Academics From Hungary

"Mathematics succeeds in dealing with tangible reality by being conceptual. We cannot cope with the full physical complexity; we must idealize."

"We wish to see... the typical attitude of the scientist who uses mathematics to understand the world around us. ...In the solution of a problem ...there are typically three phases. The first phase is entirely or almost entirely a matter of physics; the third, a matter of mathematics; and the intermediate phase, a transition from physics to mathematics. The first phase is the formulation of the physical hypothesis or conjecture; the second, its translation into equations; the third, the solution of the equations. Each phase calls for a different kind of work and demands a different attitude."

"If you cannot solve the proposed problem, try to solve first a simpler related problem."

"\frac {dy}{dx} = \frac {\omega^2x}{g}...The first derivative, the result of the differentiation of y with respect to x, was written by Leibniz in the form \frac {dy}{dx}...Leibniz's notation ...is both extremely useful and dangerous. Today, as the concepts of limit and derivative are sufficiently clarified, the use of the notation... need not be dangerous. Yet, the situation was different in the 150 years between the discovery of calculus by Newton and Leibniz and the time of Cauchy. The derivative \frac {dy}{dx} was considered as the ratio of two "infinitely small quanitites", of the infinitesimals dy and dx. ...it greatly facilitated the systematization of the rules of the calculus and gave intuitive meaning to its formulas. Yet this consideration was also obscure... it brought mathematics into disrepute... some of the best minds... such as... Berkeley, complained that calculus is incomprehensible. ...\frac {dy}{dx} is the limit of a ratio of dy to dx... Once we have realized this sufficiently clearly, we may, under certain circumstances, treat \frac {dy}{dx} so as if it were a ratio... and multiply by dx to achieve the separation of variables. We get {dy} = \frac {\omega^2x}{g}xdx"

"Even if without the Scott's proverbial thrift, the difficulty of solving differential equations is an incentive to using them parsimoniously. Happily here is a commodity of which a little may be made to go a long way. ...the equation of small oscillations of a pendulum also holds for other vibrational phenomena. In investigating swinging pendulums we were, albeit unwittingly, also investigating vibrating tuning forks."

"The differential equation of the first order \frac {dy}{dx} = f(x,y) ...prescribes the slope \frac {dy}{dx} at each point of the plane (or at each point of a certain region of the plane we call the field"). ...a differential equation of the first order... can be conceived intuitively as a problem about the steady flow of a river: Being given the direction of the flow at each point, find the streamlines. ...It leaves open the choice between the two possible directions in the line of a given slope. Thus... we should say specifically "direction of an unoriented straight line" and not merely "direction.""

"Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper."

"There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn't say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann."

"Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements."

"Euclid's manner of exposition, progressing relentlessly from the data to the unknown and from the hypothesis to the conclusion, is perfect for checking the argument in detail but far from being perfect for making understandable the main line of the argument."

"The future cannot be predicted, but futures can be invented. It was man's ability to invent which has made human society what it is."

"It would be pleasant to believe that the age of pessimism is now coming to a close, and that its end is marked by the same author who marked its beginning: Aldous Huxley. After thirty years of trying to find salvation in mysticism, and assimilating the Wisdom of the East, Huxley published in 1962 a new constructive utopia, The Island. In this beautiful book he created a grand synthesis between the science of the West and the Wisdom of the East, with the same exceptional intellectual power which he displayed in his Brave New World. (His gaminerie is also unimpaired; his close union of eschatology and scatology will not be to everybody's tastes.) But though his Utopia is constructive, it is not optimistic; in the end his island Utopia is destroyed by the sort of adolescent gangster nationalism which he knows so well, and describes only too convincingly. This, in a nutshell, is the history of thought about the future since Victorian days. To sum up the situation, the sceptics and the pessimists have taken man into account as a whole; the optimists only as a producer and consumer of goods. The means of destruction have developed pari passu with the technology of production, while creative imagination has not kept pace with either. The creative imagination I am talking of works on two levels. The first is the level of social engineering, the second is the level of vision. In my view both have lagged behind technology, especially in the highly advanced Western countries, and both constitute dangers."

