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Norbert Wiener

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Mathematician

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“A proof represents a logical process which has come to a definitive conclusion in a finite number of stages. However, a logical machine following definite rules need never come to a conclusion. It may go on grinding through different stages without ever coming to a stop, either by describing a pattern of activity of continually increasing complexity, or by going into a repetitive process like the end of a chess game in which there is a continuing cycle of perpetual check. This occurs in the case of some of the paradoxes of Cantor and Russell. Let us consider the class of all classes which are not members of themselves. Is this class a member of itself? If it is, it is certainly not a member of itself; and if it is not, it is equally certainly a member of itself. A machine to answer this question would give the successive temporary answers: “yes,” “no,” “yes,” “no,” and so on, and would never come to equilibrium. Bertrand Russell’s solution of his own paradoxes was to affix to every statement a quantity, the so-called type, which serves to distinguish between what seems to be formally the same statement, according to the character of the objects with which it concerns itself—whether these are “things,” in the simplest sense, classes of “things,” classes of classes of “things,” etc. The method by which we resolve the paradoxes is also to attach a parameter to each statement, this parameter being the time at which it is asserted. In both cases, we introduce what we may call a parameter of uniformization, to resolve an ambiguity which is simply due to its neglect.”

“What I have said about the newspapers and the movies applies equally to the radio, to television, and even to bookselling. Thus we are in an age where the enormous per capita bulk of communication is met by an ever-thinning stream of total bulk of communication. More and more we must accept a standardized inoffensive and insignificant product which, like the white bread of the bakeries, is made rather for its keeping and selling properties than for its food value. This is fundamentally an external handicap of modern communication, but it is paralleled by another which gnaws from within. This is the cancer of creative narrowness and feebleness. In the old days, the young man who wished to enter the creative arts might either have plunged in directly or prepared himself by a general schooling, perhaps irrelevant to the specific tasks he finally undertook, but which was at least a searching discipline of his abilities and taste. Now the channels of apprenticeship are largely silted up. Our elementary and secondary schools are more interested in formal classroom discipline than in the intellectual discipline of learning something thoroughly, and a great deal of the serious preparation for a scientific or a literary course is relegated to some sort of graduate school or other.”

“Thus the nerve may be taken to be a relay with essentially two states of activity: firing and repose. Leaving aside those neurons which accept their messages from free endings or sensory end organs, each neuron has its message fed into it by other neurons at points of contact known as synapses. For a given outgoing neuron, these vary in number from a very few to many hundred. It is the state of the incoming impulses at the various synapses, combined with the antecedent state of the outgoing neuron itself, which determines whether it will fire or not. If it is neither firing nor refractory, and the number of incoming synapses which “fire” within a certain very short fusion interval of time exceeds a certain threshold, then the neuron will fire after a known, fairly constant synaptic delay. This is perhaps an oversimplification of the picture: the “threshold” may not depend simply on the number of synapses but on their “weight” and their geometrical relations to one another with respect to the neuron into which they feed; and there is very convincing evidence that there exist synapses of a different nature, the so-called “inhibitory synapses,” which either completely prevent the firing of the outgoing neuron or at any rate raise its threshold with respect to stimulation at the ordinary synapses. What is pretty clear, however, is that some definite combinations of impulses on the incoming neurons having synaptic connections with a given neuron will cause it to fire, while others will not cause it to fire. This is not to say that there may not be other, non-neuronic influences, perhaps of a humoral nature, which produce slow, secular changes tending to vary that pattern of incoming impulses which is adequate for firing.”

“As in the case of the individual, not all the information which is available to the race at one time is accessible without special effort. There is a well-known tendency of libraries to become clogged by their own volume; of the sciences to develop such a degree of specialization that the expert is often illiterate outside his own minute specialty. Dr. Vannevar Bush has suggested the use of mechanical aids for the searching through vast bodies of material. These probably have their uses, but they are limited by the impossibility of classifying a book under an unfamiliar heading unless some particular person has already recognized the relevance of that heading for that particular book. In the case where two subjects have the same techniques and intellectual content but belong to widely separated fields, this still requires some individual with an almost Leibnizian catholicity of interest.”

“Now there is no normal process except death which completely clears the brain from all past impressions; and after death, it is impossible to set it going again. Of all normal processes, sleep comes the nearest to a non-pathological clearing. How often we find that the best way to handle a complicated worry or an intellectual muddle is to sleep over it! However, sleep does not clear away the deeper memories, nor indeed is a sufficiently malignant state of worry compatible with an adequate sleep. We are thus often forced to resort to more violent types of intervention in the memory cycle. The more violent of these involve a surgical intervention into the brain, leaving behind it permanent damage, mutilation, and the abridgment of the powers of the victim, as the mammalian central nervous system seems to possess no powers whatever of regeneration. The principal type of surgical intervention which has been practiced is known as prefrontal lobotomy, and consists in the removal or isolation of a portion of the prefrontal lobe of the cortex. It has recently been having a certain vogue, probably not unconnected with the fact that it makes the custodial care of many patients easier. Let me remark in passing that killing them makes their custodial care still easier. However, prefrontal lobotomy does seem to have a genuine effect on malignant worry, not by bringing the patient nearer to a solution of his problems but by damaging or destroying the capacity for maintained worry, known in the terminology of another profession as the conscience. More generally, it appears to limit all aspects of the circulating memory, the ability to keep in mind a situation not actually presented. The various forms of shock treatment—electric, insulin, metrazol—are less drastic methods of doing a very similar thing. They do not destroy brain tissue or at least are not intended to destroy it, but they do have a decidedly damaging effect on the memory. In so far as this concerns the circulating memory, and in so far as this memory is chiefly damaged for the recent period of mental disorder, and is probably scarcely worth preserving anyhow, shock treatment has something definite to recommend it as against lobotomy; but it is not always free from deleterious effects on the permanent memory and the personality. As it stands at present, it is another violent, imperfectly understood, imperfectly controlled method to interrupt a mental vicious circle. This does not prevent its being in many cases the best thing we can do at present.”

