On Artificial Intelligence I

"There is no security against the ultimate development of mechanical consciousness, in the fact of machines possessing little consciousness now. A mollusc has not much consciousness. Reflect upon the extraordinary advance which machines have made during the last few hundred years, and note how slowly the animal and vegetable kingdoms are advancing. The more highly organized machines are creatures not so much of yesterday, as of the last five minutes, so to speak, in comparison with past time." (Samuel Butler, "Erewhon: Or, Over the Range", 1872)

"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", 1950)

"The following are some aspects of the artificial intelligence problem: […] If a machine can do a job, then an automatic calculator can be programmed to simulate the machine. […] It may be speculated that a large part of human thought consists of manipulating words according to rules of reasoning and rules of conjecture. From this point of view, forming a generalization consists of admitting a new word and some rules whereby sentences containing it imply and are implied by others. This idea has never been very precisely formulated nor have examples been worked out. […] How can a set of (hypothetical) neurons be arranged so as to form concepts. […] to get a measure of the efficiency of a calculation it is necessary to have on hand a method of measuring the complexity of calculating devices which in turn can be done. […] Probably a truly intelligent machine will carry out activities which may best be described as self-improvement. […] A number of types of 'abstraction' can be distinctly defined and several others less distinctly. […] the difference between creative thinking and unimaginative competent thinking lies in the injection of a some randomness. The randomness must be guided by intuition to be efficient." (John McCarthy et al, "A Proposal for the Dartmouth Summer Research Project on Artificial Intelligence", 1955)

"We shall therefore say that a program has common sense if it automatically deduces for itself a sufficient wide class of immediate consequences of anything it is told and what it already knows. [...] Our ultimate objective is to make programs that learn from their experience as effectively as humans do." (John McCarthy, "Programs with Common Sense", 1958)

"When intelligent machines are constructed, we should not be surprised to find them as confused and as stubborn as men in their convictions about mind-matter, consciousness, free will, and the like." (Marvin Minsky, "Matter, Mind, and Models", Proceedings of the International Federation of Information Processing Congress Vol. 1 (49), 1965)

"Artificial intelligence is the science of making machines do things that would require intelligence if done by men." (Marvin Minsky, 1968)

"Artificial intelligence is based on the assumption that the mind can be described as some kind of formal system manipulating symbols that stand for things in the world. Thus it doesn't matter what the brain is made of, or what it uses for tokens in the great game of thinking. Using an equivalent set of tokens and rules, we can do thinking with a digital computer, just as we can play chess using cups, salt and pepper shakers, knives, forks, and spoons. Using the right software, one system (the mind) can be mapped onto the other (the computer)." (George Johnson, Machinery of the Mind: Inside the New Science of Artificial Intelligence, 1986)

"The deep paradox uncovered by AI research: the only way to deal efficiently with very complex problems is to move away from pure logic. [...] Most of the time, reaching the right decision requires little reasoning.[...] Expert systems are, thus, not about reasoning: they are about knowing. [...] Reasoning takes time, so we try to do it as seldom as possible. Instead we store the results of our reasoning for later reference." (Daniel Crevier, "The Tree of Knowledge", 1993)

Mathematics as Game I

"So is not mathematical analysis then not just a vain game of the mind? To the physicist it can only give a convenient language; but isn't that a mediocre service, which after all we could have done without; and, it is not even to be feared that this artificial language be a veil, interposed between reality and the physicist's eye? Far from that, without this language most of the initimate analogies of things would forever have remained unknown to us; and we would never have had knowledge of the internal harmony of the world, which is, as we shall see, the only true objective reality." (Henri Poincaré, "The Value of Science", 1905)

"Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise." (David Hilbert, "Natur und Mathematisches Erkennen", 1919–20) 

