Jews From Lithuania

"Copy nature and you infringe on the work of our Lord. Interpret nature and you are an artist."

"I am the most curious of all to see what will be the next thing that I will do."

"Imagination is a very precise thing, you know — it is not fantasy. Remember, the other day I gave you the example of what I mean, what the difference between fantasy and imagination is. I gave you the example of the man who invented the of the man who invented the wheel while he was observing another man walking."

"For me sculpture is divinity. This is the only answer that I could find for myself. Art is man's distinctly human way of fighting death. Through art, man achieves immortality and in this immortality we find God."

"Cubism is not a formula, it is not a school. Cubism is a philosophy, a point of view in the universe. It is like standing at a certain point on a mountain and looking around. If you go higher, things will look different; if you go lower, again they will look different. It is a point of view."

"All my life as an artist I have asked myself: What pushes me continually to make sculpture? I have found the answer — at least the answer for myself. Art is an action against death. It is denial of death."

"The period during the First World War was a very exciting time in Paris, with artists, philosophers, and poets continually discussing and arguing about the work with which they were involved. Although I myself am little concerned with abstract theory, I certainly do think of cubism as a form of emancipation essentially different from artistic movements that had preceded it. Thus, impressionism, while it was a revolutionary technique, was still an essentially naturalistic movement concerned with a precise examination of the nature of light and the effect of changing lights on representational scenes and objects. Cubism did add a new dimension to painting and sculpture, a dimension that changed our way of looking at nature and the work of art."

"I remember one day when Juan Gris told me about a bunch of grapes he had seen in a painting by Picasso. The next day these grapes appeared in a painting by Gris, this time in a bowl; and the day after, the bowl appeared in a painting by Picasso."

"Jacques Lipchitz and Marc Chagall were among the European artists who settled in New York City during the war. Just before and after he arrived in 1941, Lipchitz gave his works such titles as Flight (1940), The Exile's Path (1941), The Rape of Europa (1941), and Theseus and the Minotaur (1942)."

"The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."

"According to the special theory there is a finite limit to the speed of causal chains, whereas classical causality allowed arbitrarily fast signals. Foundational studies... soon revealed that this departure from classical causality in the special theory is intimately related to its most dramatic consequences: the relativity of simultaneity, time dilation, and length contraction. By now it had become clear that these kinematical effects are best seen as consequences of Minkowski space-time, which in turn incorporates a nonclassical theory of causal structure. However, it has not widely been recognized that the converse of this proposition is also true: the causal structure of Minkowski space-time contains within itself the entire geometry (topoligical and metrical structure) of Minkowski space-time. ...The problem of the independence of topological and metrical structures of space-time was clearly recognized by early writers on relativity such as Russell (1954) and, of course, Eddington..."

"In 1908 the famous mathematician Minkowski made a remarkable discovery concerning the Lorentz formulae. He showed that, although each observer has his own private space and private time, a public concept which is the same for all observers can be formed by combining space and time as a kind of 'distance' by multiplying it by the velocity of light, c; in other words, with any time interval we can associate a definite spatial interval, namely the distance which light can travel in empty space in that period. If, according to a particular observer, the difference in time between any two events is T, this associated spatial interval is cT. Then, if R is the space-distance between these two events, Minkowski showed that the difference of the squares of cT and R has the same value for all observers in uniform relative motion. The square root of this quantity is called the space-time interval between two events. Hence, although time and three-dimensional space depend on the observer, this new concept of space-time is the same for all observers."

"Minkowski calls a spatial point existing at a temporal point a world point. These coordinates are now called 'space-time coordinates'. The collection of all imaginable value systems or the set of space-time coordinates Minkowski called the world. This is now called the manifold. The manifold is four-dimensional and each of its space-time points represents an event."

"Minkowski, building on Einstein's work, had now discovered that the Universe is made of a four-dimensional "spacetime" fabric that is absolute, not relative."

"In a Newtonian view, space and time are separate and different. Symmetries of the laws of physics are combinations of rigid motions of space and an independent shift in time. But... these transformations do not leave Maxwell's equations invariant. Pondering this, the mathematicians Henri Poincaré and Hermann Minkowski were led to a new view of the symmetries of space and time, on a purely mathematical level. If they had described these symmetries in physical terms, they would have beaten Einstein to relativity, but they avoided physical speculations. They did understand that symmetries in the laws of electromagnetism do not affect space and time independently but mix them up. The mathematical scheme describing these intertwined changes is known as the Lorentz group, after the physicist, Hendrik Lorentz."

