Jews From Germany

"Man is always more than he can know of himself; consequently, his accomplishments, time and again, will come as a surprise to him."

"“We cannot have another world war. War is the wrong word. We should ban the term ‘World War III’ and say instead apocalypse or holocaust.”"

"These are the people who hate themselves because they haven't come to terms with their helplessness. They feel threatened by helplessness itself, not by those who caused or reinforced the feeling, and this is what produces their boundless rage. Therefore, they repress their helplessness, which has made them feel rejected and despised, at the same time oppressing their 'oppressors' contempt for them."

"Our own vitality as well as that of others frightens us, if it still manages to surface, we respond with rage and turn against our own freedom. It is vitality itself that we are opposing."

"Even measured by Wiener's standards Cybernetics is a badly organised work — a collection of misprints, wrong mathematical statements, mistaken formulas, splendid but unrelated ideas, and logical absurdities. It is sad that this work earned Wiener the greater part of his public renown, but this is an afterthought. At that time mathematical readers were more fascinated by the richness of its ideas than by its shortcomings."

"Horizontal mathematising leads from the world of life to the world of symbols."

"[Guided reinvention is] striking a subtle balance between the freedom of inventing and the force of guiding, between allowing the learner to please himself and asking him to please the teacher. Moreover, the learner’s free choice is already restricted by the “re” of “reinvention”. The learner shall invent something that is new to him but well-known to the guide."

"Learners should be allowed to find their own levels and explore the paths leading there with as much and as little guidance as each particular case requires."

"Angles are measured by arcs, such that 360° and 2π correspond to each other."

"Geometry is grasping space. And since it is about the education of children, it is grasping that space in which the child lives, breathes and moves. The space that the child must learn to know, explore, conquer, in order to live, breathe and move better in it."

"Euclid defines the angle as an inclination of lines…he meant halflines, because otherwise he would not be able to distinguish adjacent angles from each other… Euclid does not know zero angles, nor straight and bigger than straight angles…Euclid takes the liberty of adding angles beyond two and even four right angles; the result cannot be angles according to the original definitions…Nevertheless one feels that Euclid’s angle concept is consistent."

"Vertical mathematising is the most likely part of the learning process for the bonds with reality to be loosened and eventually cut."

"No doubt once it was real progress when developers and teachers offered learners tangible material in order to teach them arithmetic of whole number... The best palpable material you can give the child is its own body."

"Grasping spatial gestalts as figures is mathematizing of space. Arranging the properties of a parallelogram such that a particular one pops up to base the others on it in order to arrive at a definition of parallelogram, that is mathematizing the conceptual field of the parallelogram."

"Space and the bodies around us are early mental objects... Name-giving is a first step towards consciousness."

"The subject of a science is never well circumscribed and there is little use sharpening its definition. However, nobody will deny that physics deals with nature and sociology with human society in some of their aspects. With logic, it is another matter. Logic is usually understood nowadays as a study of certain formal systems, though in former times there were philosophers who held that the subject matter of logic was the formal rules of human thought. In the latter sense it would be an empirical rather than a formal science, though its empirical subject matter would still be fundamentally different from that of psychology of thinking. One interpretation of logic does not exclude the other. Formal approaches are often easier than empirical ones, and for this reason one can understand why logic as a study of formal systems has till now made more progress than logic as a study of the formal rules of thought, even if restricted to scientific thought."

"The case of methodology is analogous though less clear. Nobody would object to the subject of methodology being science, or some pseudo science. On closer inspection, however, this agreement is no more than a verbal coincidence. It rests on what is meant by science, as reported as a subject of methodology. In fact the subject methodologists call science is more often than not different from what scientists call science. Methodologists are inclined to consider a science as a linguistic system whereas the scientist would only admit that his science has a language, not that it is a language."

"In appearance and behaviour, Norbert Wiener was a baroque figure, short, rotund, and myopic, combining these and many qualities in extreme degree. His conversation was a curious mixture of pomposity and wantonness. He was a poor listener. His self-praise was playful, convincing and never offensive. He spoke many languages but was not easy to understand in any of them. He was a famously bad lecturer."

