Academics From Switzerland

"Euler and Ramanujan are mathematicians of the greatest importance in the history of constants (and of course in the history of Mathematics ...)"

"Euler's step was daring. In strict logic, it was an outright fallacy... Yet it was justified by analogy, by the analogy of the most successful achievements of a rising science that he called... "Analysis of the Infinite." Other mathematicians, before Euler, passed from finite differences to infinitely small differences, from sums with a finite number of terms to sums with an infinity of terms, from finite products to infinite products. And so Euler passed from equations of a finite degree (algebraic equations) to equations of infinite degree, applying the rules made for the finite... This analogy... is beset with pitfalls. How did Euler avoid them? ...Euler's reasons are not demonstrative. Euler does not reexamine the grounds for his conjecture... only its consequences. ...He examines also the consequences of closely related analogous conjectures... Euler's reasons are, in fact, inductive."

"It is the invaluable merit of the great Basle mathematician Leonard Euler, to have freed the analytical calculus from all geometric bounds, and thus to have established analysis as an independent science, which from his time on has maintained an unchallenged leadership in the field of mathematics."

"In 1736, during his first stay in St. Petersburg, Euler tackled the now famous problem of the seven bridges of Königsberg. His contribution to this problem is often cited as the birth of graph theory and topology."

"I discovered the works of Euler and my perception of the nature of mathematics underwent a dramatic transformation. I was de-Bourbakized, stopped believing in sets, and was expelled from the Cantorian paradise. I still believe in abstraction, but now I know that one ends with abstraction, not starts with it. I learned that one has to adapt abstractions to reality and not the other way around. Mathematics stopped being a science of theories but reappeared to me as a science of numbers and shapes."

"Perhaps the most surprising thing about mathematics is that it is so surprising. The rules which we make up at the beginning seem ordinary and inevitable, but it is impossible to foresee their consequences. These have only been found out by long study, extending over many centuries. Much of our knowledge is due to a comparatively few great mathematicians such as Newton, Euler, Gauss, or Riemann; few careers can have been more satisfying than theirs. They have contributed something to human thought even more lasting than great literature, since it is independent of language."

"As analysis was more cultivated, it gained a predominancy over geometry; being found to be a far more powerful instrument for obtaining results; and possessing a beauty and an evidence, which, though different from those of geometry, had great attractions for minds to which they became familiar. The person who did most to give to analysis the generality and symmetry which are now its pride, was also the person who made Mechanics analytical; I mean Euler."

"People are like stained-glass windows. They sparkle and shine when the sun is out, but when the darkness sets in, their true beauty is revealed only if there is a light from within."

"The Swiss-born psychiatrist Elisabeth Kubler-Ross changed western cultural resistance to dealing with death, and the teaching of how to accept it... Kubler-Ross's best known contribution to the study, thanatology, that she had helped to create, was the five stages of dying people go through. She described them - denial, anger, bargaining, depression and acceptance - in her bestseller On Death And Dying (1969), written in two months. Not everyone experiences all five, she cautioned, but at least two are always present. The definition, reached after scores of interviews with people facing imminent death, helped the medical profession to deal with a factor it had long refused to acknowledge, especially in the US... She wrote more than 20 books.. A firm believer in a god and the life hereafter, she became fascinated with near-death experiences and an advocate for people's stories of seeing a shining light and familiar faces, before being brought back from the brink."

"Dying is something we human beings do continuously, not just at the end of our physical lives on this earth."

"Those who have been immersed in the tragedy of massive death during wartime, and who have faced it squarely, never allowing their senses and feelings to become numbed and indifferent, have emerged from their experiences with growth and humanness greater than that achieved through almost any other means."

"It is difficult to accept death in this society because it is unfamiliar. In spite of the fact that it happens all the time, we never see it."

"Those who have the strength and the love to sit with a dying patient in the silence that goes beyond words will know that this moment is neither frightening nor painful, but a peaceful cessation of the functioning of the body."