"Ever since Hermann Minkowski's now infamous comments in 1908 concerning the proper way to view space-time, the debate has raged as to whether or not the universe should be viewed as a four-dimensional, unified whole wherein the past, present, and future are regarded as equally real or whether the views espoused by the possibilists, historicists, and presentests regarding the unreality of the future (and, for presentests, the past) are more accurate. Now, a century after Minkowski's proposed block universe first sparked debate, we present a new, more conclusive argument in favor of eternalism."

"When he enrolled as a student in the Polytechnic, Einstein developed a know-it-all attitude, and he paid little attention to Minkowski's lectures and skipped many. Minkowski described him as a "lazy dog," and years later, upon the publication of the theory of relativity, he commented, "I really would not have believed him capable of it.""

"Minkowski's idea and the solution of the twin paradox can best be explained by means of an analogy between space and spacetime... Time as a fourth dimension rests vertically on the other three—just as in space the vertical juts out of the two-dimensional plane as a third dimension. Distances through spacetime comprise four dimensions, just as space has three. The more you go in one direction, the less is left for the others. When a rigid body is at rest and does not move in any of the three dimensions, all of its motion takes place on the time axis. It simply grows older. ...The faster he moves away from his frame of reference... and covers more distance in the three dimensions of space, the less of his motion through spacetime as a whole is left over for the dimension of time. ...Whatever goes into space is deducted from time. ...In comparison with the distances light travels, all distances in the dimensions of space, even those involving airplane travel, are so very small that we essentially move only along the time axis, and we age continually. Only if we are able to move away from our frame of reference very quickly, like the traveling twin... would the elapsed time shrink to near zero, as it approached the speed of light. Light itself... covers its entire distance through spacetime only in the three dimensions of space... Nothing remains for the additional dimension... the dimension of time... Because light particles do not move in time, but with time, it can be said that they do not age. For them "now" means the same thing as "forever." They always "live" in the moment. Since for all practical purposes we do not move in the dimensions of space, but are at rest in space, we move only along the time axis. This is precisely the reason we feel the passage of time. Time virtually attaches to us."

"The geometrical theory of numbers... first gained prominence when Hermann Minkowski (1793-1909), who served as professor of mathematics at several universities, published his Geometrie der Zahlen (1896)."

"The discovery of Minkowski... is to be found... in the fact of his recognition that the four-dimensional space-time continuum of the theory of relativity, in its most essential formal properties, shows a pronounced relationship to the three-dimensional continuum of Euclidean geometrical space. In order to give due prominence to this relationship, however, we must replace the usual time co-ordinate t by an imaginary magnitude, \sqrt -1\cdot ct, proportional to it. Under these conditions, the natural laws satisfying the demands of the (special) theory of relativity assume mathematical forms, in which the time co-ordinate plays exactly the same role as the three space-coordinates. Formally, these four co-ordinates correspond exactly to the three space co-ordinates in Euclidean geometry. ...These inadequate remarks can give the reader only a vague notion of the important idea contributed by Minkowski. Without it the general theory of relativity... would perhaps have got no farther than its long clothes."

"A four dimensional continuum described by the co ordinates x1, x2, x3, x4, was called "world" by Minkowski, who also termed a point-event a "world point." From a "happening" in three-dimensional space, physics becomes, as it were, an "existence" in the four-dimensional world. This four dimensional "world" bears a close similarity to the three-dimensional "space" of Euclidean analytical geometry. ...We can regard Minkowski's "world" in a formal manner as a four-dimensional Euclidean space (with imaginary time co-ordinate); the Lorentz transformation corresponds to a "rotation" of the co-ordinate system in the four-dimensional world."

"With the rejection of such classical absolutes as length and duration, our ability to conceive of an objective impersonal world, independent of the presence of an observer, seems to be imperiled. The great merit of Minkowski was to show that an absolute world could nevertheless be imagined, although it was a far different world from that of classical physics. In Minkowski's world the absolute which supersedes the absolute length and duration of classical physics is the Einsteinian interval. ... Thus suppose that, as measured in our Galilean frame of reference, two flashes occur at points A and B, situated at a distance l apart, and suppose the flashes are separated in time by an interval t. If we change our frame of reference, both l and t will change in value, becoming l and t respectively, exhibiting by their changes the relativity of length and duration. In Minkowski's words, "Henceforth space and time themselves are mere shadows." On the other hand, the mathematical construct l^2 - c^2t^2 will remain invariant, and so we shall have l^2 - c^2t^2 = l'^2 - c^2t'^2. It is this invariant expression, which involves both length and duration, or both space and time, which constitutes the Einsteinian interval; and the objective world which it cannotes is the world of four-dimensional space-time. The Einsteinian interval... remains the same for all observers, just as distance alone or duration alone were mistakenly believed to remain the same for all observers in classical physics. ...the Einsteinian interval still remains an invariant as measured for all frames of reference, whether accelerated or not. In the case of accelerated frames, however, we must restrict our attention to Einsteinan intervals of infinitesimal magnitude, and then add up the intervals when finite magnitudes are involved."