"The present book is not a methodology of mathematics in the sense that I will systematically show how some teaching matter should taught; it is not even a systematic analysis of subject matter. I hardly ever refer to well-organized classroom experiments evaluated by statistical methods, nor do I cite experimental results of developmental psychology or the psychology of learning. Maybe the most striking feature is that this book contains few quotations. I will try to justify all these features."

"The classic instrument to measure drawn angles and to draw angles of a given measure is the — essentially half a circular ring, subdivided by ray segments into 180 degrees. For reasons I was unable to find out, this instrument has recently been superseded by an isosceles right triangle — called geo-triangle, solid, transparant, made of plastic — with an angular division radiating from the midpoint of the hypotenuse to the other sides. Well, inside the triangle half a circle with the midpoint of the hypotenuse as its centre is indicated, and from the position of the degree numbers it becomes clear that it is the semicircle that really matters. One is inclined to say "an outrageously misleading instrument"..."

"Our mathematical concepts, structures, ideas have been invented as tools to organise the phenomena of the physical, social and mental world. Phenomenology of a mathematical concept, structure, or idea means describing it in its relation to the phenomena for which it was created, and to which it has extended in the learning process of mankind, and, as far as this description is concerned with the learning process of the young generation, it is didactical phenomenology, a way to show the teacher the places where the learner might step into the learning process of mankind."

"No scientist is as model minded as is the statistician; in no other branch of science is the word model as often and consciously used as in statistics."

"No mathematical idea has ever been published in the way it was discovered. Techniques have been developed and are used, if a problem has been solved, to turn the solution procedure upside down, or if it is a larger complex of statements and theories, to turn definitions into propositions, and propositions into definitions, the hot invention into icy beauty. This then if it has affected teaching matter, is the didactical inversion, which as it happens may be anti-didactical. Rather than behaving anti-didactically, one should recognise that the learner is entitled to recapitulate in a fashion of mankind. Not in the trivial matter of an abridged version, but equally we cannot require the new generation to start at the point where their predecessors left off."

"Science should be distinguished from technique and its scientific instrumentation, technology. Science is practised by scientists, and techniques by ‘engineers’ — a term that in our terminology includes physicians, lawyers, and teachers. If for the scientist knowledge and cognition are primary, it is action and construction that characterises the work of the engineer, though in fact his activity may be based on science. In history, technique often preceded science."

"[The goal of developmental research is to] consciously experience, describe and justify the cyclic process of development and research so that it can be passed on to others in such a way that they can witness and relive the experience."

"A true aphorism legitimates itself; whoever feels the need to legitimate an aphorism, admits that it is illegal. The surface of an aphorism should conceal profound truth. The claim that everybody can learn everything is superficial, but is as wrong as it can be. As a matter of fact, it is no aphorism but an advertising slogan, and the excuse that it is an aphorism, is a mere wink: in advertising you cannot do without exaggerating. But even as a wink it does not become more true."

"No statistician present at this moment will have been in doubt about the meaning of my words when I mentioned the common statistical model. It must be a stochastic device producing random results. Tossing coins or a dice or playing at cards are not flexible enough. The most general chance instrument is the urn filled with balls of different colours or with tickets bearing some ciphers or letters. This model is continuously used in our courses as a didactic tool, and in our statistical analyses as a means of translating realistic problems into mathematical ones. In statistical language " urn model " is a standard expression."

"While studying antiaircraft fire control, Wiener may have conceived the idea of considering the operator as part of the steering mechanism and of applying to him such notions as feedback and stability, which had been devised for mechanical systems and electrical circuits. No doubt this kind of analogy had been operative in Wiener’s mathematical work from the beginning and sometimes had even been productive. As time passed, such flashes of insight were more consciously put to use in a sort of biological research for which Wiener consulted all kinds of people, except mathematicians, whether or not they had anything to do with it. Cybernetics, or Control and Communication in the Animal and the Machine (1948) is a rather eloquent report of these abortive attempts, in the sense that it shows there is not much to be reported. The value and influence of Cybernetics, and other publications of this kind, should not, however, be belittled. It has contributed to popularizing a way of thinking in communication theory terms, such as feedback, information, control, input, output, stability, homeostasis, prediction, and filtering . On the other hand, it also has contributed to spreading mistaken ideas of what mathematics really means"

"Educational technique needs a philosophy, which is a matter of faith rather than of science."

