On Beliefs (1970-1979)

"Implication is thus the very texture of our web of belief, and logic is the theory that traces it." (Willard v O Quine, "The Web of Belief", 1970)

"Models are to be used, but not to be believed." (Henri Theil,"Principles of Econometrics", 1971)

"Some facts are so incredible that they are believed at once, for no one could possibly have imagined them." (Arthur C Clarke, "The Lost Worlds of 2001", 1972)

"In the province of the mind, what one believes to be true is true or becomes true, within certain limits to be found experientially and experimentally. These limits are further beliefs to be transcended. In the mind, there are no limit. […] In the province of connected minds, what the network believes to be true, either is true or becomes true within certain limits to be found experientially and experimentally. These limits are further beliefs to be transcended. In the network's mind there are no limits."(John C Lilly, "The Human Biocomputer", 1974)

"Meanwhile, for those who are not aware of it, it is necessary to mention that in the conception we follow and sustain here only subjective probabilities exist - i.e. the degree of belief in the occurrence of an event attributed by a given person at a given instant and with a given set of in information. This is in contrast to other conceptions which limit themselves to special types of cases in which they attribute meaning to 'objective probabilities' (for instance, cases of symmetry as for dice etc., 'statistical' cases of 'repeatable' events, etc.)." (Bruno de Finetti, "Theory of Probability", 1974)

"Probability, too, if regarded as something endowed with some kind of objective existence, is no less a misleading misconception, an illusory attempt to exteriorize or materialize our true probabilistic beliefs." (Bruno de Finetti, "Theory of Probability", 1974)

"If physics leads us today to a world view which is essentially mystical, it returns, in a way, to its beginning, 2,500 years ago. […] Eastern thought and, more generally, mystical thought provide a consistent and relevant philosophical background to the theories of contemporary science; a conception of the world in which scientific discoveries can be in perfect harmony with spiritual aims and religious beliefs. The two basic themes of this conception are the unity and interrelation of all phenomena and the intrinsically dynamic nature of the universe. The further we penetrate into the submicroscopic world, the more we shall realize how the modern physicist, like the Eastern mystic, has come to see the world as a system of inseparable, interacting and ever-moving components with the observer being an integral part of this system." (Fritjof Capra, "The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism", 1975)

"I find it more difficult, but also much more fun, to get the right answer by indirect reasoning and before all the evidence is in. It’s what a theoretician does in science. But the conclusions drawn in this way are obviously more risky than those drawn by direct measurement, and most scientists withhold judgment until there is more direct evidence available. The principal function of such detective work - apart from entertaining the theoretician - is probably to so annoy and enrage the observationalists that they are forced, in a fury of disbelief, to perform the critical measurements." (Carl Sagan, "The Cosmic Connection: An Extraterrestrial Perspective", 1975)

"All proofs inevitably lead to propositions which have no proof! All things are known because we want to believe in them." (Frank Herbert, "Children of Dune", 1976)

"People are entirely too disbelieving of coincidence. They are far too ready to dismiss it and to build arcane structures of extremely rickety substance in order to avoid it. I, on the other hand, see coincidence everywhere as an inevitable consequence of the laws of probability, according to which having no unusual coincidence is far more unusual than any coincidence could possibly be." (Isaac Asimov, "The Planet That Wasn't", 1976)

"In science we always know much less than we believe we do." (Erwin Chargaff, "Uncertainties Great, Is the Gain Worth the Risk?", Chemical and Engineering News, 1977)

"The so-called exact sciences often are not as exact as is commonly believed. How often they infer the existence of a hat from the emergence of a rabbit!" (Erwin Chargaff, "Voices in the Labyrinth: Nature, Man and Science", 1977)

"Many people believe that reasoning, and therefore science, is a different activity from imagining. But this is a fallacy […] Reasoning is constructed with movable images just as certainly as poetry is." (Jacob Bronowski, "Visionary Eye", 1978)

On Beliefs (1960-1969)

"For imagination sets the goal picture which our automatic mechanism works on. We act, or fail to act, not because of will, as is so commonly believed, but because of imagination." (Maxwell Maltz, "Psycho-Cybernetics", 1960)

"[Science fiction is] that class of prose narrative treating of a situation that could not arise in the world we know, but which is hypothesised on the basis of some innovation in science or technology, or pseudo-science or pseudo-technology, whether human or extra-terrestrial in origin. It is distinguished from pure fantasy by its need to achieve verisimilitude and win the 'willing suspension of disbelief' through scientific plausibility." (Kingsley Amis, "New Maps of Hell", 1960)

"The null-hypothesis significance test treats ‘acceptance’ or ‘rejection’ of a hypothesis as though these were decisions one makes. But a hypothesis is not something, like a piece of pie offered for dessert, which can be accepted or rejected by a voluntary physical action. Acceptance or rejection of a hypothesis is a cognitive process, a degree of believing or disbelieving which, if rational, is not a matter of choice but determined solely by how likely it is, given the evidence, that the hypothesis is true. (William W Rozeboom, "The fallacy of the null–hypothesis significance test", Psychological Bulletin 57, 1960)

"Freedom can be manifested only in the void of beliefs, in the absence of axioms, and only where the laws have no more authority than a hypothesis." (Emil Cioran, "History and Utopia", 1960)

"A world view is not merely a philosophical by-product of each culture, like a shadow, but the very skeleton of concrete cognitive assumptions on which the flesh of customary behavior is hung. World view, accordingly, may be expressed, more or less systematically in cosmology, philosophy, ethics, religious ritual, scientific belief, and so on, but it is implicit in almost every act. In Parsonian terms, it constitutes the set of cognitive orientations of the members of a society." (Anthony F C Wallace, "Culture and Personality", 1961)