"Watching a peaceful death of a human being reminds us of a falling star; one of a million lights in a vast sky that flares up for a brief moment only to disappear into the endless night forever."

"Guilt is perhaps the most painful companion of death."

"There is not much sense in suffering, since drugs can be given for pain, itching, and other discomforts. The belief has long died that suffering here on earth will be rewarded in heaven. Suffering has lost its meaning."

"We have to ask ourselves whether medicine is to remain a humanitarian and respected profession or a new but depersonalized science in the service of prolonging life rather than diminishing human suffering."

"Learn to get in touch with silence within yourself and know that everything in this life has a purpose. There are no mistakes, no coincidences; all events are blessings given to us to learn from. There is no need to go to India or anywhere else to find peace. You will find that deep place of silence right in your room, your garden or even your bathtub."

"We make progress in society only if we stop cursing and complaining about its shortcomings and have the courage to do something about them."

"As far as service goes, it can take the form of a million things. To do service, you don't have to be a doctor working in the slums for free, or become a social worker. Your position in life and what you do doesn't matter as much as how you do what you do."

"The child is a realist in every domain of thought, and it is therefore natural that in the moral sphere he should lay more stress on the external, tangible element than on the hidden motive."

"Much research in psychology has been more concerned with how large groups of people behave than about the particular ways in which each individual person thinks... too statistical. I find this disappointing because, in my view of the history of psychology, far more was learned, for example, when Jean Piaget spent several years observing the ways that three children developed, or when Sigmund Freud took several years to examine the thinking of a rather small number of patients."

"At one time, many philosophers held that faultless "laws of thought" were somehow inherent, a priori, in the very nature of mind. This belief was twice shaken in the past century; first when Russell and his successors showed how the logic men employ can be defective, and later when Freud and Piaget started to reveal the tortuous ways in which our minds actually develop."

"There are in existence two distinct ideas of justice. We say that an award is unjust when it penalizes the innocent, rewards the guilty, or when, in general, it fails to be meted out in exact proportion to the merit or guilt in question. On the other hand, we say that a division is unjust when it favors some at the expense of others. In this second adaptation of the term, the idea of justice implies only the idea of equality. In the first acceptation of the term, the notion of justice is inseparable from that of the reward and punishment, and is defined by the correlation between acts and their retribution."

"The relations between parents and children are certainly not only those of constraint. There is spontaneous mutual affection, which from the first prompts the child to acts of generosity and even of self-sacrifice, to very touching demonstrations which are in no way prescribed. And here no doubt is the starting point for that morality of good which we shall see developing alongside of the morality of right or duty, and which in some persons completely replaces it."

"The majority of parents are poor psychologists and give their children the most questionable moral trainings. It is perhaps in this domain that one realized most how keenly how immoral it can be to believe too much in morality, and how much more precious is a little humanity than all the rules in the world. Thus the adult leads the child to the notion of objective responsibility, and consolidates in consequence a tendency that is already natural to the spontaneous mentality of little children."

"To perceive is to construct intellectually, and if the child draws things as he conceives them, it is certainly because he cannot perceive them without conceiving them. But to give up gradually the spurious absolutes situated away and apart from the context of relations that has been built up during experience itself is the work of a superior kind of rationality. When the child comes to draw things as he sees them, it will be precisely because he has given up taking isolated objects in and for themselves and has begun to construct real systems of relations which take account of the true perspective in which things are connected."

"As Bovet has demonstrated in the field of morals, rules do not appear in the mind of the child as innate facts, but as facts that are transmitted to him by his seniors, and to which from his tenderest years he has to conform by means of a sui generis form of adaptation. This, of course, does not prevent some rules from containing more than others an element of rationality, thus corresponding to the deepest fundamental constants of human nature. But whether they be rational or simply a matter of usage and consensus of opinion, rules imposed on the childish mind by adult constraint do begin by presenting a more or less uniform character of exteriority and sheer authority. So that instead of passing smoothly from an early individualism (the "social" element of the first months is only biologically social, so to speak, inside the individual, and therefore individualistic) to a state of progressive cooperation, the child is from his first year onwards in the grip of coercive education which goes straight on and ends by producing what Claprède has so happily called a veritable "short circuit.""

