Refugees

"It is seen that continued shuffling may reasonably be expected to produce perfect "randomness" and to eliminate all traces of the original order. It should be noted, however, that the number of operations required for this purpose is extremely large."

"Physical irreversibility manifests itself in the fact that, whenever the system is in a state far removed from equilibrium, it is much more likely to move toward equilibrium, than in the opposite direction."

"The fact that the mean recurrence time is infinite implies that the chance fluctuations in an individual prolonged coin-tossing game are far removed from the familiar pattern governed by the normal distribution."

"It is not necessary to think of gambling places; the statistician who applies statistical tests is engaged in a dignified sort of gambling, and in his case the distribution of the random variables changes from occasion to occasion."

"This faulty intuition as well as many modern applications of probability theory are under the strong influence of traditional misconceptions concerning the meaning of the law of large numbers and of a popular mystique concerning a so-called law of averages."

"Much harm was done by the misleading suggestive power of this name. It must be understood that a fair game may be distinctly unfavorable to the player."

"The classical theory of probability was devoted mainly to a study of the gamble's gain, which is again a random variable; in fact, every random variable can be interpreted as the gain of a real or imaginary gambler in a suitable game."

"It has been suggested that an army of monkeys might be trained to pound typewriters at random in the hope that ultimately great works of literature would be produced. Using a coin for the same purpose may save feeding and training expenses and free the monkeys for other monkey business."

"Note the situation is different when the player is permitted to vary his stakes. In this case there exist advantageous strategies, and the game depends on the strategy."

"Warning. It is usual to read into the law of large numbers things which it definitely does not imply. If Peter and Paul toss a perfect coin 10,000 times, it is customary to expect that Peter will be in the lead roughly half the time. This is not true. In a large number of different coin-tossing games it is reasonable to expect that any fixed moment heads will be in the lead in roughly half of all cases. But it is quiet likely that the player who ends at the winning side has been in the lead for practically the whole duration of the game. Thus, contrary to widespread belief, the time average for any individual game has nothing to do with the ensemble average at any given moment."

"The man in the street, and also the philosopher K. Marbe, believe that after a run of seventeen heads tail becomes more probable. This argument has nothing to do with imperfections of physical coins; it endows nature with memory, or, in our terminology, it denies the stochastic independence of successive trials. Marbe's theory cannot be refuted by logic but is rejected because of empirical support."

"It is a common fallacy to believe that the law of large numbers acts as a force endowed with memory seeking to return to the original state, and many wrong conclusions have been drawn from this assumption."

"The theory of independent experiments is the analytically simplest and most advanced part of probability theory."

"Infinite product spaces are the natural habitat of probability theory."

"The notion of conditional probability is a basic tool of probability theory, and it is unfortunate that its great simplicity is somewhat obscured by a singularly clumsy terminology."

"To every event defined for the original random walk there corresponds an event of equal probability in the dual random walk, and in this way almost every probability relation has its dual."

"Simple methods will soon lead us to results of far reaching theoretical and practical importance. We shall encounter theoretical conclusions which not only are unexpected but actually come as a shock to intuition and common sense. They will reveal that commonly accepted notions concerning chance fluctuations are without foundation and that the implications of the law of large numbers are widely misconstrued."

"This means that if in a city seven accidents occur each week, then (assuming that all possible distributions are equally likely) practically all weeks will contain days with two or more accidents, and on the average only one week out of 165 will show a uniform distribution of one accident per day."

"When a coin is tossed, it does not necessarily fall heads or tails; it can roll away or stand on its edge."

"Only yesterday the practical things of today were decried as impractical, and the theories which will be practical tomorrow will always be branded as valueless games by the practical man of today."

"Historically, the original purpose of the theory of probability was to describe the exceedingly narrow domain of experience connected with games of chance, and the main effort was directed to the calculation of certain probabilities."

"The philosophy of the foundations of probability must be divorced from mathematics and statistics, exactly as the discussion of our intuitive space concept is now divorced from geometry."

"The manner in which mathematical theories are applied does not depend on preconceived ideas; it is a purposeful technique depending on, and changing with, experience."