"All our language is composed of brief little dreams; and the wonderful thing is that we sometimes make of them strangely accurate and marvelously reasonable thoughts. […] What should we be without the help of that which does not exist? Very little. And our unoccupied minds would languish if fables, mistaken notions, abstractions, beliefs, and monsters, hypotheses, and the so-called problems of metaphysics did not people with beings and objectless images our natural depths and darkness. Myths are the souls of our actions and our loves. We cannot act without moving towards a phantom. We can love only what we create." (Paul Valéry,"The Outlook for Intelligence", 1962)

"The important distinction between science and those other systematizations [i.e., art, philosophy, and theology] is that science is self-testing and self-correcting. Here the essential point of science is respect for objective fact. What is correctly observed must be believed [...] the competent scientist does quite the opposite of the popular stereotype of setting out to prove a theory; he seeks to disprove it. (George G Simpson, "Notes on the Nature of Science", 1962)

"Science, indeed, tells us a very great deal less about the universe than we have been accustomed to suppose, and there is no reason to believe that all we can ever know must be couched in terms of its thin and largely arbitrary abstractions." (John W N Sullivan, "Art and Reality", 1964)

"There are metaphysical problems, which cannot be disposed of by declaring them meaningless. For, as I have repeatedly said, they are ‘beyond physics’ indeed and demand an act of faith. We have to accept this fact to be honest. There are two objectionable types of believers: those who believe the incredible and those who believe that ‘belief’ must be discarded and replaced by 'the scientific method'." (Max Born, "Natural Philosophy of Cause and Chance", 1964)

"The belief that there is only one truth and that oneself is in possession of it, seems to me the deepest root of all that is evil in the world." (Max Born, "Natural Philosophy of Cause and Chance", 1964)

"There are metaphysical problems, which cannot be disposed of by declaring them meaningless. For, as I have repeatedly said, they are ‘beyond physics’ indeed and demand an act of faith. We have to accept this fact to be honest. There are two objectionable types of believers: those who believe the incredible and those who believe that ‘belief’ must be discarded and replaced by 'the scientific method'." (Max Born, "Natural Philosophy of Cause and Chance", 1964)

"The fact that theories are not subject to absolute and final proof has led to a serious vulgar misapprehension. Theory is contrasted with fact as if the two had no relationship or were antitheses: 'Evolution is only a theory, not a fact'. Of course, theories are not facts. They are generalizations about facts and explanations of facts, based on and tested by facts. As such they may be just as certain - merit just as much confidence - as what are popularly termed 'facts'. Belief that the sun will rise tomorrow is the confident application of a generalization. The theory that life has evolved is founded on much more evidence than supports the generalization that the sun rises every day. In the vernacular, we are justified in calling both 'facts'." (George G Simpson, Life: An Introduction to Biology, 1965)

"The most natural way to give an independence proof is to establish a model with the required properties. This is not the only way to proceed since one can attempt to deal directly and analyze the structure of proofs. However, such an approach to set theoretic questions is unnatural since all our intuition come from our belief in the natural, almost physical model of the mathematical universe." (Paul J Cohen, "Set Theory and the Continuum Hypothesis", 1966)

"Up until now most economists have concerned themselves with linear systems, not because of any belief that the facts were so simple, but rather because of the mathematical difficulties involved in nonlinear systems [... Linear systems are] mathematically simple, and exact solutions are known. But a high price is paid for this simplicity in terms of special assumptions which must be made." (Paul A Samuelson, "Foundations of Economic Analysis", 1966)

"It is now natural for us to try to derive the laws of nature and to test their validity by means of the laws of invariance, rather than to derive the laws of invariance from what we believe to be the laws of nature." (Eugene P Wigner, "Symmetries and Reflections", 1967)

"Most of our beliefs about complex organizations follow from one or the other of two distinct strategies. The closed-system strategy seeks certainty by incorporating only those variables positively associated with goal achievement and subjecting them to a monolithic control network. The open-system strategy shifts attention from goal achievement to survival and incorporates uncertainty by recognizing organizational interdependence with environment. A newer tradition enables us to conceive of the organization as an open system, indeterminate and faced with uncertainty, but subject to criteria of rationality and hence needing certainty." (James D Thompson, "Organizations in Action", 1967)

"[…] the social scientist who lacks a mathematical mind and regards a mathematical formula as a magic recipe, rather than as the formulation of a supposition, does not hold forth much promise. A mathematical formula is never more than a precise statement. It must not be made into a Procrustean bed - and that is what one is driven to by the desire to quantify at any cost. It is utterly implausible that a mathematical formula should make the future known to us, and those who think it can, would once have believed in witchcraft. The chief merit of mathematicization is that it compels us to become conscious of what we are assuming." (Bertrand de Jouvenel, "The Art of Conjecture", 1967)

"The higher we climb the ladder of epistemic abstraction the less we ourselves appear in our picture of the world and the better we are at explaining our own experiences. On the other hand, by remaining close to the senses we will not transcend superficial, anthropocentric world views. In short, although experience is a test of our theories it is not the stuff our theories are made of or even the referent of physical theories: human experience proper is the subject of nonphysical sciences like psychology. These platitudes had to be stated on account of the widespread belief that in physics only observational predicates matter - a belief inherited from philosophies at variance with science." (Mario Bunge, "Foundations of Physics", 1967)

"An algorithm must be seen to be believed, and the best way to learn what an algorithm is all about is to try it." (Donald E Knuth, The Art of Computer Programming Vol. I, 1968)

On Belief (1950-1959)

"A computer would deserve to be called intelligent if it could deceive a human into believing that it was human." (Alan Turing, "Computing Machinery and Intelligence", Mind Vol. 59, 1950)

"[…] the chief reason in favor of any theory on the principles of mathematics must always be inductive, i.e., it must lie in the fact that the theory in question enables us to deduce ordinary mathematics. In mathematics, the greatest degree of self-evidence is usually not to be found quite at the beginning, but at some later point; hence the early deductions, until they reach this point, give reasons rather from them, than for believing the premises because true consequences follow from them, than for believing the consequences because they follow from the premises." (Alfred N Whitehead, "Principia Mathematica", 1950)