"A serious threat to the very life of science is implied in the assertion that mathematics is nothing but a system of conclusions drawn from definitions and postulates that must be consistent but otherwise may be created by the free will of the mathematician. If this description were accurate, mathematics could not attract any intelligent person. It would be a game with definitions, rules and syllogisms, without motivation or goal." (Richard Courant & Herbert Robbins, "What Is Mathematics?", 1941)

"Geometry, whatever others may think, is the study of different shapes, many of them very beautiful, having harmony, grace and symmetry. […] Most of us, if we can play chess at all, are content to play it on a board with wooden chess pieces; but there are some who play the game blindfolded and without touching the board. It might be a fair analogy to say that abstract geometry is like blindfold chess – it is a game played without concrete objects." (Edward Kasner & James R Newman, "New Names for Old", 1956) 

"To the average mathematician who merely wants to know that his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency." (Paul Cohen, "Axiomatic set theory, American Mathematical Society", 1971)

"There is an infinite regress in proofs; therefore proofs do not prove. You should realize that proving is a game, to be played while you enjoy it and stopped when you get tired of it." (Imre Lakatos, "Proofs and Refutations", 1976)

"The way the mathematics game is played, most variations lie outside the rules, while music can insist on perfect canon or tolerate a casual accompaniment." (Marvin Minsky, "Music, Mind, and Meaning", 1981)

"If doing mathematics or science is looked upon as a game, then one might say that in mathematics you compete against yourself or other mathematicians; in physics your adversary is nature and the stakes are higher." (Mark Kac, "Enigmas Of Chance", 1985)

"Mathematicians are used to game-playing according to a set of rules they lay down in advance, despite the fact that nature always writes her own. One acquires a great deal of humility by experiencing the real wiliness of nature." (Philip W Anderson, "More and Different: Notes from a Thoughtful Curmudgeon", 2011)

"Often the key contribution of intuition is to make us aware of weak points in a problem, places where it may be vulnerable to attack. A mathematical proof is like a battle, or if you prefer a less warlike metaphor, a game of chess. Once a potential weak point has been identified, the mathematician’s technical grasp of the machinery of mathematics can be brought to bear to exploit it." (Ian Stewart, "Visions of Infinity", 2013)

Game Theory II

"A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution." (Richard A Epstein, "The Theory of Gambling and Statistical Logic" [Revised Edition], 1977)

"Game theory is a collection of mathematical models designed to study situations involving conflict and/or cooperation. It allows for a multiplicity of decision makers who may have different preferences and objectives. Such models involve a variety of different solution concepts concerned with strategic optimization, stability, bargaining, compromise, equity and coalition formation." (Notices of the American Mathematical Society Vol. 26 (1), 1979) 

"A finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play." (James P Cars, "Finite and Infinite Games: A Vision of Life as Play and Possibility", 1986)

"Game theory is a theory of strategic interaction. That is to say, it is a theory of rational behavior in social situations in which each player has to choose his moves on the basis of what he thinks the other players' countermoves are likely to be." (John Harsanyi, "Games with Incomplete Information", The American Economic Review Vol. 85 (3), 1997)

"In principle, every social situation involves strategic interaction among the participants. Thus, one might argue that proper understanding of any social situation would require game-theoretic analysis. But in actual fact, classical economic theory did manage to sidestep the game-theoretic aspects of economic behavior by postulating perfect competition, i. e., by assuming that every buyer and every seller is very small as compared with the size of the relevant markets, so that nobody can significantly affect the existing market prices by his actions." (John Harsanyi, "Games with Incomplete Information" 1997)

"Like all of mathematics, game theory is a tautology whose conclusions are true because they are contained in the premises." (Thomas Flanagan, "Game Theory and Canadian Politics", 1998)

"I think game theory creates ideas that are important in solving and approaching conflict in general." Robert Aumann, 2005)

"The players in a game are said to be in strategic equilibrium (or simply equilibrium) when their play is mutually optimal: when the actions and plans of each player are rational in the given strategic environment - i. e., when each knows the actions and plans of the others." (Robert Aumann, "War and Peace", 2005)

