jews-from-the-netherlands

"The word “prostitution” was not allowed to be mentioned in proper company.... How often have I tried in vain to throw down that wall of prejudice and routine! I am thinking, among other things, of a dispute with one of my professors. Completely in good faith, "Professor" proclaimed the position held by almost everyone at the time, that for a man satisfying his sex drive was a requirement of health and that it was therefore in the community's interest to ensure that by satisfying that drive no or minimal damage was done to his health. “If that is really your opinion,” I replied, “you are morally obliged to make your daughters available for this purpose.”"

"I would like to tell you about a not unpleasant experience that I had in the first years of my career... After prolonged treatment, I was able to assure the wife of an Amsterdam patrician that she was cured of a serious gynecological ailment, which she had suffered for many years. As was customary in those years, I submitted my account at the start of the new year. A few days later I received a visit from the husband of my ex-patient.... “What gave you the idea!” he shouted, full of indignation. “You must surely know that no one thinks of paying women's work as highly as work done by men.”.... “Did you then,” I asked very calmly, “when your wife was indeed seriously ill, seek inferior and therefore cheap medical help for her? I suspect that it was primarily good help you sought. I thought that was why you turned to me, the only female doctor in the Netherlands.” “Are you,” I asked further, “are you really seriously complaining about a bill based on the rates set by my male colleagues? You should rather appreciate that I adhere to this, instead of relying on the privileged position of being the only female doctor in the country for the time being and therefore being paid more expensively than the other Amsterdam physicians.” ....his wife came to pay the bill a few days later...."

"The sky is full of birds, the purple lupins stand up so regally and peacefully, two little old women have sat down on the box for a chat, the sun is shining on my face — and right before our eyes, mass murder. The whole thing is simply beyond comprehension."

"There is a really deep well inside me. And in it dwells God. Sometimes I am there, too. But more often stones and grit block the well, and God is buried beneath. Then He must be dug out again."

"And if God does not help me to go on, then I shall have to help God. — The surface of the earth is gradually turning into one great prison camp, and soon there will be nobody left outside. … I don't fool myself about the real state of affairs, and I've even dropped the pretense that I'm out to help others. I shall merely try to help God as best I can, and if I succeed in doing that, then I shall be of use to others as well. But I mustn't have heroic illusions about that either."

"Dear God, these are anxious times. Tonight for the first time I lay in the dark with burning eyes as scene after scene of human suffering passed before me. I shall promise You one thing, God, just one very small thing: I shall never burden my today with cares about my tomorrow, although that takes some practice. Each day is sufficient unto itself. I shall try to help You, God, to stop my strength ebbing away, though I cannot vouch for it in advance. But one thing is becoming increasingly clear to me: that You cannot help us, that we must help You to help ourselves. And that is all we can manage these days and also all that really matters: that we safeguard that little piece of You, God, in ourselves. And perhaps in others as well. Alas, there doesn't seem to be much You Yourself can do about our circumstances, about our lives. Neither do I hold You responsible. You cannot help us, but we must help You and defend Your dwelling place inside us to the last."

"You have made me so rich, oh God, please let me share Your beauty with open hands. My life has become an uninterrupted dialogue with You, oh God, one great dialogue. At night, when I lie in my bed and rest in You, oh God, tears of gratitude run down my face, and that is my prayer."

"The absence of hatred in no way implies the absence of moral indig­nation."

"By ignoring and evading rather than altogether abolishing obsolete rules and regulations, eighteenth century Britain moved slowly toward a free market society."

"Whether the medieval episode is being regarded as itself revolutionary or as an indispensable run-up to the Scientific Revolution or not even that, just about every historian of science keeps treating it as the immediate predecessor to whatever revolutionary things happened in the 17th century."

"The distinction between micro- and macro inventions matters because they appeared to be governed by different laws. Micro-inventions generally result from an intentional search for improvements, and are understandable -if not predictable- by economic forces. They are guided, at least to some extent, by the laws of supply and demand and by the intensity of search and the resources committed to them, and thus by signals emitted by the price mechanism. Furthermore, in so far as micro inventions are the by-products of experience through learning by doing or learning by using they are correlated with output or investment. Macroinventions are more difficult to understand, and seem to be governed by individual genius and luck as much as by economic forces. Often they are based on some fortunate event, in which an inventor stumbles on one thing while looking for another, arrives at the right conclusion for the wrong reason, or brings to bear a seemingly unrelated body of knowledge that just happen to hold the clue to the right solution. The timing of these inventions is consequently often hard to explain. Much of the economic literature dealing with the generation of technological progress through market mechanisms and incentive devices thus explain only part of the story. This does not mean that we have to give up the attempt to try to understand macroinventions. We must, however, look for explanations largely outside the trusted and familiar market mechanisms relied upon by economists."