"The urn model is to be the expression of three postulates: (1) the constancy of a probability distribution, ensured by the solidity of the vessel, (2) the randomcharacter of the choice, ensured by the narrowness of the mouth, which is to prevent visibility of the contents and any consciously selective choice, (3) the independence of successive choices, whenever the drawn balls are put back into the urn. Of course in abstract probability and statistics the word " choice " can be avoided and all can be done without any reference to such a model. But as soon as the abstract theory is to be applied, random choice plays an essential role."

"If you want truly to understand something, try to change it."

"In 1946, a Macy Foundation interdisciplinary conference was organized to use the model provided by "feedback systems," honorifically referred to in earlier conferences as "teleological mechanisms," and later as "cybernetics," with the expectation that this model would provide a group of sciences with useful mathematical tools and, simultaneously, would serve as a form of cross-disciplinary communication. Out of the deliberations of this group came a whole series of fruitful developments of a very high order. Kurt Lewin (who died in 1947) took away from the first meeting the term "feedback". He suggested ways in which group processes, which he and his students were studying in a highly disciplined, rigorous way, could be improved by a "feedback process," as when, for example, a group was periodically given a report on the success or failure of its particular operations."

"A successful individual typically sets his next goal somewhat but not too much above his last achievement. In this way he steadily raises his level of aspiration... The unsuccessful individual on the other hand, tends to show one of two reactions: he sets his goal very low, frequently below his past achievement... or he sets his goals far above his abilities."

"The scope of time ahead which influences present behavior, and is therefore to be regarded as part of the present life-space, increases during development. This change in time perspective is one of the most fundamental facts of development. Adolescence seems to be a period of particularly deep change in respect to time perspective. The change can be partly described as a shift in scope. Instead of days, weeks, or months, now years ahead are considered in certain goals. Even more important is the way in which these future events influence present behavior. The ideas of a child of six or eight in regard to his occupation as an adult are not likely to be based on sufficient knowledge of the factors which might help or interfere with the realization of these ideas. They might be based on relatively narrow but definite expectations or might have a dream or playlike character. In other words, "ideal goals" and "real goals" for the distant future are not much distinguished, and this future has more the fluid character of the level of irreality. In adolescence a definite differentiation in regard to the time perspective is likely to occur. Within those parts of the life-space which represent the future, levels of reality and irreality are gradually being differentiated."

"To instigate changes toward democracy a situation has to be created for a certain period where the leader is sufficiently in control to rule out influences he does not want and to manipulate the situation to a sufficient degree. The goal of the democratic leader in this transition period will have to be the same as any good teacher, namely to make himself superfluous, to be replaced by indigenous leaders from the group."

"A certain area within a channel may function as a “gate”; the constellation of the forces before and after the gate region is decisively different in such a way that the passing or not passing of the unit through the whole channel depends to a high degree upon what happens in the gate region. This holds not only for food channels but also for the travelling of a news item through certain communication channels in a group, for movement of goods, and the social locomotion of individuals in many organizations."

"The survival and development of democracy depends not so much on the development of democratic ideals which are wide-spread and strong. Today, more than ever before, democracy depends upon the development of efficient forms of democratic social management and upon the spreading of the skill in such management to the common man."

"Planning starts usually with something like a general idea. For one reason or another it seems desirable to reach a certain objective, and how to reach it is frequently not too clear. The first step then is to examine the idea carefully in the light of the means available. Frequently more fact-finding about the situation is required. If this first period of planning is successful, two items emerge: namely, an ‘over-all plan’ of how to reach the objective and secondly, a decision in regard to the first step of action. Usually this planning has also somewhat modified the original idea. The next period is devoted to executing the first step of the original plan."