"For the fundamental fact of human psychology is that society, instead of remaining almost entirely inside the individual organism as in the case of animals prompted by their instincts, becomes crystallized almost entirely outside the individuals. In other words, social rules, as Durkheim has so powerfully shown, whether they be linguistic, moral, religious, or legal, etc., cannot be constituted, transmitted or preserved by means of an internal biological heredity, but only through the external pressure exercised by individuals upon each other."

"The notion of good, which generally speaking, appears later than the notion of pure duty, particularly in the case of the child, is perhaps the final conscious realization of something that is the primary condition of the moral life — the need for reciprocal affection. And since moral realism is, on the contrary, the result of constraint exercised by the adult on the child, it may perhaps be a secondary growth in comparison to the simple aspiration after good, while still remaining the first notion to be consciously realized when the child begins to reflect upon morality and to attempt formulation."

"One must have felt a real desire to exchange thoughts with others in order to discover all that a lie can involve. And this interchange of thoughts is from the first not possible between adults and children, because the initial inequality is too great and the child tries to imitate the adult and at the same time to protect himself against him rather than really to exchange thoughts with him. The situation we have described is thus almost the necessary outcome of unilateral respect. The spirit of the command having failed to be assimilated, the letter alone remains. Hence the phenomenon we have been observing. The child thinks of a lie as "what isn't true," independently of the subject's intentions. He even goes so far as to compare lies to those linguistic taboos, "naughty words." As for the judgment of responsibility, the further a lie is removed from reality, the more serious is the offense. Objective responsibility is thus the inevitable result of unilateral respect in its earliest stage."

"Thus we see that the child is almost led to tell lies — or what seem to us lies from our point of view — by the very structure of his spontaneous thought. Given this situation, what will be the result of the laws laid down by adults about truthfulness? On the occasion of the first very obvious lies, or of those connected with some offense or other and told therefore with the object of averting punishment or scolding, the parents point out to the child that he has just done something very wrong and thus inculcate in him the respect for truth."

"It is as his own mind comes into contact with others that truth will begin to acquire value in the child's eyes and will consequently become a moral demand that can be made upon him. As long as the child remains egocentric, truth as such will fail to interest him and he will see no harm in transposing facts in accordance with his desires."

"In this way things, external objects, are assimilated to more or less ordered motor schemas, and in this continuous assimilation of objects the child's own activity is the starting point of play. Not only this, but when to pure movement are added language and imagination, the assimilation is strengthened, and wherever the mind feels no actual need for accommodating itself to reality, its natural tendency will be to distort the objects that surround it in accordance with its desires or its fantasy, in short to use them for its satisfaction. Such is the intellectual egocentrism that characterizes the earliest form of child thought."

"The need to speak the truth and even to seek it for oneself is only conceivable in so far as the individual thinks and acts as one of a society, and not of any society (for it is just the constraining relations between superior and inferior that often drive the latter to prevarication) but of a society founded on reciprocity and mutual respect, and therefore on cooperation."

"The child who defines a lie as being a "naughty word" knows perfectly well that lying consists in not speaking the truth. He is not, therefore, mistaking one thing for another, he is simply identifying them one with another by what seems to us a quaint extension of the word "lie"."