"An equilibrium is not always an optimum; it might not even be good. This may be the most important discovery of game theory." (Ivar Ekeland, "The Best of All Possible Worlds", 2006)

"Game theory brings to the chaos–theory table the idea that generally, societies are not designed, and that most situations don't come with a rulebook. Instead, people have their own plans and designs on how things should fit together. They want to determine how the game is played, and they see societal designers as myopic busybodies who would imprison them with their theories." (Lawrence K Samuels, "In Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

Game Theory I

"The implication of game theory, which is also the implication of the third image, is, however, that the freedom of choice of any one state is limited by the actions of the others." (Kenneth Waltz, "Man, the State, and War", 1959)

"At present game theory has, in my opinion, two important uses, neither of them related to games nor to conflict directly. First, game theory stimulates us to think about conflict in a novel way. Second, game theory leads to some genuine impasses, that is, to situations where its axiomatic base is shown to be insufficient for dealing even theoretically with certain types of conflict situations... Thus, the impact is made on our thinking process themselves, rather than on the actual content of our knowledge. (Anatol Rapoport, "Fights, games, and debates", 1960)

"It is the shortcomings of game theory (as originally formulated) which force the consideration of the role of ethics, of the dynamics of social structure, and of social structure and of individual psychology in situations of conflict." (Anatol Rapoport, "Fights, games, and debates", 1960)

"Although the drama of games of strategy is strongly linked with the psychological aspects of the conflict, game theory is not concerned with these aspects. Game theory, so to speak, plays the board. It is concerned only with the logical aspects of strategy." (Anatol Rapoport, "The Use and Misuse of Game Theory", Scientific American 207, 1962)

"Game theory applies to a very different type of conflict, now technically called a game. The well-known games such as poker, chess, ticktacktoe and so forth are games in the strict technical Bark and counterbark sense. But what makes parlor games is not their entertainment value or detachment from real life." (Anatol Rapoport, "The Use and Misuse of Game Theory", Scientific American 207, 1962)

"Whether game theory leads to clear-cut solutions, to vague solutions, or to impasses, it does achieve 

one thing. In bringing techniques of logical and mathematical analysis gives men an opportunity to bring conflicts up from the level of fights, where the intellect is beclouded by passions, to the level of games, where the intellect has a chance to operate." (Anatol Rapoport, "The Use and Misuse of Game Theory", Scientific American 207, 1962)

"[Game theory is] essentially a structural theory. It uncovers the logical structure of a great variety of conflict situations and describes this structure in mathematical terms. Sometimes the logical structure of a conflict situation admits rational decisions; sometimes it does not." (Anatol Rapoport, "Prisoner's dilemma: A study in conflict and cooperation", 1965)

"Evolutionary game theory is a way of thinking about evolution at the phenotypic level when the fitnesses of particular phenotypes depend on their frequencies in the population." (John M Smith, "Evolution and the Theory of Games", 1973)

"Strategy in complex systems must resemble strategy in board games. You develop a small and useful tree of options that is continuously revised based on the arrangement of pieces and the actions of your opponent. It is critical to keep the number of options open. It is important to develop a theory of what kinds of options you want to have open." (John H Holland, [presentation] 2000)

"Game theory postulates rational behavior for each participant. Each player is conscious of the rules and behaves in accordance with them, each player has sufficient knowledge of the situation in which he or she is involved to be able to evaluate what the best option is when it comes to taking action (a move), and each player takes into account the decisions that might be made by other participants and their repercussions with respect to his or her own decision. Game theory about zero-sum games with two participants is relevant for chess. In this type of situation, each action that is favorable to one participant (player) is proportionally unfavorable for the opponent. Thus, the gain of one represents the loss of the other." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)