"As a set of cognitive beliefs, religion is a speculative hypothesis of an extremely low order of probability." (Sidney Hook, The Partisan Review, 1950)

"It is a common fallacy to believe that the law of large numbers acts as a force endowed with memory seeking to return to the original state, and many wrong conclusions have been drawn from this assumption." (William Feller, "An Introduction To Probability Theory And Its Applications", 1950)

"[…] no one believes an hypothesis except its originator but everyone believes an experiment except the experimenter. (William I B Beveridge, "The Art of Scientific Investigation", 1950)

"The hypothesis is the principal intellectual instrument in research. Its function is to indicate new experiments and observations and it therefore sometimes leads to discoveries even when not correct itself. We must resist the temptation to become too attached to our hypothesis, and strive to judge it objectively and modify it or discard it as soon as contrary evidence is brought to light. Vigilance is needed to prevent our observations and interpretations being biased in favor of the hypothesis. Suppositions can be used without being believed." (William I B Beveridge, "The Art of Scientific Investigation", 1950)

"The belief in science has replaced in large measure, the belief in God. Even where religion was regarded as compatible with science, it was modified by the mentality of the believer in scientific truth." (Hans Reichenbach, "The Rise of Scientific Philosophy", 1951)

"The older physicist believed in Nature and thought of himself as making experiments to see what She was like. She was there whether he could observe her or not. But the modern physicist thinks first of all of what he observes in his experiments and is not interested in anything that he cannot possibly observe. He looks for relations between his observations and ignores everything else. But he still expresses his results as though they were discoveries of the essence of Nature, because he is so used to this way of speaking that he does not realise that his discoveries no longer conform to it. When they are expressed as the characteristics of a world existing outside us and independently of us, which causes our experience by its impact on our sense organs, these discoveries require such a world to have contradictory properties. Hence, by retaining this form of expression, the physicist finds himself presenting his perfectly rational achievements as though they were nonsensical. (Herbert Dingle, "The Scientific Adventure", British Journal for the Philosophy of Science, 1952)

"The trouble seems to lie chiefly in the assumption that mathematics is by nature something absolute, unchanging with time and place, and therefore capable of being identified once the genius with the eye sharp enough to perceive and characterize it appears on the human scene. And, since mathematics is nothing of the sort (although the layman will probably go on for centuries hence believing that it is), only failure can ensue from the attempt so to characterize it." (Raymond L Wilder, "Introduction to the Foundations of Mathematics", 1952)

On Beliefs (1900-1924)

"Induction applied to the physical sciences is always uncertain, because it rests on the belief in a general order of the universe, an order outside of us." (Henri Poincaré, "Science and Hypothesis", 1901)

"Let us notice first of all, that every generalization implies in some measure the belief in the unity and simplicity of nature." (Jules H Poincaré, "Science and Hypothesis", 1901)

"Besides it is an error to believe that rigour is the enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous method is at the same time the simpler and the more easily comprehended. The very effort for rigor forces us to find out simpler methods of proof." (David Hilbert,"Mathematical Problems", Bulletin of the American Mathematical Society Vol. 8, 1902)

"To undertake the calculation of any probability, and even for that calculation to have any meaning at all, we must admit, as a point of departure, an hypothesis or convention which has always something arbitrary about it. In the choice of this convention we can be guided only by the principle of sufficient reason. Unfortunately, this principle is very vague and very elastic, and in the cursory examination we have just made we have seen it assume different forms. The form under which we meet it most often is the belief in continuity, a belief which it would be difficult to justify by apodeictic reasoning, but without which all science would be impossible. Finally, the problems to which the calculus of probabilities may be applied with profit are those in which the result is independent of the hypothesis made at the outset, provided only that this hypothesis satisfies the condition of continuity." (Henri Poincaré, "Science and Hypothesis", 1901)

"A belief in a proposition is a controlled and contented habit of acting in ways that will be productive of desired results only if the proposition is true; An affirmation is an act of an utterer of a proposition to an interpreter, and consists, in the first place, in the deliberate exercise, in uttering the proposition, of a force tending to determine a belief in it in the mind of the interpreter." (Charles S Peirce, "New Elements" ["Kaina stoiceia"], 1904)

"The most violent revolutions in an individual's beliefs leave most of his old order standing. Time and space, cause and effect, nature and history, and one's own biography remain untouched. New truth is always a go-between, a smoother-over of transitions. It marries old opinion to new fact so as ever to show a minimum of jolt, a maximum of continuity." (William James, "What Pragmatism Means", 1907)

"[…] the chief reason in favor of any theory on the principles of mathematics must always be inductive, i.e., it must lie in the fact that the theory in question enables us to deduce ordinary mathematics. In mathematics, the greatest degree of self-evidence is usually not to be found quite at the beginning, but at some later point; hence the early deductions, until they reach this point, give reasons rather from them, than for believing the premises because true consequences follow from them, than for believing the consequences because they follow from the premises." (Alfred N Whitehead, "Principia Mathematica", 1910)  

"The belief that mathematics, because it is abstract, because it is static and cold and gray, is detached from life, is a mistaken belief. Mathematics, even in its purest and most abstract estate, is not detached from life. It is just the ideal handling of the problems of life, as sculpture may idealize a human figure or as poetry or painting may idealize a figure or a scene. Mathematics is precisely the ideal handling of the problems of life, and the central ideas of the science, the great concepts about which its stately doctrines have been built up, are precisely the chief ideas with which life must always deal and which, as it tumbles and rolls about them through time and space, give it its interests and problems, and its order and rationality." (Cassius J Keyser, "The Humanization of the Teaching of Mathematics", 1912)

"It is experience which has given us our first real knowledge of Nature and her laws. It is experience, in the shape of observation and experiment, which has given us the raw material out of which hypothesis and inference have slowly elaborated that richer conception of the material world which constitutes perhaps the chief, and certainly the most characteristic, glory of the modern mind." (Arthur J Balfour, "The Foundations of Belief", 1912)