“One of my father’s purposes in going to Vienna was to see a journalist by the name of Karl Kraus. I do not know what they discussed, though they probably concerned themselves with Jewish matters and quite possibly with the problem of the translation into literary German of the Yiddish poems of Moritz Rosenfeld, the New York garment worker-poet, whom father had ‘‘discovered.’’ I remember being taken into Kraus’s apartment in an old-fashioned Vienna apartment house, and there I remember what seemed to me a confusion and disorder which I have never seen equaled elsewhere.”

“If we use, to achieve our purposes, a mechanical agency with whose operation we cannot efficiently interfere once we have started it, because the action is so fast and irrevocable that we have not the data to intervene before the action is complete, then we had better be quite sure that the purpose put into the machine is the purpose which we really desire and not merely a colorful imitation of it.”

“We have contributed to the initiation of a new science which, as I have said, embraces technical developments with great possibilities for good and for evil. We can only hand it over into the world that exists about us, and this is the world of Belsen and Hiroshima. We do not even have the choice of suppressing these new technical developments. They belong to the age, and the most any of us can do by suppression is to put the development of the subject into the hands of the most irresponsible and most venal of our engineers. The best we can do is to see that a large public understands the trend and the bearing of the present work, and to confine our personal efforts to those fields, such as physiology and psychology, most remote from war and exploitation. As we have seen, there are those who hope that the good of a better understanding of man and society which is offered by this new field of work may anticipate and outweigh the incidental contribution we are making to the concentration of power (which is always concentrated, by its very conditions of existence, in the hands of the most unscrupulous). I write in 1947, and I am compelled to say that it is a very slight hope.”

“The mechanical brain does not secrete thought "as the liver does bile," as the earlier materialists claimed, nor does it put it out in the form of energy, as the muscle puts out its activity. Information is information, not matter or energy. No materialism which does not admit this can survive at the present day.”

“We are in the position of the man who has only two ambitions in life. One is to invent the universal solvent which will dissolve any solid substance, and the second is to invent the universal container which will hold any liquid. Whatever this inventor does, he will be frustrated.”

“What sometimes enrages me and always disappoints and grieves me is the preference of great schools of learning for the derivative as opposed to the original, for the conventional and thin which can be duplicated in many copies rather than the new and powerful, and for arid correctness and limitation of scope and method rather than for universal newness and beauty, wherever it may be seen.”

“The sense of tragedy is that the world is not a pleasant little nest made for our protection, but a vast and largely hostile environment, in which we can achieve great things only by defying the gods; and that this defiance inevitably brings its own punishment.”

“There are fields of scientific work...which have been explored from the different sides of pure mathematics, statistics, electrical engineering, and neurophysiology...in which every single notion receives a separate and different name from each group, and in which important work has been triplicated or quadruplicated, while still other important work is delayed by the unavailability in one field of results that may have already become classical in the next field.”

“I may remark parenthetically that the modern apparatus of the theory of small samples, once it goes beyond the determination of its own specially defined parameters and becomes a method for positive statistical inference in new cases, does not inspire me with any confidence unless it is applied by a statistician by whom the main elements of the dynamics of the situation are either explicitly known or implicitly felt.”

“Science is better paid than at any time in the past. The results of this pay have been to attract into science many of those for whom the pay is the first consideration, and who scorn to sacrifice immediate profit for the freedom of development of their own concept. Moreover, this inner development, important and indispensable as it may be to the world of science in the future, generally does not have the tendency to put a single cent into the pockets of their employers.”

“The idea that information can be stored in a changing world without an overwhelming depreciation of its value is false. It is scarcely less false than the more plausible claim that after a war we may take our existing weapons, fill their barrels with information.”

“Progress imposes not only new possibilities for the future but new restrictions. It seems almost as if progress itself and our fight against the increase of entropy intrinsically must end in the downhill path from which we are trying to escape.”

“Just as entropy is a measure of disorganization, the information carried by a set of messages is a measure of organization. In fact, it is possible to interpret the information carried by a message as essentially the negative of its entropy, and the negative logarithm of its probability. That is, the more probable the message, the less information it gives. Cliches, for example, are less illuminating than great poems.”