On Mechanisms I: On Pendulum

"Science gains from it [the pendulum] more than one can expect. With its huge dimensions, the apparatus presents qualities that one would try in vain to communicate by constructing it on a small [scale], no matter how carefully. Already the regularity of its motion promises the most conclusive results. One collects numbers that, compared with the predictions of theory, permit one to appreciate how far the true pendulum approximates or differs from the abstract system called 'the simple pendulum'." (Jean-Bernard-Léon Foucault, "Demonstration Experimentale du Movement de Rotation de la Terre", 1851)

"The force acting on the pendulum is proportional to its active mass, its inertia is proportional to its passive mass, so that the period will depend on the ratio of the passive and the active mass. Consequently the fact that the period of all these different pendulums was the same, proves that this ratio is a constant, and can be made equal to unity by a suitable choice of units, i. e., the inertial and the gravitational mass are the same." (Willem de Sitter, "The Astronomical Aspect of the Theory of Relativity", 1933)

"[…] we must be clear about how a 'system' is to be defined. Our first impulse is to point at the pendulum and to 'the system is that thing there' . This method, however, has a fundamental disadvantage: every material object contains no less than an infinity of variables and therefore of possible systems. The real pendulum, for instance, has not only length and position; it has also mass, temperature, electric conductivity, crystalline structure, chemical impurities, some radio-activity, velocity, reflecting power, tensile strength, a surface film of moisture, bacterial contamination, an optical absorption, elasticity, shape, specific gravity, and so on and on. Any suggestion that we should study 'all' the facts is unrealistic, and actually the attempt is never made. What is try is that we should pick out and study the facts that are relevant to some main interest that is already given." (W Ross Ashby, "An Introduction to Cybernetics", 1956)

"[…] the equation of small oscillations of a pendulum also holds for other vibrational phenomena. In investigating swinging pendulums we were, albeit unwittingly, also investigating vibrating tuning forks." (George Pólya, "Mathematical Methods in Science", 1977)

"Linking topology and dynamical systems is the possibility of using a shape to help visualize the whole range of behaviors of a system. For a simple system, the shape might be some kind of curved surface; for a complicated system, a manifold of many dimensions. A single point on such a surface represents the state of a system at an instant frozen in time. As a system progresses through time, the point moves, tracing an orbit across this surface. Bending the shape a little corresponds to changing the system's parameters, making a fluid more visous or driving a pendulum a little harder. Shapes that look roughly the same give roughly the same kinds of behavior. If you can visualize the shape, you can understand the system. (James Gleick, "Chaos: Making a New Science", 1987)

"Linking topology and dynamical systems is the possibility of using a shape to help visualize the whole range of behaviors of a system. For a simple system, the shape might be some kind of curved surface; for a complicated system, a manifold of many dimensions. A single point on such a surface represents the state of a system at an instant frozen in time. As a system progresses through time, the point moves, tracing an orbit across this surface. Bending the shape a little corresponds to changing the system's parameters, making a fluid more visous or driving a pendulum a little harder. Shapes that look roughly the same give roughly the same kinds of behavior. If you can visualize the shape, you can understand the system." (James Gleick, "Chaos: Making a New Science", 1987)

"Dynamical systems that vary continuously, like the pendulum and the rolling rock, and evidently the pinball machine when a ball’s complete motion is considered, are technically known as flows. The mathematical tool for handling a flow is the differential equation. A system of differential equations amounts to a set of formulas that together express the rates at which all of the variables are currently changing, in terms of the current values of the variables." (Edward N Lorenz, "The Essence of Chaos", 1993)

"Just as few concrete physical systems are strictly deterministic in their behavior, so very few are strictly linear. The great importance of linearity lies in a combination of two circumstances. First, many tangible phenomena behave approximately linearly over restricted periods of time or restricted ranges of the variables, so that useful linear mathematical models can simulate their behavior. A pendulum swinging through a small angle is a nearly linear system. Second, linear equations can be handled by a wide variety of techniques that do not work with nonlinear equations." (Edward N Lorenz, "The Essence of Chaos", 1993)