"The critical mathematician has abandoned the search for truth. He no longer flatters himself that his propositions are or can be known to him or to any other human being to be true; and he contents himself with aiming at the correct, or the consistent. The distinction is not annulled nor even blurred by the reflection that consistency contains immanently a kind of truth. He is not absolutely certain, but he believes profoundly that it is possible to find various sets of a few propositions each such that the propositions of each set are compatible, that the propositions of each such set imply other propositions, and that the latter can be deduced from the former with certainty. That is to say, he believes that there are systems of coherent or consistent propositions, and he regards it his business to discover such systems. Any such system is a branch of mathematics." (Cassius J Keyser, Science, New Series, Vol. 35 (904), 1912)

"It is only when one looks not towards the outside, at their utility, but within mathematics itself at the relationship among the unused parts that one sees the other, real face of this science. It is not goal-oriented but uneconomical and passionate… (The mathematician) believes that what he is doing will probably eventually lead to some practical cash value, but this is not what spurs him on; he serves the truth, which is to say his destiny, not its purpose. The result may be economical a thousand times over; what is immanent is a total surrender and a passionate devotion." (Robert Musil, "The Mathematical Man", 1913)

"In fact, the opposition of instinct and reason is mainly illusory. Instinct, intuition, or insight is what first leads to the beliefs which subsequent reason confirms or confutes; but the confirmation, where it is possible, consists, in the last analysis, of agreement with other beliefs no less instinctive. Reason is a harmonising, controlling force rather than a creative one. Even in the most purely logical realms, it is insight that first arrives at what is new." (Bertrand Russell,"Our Knowledge of the External World", 1914)

"The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another." (Henri Poincaré, 1913)

"It seems rather futile, if such be the normal history of hypothetical models, to inflict on us the labor of learning abstruse hypotheses which continually revamp old metaphysical terms and merely dress them up in new transcendental symbols. It is a valuable exercise to strip hypotheses of their technical phraseology; to change those words which deceive our minds into believing that a clear idea has been conveyed, when, in fact, they have merely been wrenched from any real significance." (Louis T More, "The Limitations of Science", 1915)

"It [science] involves an intelligent and persistent endeavor to revise current beliefs so as to weed out what is erroneous, to add to their accuracy, and, above all, to give them such shape that the dependencies of the various facts upon one another may be as obvious as possible." (John Dewey, "Democracy and Education", 1916)

"Science herself consults her heart when she lays it down that the infinite ascertainment of fact and correction of false belief are the supreme goods for man." (William James, "Selected Papers on Philosophy", 1918)

"We must have a logical intuition of the probable relations between propositions. Once the existence of this relation between evidence and conclusion, the latter becomes the subject of the degree of belief." (John M Keynes, "Treatise on Probability", 1921)

"A hypothesis or theory is clear, decisive, and positive, but it is believed by no one but the man who created it. Experimental findings, on the other hand, are messy, inexact things, which are believed by everyone except the man who did the work." (Harlow Shapley, "Review of Scientific Instruments" Vol. 6, 1922)

"The question whether any branch of science can ever become purely deductive is easily answered. It cannot. If science deals with the external world, as we believe it does, and not merely with the relations of propositions then no branch of science can ever be purely deductive. Deductive reasoning by itself can never tell us about facts. The use of deduction in science is to serve as a calculus to make our observations go further, not to take the place of observation." (Arthur D Ritchie, "Scientific Method: An Inquiry into the Character and Validity of Natural Laws", 1923)

On Beliefs (1800-1899)

"Man must cling to the belief that the incomprehensible is comprehensible. Else he would give up investigating. " (Johann Wolfgang von Goethe, "Maxims and Reflections", 1829)

"So it happens at times that a person believes that he has a world-view, but that there is yet one particular phenomenon that is of such a nature that it baffles the understanding, and that he explains differently and attempts to ignore in order not to harbor the thought that this phenomenon might overthrow the whole view, or that his reflection does not possess enough courage and resolution to penetrate the phenomenon with his world-view." (Søren Kierkegaard, 1844)

"By degree of probability we really mean, or ought to mean, degree of belief [...] Probability then, refers to and implies belief, more or less, and belief is but another name for imperfect knowledge, or it may be, expresses the mind in a state of imperfect knowledge." (Augustus De Morgan, "Formal Logic: Or, The Calculus of Inference, Necessary and Probable", 1847)

"SYSTEM (to place together) - is a full and connected view of all the truths of some department of knowledge. An organized body of truth, or truths arranged under one and the same idea, which idea is as the life or soul which assimilates all those truths. No truth is altogether isolated. Every truth has relation to some other. And we should try to unite the facts of our knowledge so as to see them in their several bearings. This we do when we frame them into a system. To do so legitimately we must begin by analysis and end with synthesis. But system applies not only to our knowledge, but to the objects of our knowledge. Thus we speak of the planetary system, the muscular system, the nervous system. We believe that the order to which we would reduce our ideas has a foundation in the nature of things. And it is this belief that encourages us to reduce our knowledge of things into systematic order. The doing so is attended with many advantages. At the same time a spirit of systematizing may be carried too far. It is only in so far as it is in accordance with the order of nature that it can be useful or sound. (William Fleming, "Vocabulary of philosophy, mental, moral, and metaphysical; with quotations and references; for the use of students", 1857)

"The world is devoted to physical science, because it believes theses discoveries will increase its capacity of luxury and self-indulgence. But the pursuit of science only leads to the insoluble." (Benjamin Disraeli, "Lothair", 1870)

"The philosopher believes that the value of his philosophy lies in the whole, in the building: posterity discovers it in the bricks with which he built and which are then often used again for better building: in the fact, that is to say, that building can be destroyed and nonetheless possess value as material." (Friedrich Nietzsche, "Human, all-too-human", 1878)