"It is when the child is accustomed to act from the point of view of those around him, when he tries to please rather than to obey, that he will judge in terms of intentions. So that taking intentions into account presupposes cooperation and mutual respect. Only those who have children of their own know how difficult it is to put this into practice. Such is the prestige of parents in the eyes of the very young child, that even if they lay down nothing in the form of general duties, their wishes act as law and thus give rise automatically to moral realism (independently, of course, of the manner in which the child eventually carries out these desires). In order to remove all traces of moral realism, one must place oneself on the child's own level, and give him a feeling of equality by laying stress on one's own obligations and one's own deficiencies. In this way the child will find himself in the presence, not of a system of commands requiring ritualistic and external obedience, but of a system of social relations such that everyone does his best to obey the same obligations, and does so out of mutual respect. The passage from obedience to cooperation thus marks a progress analogous to that of which we saw the effects in the evolution of the game of marbles: only in the final stage does the morality of intention triumph over the morality of objective responsibility. When parents do not trouble about such considerations as these, when they issue contradictory commands and are inconsistent in the punishments they inflict, then, obviously, it is not because of moral constraint but in spite of and as a reaction against it that the concern with intentions develops in the child. Here is a child, who, in his desire to please, happens to break something and is snubbed for his pains, or who in general sees his actions judged otherwise than he judges them himself. It is obvious that after more or less brief periods of submission, during which he accepts every verdict, even those that are wrong, he will begin to feel the injustice of it all. Such situations can lead to revolt. But if, on the contrary, the child finds in his brothers and sisters or in his playmates a form of society which develops his desire for cooperation and mutual sympathy, then a new type of morality will be created in him, a morality of reciprocity and not of obedience. This is the true morality of intention and of subjective responsibility."

"In real life the child is in the presence, not of isolated acts, but of personalities that attract or repel him as a global whole. He grasps people's intentions by direct intuition and cannot therefore abstract from them. He allows, more or less justly, for aggravating and attenuating circumstances. This is why the stories told by the children themselves often give rise to different evaluations from those suggested by the experimenter's stories."

"The discussion of the game of marbles seems to have led us into rather deep waters. But in the eyes of children the history of the game of marbles has quite as much importance as the history of religion or of forms of government. It Is a history, moreover, that is magnificently spontaneous; and it was therefore perhaps not entirely useless to seek to throw light on the child's judgment of moral value by a preliminary study of the social behaviour of children amongst themselves."

"Generally speaking, one can say that motor intelligence contains the germs of completed reason. But it gives promise of more than reason pure and simple. From the moral as from the intellectual point of view, the child is born neither good nor bad, but master of his destiny. Now, if there is intelligence in the schemas of motor adaptation, there is also the element of play. The intentionality peculiar to motor activity is not a search for truth but the pursuit of a result, whether objective or subjective; and to succeed is not to discover a truth."

"If mutual respect does derive from unilateral respect, it does so by opposition."

"There is little mysticism without an element of transcendence, and conversely, there is no transcendence without a certain degree of egocentrism. It may be that the genesis of these experiences is to be sought in the unique situation of the very young child in relation to adults. The theory of the filial origin of the religious sense seems to us singularly convincing in this connection."

"Egocentrism in so far as it means confusion of the ego and the external world, and egocentrism in so far as it means lack of cooperation, constitute one and the same phenomenon. So long as the child does not dissociate his ego from the suggestions coming from the physical and from the social world, he cannot cooperate, for in order to cooperate one must be conscious of one's ego and situate it in relation to thought in general. And in order to become conscious of one's ego, it is necessary to liberate oneself from the thought and will of others. The coercion exercised by the adult or the older child is therefore inseparable from the unconscious egocentrism of the very young child."

"Every observer has noted that the younger the child, the less sense he has of his own ego. From the intellectual point of view, he does not distinguish between external and internal, subjective and objective. From the point of view of action, he yields to every suggestion, and if he does oppose to other people's wills — a certain negativism which has been called "the spirit of contradiction" — this only points to his real defenselessness against his surroundings. A strong personality can maintain itself without the help of this particular weapon. The adult and the older child have complete power over him. They impose their opinions and their wishes, and the child accepts them without knowing that he does so. Only — and this is the other side of the picture — as the child does not dissociate his ego from the environment, whether physical or social, he mixes into all his thoughts and all his actions, ideas and practices that are due to the intervention of his ego and which, just because he fails to recognize them as subjective, exercise a check upon his complete socialization. From the intellectual point of view, he mingles his own fantasies with accepted opinions, whence arise pseudo lies (or sincere lies), syncretism, and all the features of child thought. From the point of view of action, he interprets in his own fashion the examples he has adopted, whence the egocentric form of play we were examining above. The only way of avoiding these individual refractions would lie in true cooperation, such that both child and senior would each make allowance for his own individuality and for the realities that were held in common."

