Academics From Italy

"Full use of Lagrange's own made the unification of the varied principles of statistics and dynamics possible—in statistics by the use of the principle of virtual velocities, in dynamics by the use of . This led... to generalized coordinates and to the equation of motion in their "Lagrangian" form... Newton's geometrical approach was now fully discarded; Lagrange's book was a triumph of pure analysis."

"I cannot say whether I will still be doing geometry ten years from now. It also seems to me that the mine has maybe already become too deep and unless one finds new veins it might have to be abandoned. Physics and chemistry now offer a much more glowing richness and much easier exploitation. Also, the general taste has turned entirely in this direction, and it is not impossible that the place of Geometry in the Academies will someday become what the role of the Chairs of Arabic at the universities is now."

"We have already various treatises on Mechanics, but the plan of this one is entirely new. I intend to reduce the theory of this Science, and the art of solving problems relating to it, to general formulae, the simple development of which provides all the equations necessary for the solution of each problem. I hope that the manner in which I have tried to attain this object will leave nothing to be desired. No diagrams will be found in this work. The methods that I explain require neither geometrical, nor mechanical, constructions or reasoning, but only algebraical operations in accordance with regular and uniform procedure. Those who love Analysis will see with pleasure that Mechanics has become a branch of it, and will be grateful to me for having thus extended its domain."

"As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company, they drew from each other fresh vitality and thenceforward marched on at a rapid pace toward perfection."

"An ancient writer said that arithmetic and geometry are the wings of mathematics; I believe one can say without speaking metaphorically that these two sciences are the foundation and essence of all the sciences which deal with quantity. Not only are they the foundation, they are also, as it were, the capstones; for, whenever a result has been arrived at, in order to use that result, it is necessary to translate it into numbers or into lines; to translate it into numbers requires the aid of arithmetic, to translate it into lines necessitates the use of geometry."

"Newton was the greatest genius that ever existed, and the most fortunate, for we cannot find more than once a system of the world to establish."

"Lagrange... was the first to draw sharply the line of demarcation between physics and metaphysics. The mechanical ideas of Descartes, Leibnitz, Maupertius, and even of Euler, had proved to be more or less hazy and unfruitful from a failure to separate those two distinct regions of thought. Lagrange put an end to this confusion, for no serious attempt has since been made to derive the laws of mechanics from a metaphysical basis."

"The great masters of modern analysis are Lagrange, Laplace, and Gauss, who were contemporaries. It is interesting to note the marked contrast in their styles. Lagrange is perfect both in form and matter, he is careful to explain his procedure, and though his arguments are general they are easy to follow. Laplace on the other hand explains nothing, is indifferent to style, and, if satisfied that his results are correct, is content to leave them either with no proof or with a faulty one. Gauss is as exact and elegant as Lagrange, but even more difficult to follow than Laplace, for he removes every trace of the analysis by which he reached his results, and studies to give a proof which while rigorous shall be as concise and synthetical as possible."

"Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty [of the parallel axiom]. He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him which he had not observed : he muttered II faut que fy songe encore, and put the paper in his pocket."

"The mathematician is perfect only in so far as he is a perfect being, in so far as he perceives the beauty of truth; only then will his work be thorough, transparent, comprehensive, pure, clear, attractive and even elegant. All this is necessary to resemble Lagrange."

"Lagrange, struck with the circumstance that the calculus had never given any inequalities but such as were periodical, applied himself to the investigation of a general question, from which he found by a method peculiar to himself and independent of any approximation, that the inequalities produced by the mutual action of the planets must in effect be all periodical; that the periodical changes are confined within narrow limits; that none of the planets ever has been or ever can be a comet moving in a very eccentric orbit; but that the planetary system oscillates as it were round a medium state from which it never deviates far: that amid all the changes which arise from the mutual actions of the planets, two things remain perpetually the same, viz. the length of the greater axis of the ellipse which the planet describes, and its periodical time round the sun; or, which is the same thing, the mean distance of each planet from the sun and its mean motion remain constant. The plane of the orbit varies, the species of the ellipse and its eccentricity change, but never, by any means whatever, the greater axis of the ellipse, or the time of the entire revolution of the planet. The discovery of this great principle, which we may consider as the bulwark that secures the stability of our system, and excludes all access to confusion and disorder, must render the name of Lagrange for ever memorable in science, and ever revered by those who delight in the contemplation of whatever is excellent and sublime. After Newton's discovery of the elliptic orbits of the planets from gravitation, Langrange's discovery of their periodical inequalities is, without doubt, the noblest truth in physical astronomy, and in respect of the doctrine of final causes, it may truly be regarded as the greatest of all."