"The bewildered novice in chess moves cautiously, recalling individual rules, whereas the experienced player absorbs a complicated situation at a glance and is unable to account rationally for his intuition. In like manner mathematical intuition grows with experience, and it is possible to develop a natural feeling for concepts such as four dimensional space."

"The results concerning fluctuations in coin tossing show the widely held beliefs about the law of large numbers are fallacious. They were so amazing and so at variance with common intuition that even sophisticated colleagues doubted that coins actually misbehave as theory predicts."

"When this book was first conceived (more than 25 years ago) few mathematicians outside the Soviet Union recognized probability as a legitimate branch of mathematics."

"You truly are an extraordinary man, Mr Sandeen. Nobody I know counts weeks. That is absolutely marvelous."

"The course of history as a whole is no object of experience; history has no eidos, because the course of history extends into the unknown future."

"What was novel in Voegelin’s thought was that he wedded that commonplace to a theory of history, suggesting that a universal process of symbolization was surreptitiously at work in human civilization, giving world history a discernible direction."

"The great line of demarcation in modern politics, Eric Voegelin used to point out, is not a division between liberals on one side and totalitarians on the other. No, on one side of that line are all those men and women who fancy that the temporal order is the only order, and that material needs are their only needs, and that they may do as they like with the human patrimony. On the other side of that line are all those people who recognize an enduring moral order in the universe, a constant human nature, and high duties toward the order spiritual and the order temporal."

"The Nazis' opponents also recognized the pseudo-religious character of the movement. As the Catholic exile Eric Voegelin put it, Nazism was 'an ideology akin to Christian heresies of redemption in the here and now . . . fused with post-Enlightenment doctrines of social transformation'. The journalist Konrad Heiden called Hitler 'a pure fragment of the modern mass soul' whose speeches always ended 'in overjoyed redemption'. An anonymous Social Democrat called the Nazi regime a 'counter-church'. Two individuals as different as Eva Klemperer, wife of the Jewish-born philologist Victor, and the East Prussian conservative Friedrich Reck-Malleczewen could agree in likening Hitler to the sixteenth-century Anabaptist Jan of Leyden."

"Voegelin’s was a lapsarian story, like Weaver’s, but told with a deeper knowledge of languages and the past. The timescale ran from preclassical times to the present. He elaborated an overarching tale of humanity’s fall into modernity in many essays, in an eight-volume history of political ideas written for college use, and in his main work, the five-volume Order and History (1956–87). For Voegelin, the “ismatic” apple that prompted our fall into modernity was not nominalism but gnosticism. By “gnosticism,” he meant a corrosive error about the nature of social norms, made originally by puritanical, mystic religious sects—the Gnostics—in the early Christian period. The gnostic error on Voegelin’s telling became pervasive in later myth, religion, and politics. The error was to confuse norms binding together present society with idealized depictions of a hoped-for future society. To that simple-sounding thought—that aiming to remake society was chasing a fantasy—Voegelin gave rich historico-philosophical clothing."

"The three mid-twentieth-century master painters of liberal disorder considered here—Richard Weaver, Eric Voegelin and Alasdair MacIntyre—all worked in the United States. Voegelin and MacIntyre were European emigrés. They wrote with a historical and geographic broad sweep. By the “West” they meant, willy-nilly, the classical Mediterranean world, medieval Christendom, and present-day rich, non-Communist nations. All took for granted a pervasive spiritual decline. None focused topically on this or that particular social harm or its solution. They wrote as if Western troubles were, if not of one kind, at any rate from a common source in a collective moral disorder. The scholastic and historical detail was imposing. With Voegelin, it was overwhelming. Despite the detail, however, the appeal of the picture lay in its simplicity and familiarity. Each told a time-honored story of Luciferan pride and fall. What liberals saw as progress, these thinkers took for ruinous and merited decline. Reversing decline, supposing that reversal were possible, was a matter of morals and how to think about morals. Each had a social diagnosis, a historical story, and a suggested cure. On the diagnosis, they concurred. We were suffering from liberal modernity. On the timing of its onset they differed: the twelfth century, perhaps earlier (Voegelin); the fourteenth century (Weaver); eighteenth-century Enlightenment (MacIntyre). The suggested cure was to rebuff liberal efforts to privatize morality and put morality back into politics and public life. Weaver, Voegelin, and MacIntyre opened paths toward present-day “values” conservatism. They pointed to a sphere of politics that conservatives might hope to claim as their own."