"Incomplete knowledge of the future, and also of the past of the transmitter from which the future might be constructed, is at the very basis of the concept of information. On the other hand, complete ignorance also precludes communication; a common language is required, that is to say an agreement between the transmitter and the receiver regarding the elements used in the communication process... [The information of a message can] be defined as the 'minimum number of binary decisions which enable the receiver to construct the message, on the basis of the data already available to him.' These data comprise both the convention regarding the symbols and the language used, and the knowledge available at the moment when the message started."

"I do not know of anything in modern poetry as violently hostile to contemporary life as was the poetry of T. S. Eliot, which so perfectly fitted the mood of the young people between the two wars. I also find much more benevolence towards humanity in younger historians than there was in Spengler or in Toynbee. Still, it is not difficult to sense the disgust of the intellectuals at the new prosperous working class, 'with their eyes glued to the television screen,' who have become indifferent to radical ideas."

"The historical Jesus can be retrieved only within the context of first-century Galilean Judaism.... Against this background, what kind of picture of Jesus emerges from the Gospels? That of a rural holy man, initially a follower of the movement of repentance launched by another holy man, John the Baptist. In the hamlets and villages of Lower Galilee and the lakeside, Jesus set out to preach the coming of the Kingdom of God within the lifetime of his generation and outlined the religious duties his simple listeners were to perform to prepare themselves for the great event."

"If one had to single out the most revolutionary novelty furnished by Qumran, its contribution to our understanding of the genesis of Jewish literary compositions could justifiably be our primary choice."

"The account of the discovery of the Dead Sea Scrolls, as the manuscripts are inaccurately designated, and of the half a century of intense research that followed, is in itself a fascinating as well as an exasperating story."

"The absence from the Dead Sea Scrolls of historical texts proper should not surprise us. Neither in the inter-Testamental period, nor in earlier biblical times, was the recording of history as we understand it a strong point among the Jews."

"This is a simple and moving message, which Jesus formulated in his own language for his simple Galilean audience, about God, the heavenly Father, on the dignity of all human beings as children of God, on life turned into worship by total trust, on an overwhelming sense of urgency to do one’s duty without procrastination, on the sanctification of the here and now, and above all on the love of God through the love of one’s neighbour."

"Not all Constructivists concentrate so strongly on reality. There are those for whom inner life plays an important part, such as the non-Russian Moholy Nagy, Kassak, and Baumeister etc. Their art painting figures often have a more symbolic meaning.. .Sometimes without any direct connection to reality.. .Moholy Nagy’s work is 'l’art pour l’art' - as opposed to El Lissitsky who is demonstrative.. ..in as much as he propagates the Bolshevist morale of not dreaming but doing."

"Designing is not a profession but an attitude."

"Moholy Nagy, [in contrast to El Lissitsky ], does not muddle the various technical areas, but limits each technique to its own area. Later, when he applies himself more to photography and film [in America], he champions pure photography and film and opposes the imitation of the art of painting in these areas."

"My talent lies in the expression of my life and creative power through light, colour and form. As a painter I can convey the essence of life."

"The photogram, image formation outside the camera is the real key to photography,it embodies the essence... that allows us to capture light on light sensitive material without the use of any camera."

"The experience of space is not a privilege of the gifted few, but a biological function."

"Where in the Schrödinger equation do you put the joy of being alive?"

"In science, it is not speed that is the most important. It is the dedication, the commitment, the interest and the will to know something and to understand it — these are the things that come first."

"A possible explanation of the physicist's use of mathematics to formulate his laws of nature is that he is a somewhat irresponsible person. As a result, when he finds a connection between two quantities which resembles a connection well-known from mathematics, he will jump at the conclusion that the connection is that discussed in mathematics simply because he does not know of any other similar connection."

