Mind

"How much of a person's competence is based on knowing which actions not to take? We usually think of a person's abilities in positive terms... But one could take the opposite view that "An expert is someone who rarely slips up—because of knowing what not to do." However, this subject was rarely discussed in the twentieth-century—except, perhaps most notably, in Sigmund Freud's analysis."

"We have not overthrown the divine right of kings to fall down before the divine right of experts."

"I think the people in this country have had enough of experts."

"No lesson seems to be so deeply inculcated by the experience of life as that you should never trust experts. If you believe doctors, nothing is wholesome: if you believe the theologians, nothing is innocent: if you believe the soldiers, nothing is safe. They all require their strong wine diluted by a very large admixture of insipid common sense."

"There appear to be no integrating forces, no unified meaning, no true inner understanding of phenomena in our experience of the world. Experts can explain anything in the objective world to us, yet we understand our own lives less and less. In short, we live in the postmodern world, where everything is possible and almost nothing is certain."

"An expert is someone who knows some of the worst mistakes that can be made in his subject, and how to avoid them."

"Experts bring light to dark places."

"If a man is trained, purely and simply, to be expert and contented in a particular task he will not innovate; Freud would have remained an anatomist, Marx a philosopher, Darwin a field-naturalist."

"In choosing people for specific jobs previous experience should not be a guide. I never put a man in the job which he thought he knew. Often the 'experts' make the worst possible Ministers in their own fields. In this country we prefer rule by amateurs."

"An expert is a person who has found out by his own painful experience all the mistakes that one can make in a very narrow field."

"The prevailing situation of criticism ... has given rise to a cult of professional expertise whose effect in general is pernicious. For the intellectual class, expertise has usually been a service rendered, and sold, to the central authority of society. This is the trahison des clercs of which Julien Benda spoke in the 1920s. Expertise in foreign affairs, for example, has usually meant the legitimization of the conduct of foreign policy and, what is more to the point, a sustained investment in revalidating the role of experts in foreign affairs. The same sort of thing is true of literary critics and professional humanists, except that their expertise is based upon noninterference in what Vico grandly calls the world of nations but which prosaically might just as well be called “the world.” We tell our students and our general constituency that we defend the classics, the virtues of a liberal education, and the precious pleasures of literature even as we also show ourselves to be silent (perhaps incompetent) about the historical and social world in which all these things take place. ..."

"Knowledge is one of the scarcest of all resources. Glib generalities abound, but specific hard facts about particular places and particular things at particular times that are relevant to economic decisions are something entirely different and much more scarce. In some respects, governments are better able to assemble vast amounts of knowledge, but the kind of knowledge involved is often in the form of statistical or verbal generalities known as “expertise,” which is no substitute for the kind of concrete knowledge that someone in the middle of a particular economic situation has. Just picking the right location for a particular business in a particular community can be the difference between profits and bankruptcy, even though that kind of knowledge may not be exciting from an intellectual standpoint. Experts may indeed have far more knowledge than the average amount of knowledge among individuals in the general population but the total amount of knowledge among millions of people in the general population vastly exceeds the total knowledge that any group of experts can assemble."

"In the media age, everybody was famous for 15 minutes. In the Wikipedia age, everybody can be an expert in five minutes. Special bonus: You can edit your own entry to make yourself seem even smarter."

"Don't take too seriously all that the neighbors say. Don't be overawed by what the experts say. Don't be afraid to trust your own common sense."

"Experto credite."

"It is very pleasant to follow one's inclinations ; but, unfortunately, we cannot follow them all. They are like the teeth sown by Cadmus ; they spring up, get in each other's way, and fight."

"Inclination never wants an excuse — and, if one won't do, there are a dozen others soon found."

"For positivism, which has assumed the judicial office of enlightened reason, to speculate about intelligible worlds is no longer merely forbidden but senseless prattle. ... For the scientific temper, any deviation of thought from the business of manipulating the actual, any stepping outside the jurisdiction of existence, is no less senseless and self-destructive than it would be for the magician to step outside the magic circle drawn for his incantation; and in both cases violation of the taboo carries a heavy price for the offender."