"That which is provable, ought not to be believed in science without proof" (Richard Dedekind,"Was sind und was sollen die Zahlen?", 1888)

"Every probability - and most of our common, working beliefs are probabilities - is provided with buffers at both ends, which break the force of opposite opinions clashing against it; but scientific certainty has no spring in it, no courtesy, no possibility of yielding. All this must react on the minds which handle these forms of truth. (Oliver W Holmes, "The Autocrat of the Breakfast-Table", 1891)

"Metaphysics is the finding of bad reasons for what we believe upon instinct, but to find these reasons is no less an instinct." (Francis H Bradley,"Appearance and Reality: A Metaphysical Essay", 1893)

"For the truly scientific man, the hypothesis is destined solely to enable him to get the facts of nature in some definite order, an order which shall make apparent their connection with the great order and harmony which is believed to be present in the universe." (James M Baldwin, "The Processes of Life Revealed by the Microscope: A Plea for Physiological Histology", Science N.S. Vol. 2 (34), 1895)

"Science for the past is a description, for the future a belief." (Karl Pearson, "The Grammar of Science", 1892)

W Brian Arthur - Collected Quote

"A technology that by chance gains an early lead in adoption may eventually 'corner the market' of potential adopters, with the other technologies becoming locked out." (W Brian Arthur, "Competing Technologies, Increasing Returns and Lock-in by Historical Events", 1989)

"In many parts of the economy, stabilizing forces appear not to operate. Instead, positive feedback magnifies the effects of small economic shifts; the economic models that describe such effects differ vastly from the conventional ones. Diminishing returns imply a single equilibrium point for the economy, but positive feedback - increasing returns - makes for many possible equilibrium points. There is no guarantee that the particular economic outcome selected from among the many alternatives will be the ‘best’ one." (W Brian Arthur, "Returns and Path Dependence in the Economy", 1994)

"Complexity is looking at interacting elements and asking how they form patterns and how the patterns unfold. It’s important to point out that the patterns may never be finished. They’re open-ended. In standard science this hit some things that most scientists have a negative reaction to. Science doesn’t like perpetual novelty." (W Brian Arthur, 1999)

"Complexity theory is really a movement of the sciences. Standard sciences tend to see the world as mechanistic. That sort of science puts things under a finer and finer microscope. […] The movement that started complexity looks in the other direction. It’s asking, how do things assemble themselves? How do patterns emerge from these interacting elements? Complexity is looking at interacting elements and asking how they form patterns and how the patterns unfold. It’s important to point out that the patterns may never be finished. They’re open-ended. In standard science this hit some things that most scientists have a negative reaction to. Science doesn’t like perpetual novelty." (W Brian Arthur, "Coming from Your Inner Self", 1999)

"Our deepest hope as humans lies in technology; but our deepest trust lies in nature. These forces are like tectonic plates grinding inexorably into each other in one, long, slow collision. This collision is not new, but more than anything else it is defining our era. Technology is steadily creating the dominant issues and upheavals of our time." (W Brian Arthur, "The Nature of Technology: What It Is and How It Evolves", 2009)

"A belief model is clung to not because it is 'correct'  - there is no way to know this - but rather because it has worked in the past and must cumulate a record of failure before it is worth discarding. In general, there may be a constant slow turnover of hypotheses acted upon. One could speak of this as a system of temporarily fulfilled expectations - beliefs or models or hypotheses that are temporarily fulfilled (though not perfectly), which give way to different beliefs or hypotheses when they cease to be fulfilled." (W Brian Arthur, "Complexity and the Economy", 2015) 

"An event occurring at one node will cause a cascade of events: often this cascade or avalanche propagates to affect only one or two further elements, occasionally it affects more, and more rarely it affects many. The mathematical theory of this - which is very much part of complexity theory - shows that propagations of events causing further events show characteristic properties such as power laws (caused by many and frequent small propagations, few and infrequent large ones), heavy tailed probability distributions (lengthy propagations though rare appear more frequently than normal distributions would predict), and long correlations (events can and do propagate for long distances and times)." (W Brian Arthur, "Complexity and the Economy", 2015) 

"Complexity economics holds that the economy is not necessarily in equilibrium, that computation as well as mathematics is useful in economics, that increasing as well as diminishing returns may be present in an economic situation, and that the economy is not something given and existing but forms from a constantly developing set of institutions, arrangements, and technological innovations." (W Brian Arthur, "Complexity and the Economy", 2015)

"Complexity economics is not a special case of neoclassical economics. On the contrary, equilibrium economics is a special case of nonequilibrium and hence complexity economics. Complexity economics, we can say, is economics done in a more general way. Equilibrium of course will remain a useful first-order approximation, useful for situations in economics that are well-defined, rationalizable, and reasonably static, but it can no longer claim to be the center of economics. Moving steadily to the center is an economics that can handle interactions more generally, that can recognize nonequilibrium phenomena, that can deal with novelty, formation and change." (W Brian Arthur, "Complexity and the Economy", 2015)

"Complexity is not a theory but a movement in the sciences that studies how the interacting elements in a system create overall patterns, and how these overall patterns in turn cause the interacting elements to change or adapt. It might study how individual cars together act to form patterns in traffic, and how these patterns in turn cause the cars to alter their position. Complexity is about formation - the formation of structures - and how this formation affects the objects causing it." (W Brian Arthur, "Complexity and the Economy", 2015)

"In the 'computation' that is the economy, large and small probabilistic events at particular non-repeatable moments determine the attractors fallen into, the temporal structures that form and die away, the technologies that are brought to life, the economic structures and institutions that result from these, the technologies and structures that in turn build upon these; indeed the future shape of the economy - the future path taken. The economy at all levels and at all times is path dependent. History again becomes important. And time reappears." (W Brian Arthur, "Complexity and the Economy", 2015)