"Mixture of assimilation to earlier schemas and adaptation to the actual conditions of the situation is what defines motor intelligence. But — and this is where rules come into existence — as soon as a balance is established between adaptation and assimilation, the course of conduct adopted becomes crystallized and ritualized. New schemas are even established which the child looks for and retains with care, as though they were obligatory or charged with efficacy."

"The motor rule. In its beginnings the motor rule merges into habit. During the first few months of an infant's life, its manner of taking the breast, of laying its head on the pillow, etc., becomes crystallized into imperative habits. This is why education must begin in the cradle. To accustom the infant to get out of its own difficulties or to calm it by rocking it may be to lay the foundations of a good or of a bad disposition. But not every habit will give rise to the knowledge of a rule. The habit must first be frustrated, and the ensuing conflict must lead to an active search for the habitual. Above all, the particular succession must be perceived as regular, i.e. there must be judgment or consciousness of regularity (Regelbewusstseiri). The motor rule is therefore the result of a feeling of repetition which arises out of the ritualization of schemas of motor adaptation."

"A second prefatory question faces us: that of society and the individual. We have sought to contrast the child and the civilized adult on the ground of their respective social attitudes. The baby (at the stage of motor intelligence) is asocial, the egocentric child is subject to external constraint but has little capacity for cooperation, the civilized adult of to-day presents the essential character of cooperation between differentiated personalities who regard each other as equals. There are therefore three types of behavior: motor behavior, egocentric behavior (with external constraint), and cooperation. And to these three types of social behavior there correspond three types of rules: motor rules, rules due to unilateral respect, and rules due to mutual respect. But here again, one must beware of laying down the law: for things are motor, individual and social all at once. As we shall have occasion to show, rules of cooperation are in some respects the outcome of the rules of coercion and of the motor rules. On the other hand, coercion is applied during the first days of an infant's life, and the earliest social relations contain the germs of cooperation. Here again, it is not so much a question of these successive features themselves as of the proportions in which they are present. Moreover, the way in which conscious realization and the time-lag from one level to another come into play is a further bar to our arranging these phenomena in a strict sequence, as though they made a single appearance and then disappeared from the scene once and for all."

"Between the various types of rules which we shall give there will therefore be at once continuity of function and difference of structure. This renders arbitrary any attempt to cut mental reality up into stages. The matter is further complicated by the "Law of conscious realization" and the resulting time-lag. The appearance of a new type of rule on the practical plane does not necessarily mean that this rule will come into the subject's consciousness, for each mental operation has to be relearned on the different planes of action and of thought."

"In certain circumstances where he experiments in new types of conduct by cooperating with his equals, the child is already an adult. There is an adult in every child and a child in every adult. … There exist in the child certain attitudes and beliefs which intellectual development will more and more tend to eliminate: there are others which will acquire more and more importance. The later are not derived from the former but are partly antagonistic to them."

"When the child imitates the rules practiced by his older companions he feels that he is submitting to an unalterable law, due, therefore, to his parents themselves. Thus the pressure exercised by older on younger children is assimilated here, as so often, to adult pressure. This action of the older children is still constraint, for cooperation can only arise between equals. Nor does the submission of the younger children to the rules of the older ones lead to any sort of cooperation in action; it simply produces a sort of mysticism, a diffused feeling of collective participation, which, as in the case of many mystics, fits in perfectly well with egocentrism. For we shall see eventually that cooperation between equals not only brings about a gradual change in the child's practical attitude, but that it also does away with the mystical feeling towards authority."