"A deep sense of humor and an unusual ability for telling stories and jokes endeared Johnny even to casual acquaintances. He could be blunt when necessary, but was never pompous. A mind of von Neumann's inexorable logic had to understand and accept much that most of us do not want to accept and do not even wish to understand. This fact colored many of von Neumann's moral judgments. "It is just as foolish to complain that people are selfish and treacherous as it is to complain that the magnetic field does not increase unless the electric field has a curl. Both are laws of nature." Only scientific intellectual dishonesty and misappropriation of scientific results could rouse his indignation and ire — but these did — and did almost equally whether he himself, or someone else, was wronged."

"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve."

"His playing was free, poetic, replete with imaginative shadings, and, at the same time, characterized by noble, artistic repose. And his technique, his virtuosity? I hesitate to speak if it. It suffices to observe that he has not lost it but has rather added to it in clarity and moderation. What a remarkable man! After a life incomparably rich and active, full of excitement, passion, and pleasure, he returns at the age of sixty-two and plays the most difficult music with the ease and strength and freshness of a youth…."

"I carry a deep sadness of the heart which must now and then break out in sound."

"Perhaps the greatest source of wonder in Liszt's life was that he composed anything at all, let alone anything of lasting greatness. The man who, from an early age, had crisscrossed Europe as the greatest travelling virtuoso, providing, with the onset of puberty, much material for gossip columns, might have been forgiven for taking the Wildean view, 'My art is my life', and leaving it at that. [...] Exactly how Liszt could have found the time to compose is difficult to imagine."

"Wasting time is one of the worst faults of the world. Life is so short, every moment is so precious and yet, we live as if life will never end."

"Sorrowful and great is the artist's destiny."

"When you write the story of two happy lovers, place them on the shores of Lake Como. I do not know a district more manifestly blessed by heaven; I've never seen another where the charms of a life of love would seem more natural [...] and start it with these words: "On the shores of Lake Como.""

"Composer, teacher, Abbé, Casanova, writer, sage, pioneer and champion of new music, philanthropist, philosopher and one of the greatest pianists in history, Franz Liszt was the very embodiment of the Romantic spirit. He worked in every field of music except ballet and opera and to each field he contributed a significant development."

"Brahms' Variations are better than mine, but mine were written before his."

"Mannheim also realized that the enlarged concept of ideology in Marxism raises a fundamental problem of knowledge. By denouncing something as "ideological," one takes an ideological position. Mannheim sees this as a spiritual and intellectual crisis in what is now a "Post-Marxist world". Our world is a polemical conflict between different worldviews, each labeling the other as "ideology." There are no criteria common to all with which to arbitrate the validity of one cultural perspective versus another. Even the class consciousness of the proletariat becomes one perspective among many."

"Mannheim notes that utopia not only shares with ideology a noncongruence with reality, but that utopia offers a perspective critical of the given reality, thus exposing the gap between what is and an ideal of what should be. Utopia, in challenging the existing order, is always a projection into possible futures; whereas, ideology, in legitimating the existing order, is directed toward perpetuating the past. Utopia tends to be the tool of social groups seeking ascendancy; while ideology tends to be the tool of dominant groups seeking to assuage their own sense of failing and justify the inadequacy of the status quo. Ideology and utopia are about power."