"David Hilbert—the undisputed, foremost living mathematician in the world and lifelong close friend and collaborator of the by then deceased Minkowski—had already presented to the Göttingen Academy his own version of the same equations a few days earlier [than Einstein]. Although Minkowski and Hilbert accomplished their most important achievements in pure mathematical fields, their respective contributions to relativity should in no sense be seen as merely occasional excursions into the field of theoretical physics. Minkowski and Hilbert were motivated by much more than a desire to apply their exceptional mathematical abilities opportunistically... On the contrary, Minkowski's and Hilbert's contributions to relativity are best understood as an organic part of their overall scientific careers."

"Not only the physical but also the intellectual landscape of German-language mathematics in the early 1930s would be impossible to imagine without Gernan-Jewish mathematicians. Indeed, some fields of mathematics were completely transformed by their contributions. Number theory was transformed by Hermann Minkowski and Edmund Landau, algebra by Ernst Steinitz and Emmy Noether, set theory and general topology by Felix Hausdorff, Abraham Fraenkel and several others—to mention but a few examples."

"Many authors say that classical mechanics stand in opposition to the relativity postulate, which is taken to be the basic of the new Electro-dynamics"

"It would be very unsatisfactory if the new way of looking at the time-concept, which permits a Lorentz transformation, were to be confined to a single part of Physics."

"By laying down the relativity postulate from the outset, sufficient means have been created for deducing henceforth the complete series of Laws of Mechanics from the principle of conservation of energy (and statements concerning the form of the energy) alone."

"The assumption of the contraction of the electron in Lorentz's theory must be introduced at an earlier stage than Lorentz has actually done."

"H. A. Lorentz has found out the Relativity theorem and has created the Relativity postulate as a hypothesis that electrons and matter suffer contractions in consequence of their motion according to a certain law. A. Einstein has brought out the point very clearly, that this postulate is not an artificial hypothesis but is rather a new way of comprehending the time-concept, which is forced upon us by observation of natural phenomena."

"[Zurich,] where the students, even the most capable among them, ... are accustomed to get everything spoon-fed."

"It came as a tremendous surprise, for in his student days Einstein had been a lazy dog... He never bothered about mathematics at all."

"Oh, that Einstein, always cutting lectures... I really would not believe him capable of it."

"The rigid electron is in my view a monster in relation to Maxwell's equations, whose innermost harmony is the principle of relativity."

"The word postulate of relativity... appears to me very stale... I should rather like to give this statement the name Postulate of the absolute world (or briefly, world-postulate)."

"The whole world appears resolved into such world-lines. And I should like to say beforehand that, according to my opinion, it would be possible for the physical laws to find their fullest expression as correlations of these world-lines."

"Summits like those in Geneva promote hope. But hope without action is hopeless. Our enthusiasm for the positive spirit in these deliberations must not blind us to the absence of genuine progress toward disarmament. Twenty-four nuclear bombs are being added weekly to world arsenals."

"If we are to succeed, this vision must possess millions of people. We must convince each generation that they are but transient passengers on this planet earth. It does not belong to them. They are not free to doom generations yet unborn. They are not at liberty to erase humanity's past nor dim its future. Only life itself can lay claim to sacred continuity. The magnitude of the danger and its imminence must bring the human family together in common pursuit of peace denied throughout the century. On the threshold of a new millennium the achievement of world peace is no longer remote, for it is beckoned by the unleashing of the deepest spiritual forces embedded in humankind when threatened with extinction. The reason, the creativeness, and the courage that human beings possess foster an abiding faith that what humanity creates, humanity can and will control."

"We must hold fast to the dream that reason will prevail. The world today is full of anguish and dread. As great as is the danger, still greater is the opportunity. If science and technology have catapulted us to the brink of extinction, the same ingenuity has brought humankind to the boundary of an age of abundance. Never before was it possible to feed all the hungry. Never before was it possible to shelter all the homeless. Never before was it possible to teach all the illiterates. Never before were we able to heal so many afflictions. For the first time science and medicine can diminish drudgery and pain. Only those who see the invisible can do the impossible. But in order to do the impossible, in the words of Jonathan Schell, we ask "not for our personal survival: we ask only that we be survived. We ask for assurance that when we die as individuals, as we know we must, mankind will live on"."

"Combatting the nuclear threat has been our exclusive preoccupation, since we are dedicated to the proposition that to insure the conditions of life, we must prevent the conditions of death. Ultimately, we believe people must come to terms with the fact that the struggle is not between different national destinies, between opposing ideologies, but rather between catastrophe and survival. All nations share a linked destiny; nuclear weapons are their shared enemy."