"In discussing the distinction between minor inventions, whose cumulative impact is decisive in productivity growth, and major technological breakthroughs, it may be useful to draw an analogy between the history of technology and the modem theory of evolution ( ... ) Some biologists distinguish between micro-mutations, which are small changes in an existing species and which gradually alter its features, and macromutations, which creates new species. The distinction between the two could provide a useful analogy for our purposes. I define micro inventions as the small, incremental steps that improve, adapt an extremeline existing techniques already in use, reducing costs, improving form and function, increasing durability, and reducing energy and raw material requirements. Macroinventions, on the other hand, are those inventions in which a radical new idea, without clear precedent, emerges more or less ab nihilo. In terms of sheer numbers, micro inventions are far more frequent and account for most gains in productivity. Macroinventions, however, are equally crucial in technological history."

"The clash between reason and Portuguese experience. Hooykaas' starting point is the intellectual challenge which, from the early 15th century onward, was posed by the discoveries of the Portuguese mariners... There follows an array of fascinating accounts of, and quotations from, works by contemporary authors who were compelled to face as facts numerous phenomena the ancients had been quite sure could not possibly be observed because they were bound not to exist. Examples are Aristotle's denial that the tropics could be inhabited; Ptolemy's mathematically derived conviction that all dry land is confined to part of the Northern Hemisphere, and so on. ...In Hooykaas' view we are witnessing here a birth of 'natural history' in the domain of the hard and given fact... The narrow world of sense-data to which the ancient natural philosophers had confined their all-too-rational speculations was now being blown to pieces. And this was not being done by fellow natural philosophers, but rather at the urging of scarcely literate sailors!"

"Hooykaas (1972, p. 100) writes that especially commercial and industrial cities were intellectually dynamic, far more so than sleepy university towns. These cities also tended to be more tolerant of different religions and multilingual. Modern research has found that especially cities involved in Atlantic trade were institutionally dynamic."

"Before the Industrial Revolution all techniques in use were supported by very narrow epistemic bases. That is to say, the people who invented them did not have much of a clue as to why and how they worked. The pre-1750 world produced, and produced well. It made many path-breaking inventions. But it was a world of engineering without mechanics, iron-making without metallurgy, farming without soil science, mining without geology, water-power without hydraulics, dye-making without organic chemistry, and medical practice without microbiology and immunology. The main point to keep in mind here is that such a lack of an epistemic base does not necessarily preclude the development of new techniques through trial and error and simple serendipity. But it makes the subsequent wave of micro-inventions that adapt and improve the technique and create the sustained productivity growth much slower and more costly. If one knows why some device works, it becomes easier to manipulate and debug it, to adapt to new uses and changing circumstances. Above all, one knows what will not work and thus reduce the costs of research and experimentation."

"Economists have traditionally been leery at mentalités as a factor in long-term economic development. In the budding literature on the economic rise of the West, such factors have been ignored or curtly dismissed. In the past, economists’ hostility to religious factors stems from the incompleteness of such theories. Attitudes were a matter of degree, not of absolutes."

"Technological systems, like all cultural systems, must have some built-in stability."

"What made the West successful was neither capitalism, nor science, nor an historical accident such as a favourable geography. Instead, political and mental diversity combined to create an ever changing panorama of technologically creative societies."

"If England led the rest of the world in the Industrial Revolution, it was despite, not because of her formal education system."

"As Hooykaas (1972, p. 101) argued, the pervasiveness of religion meant that for any idea to become socially acceptable, it made a huge difference whether it was resisted, tolerated, or sponsored by prevalent religious beliefs."

"The physical and social environment is important in determining the actions of individuals, although it is not solely responsible for the outcome."

"The distinction between micro- and macroinventions is useful because, as historians of technology emphasize, the word first is hazardous in this literature. . Many technological breakthroughs had a history that began before the event generally regarded as “the invention,” and almost all macroinventions required subsequent improvements to make them operational. Yet in a large number of cases, one or two identifiable events were crucial. Without such breakthroughs technological progress would eventually fizzle out."

"Knowledge may have been sought for its own sake or with a view to achieving certain practical improvements."

"All arguments based on the unequal status of texts are questionable. In principle, all ancient readings have an equal status, without relation to the text or translation in which they are found."

"To a large extent textual evaluation cannot be bound by any fixed rules. It is an art in the full sense of the word, a faculty which can be developed, guided by intuition based on wide experience."

"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."

"[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."

"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."

"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."

"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."

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

"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."

"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."

"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."

"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"

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

"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."

"[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."

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

"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."

"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."

"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."

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

"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."

"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."

"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"..."