"Our National wish and purpose are only to be amused; our National religion is the performance of church ceremonies, and preaching of soporific truth (or untruths) to keep the mob quietly at work, while we amuse ourselves; and the necessity for this amusement is fastening on us, as a feverous disease of parched throat and wandering eyes—senseless, dissolute, merciless."

"Like one who has eaten and drunk too much and vomits painfully, and then feels better, so did the restless man wish he could rid himself with one terrific heave of these pleasures, of these habits of this entirely senseless life. … It seemed to him that he had spent his life in an entirely worthless and senseless manner; he retained nothing vital, nothing in any way precious or worth while. He stood alone, like a shipwrecked man on the shore."

"When we see a great man desiring power instead of his real goal we soon recognize that he is sick, or more precisely that his attitude to his work is sick. He overreaches himself, the work denies itself to him, the incarnation of the spirit no longer takes place, and to avoid the threat of senselessness he snatches after empty power. This sickness casts the genius on to the same level as those hysterical figures who, being by nature without power, slave for power, in order that they may enjoy the illusion that they are inwardly powerful, and who in this striving for power cannot let a pause intervene, since a pause would bring with it the possibility of self-reflection and self-reflection would bring collapse."

"My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.)"

"The argument “I may be dreaming” is senseless for this reason: if I am dreaming, this remark is being dreamed as well—and indeed it is also being dreamed that these words have any meaning."

"Although we acquire the skill of understanding words by experience, so that we know the correlations between them and things, between words and other words, and between words and feelings and actions, we do not do it by inductive reasoning. Nor must we think that we do it by deductive reasoning... In the main, words are cues rather than clues."

"It seems that scientists are often attracted to beautiful theories in the way that insects are attracted to flowers — not by logical deduction, but by something like a sense of smell."

"The Greeks... discovered mathematics and the art of deductive reasoning. Geometry, in particular, is a Greek invention, without which modern science would have been impossible."

"But in connection with mathematics the one-sidedness of the Greek genius appears: it reasoned deductively from what appeared self-evident, not inductively from what had been observed. Its amazing successes in the employment of this method misled not only the ancient world, but the greater part of the modern world also."

"The influence of geometry upon philosophy and scientific method has been profound. Geometry, as established by the Greeks, starts with axioms which are (or are deemed to be) self-evident, and proceeds, by deductive reasoning, to arrive at theorems which are very far from self-evident. The axioms and theorems are held to be true of actual space, which is something given in experience. It thus appeared to be possible to discover things about the actual world by first noticing what is self-evident and then using deduction. This view influenced Plato and Kant, and most of the intermediate philosophers. ...The eighteenth century doctrine of natural rights is a search for Euclidean axioms in politics. The form of Newton's Principia, in spite of its admittedly empirical material, is entirely dominated by Euclid. Theology, in its exact scholastic forms, takes its style from the same source."

"Descartes was an eminent mathematician, and it would seem that the bent of his mind led him to overestimate the value of deductive reasoning from general principles, as much as Bacon had underestimated it."

"I may as well say at once that I do not distinguish between inference and deduction. What is called induction appears to me to be either disguised deduction or a mere method of making plausible guesses."

"It has only been very slowly that scientific method, which seeks to reach principles inductively from observation of particular facts, has replaced the Hellenic belief in deduction from luminous axioms derived from the mind of the philosopher."

"Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. Both these points would belong to applied mathematics. We start, in pure mathematics, from certain rules of inference, by which we can infer that if one proposition is true, then so is some other proposition. These rules of inference constitute the major part of the principles of formal logic. We then take any hypothesis that seems amusing, and deduce its consequences. If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate."