"Mathematics is a technique, a tool, albeit a sophisticated one. Theory is something different. Theory lies in the discovery, understanding, and explaining of phenomena present in the world. Mathematics facilitates this - enormously - but then so does computation. Naturally, there is a difference. Working with equations allows us to follow an argument step by step and reveals conditions a solution must adhere to, whereas computation does not. But computation - and this more than compensates - allows us to see phenomena that equilibrium mathematics does not. It allows us to rerun results under different conditions, exploring when structures appear and don’t appear, isolating underlying mechanisms, and simplifying again and again to extract the bones of a phenomenon. Computation in other words is an aid to thought, and it joins earlier aids in economics - algebra, calculus, statistics, topology, stochastic processes - each of which was resisted in its time. The computer is an exploratory lab for economics, and used skillfully, a powerful generator for theory." (W Brian Arthur, "Complexity and the Economy", 2015)

"Technological disruption acts on a somewhat slower timescale than the Brownian motion of uncertainty. But if anything it causes larger upheavals. And by itself it induces further uncertainty: businesses and industries simply do not know what technologies will enter their space next. Both uncertainty and technology then give us an economy where agents have no determinate means to make decisions." (W Brian Arthur, "Complexity and the Economy", 2015)

"The failures of economics in the practical world are largely due to seeing the economy in equilibrium. […] Equilibrium thinking cannot 'see' such exploitation in advance for a subtle reason: by definition, equilibrium is a condition where no agent has any incentive to diverge from its present behavior, therefore exploitive behavior cannot happen. And it cannot see extreme market behavior easily either:  divergences are quickly corrected by countervailing forces. By its base assumptions, equilibrium economics is not primed to look for exploitation of parts of the economy or for system breakdowns." (W Brian Arthur, "Complexity and the Economy", 2015)

"Under equilibrium by definition there is no scope for improvement or further adjustment, no scope for exploration, no scope for creation, no scope for transitory phenomena, so anything in the economy that takes adjustment - adaptation, innovation, structural change, history itself - must be bypassed or dropped from theory. The result may be a beautiful structure, but it is one that lacks authenticity, aliveness, and creation." (W Brian Arthur, "Complexity and the Economy", 2015)

"We carry out localized deductions based on our current hypotheses and act on them. As feedback from the environment comes in, we may strengthen or weaken our beliefs in our current hypotheses, discarding some when they cease to perform, and replacing them as needed with new ones. In other words, when we cannot fully reason or lack full definition of the problem, we use simple models to fill the gaps in our understanding. Such behavior is inductive." (W Brian Arthur, "Complexity and the Economy", 2015)

"As we begin to understand complex systems, we begin to understand that we're part of an ever-changing, interlocking, non-linear, kaleidoscopic world." (W Brian Arthur)

Herbert Read - Collected Quotes

"A poem therefore is to be defined as a structure of words whose sound constitutes a rhythmical unity, complete in itself, irrefragable, unanalyzable, completing its symbolic references within the ambit of its sound effects." (Herbert Read, "What is a Poem", 1926)

"The words in a poem, (or more exactly, syllables) are vocal signs that convey an intangible essence (the pattern of feeling) that vanishes the moment we approach it with an analytical intelligence." (Herbert Read, "What is a Poem", 1926)

"There is no beauty in anything rational. Beauty emerges from the unknown, often from the inane, generally irrational, as unforseen combinations." (Herbert Read, "Phases in English Poetry", 1928)

"All art originates in an act of intuition or vision." (Herbert Read, "Form in Modern Poetry", 1948)

"Poetry is properly speaking a transcendental quality, a sudden transformation in which words assume a particular influence." (Herbert Read, "Form in Modern Poetry", 1948)

"The difference between poetry and prose is not one of surface qualities, or form, or mode of expression, but of essence. The state of mind in which poetry originates must either seek poetic expression or it must not be expressed." (Herbert Read, "Form in Modern Poetry", 1948)

"Words, their sound and even their very appearance, are, of course, everything to he poet." (Herbert Read, "Form in Modern Poetry", 1948)

"Beauty had been born, not, as we so often conceive it nowadays, as an ideal of humanity, but as measure, as the reduction of the chaos of appearances to the precision of linear symbols. Symmetry, balance, harmonic division, mated and mensurated intervals – such were its abstract characteristics." (Herbert Read, "Icon and Idea: The Function of Art in the Development of Human Consciousness", 1955)

"Intellect begins with the observation of nature, proceeds to memorize and classify the facts thus observed, and by logical deduction builds up that edifice of knowledge properly called science. But admittedly we also know by feeling, and we can combine the two faculties, and present knowledge in the guise of art." (Herbert Read, "Selected Writings: Poetry and Criticism", 1963)

"Progress is measured by richness and intensity of experience - by a wider and deeper apprehension of the significance and scope of human existence." (Herbert Read, "Selected writings: poetry and criticism", 1963)

"The most general law in nature is equity - the principle of balance and symmetry which guides the growth of forms along the lines of the greatest structural efficiency." (Herbert Read, "Selected Writings: Poetry and Criticism", 1963)

"The work of art [...] is an instrument for tilling the human psyche, that it may continue to yield a harvest of vital beauty." (Herbert Read, "Collected Poems", 1966)

On Consistence (Unsourced)

"[...] a hypothesis test tells us whether the observed data are consistent with the null hypothesis, and a confidence interval tells us which hypotheses are consistent with the data." (William C Blackwelder)

"Consistency is the enemy of enterprise, just as symmetry is the enemy of art." (George B Shaw)

"Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number." (Georg Cantor)

"Facts and values are entangled in science. It's not because scientists are biased, not because they are partial or influenced by other kinds of interests, but because of a commitment to reason, consistency, coherence, plausibility and replicability. These are value commitments." (Alva Noë)

"Instead of seeking to attain consistency and uniformity of system, as some modern writers have attempted, by banishing this thought of time from the higher Algebra, I seek to attain the same object, by systematically introducing it into the lower or earlier parts of the science." (Sir William R Hamilton)

