about what one wants rather than how one wants to do it. The trouble with machine code, of course, is that when you look at a random section of machine code you don't know what properties of the instructions the programmer really wanted to exploit."

"The glory of God is not contingent on man's good will, but all existence subserves his purposes. The system of the universe is as a celestial poem, whose beauty is from all eternity, and must not be marred by human interpolations. Things proceed as they were ordered, in their nice, and well-adjusted, and perfect harmony; so that as the hand of the skilful artist gathers music from the harp-strings, history calls it forth from the well-tuned chords of time. Not that this harmony can be heard during the tumult of action. Philosophy comes after events, and gives the reason of them, and describes the nature of their results. The great mind of collective man may, one day, so improve in self-consciousness as to interpret the present and foretell the future; but as yet, the end of what is now happening, though we ourselves partake in it, seems to fall out by chance. All is nevertheless one whole; individuals, families, peoples, the race, march in accord with the Divine will; and when any part of the destiny of humanity is fulfilled, we see the ways of Providence vindicated. The antagonisms of imperfect matter and the perfect idea, of liberty and necessary law, become reconciled. What seemed irrational confusion, appears as the web woven by light, liberty and love. But this is not perceived till a great act in the drama of life is finished. The prayer of the patriarch, when he desired to behold the Divinity face to face, was denied; but he was able to catch a glimpse of Jehovah, after He had passed by; and so it fares with our search for Him in the wrestlings of the world. It is when the hour of conflict is over, that history comes to a right understanding of the strife, and is ready to exclaim: "Lo! God is here, and we knew it not.""

"The unchanging character of law is the only basis on which continuous action can rest. Without it man would be but as the traveller over endless morasses; the builder on quicksands; the mariner without compass or rudder, driven successively whithersoever changing winds may blow. The universe is the reflex and image of its Creator. "The true work of art," says Michael Angelo, "is but a shadow of the Divine perfections." We may say in a more general manner, that Beauty Itself Is But The Sensible Image Of The Infinite; that all creation is a manifestation of the Almighty; not the result of caprice, but the glorious display of his perfection; and as the universe thus produced, is always in the course of change, so its regulating mind is a living Providence, perpetually exerting itself anew. If his designs could be thwarted, we should lose the great evidence of his unity, as well as the anchor of our own hope. Harmony is the characteristic of the intellectual system of the universe; and immutable laws of moral existence must pervade all time and all space, all ages and all worlds."

"The progress of man consists in this, that he himself arrives at the perception of truth. The Divine mind, which is its source, left it to be discovered, appropriated and developed by finite creatures. The life of an individual is but a breath; it comes forth like a flower, and flees like a shadow. Were no other progress, therefore, possible than that of the individual, one period would have little advantage over another. But as every man partakes of the same faculties and is consubstantial with all, it follows that the race also has an existence of its own; and this existence becomes richer, more varied, free and complete, as time advances. Common Sense implies by its very name, that each individual is to contribute some share toward the general intelligence. The many are wiser than the few; the multitude than the philosopher; the race than the individual; and each successive generation than its predecessor."

"No science has been reached, no thought generated, no truth discovered, which has not from all time existed potentially in every human mind. The belief in the progress of the race does not, therefore, spring from the supposed possibility of his acquiring new faculties, or coming into the possession of a new nature. Still less does truth vary. They speak falsely who say that truth is the daughter of time; it is the child of eternity, and as old as the Divine mind. The perception of it takes place in the order of time; truth itself knows nothing of the succession of ages. Neither does morality need to perfect itself; it is what it always has been, and always will be. Its distinctions are older than the sea or the dry land, than the earth or the sun. The relation of good to evil is from the beginning, and is unalterable."

"The prejudices of ignorance are more easily removed than the prejudices of interest; the first are blindly adopted; the second wilfully preferred."

"The exact measure of the progress of civilization is the degree in which the intelligence of the common mind has prevailed over wealth and brute force."

"Sedition is bred in the lap of luxury and its chosen emissaries are the beggared spendthrift and the impoverished libertine."

"The best government rests on the people and not on the few, on persons and not on property, on the free development of public opinion and not on authority."

"By common consent grey hairs are a crown of glory; the only object of respect that can never excite envy."