"The two great conceptual revolutions of twentieth-century science, the overturning of classical physics by Werner Heisenberg and the overturning of the foundations of mathematics by Kurt Gödel, occurred within six years of each other within the narrow boundaries of German-speaking Europe. ...A study of the historical background of German intellectual life in the 1920s reveals strong links between them. Physicists and mathematicians were exposed simultaneously to external influences that pushed them along parallel paths. ...Two people who came early and strongly under the influence of Spengler's philosophy were the mathematician Hermann Weyl and the physicist Erwin Schrödinger. ...Weyle and Schrödinger agreed with Spengler that the coming revolution would sweep away the principle of physical causality. The erstwhile revolutionaries David Hilbert and Albert Einstein found themselves in the unaccustomed role of defenders of the status quo, Hilbert defending the primacy of formal logic in the foundations of mathematics, Einstein defending the primacy of causality in physics. In the short run, Hilbert and Einstein were defeated and the Spenglerian ideology of revolution triumphed, both in physics and in mathematics. Heisenberg discovered the true limits of causality in atomic processes, and Gödel discovered the limits of formal deduction and proof in mathematics. And, as often happens in the history of intellectual revolutions, the achievement of revolutionary goals destroyed the revolutionary ideology that gave them birth. The visions of Spengler, having served their purpose, rapidly became irrelevant."

"The two operations of our understanding, intuition and deduction, on which alone we have said we must rely in the acquisition of knowledge."

"Experience has convinced me that the proper way of teaching is to bring together that which is simple from all quarters, and, if I may use such a phrase, to draw upon the surface of the subject a proper mean between the line of closest connexion and the line of easiest deduction. This was the method followed by Euclid, who, fortunately for us, never dreamed of a geometry of triangles, as distinguished from a geometry of circles, or a separate application of the arithmetics of addition and subtraction; but made one help out the other as he best could."

"Robert [Grosseteste] became much interested in science and scientific method … He was conscious of the dual approach by means of induction and deduction (resolution and composition); i.e., from the empirical knowledge one proceeds to probable general principles, and from these as premises one them derives conclusions which constitute verifications or falsifications of the principles. This approach to science was not that far removed from Aristotle ..."

"The long chains of simple and easy reasonings by means of which geometers are accustomed to reach the conclusions of their most difficult demonstrations, had led me to imagine that all things, to the knowledge of which man is competent, are mutually connected in the same way, and that there is nothing so far removed from us as to be beyond our reach, or so hidden that we cannot discover it, provided only we abstain from accepting the false for the true, and always preserve in our thoughts the order necessary for the deduction of one truth from another."

"I cannot see why it is necessary that every deduction from algebra should be bound to certain conventions incident to an earlier stage of mathematical learning, even supposing them to have been consistently used up to the point in question. I should not care if any one thought this treatise unalgebraical, but should only ask whether the premises were admissible and the conclusions logical."

"With the completion of Euclid's Elements... For the first time in history masses of isolated discoveries were unified and correlated by a single guided principle, that of rigid deduction from explicitly stated assumptions. ...Not until 1839, in the work of ...D. Hilbert, was the full impact of Euclid's methodology felt in all mathematics. Concurrently with the pragmatic demonstration of the postulational method in arithmetic, geometry, algebra, topology, the theory of point sets, and analysis which distinguished the first four decades of the twentieth century, the method became almost popular in theoretical physics in the 1930's through the work of P. A. M. Dirac. Earlier scientific essays in the method, notably by E. Mach in mechanics and A. Einstein in relativity, had shown that the postulational approach is not only clarifying but creative. Mathematicians and scientists of the conservative persuasion may feel that a science constrained by an explicitly formulated set of assumptions has lost some of its freedom... Experience shows that the only loss is denial of the privilege of making avoidable mistakes in reasoning. ...Objection to the method is neither more nor less than objection to mathematics. ...If the Pythagorean dream of a mathematized science is to be realized, all of the sciences must eventually submit to the discipline that geometry accepted from Euclid."