"In Brazil, it goes like this: communists only read communist authors, (economic) liberals only read liberal authors and so on. Each one is afraid of tarnishing their little soul with sinful thoughts. In order for someone to speak with some propriety about the communist movement, they must have previously studied the following things:"

"We see again confirmed the correlation between spiritual impotence and antirationalism: one cannot deny God and retain reason."

"But it is useless to subject this hash of uncritical language to critical questioning. We can make no sense of these sentences of Engels unless we consider them as symptoms of a spiritual disease. As a disease, however, they make excellent sense for, with great intensity, they display the symptoms of logophobia, now quite outspokenly as a desperate fear and hatred of philosophy. We even find named the specific object of fear and hatred: it is "the total context of things and of knowledge of things." Engels, like Marx, is afraid that the recognition of critical conceptual analysis might lead to the recognition of a "total context," of an order of being and perhaps even of cosmic order, to which their particular existences would be subordinate. If we may use the language of Marx: a total context must not exist as an autonomous subject of which Marx and Engels are insignificant predicates; if it exists at all, it must exist only as a predicate of the autonomous subjects Marx and Engels. Our analysis has carried us closer to the deeper stratum of theory that we are analysing at present, the meaning of logophobia now comes more clearly into view. It is not the fear of a particular critical concept, like Hegel's Idea, it is rather the fear of critical analysis in general. Submission to critical argument at any point might lead to the recognition of an order of the logos, of a constitution of being, and the recognition of such an order might reveal the revolutionary idea of Marx, the idea of establishing a realm of freedom and of changing the nature of man through revolution, as the blasphemous and futile nonsense which it is."

"The criterion of integral sanity [for Littré] is the acceptance of Positivism in its first stage. The criteria of decadence or decline are (1) a faith in transcendental reality, whether it expresses itself in the Christian form or in that of a substitute religion, (2) the assumption that all human faculties have a legitimate urge for public expression in a civilization, and (3) the assumption that love can be a legitimate guiding principle of action, taking precedence before reason. This diagnosis of mental deficiency is of an importance which can hardly be exaggerated. It is not the isolated diagnosis of Littré; it is rather the typical attitude toward the values of Western civilization which has continued among "intellectual positivists" from the time of Mill and Littré down to the neo-Positivistic schools of the Viennese type. Moreover, it has not remained confined to the schools but has found popular acceptance to such a degree that this variant of Positivism is today one of the most important mass movements. It is impossible to understand the graveness of the Western crisis unless we realize that the cultivation of values beyond Littré's formula of civilization as the dominion of man over nature and himself by means of science is considered by broad sectors of Western society to be a kind of mental deficiency."

"The tenacity of faith in this complex of ideas is certainly not caused by its merits as an adequate interpretation of man and society. The inadequacy of a pleasure-pain psychology, the poverty of utilitarian ethics, the impossibility of explaining moral phenomena by the pursuit of happiness, the uselessness of the greatest happiness of the greatest number as a principle of social ethics - all these have been demonstrated over and over again in a voluminous literature. Nevertheless, even today this complex of ideas holds a fascination for a not inconsiderable number of persons. This fascination will be more intelligible if we see the complex of sensualism and utilitarianism not as number of verifiable propositions but as the dogma of a religion of socially immanent salvation. Enlightened utilitarianism is but the first in a series of totalitarian, sectarian movements to be followed later by Positivism, Communism and National Socialism."

"One can hardly engage in a serious study of medieval Christianity without discovering among its ‘values’ the belief in a rational science of human and social order and especially of natural law. Moreover, this science was not simply a belief, but it was actually elaborated as a work of reason."

"'The order of history is the history of order.'"

"Christ is the head of the corpus mysticum, which includes all men from the beginning of the world to its end. He is not the president of a special-interest club."

"The death of the spirit is the price of progress."

"Philosophy springs from the love of being; it is man's loving endeavor to perceive the order of being and attune himself to it. Gnosis desires dominion over being; in order to seize control of being the Gnostic constructs his system. The building of systems is a gnostic form of reasoning, not a philosophical one."

"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."

"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..."

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

"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."

"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."

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

"Where are they?"