"Who has studied the works of such men as Euler, Lagrange, Cauchy, Riemann, , and Weierstrass, can doubt that a great mathematician is a great artist? The faculties possessed by such men, varying greatly in kind and degree with the individual, are analogous with those requisite for constructive art. Not every mathematician possesses in a specially high degree that critical faculty which finds its employment in the perfection of form, hi conformity with the ideal of logical completeness; but every great mathematician possesses the rarer faculty of constructive imagination."

"The questions here dealt with have occupied me since my earliest youth, when my interest for them was powerfully stimulated by the beautiful introductions of Lagrange to the chapters of his Analytic Mechanics..."

"Analytic mechanics... was brought to the highest degree of perfection by Lagrange. Lagrange's aim is ('... 1788) to dispose, once and for all, of the reasoning necessary to resolve mechanical problems, by embodying as much as possible of it in a single formula. This he did. Every case... can now be dealt with by a very simple, highly symmetrical and perspicuous schema; and whatever reasoning is left is performed by purely mechanical methods. The mechanics of Lagrange is a stupendous contribution to the economy of thought."

"It took them only an instant to cut off that head, but France may not produce another like it in a century."

"The value of his work [Mécanique Analytique] consists in the exposition of a general method by which every mechanical question may be stated in a single algebraic equation. The entire history of any mechanical system, as for example, the solar system, may thus be condensed into a single sentence; and its detailed interpretation becomes simply a question of algebra. No one who has not tried to cope with the difficulties presented by almost any mechanical problem can form a just appreciation of the great utility of such a labor-saving and thought-saving device. It has been well called 'a stupendous contribution to the economy of thought.'"

"Some years ago, an American psychologist, Abraham Maslow, felt the same kind of instinctive revolt against the 'atmosphere' of Freudian psychology, with its emphasis on sickness and neurosis, and decided that he might obtain some equally interesting results if he studied extremely healthy people. He therefore looked around for the most cheerful and well-adjusted people he could find, and asked for their co-operation in his studies. he soon discovered and interesting fact: that most extremely healthy people frequently experience of intense affirmation and certainty; Maslow called these 'peak experiences.' No one had made this discovery before because it had never struck anyone that a science calling itself 'psychology' and professing to be a science of the human mind (not merely the sick mind), ought to form its estimate of human beings by taking into account healthy minds as well as sick ones. A sick man talks obsessively about his illness; a healthy man never talks about his health; for as Pirandello points out, we take happiness for granted, and only begin to question life when we are unhappy. Hence no psychologist ever made this simple and obvious discovery about peak experiences."

"Così è (se vi pare)"

"Woe to him who doesn't know how to wear his mask, be he king or pope!"

"Anyone can be heroic from time to time, but a gentleman is something which you have to be all the time. Which isn't easy."

"E non le sembra già questa un'opinione?"

"He was simply unable to let things be foggy. Since they always are, this kept him pretty active."

"MAJORANA: There are scientists who 'happen' only once in every 500 years, like Archimedes or Newton. And there are scientists who happen only once or twice in a century, like Einstein or Bohr. FERMI: But where do I come in, Majorana? MAJORANA: Be reasonable, Enrico! I am not talking about you or me. I am talking about Einstein and Bohr."

"As astronomer Carl Sagan thought about what Fermi said Fermi paradox], he began to be alarmed. ...This could only mean that advanced civilizations destroy themselves before they get that far, a viewpoint Sagan published in 1966."