"In Mannheim’s post-Enlightenment, post-Romantic conception of democratization, social machinery that is maximally emancipatory, both over time and at any given historical moment, comes into being in a sustainable way only in a permanently revolutionary situation. That situation is one in which groups negotiate for power in a manner that continuously brings new leadership into positions for influencing or making choices for the community. The political process that Mannheim advocates in response to Fascism admits and institutionalizes the need for perpetual instability and uncertainty in order to make freedom possible; without uncertainty, or what Iser calls indeterminacy, is no freedom. Mannheim's political process is a democratized version of Trotsky's idea of "permanent revolution"…"

"Mannheim established no school. His preferred literary form was the essay and, collectively, his works contain many inconsistencies and, in places, a certain vagueness. Mannheim, himself was clear about these characteristics but appealed to his readers to see in them a sign of the provisional and experimental nature of his thinking. Of all the classical sociologists, Mannheim is the one whose biography and mode of questioning connects him most directly to the problems of our own time. Although he formulated his politics in relation to a historical situation from which we feel increasingly distant, the questions he posed in the diagnosis of conflict, on the role of the intelligentsia, on education and on democratic planning remain as pertinent as ever."

"Every bureaucracy, therefore, in accord with the peculiar emphasis on its own position, tends to generalize its own experience and to overlook the fact that the realm of administration and of smoothly functioning order represents only a part of the total political reality. Bureaucratic thought does not deny the possibility of the science of politics, but regards it as identical with the science of administration. Thus irrational factors are overlooked, and when these nevertheless force themselves to the fore, they are treated as "routine matters of state.""

"We are faced with the curiously appalling trend of modern thought, in which the absolute which was once a means of entering into communion with the divine, has now become an instrument used by those who profit from it, to distort, pervert, and conceal the meaning of the present."

"It may possibly be true that, to continue to live on and to act in a world like ours, it is vitally necessary to seek a way out of this uncertainty of multiple alternatives; and accordingly people may be led to embrace some immediate goal as if it were absolute, by which they hope to make their problems appear concrete and real. But it is not primarily the man of action who seeks the absolute and immutable, but rather it is he who wishes to induce others to hold on to the status quo because he feels comfortable and smug under conditions as they are."

"When the empirical investigator glories in his refusal to go beyond the specialized observation dictated by the traditions of his discipline, be they ever so inclusive, he is making a virtue out of a defense mechanism which insures him against questioning his presuppositions."

"In order to be transmuted into knowledge, every perception is and must be ordered and organized into categories. The extent, however, to which we can organize and express our experience in such conceptual forms is, in turn, dependent upon the frames of reference which happen to be available at a given historical moment. The concepts which we have and the universe of discourse in which we move, together with the directions in which they tend to elaborate themselves, are dependent largely upon the historical-social situation of the intellectually active and responsible members of the group."

"This first non-evaluative insight into history does not inevitably lead to relativism, but rather to relationism. Knowledge, as seen in the light of the total conception of ideology, is by no means an illusory experience, for ideology in its relational concept is not at all identical with illusion. Knowledge arising out of our experience in actual life situations, though not absolute, is knowledge none the less. The norms arising out of such actual life situations do not exist in a social vacuum, but are effective as real sanctions for conduct. Relationism signifies merely that all of the elements of meaning in a given situation have reference to one another and derive their significance from this reciprocal interrelationship in a given frame of thought. Such a system of meanings is possible and valid only in a given type of historical existence, to which, for a time, it furnishes appropriate expression. When the social situation changes, the system of norms to which it had previously given birth ceases to be in harmony with it. The same estrangement goes on with reference to knowledge and to the historical perspective. All knowledge is oriented toward some object and is influenced in its approach by the nature of the object with which it is pre-occupied. But the mode of approach to the object to be known is dependent upon the nature of the knower."

"It has become extremely questionable whether, in the flux of life, it is a genuinely worthwhile intellectual problem to seek to discover fixed and immutable ideas or absolutes. It is a more worthy intellectual task perhaps to learn to think dynamically and relationally rather than statically."

"Conflicting intellectual positions may actually come to supplement one another. It is imperative in the present transitional period to make use of the intellectual twilight which dominates our epoch and in which all values and points of view appear in their genuine relativity. We must realize once and for all that the meanings which make up our world are simply an historically determined and continuously developing structure in which man develops, and are in no sense absolute."