"The research needed for social practice can best be characterized as research for social management or social engineering. It is a type of action research, a comparative research of the conditions and effects of various forms of social action, and research leading to social action. Research that produces nothing but books will not suffice."

"An attempt to improve intergroup relations has to face a wide variety of tasks. It deals with problems of attitude and stereotypes in regard to other groups and to one's own group, with problems of development of attitudes and conduct during childhood and adolescence, with problems of housing, and the change of the legal structure of the community; it deals with problems of status and caste, with problems of economic discrimination, with political leadership and with leadership in many aspects of community life. It deals with the small social body of a family, a club or a friendship group, with the larger social body of a school or a school system, with neighborhoods and with social bodies of the size of a community, of the state, a nation and with international problems."

"The life space... includes both the person and his psychological environment. The task of explaining behavior then becomes identical with (1) finding a scientific representation of the life space (LSp) and (2) determining the function (F) which links the behavior to the life space. This function (F) is what one usually calls a law... The novelist who tells the story behind the behavior and development of an individual gives us detailed data about his parents, his siblings, his character, his intelligence, his occupation, his friends, his status. He gives us these data in their specific interrelation, that is, as part of a total situation. Psychology has to fulfill the same task with scientific instead of poetic means.... The method should be analytical in that the different factors which influence behavior have to be specifically distinguished. In science, these data have also to be represented in their particular setting within the specific situation. A totality of coexisting facts which are conceived of as mutually interdependent is called a field. Psychology has to view the life space, including the person and his environment, as one field."

"The objective of social change might concern the nutritional standard of consumption, the economic standard of living, the type of group relation, the output of a factory, the productivity of an educational team. It is important that a social standard to be changed does not have the nature of a “thing” but of a “process.”."

"The second experiment, with four leaders, makes possible a comparison of the authoritarianism and democracy of four different leaders, and the "laissez-faire" method of two different leaders. In two cases it is also possible to compare the same atmosphere, created by two different leaders with the same club. One other type of control seemed very important, the nature of the club activity, and the physical setting..."

"A business man once stated that there is nothing so practical as a good theory."

"The present report is a preliminary summary on one phase of a series of experimental studies of group life which has as its aim a scientific approach to such questions as the following : What underlies such differing patterns of group behavior as rebellion against authority, persecution of a scapegoat, apathetic submissiveness to authoritarian domination, or attack upon an outgroup? How may differences in subgroup structure, group stratification, and potency of ego- centered and group-centered goals be utilized as criteria for predicting the social resultants of different group atmospheres? Is not democratic group life more pleasant, but authoritarianism more efficient?"

"A goal can play an essential role in the psychological situation without being clearly present in consciousness."

"[Life space was defined as] the totality of facts which determine the behavior (B) of an individual (or group/organization) at a certain moment. The life space (L) represents the totality of possible events. The life space includes the person (P) and the environment (E). B = f(L) = f(P.E)"

"One should view the present situation – the status quo – as being maintained by certain conditions or forces. A culture – for instance, the food habits of a certain group at a given time – is not a static affair but a live process like a river which moves but still keeps to a recognizable form...Food habits do not occur in empty space. They are part and parcel of the daily rhythm of being awake and asleep; of being alone and in a group; of earning a living and playing; of being a member of a town, a family, a social class, a religious group . . . in a district with good groceries and restaurants or in an area of poor and irregular food supply. Somehow all these factors affect food habits at any given time. They determine the food habits of a group every day anew just as the amount of water supply and the nature of the river bed determine the flow of the river, its constancy or change."

"[Lewin formally defines a Gestalt as:] a system whose parts are dynamically connected in such a way that a change of one part results in a change of all other parts."

"Any planned social change will have to consider a multitude of factors characteristic for the particular case. The change may require a more or less unique combination of educational and organizational measures; it may depend upon quite different treatments or Ideology, expectation and organization. Still, certain general formal principles always have to be considered."