"Nothing is too wonderful to be true, if it be consistent with the laws of nature, and in such things as these, experiment is the best test of such consistency." (Michael Faraday)

"String theory is extremely attractive because gravity is forced upon us. All known consistent string theories include gravity, so while gravity is impossible in quantum field theory as we have known it, it is obligatory in string theory." (Edward Witten)

"The primary service of modern mathematics is that it alone enables us to understand the vast abstract permanences which underlie the flux of things, without requiring us to regard its self-consistent abstractions as more than specific limited instruments of thought." (George D Birkhoff)

[...] we and our models are both part of the universe we are describing. Thus a physical theory is self referencing, like in Gödel’s theorem. One might therefore expect it to be either inconsistent or incomplete. The theories we have so far are both inconsistent and incomplete. (Stephen Hawking, "Gödel and the End of the Universe")

On Consistence (2010-2019)

"The objectivist view is that probabilities are real aspects of the universe - propensities of objects to behave in certain ways - rather than being just descriptions of an observer’s degree of belief. For example, the fact that a fair coin comes up heads with probability 0.5 is a propensity of the coin itself. In this view, frequentist measurements are attempts to observe these propensities. Most physicists agree that quantum phenomena are objectively probabilistic, but uncertainty at the macroscopic scale - e.g., in coin tossing - usually arises from ignorance of initial conditions and does not seem consistent with the propensity view." (Stuart J Russell & Peter Norvig, "Artificial Intelligence: A Modern Approach", 2010)

"It is the consistency of the information that matters for a good story, not its completeness. Indeed, you will often find that knowing little makes it easier to fit everything you know into a coherent pattern. (Daniel Kahneman, "Thinking, Fast and Slow", 2011)

"Knowing the importance of luck, you should be particularly suspicious when highly consistent patterns emerge from the comparison of successful and less successful firms. In the presence of randomness, regular patterns can only be mirages. (Daniel Kahneman, "Thinking, Fast and Slow", 2011)

"The reactions that break down large molecules into small ones do not require an input of energy, but the reactions that build up large molecules require and input of energy. This is consistent with the laws of thermodynamics, which say that large, orderly molecules tend to break down into small, disorderly molecules. (Stanley A Rice, "Life of Earth: Portrait of a Beautiful, Middle-aged Stressed-out World", 2011)

"While mathematicians now recognize that there is some freedom in the choice of the axioms one uses, not any set of statements can serve as a set of axioms. In particular, every set of axioms must be logically consistent, which is another way of saying that it should not be possible to prove a particular statement simultaneously true and false using the given set of axioms. Also, axioms should always be logically independent - that is, no axiom should be a logical consequence of the others. A statement that is a logical consequence of some of the axioms is a theorem, not an axiom. (John Tabak, "Beyond Geometry: A new mathematics of space and form", 2011)

"If the distance from the mean for one variable tends to be broadly consistent with distance from the mean for the other variable (e.g., people who are far from the mean for height in either direction tend also to be far from the mean in the same direction for weight), then we would expect a strong positive correlation. If distance from the mean for one variable tends to correspond to a similar distance from the mean for the second variable in the other direction (e.g., people who are far above the mean in terms of exercise tend to be far below the mean in terms of weight), then we would expect a strong negative correlation. If two variables do not tend to deviate from the mean in any meaningful pattern (e.g., shoe size and exercise) then we would expect little or no correlation." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"Complex systems defy intuitive solutions. Even a third-order, linear differential equation is unsolvable by inspection. Yet, important situations in management, economics, medicine, and social behavior usually lose reality if simplified to less than fifth-order nonlinear dynamic systems. Attempts to deal with nonlinear dynamic systems using ordinary processes of description and debate lead to internal inconsistencies. Underlying assumptions may have been left unclear and contradictory, and mental models are often logically incomplete. Resulting behavior is likely to be contrary to that implied by the assumptions being made about' underlying system structure and governing policies. (Jay W Forrester, "Modeling for What Purpose?", The Systems Thinker Vol. 24 (2), 2013)

"A worldview is a commitment, a fundamental orientation of the heart, that can be expressed as a story or in a set of presuppositions (assumptions which may be true, partially true or entirely false) which we hold (consciously or subconsciously, consistently or inconsistently) about the basic constitution of reality, and that provides the foundations on which we live and more and have our being." (James W Sire,"Naming the Elephant: Worldview as a Concept", 2015)

"Accuracy and coherence are related concepts pertaining to data quality. Accuracy refers to the comprehensiveness or extent of missing data, performance of error edits, and other quality assurance strategies. Coherence is the degree to which data - item value and meaning are consistent over time and are comparable to similar variables from other routinely used data sources." (Aileen Rothbard, "Quality Issues in the Use of Administrative Data Records", 2015)

"Reality is necessarily viewed through a conceptual system and is inseparable from the system through which it is viewed. But reality is by definition singular - there is only one reality; there cannot be two or three. Something is either real or it is not. The notion that reality is relative or that there can be two competing and inconsistent realities is disorienting and produces untenable cognitive dissonance." (William Byers, "Deep Thinking: What Mathematics Can Teach Us About the Mind", 2015)

"The essential quality of mathematics that binds it together in a coherent way is the use of mathematical proof to deduce new results from known ones, building up a strong and consistent theory." (Ian Stewart & David Tall, "The Foundations of Mathematics" 2nd Ed., 2015)

"Like all models, people’s mental models are an abstraction of reality. They may be complete and correct, or they may have gaps or inconsistencies that are consequential to effective decision making and action. A mental model is usually less complex than the real-world phenomenon involved and tends to lag in context or time and so can easily become out of date. In many cases, people may lack conscious, well-formed mental models on issues that they have not thoroughly considered in the past. This may be challenging for decision-makers as people’s responses may seem unpredictable or irrational. (Matthew D Wood, An Introduction to Mental Modeling, [in "Mental Modeling Approach: Risk Management Application Case Studies"], 2017)