"Perhaps the signal accomplishment of the IPPNW has been the broad-based, free-flowing dialogue between physicians of the two contending power blocs. We heed Einstein's words, "Peace cannot be kept by force. It can only be achieved by understanding". In a world riven with confrontation and strife, IPPNW has become a model for cooperation among physicians from East and West, from North and South. Paranoid fantasies of a dehumanized adversary cannot withstand the common pursuit of healing and preventing illness."

"Throughout human history, when confronted with what was deemed a deadly enemy, the fixed human response has been to gather more rocks, muskets, cannons, and now nuclear bombs. While nuclear weapons have no military utility — indeed they are not weapons but instruments of genocide-this essential truth is obscured by the notion of an "evil enemy". The "myth of the other", the stereotyping and demonizing of human beings beyond recognition, is still pervasive and now exacts inordinate economic, psychologic, and moral costs. The British physicist P.M.S. Blackett anticipated this state of paranoia: "Once a nation bases its security on an absolute weapon, such as the atom bomb, it becomes psychologically necessary to believe in an absolute enemy". The imagined enemy is eventually banished from the human family and reduced to an inanimate object whose annihilation loses all moral dimension."

"As no national interest would justify inflicting genocide on the victim and suicide on the aggressor, a prevalent misconception is that nuclear war will never be fought. But the realities of our age compel an opposite assessment. In no previous epoch were adversaries so continuously and totally mobilized for instant war. It is a statistical certainly that hair-trigger readiness cannot endure as a permanent condition. Furthermore, the unrelenting growth in nuclear arsenals, the increasing accuracy of missiles, and the continuing computerization of response systems all promote instabilities which court nuclear war by technical malfunction; by miscalculation, human aberration or criminal act."

"Martin Buber suggested that evil prevailed because of the inability of man to imagine the real. Yet human beings do have that capacity. Lord Byron, a poet favored by Alfred Nobel, captured the stark essence of a post-nuclear world in his poem "Darkness":"

"Every historic period has had its Cassandras. Our era is the first in which prophecies of doom stem from objective scientific analyses."

"The hope of a benevolent civilization was shattered in the blood-soaked trenches of the First World War. The "war to end all wars" claimed sixteen million lives, and left embers which kindled an even more catastrophic conflagration. Over the sorry course of 5,000 years of endless conflicts, some limits had been set on human savagery. Moral safeguards proscribed killing unarmed civilians and health workers, poisoning drinking waters, spreading infection among children and the disabled, and burning defenseless cities. But the Second World War introduced total war, unprincipled in method, unlimited in violence, and indiscriminate in victims. The ovens of Auschwitz and the atomic incineration of Hiroshima and Nagasaki inscribed a still darker chapter in the chronicle of human brutality. The prolonged agony which left 50 million dead did not provide an enduring basis for an armistice to barbarism. On the contrary, arsenals soon burgeoned with genocidal weapons equivalent to many thousands of World War II's. The advent of the nuclear age posed an unprecedented question: not whether war would exact yet more lives but whether war would preclude human existence altogether."

"Alfred Nobel believed that the destructiveness of dynamite would put an end to war. He deeply believed that the tragic reality of mass carnage would achieve results which all the preaching of peace and goodwill had so far failed to achieve. His prophecy now must gain fulfillment. Recoiling from the abyss of nuclear extermination, the human family will finally abandon war. May we learn from barbaric and bloody deeds of the twentieth century and bestow the gift of peace to the next millennium. Perhaps in that way we shall redeem some measure of respect from generations yet to come. Having achieved peace, in the sonorous phrase of Martin Luther King, Jr. spoken here twenty-one years ago, human beings will then "rise to the majestic heights of moral maturity"."

"We physicians have focused on the nuclear threat as the singular issue of our era. We are not indifferent to other human rights and hard-won civil liberties. But first we must be able to bequeath to our children the most fundamental of all rights, which preconditions all others; the right to survival."

"We physicians protest the outrage of holding the entire world hostage. We protest the moral obscenity that each of us is being continuously targeted for extinction. We protest the ongoing increase in overkill. We protest the expansion of the arms race to space. We protest the diversion of scarce resources from aching human needs. Dialogue without deeds brings the calamity ever closer, as snail-paced diplomacy is outdistanced by missile-propelled technology. We physicians demand deeds to implement further deeds which will lead to the abolition of all nuclear weaponry. We recognise that before abolition can become a reality, the nuclear arms race must be halted."

"We physicians who shepherd human life from birth to death have a moral imperative to resist with all our being the drift toward the brink. The threatened inhabitants on this fragile planet must speak out for those yet unborn, for posterity has no lobby with politicians."