"If Fermi had been born a few years earlier, one could well imagine him discovering Rutherford's atomic nucleus, and then developing Bohr's theory of the hydrogen atom. If this sounds like hyperbole, anything about Fermi is likely to sound like hyperbole."

"There is no democracy in physics. We can't say that some second-rate guy has as much right to opinion as Fermi."

"Some recent work by E. Fermi and L. Szilard, which has been communicated to me in manuscript, leads me to expect that the element uranium may be turned into a new and important source of energy in the immediate future. Certain aspects of the situation seem to call for watchfulness and, if necessary, quick action on the part of the Administration..."

"Such a weapon goes far beyond any military objective and enters the range of very great natural catastrophes. By its very nature it cannot be confined to a military objective but becomes a weapon which in practical effect is almost one of genocide. It is clear that the use of such a weapon cannot be justified on any ethical ground which gives a human being a certain individuality and dignity even if he happens to be a resident of an enemy country... The fact that no limits exist to the destructiveness of this weapon makes its very existence and the knowledge of its construction a danger to humanity as a whole. It is necessarily an evil thing considered in any light."

"Although the problem of transmuting chemical elements into each other is much older than a satisfactory definition of the very concept of chemical element, it is well known that the first and most important step towards its solution was made only nineteen years ago by the late Lord Rutherford, who started the method of the nuclear bombardments."

"Where are they?"

"I cannot think of a single one, not even intelligence."

"I hope it won't take long."

"If I could remember the names of all these particles, I'd be a botanist."

"There are two possible outcomes: if the result confirms the hypothesis, then you've made a measurement. If the result is contrary to the hypothesis, then you've made a discovery."

"The Devil is not the Prince of Matter; the Devil is the arrogance of the spirit, faith without smile, truth that is never seized by doubt. The Devil is grim because he knows where he is going, and, in moving, he always returns whence he came."

"We live for books."

"That man is … odd," I dared say to William. "He is, or has been, in many ways a great man. But for this very reason he is odd. It is only petty men who seem normal."

"Because learning does not consist only of knowing what we must or we can do, but also of knowing what we could do and perhaps should not do."

"Books are not made to be believed, but to be subjected to inquiry. When we consider a book, we mustn't ask ourselves what it says but what it means..."

"A monk should surely love his books with humility, wishing their good and not the glory of his own curiosity; but what the temptation of adultery is for laymen and the yearning for riches is for secular ecclesiastics, the seduction of knowledge is for monks."

"There are magic moments, involving great physical fatigue and intense motor excitement, that produce visions of people known in the past. As I learned later from the delightful little book of the Abbé de Bucquoy, there are also visions of books as yet unwritten."

"I am mimetic. If I write a book set in the seventeenth century, I write in a Baroque style. If I’m writing a book set in a newspaper office, I write in Journalese."

"I don't miss my youth. I'm glad I had one, but I wouldn't like to start over."

"After all, the cultivated person's first duty is to be always prepared to rewrite the encyclopaedia."

"I don't even have an E-mail address. I have reached an age where my main purpose is not to receive messages."

"How should we deal with intrusions of fiction into life, now that we have seen the historical impact that this phenomenon can have? … Reflecting on these complex relationships between reader and story, fiction and life, can constitute a form of therapy against the sleep of reason, which generates monsters."

"To read fiction means to play a game by which we give sense to the immensity of things that happened, are happening, or will happen in the actual world. By reading narrative, we escape the anxiety that attacks us when we try to say something true about the world. This is the consoling function of narrative — the reason people tell stories, and have told stories from the beginning of time."

"The language of Europe is translation."

"The real hero is always a hero by mistake; he dreams of being an honest coward like everybody else. If it had been possible he would have settled the matter otherwise, and without bloodshed. He doesn't boast of his own death or of others'. But he does not repent. He suffers and keeps his mouth shut; if anything, others then exploit him, making him a myth, while he, the man worthy of esteem, was only a poor creature who reacted with dignity and courage in an event bigger than he was."

"In the United States, politics is a profession, whereas in Europe it is a right and a duty."