"Quaternions are not actual extensions of imaginary numbers, and they are not taking complex numbers into a multi-dimensional space on their own. Quaternion units are instances of some number-like object type, identified collectively, but they are not numbers (be it real or imaginary). In other words, they form a closed, internally consistent set of object instances; they can of course be plotted visually on a multi-dimensional space but this only is a visualization within their own definition." (Huseyin Ozel, "Redefining Imaginary and Complex Numbers, Defining Imaginary and Complex Objects", 2018)

On Consistence (2000-2009)

"Data are generally collected as a basis for action. However, unless potential signals are separated from probable noise, the actions taken may be totally inconsistent with the data. Thus, the proper use of data requires that you have simple and effective methods of analysis which will properly separate potential signals from probable noise." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"When a system is predictable, it is already performing as consistently as possible. Looking for assignable causes is a waste of time and effort. Instead, you can meaningfully work on making improvements and modifications to the process. When a system is unpredictable, it will be futile to try and improve or modify the process. Instead you must seek to identify the assignable causes which affect the system. The failure to distinguish between these two different courses of action is a major source of confusion and wasted effort in business today." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"Conventional mathematics and control theory exclude vagueness and contradictory conditions. As a consequence, conventional control systems theory does not attempt to study any formulation, analysis, and control of what has been called fuzzy systems, which may be vague, incomplete, linguistically described, or even inconsistent." (Guanrong Chen & Trung Tat Pham, "Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems", 2001)

"In essence, mathematicians wanted to prove two things: 1.Mathematics is consistent: Mathematics contains no internal contradictions. There are no slips of reason or ambiguities. No matter from what direction we approach the edifice of mathematics, it will always display the same rigor and truth. 2.Mathematics is complete: No mathematical truths are left hanging. Nothing needs adding to the system. Mathematicians can prove every theorem with total rigor so that nothing is excluded from the overall system." (F David Peat, "From Certainty to Uncertainty", 2002)

"History, as well as life itself, is complicated; neither life nor history is an enterprise for those who seek simplicity and consistency." (Jared Diamond, "Collapse: How Societies Choose to Fail or Succeed", 2005)

"A recurring concern has been whether set theory, which speaks of infinite sets, refers to an existing reality, and if so how does one ‘know’ which axioms to accept. It is here that the greatest disparity of opinion exists (and the greatest possibility of using different consistent axiom systems)." (Paul Cohen, "Skolem and pessimism about proof in mathematics". Philosophical Transactions of the Royal Society A 363 (1835), 2005)

"String theory was not invented to describe gravity; instead it originated in an attempt to describe the strong interactions, wherein mesons can be thought of as open strings with quarks at their ends. The fact that the theory automatically described closed strings as well, and that closed strings invariably produced gravitons and gravity, and that the resulting quantum theory of gravity was finite and consistent is one of the most appealing aspects of the theory." (David Gross, "Einstein and the Search for Unification", 2005)

"The worst aspect of the term 'complex' - one that condemns it to eventual extinction in my opinion - is that it is also applied to structures called 'simple'. Mathematics uses the word 'simple' as a technical term for objects that cannot be 'simplified'. Prime numbers are the kind of thing that might be called 'simple' (though in their case it is not usually done) because they cannot be written as products of smaller numbers. At any rate, some of the 'simple' structures are built on the complex numbers, so mathematicians are obliged to speak of such things as 'complex simple Lie groups'. This is an embarrassment in a subject that prides itself on consistency, and surely either the word 'simple' or the word 'complex' has to go." (John Stillwell, "Yearning for the Impossible: The Surprising Truths of Mathematics", 2006)

"The role of conceptual modelling in information systems development during all these decades is seen as an approach for capturing fuzzy, ill-defined, informal 'real-world' descriptions and user requirements, and then transforming them to formal, in some sense complete, and consistent conceptual specifications." (Janis A Burbenko jr., "From Information Algebra to Enterprise Modelling and Ontologies", Conceptual Modelling in Information Systems Engineering, 2007)

"Mathematicians are sometimes described as living in an ideal world of beauty and harmony. Instead, our world is torn apart by inconsistencies, plagued by non sequiturs and, worst of all, made desolate and empty by missing links between words, and between symbols and their referents; we spend our lives patching and repairing it. Only when the last crack disappears are we rewarded by brief moments of harmony and joy." (Alexandre V Borovik,"Mathematics under the Microscope: Notes on Cognitive Aspects of Mathematical Practice", 2009)

"Mathematicians seek a certain kind of beauty. Perhaps mathematical beauty is a constant - as far as the contents of mathematics are concerned - and yet the forms this beauty takes are certainly cultural. And while the history of mathematics surely is many stranded, one of its most important strands is formed by such cultural forms of mathematical beauty." (Reviel Netz,"Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic", 2009)

 "Obviously, the final goal of scientists and mathematicians is not simply the accumulation of facts and lists of formulas, but rather they seek to understand the patterns, organizing principles, and relationships between these facts to form theorems and entirely new branches of human thought." (Clifford A Pickover,"The Math Book", 2009)

"The reasoning of the mathematician and that of the scientist are similar to a point. Both make conjectures often prompted by particular observations. Both advance tentative generalizations and look for supporting evidence of their validity. Both consider specific implications of their generalizations and put those implications to the test. Both attempt to understand their generalizations in the sense of finding explanations for them in terms of concepts with which they are already familiar. Both notice fragmentary regularities and - through a process that may include false starts and blind alleys - attempt to put the scattered details together into what appears to be a meaningful whole. At some point, however, the mathematician’s quest and that of the scientist diverge. For scientists, observation is the highest authority, whereas what mathematicians seek ultimately for their conjectures is deductive proof." (Raymond S Nickerson, "Mathematical Reasoning: Patterns, Problems, Conjectures and Proofs", 2009)