""I exist" does not follow from "there is a thought now." The fact that a thought occurs at a given moment does not entail that any other thought has occurred at any other moment, still less that there has occurred a series of thoughts sufficient to constitute a single self. As Hume conclusively showed, no one event intrinsically points to any other. We infer the existence of events which we are not actually observing, with the help of general principle. But these principles must be obtained inductively. By mere deduction from what is immediately given we cannot advance a single step beyond. And, consequently, any attempt to base a deductive system on propositions which describe what is immediately given is bound to be a failure."

"Between the workable empiricism of the early land measurers... of ancient Egypt and the geometry of the Greeks in the sixth century before Christ, there is a great chasm. ...and the chasm is bridged by deductive reasoning applied consciously and deliberately to the practical inductions of daily life. Without the strictest deductive proof from admitted assumptions, explicitly stated as such, mathematics does not exist. This does not deny that intuition, experiment, induction, and plain guessing are important elements in mathematical invention. It merely states the criterion by which the final product of all guessing, by whatever name it be dignified, is judged to be or not to be mathematics. It is not known where or when the distinction between inductive inference—the summation of raw experience—and deductive proof from a set of postulates was first made, but it was sharply recognized by the Greek mathematicians as early as 550 B.C."

"It has fallen to the lot of one people, the ancient Greeks, to endow human thought with two outlooks on the universe neither of which has blurred appreciably in more than two thousand years. ...The first was the explicit recognition that proof by deductive reasoning offers a foundation for the structure of number and form. The second was the daring conjecture that nature can be understood by human beings through mathematics, and that mathematics is the language most adequate for idealizing the complexity of nature into appreciable simplicity. Both are attributed by persistent Greek tradition to Pythagoras in the sixth century before Christ. ...there is an equally persistent tradition that it was Thales... who first proved a theorem in geometry. But there seems to be no claim that Thales... proposed the inerrant tactic of definitions, postulates, deductive proof, theorem as a universal method in mathematics. ...in attributing any specific advance to Pythagoras himself, it must be remembered that the Pythagorean brotherhood was one of the world's earliest unpriestly cooperative scientific societies, if not the first, and that its members assigned the common work of all by mutual consent to their master."

"Dumb parts, properly connected into a swarm, yield smart results."

"Human beings suffer from a 'centralized mindset'; they would like to assign the coordination of activities to a central command. But the way social insects form highways and other amazing structures such as bridges, chains, nests (by the way, African fungus-growing termites have invented air conditioning) and can perform complex tasks (nest building, defense, cleaning, brood care, foraging, etc) is very different: they self-organize through direct and indirect interactions."

"The most amazing thing about social insect colonies is that there's no individual in charge. If you look at a single ant, you may have the impression that it is behaving, if not randomly, at least not in synchrony with the rest of the colony. You feel that it is doing its own things without paying too much attention to what the others are doing."

"when software systems become so intractable that they can no longer be controlled, swarm intelligence offers an alternative way of designing an ‘intelligent’ systems, in which autonomy, emergence, and distributed functioning replace control, preprogramming, and centralization."

"Swarm Intelligence can be defined more precisely as: Any attempt to design algorithms or distributed problem-solving methods inspired by the collective behavior of the social insect colonies or other animal societies. The main properties of such systems are flexibility, robustness, decentralization and self-organization."

"These nature-inspired algorithms gradually became more and more attractive and popular among the evolutionary computation research community, and together they were named swarm intelligence, which became the little brother of the major four evolutionary computation algorithms."

"Swarm intelligence illustrates the complex and holistic way in which the world operates. Order is created from chaos; patterns are revealed; and systems are free to work out their errors and problems at their own level. What natural systems can teach humanity is truly amazing."

"Mindfulness is present-moment awareness. It takes place in the here and now. It is the observance of what is happening right now, in the present. It stays forever in the present, perpetually on the crest of the ongoing wave of passing time."