"Systems that vary deterministically as time progresses, such as mathematical models of the swinging pendulum, the rolling rock, and the breaking wave, and also systems that vary with an inconsequential amount of randomness - possibly a real pendulum, rock, or wave - are technically known as dynamical systems." (Edward N Lorenz, "The Essence of Chaos", 1993)

"Most of us use the word 'chaos' rather loosely to represent anything that occurs randomly, so it is natural to think that the motion described by the erratic pendulum above is completely random. Not so. The scientific definition of chaos is different from the one you may be used to in that it has an element of determinism in it. This might seem strange, as determinism and chaos are opposites of one another, but oddly enough they are also compatible." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"One of the reasons we deal with the pendulum is that it is easy to plot its motion in phase space. If the amplitude is small, it's a two-dimensional problem, so all we need to specify it completely is its position and its velocity. We can make a two-dimensional plot with one axis (the horizontal), position, and the other (the vertical), velocity." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"A pendulum swings in a circle, so there is a lowest point that it can possibly reach - hanging vertically downwards. Any change in potential energy must be compensated by an equal and opposite change in kinetic energy: if the bob gets higher, it has to move more slowly; if it gets lower, it has to move faster. Imagine grabbing the pendulum by its bob and raising it to some chosen height. Hold it steady. Your hand did some work, and increased the bob's potential energy. The kinetic energy is zero because the pendulum is not moving. Now let go, and from now on let the pendulum move as it wishes. Gravity pulls the bob downwards, so the potential energy decreases. Kinetic energy must increase to compensate, so the weight starts to fall. At some stage the bob must reach the lowest point of the circle: here its potential energy is zero, so all of the energy has become kinetic. Not only is it moving at this point - it is moving as fast as it can possibly go." (Ian Stewart, "The Magical Maze: Seeing the world through mathematical eyes", 1997)

"Real dynamical problems typically involve nonlinear differential equations of second order, but these often simplify greatly if we investigate small oscillations about a position of equilibrium. Coupled oscillators are particularly interesting, an early example being the double pendulum, first studied by Euler and Daniel Bernoulli in the 1730s." (David Acheson, "From Calculus to Chaos: An Introduction to Dynamics", 1997)

"Financial markets are supposed to swing like a pendulum: They may fluctuate wildly in response to exogenous shocks, but eventually they are supposed to come to rest at an equilibrium point and that point is supposed to be the same irrespective of the interim fluctuations." (George Soros, "The Crisis of Global Capitalism", 1998)

"According to quantum theory, the ground state, or lowest energy state, of a pendulum is not just sitting at the lowest energy point, pointing straight down. That would have both a definite position and a definite velocity, zero. This would be a violation of the uncertainty principle, which forbids the precise measurement of both position and velocity at the same time. The uncertainty in the position multiplied by the uncertainty in the momentum must be greater than a certain quantity, known as Planck's constant - a number that is too long to keep writing down, so we use a symbol for it: ħ." (Stephen W Hawking, "The Universe in a Nutshell", 2001)

"So the ground state, or lowest energy state, of a pendulum does not have zero energy, as one might expect. Instead, even in its ground state a pendulum or any oscillating system must have a certain minimum amount of what are called zero point fluctuations. These mean that the pendulum won't necessarily be pointing straight down but will also have a probability of being found at a small angle to the vertical. Similarly, even in the vacuum or lowest energy state, the waves in the Maxwell field won't be exactly zero but can have small sizes. The higher the frequency (the number of swings per minute) of the pendulum or wave, the higher the energy of the ground state." (Stephen W Hawking, "The Universe in a Nutshell", 2001)

"[…] some systems (system is just a jargon for anything, like the swinging pendulum or the Solar System, or water dripping from a tap)  are very sensitive to their starting conditions, so that a tiny difference in the initial ‘push’ you give them causes a big difference in where they end up, and there is feedback, so that what a system does affects its own behavior."(John Gribbin, "Deep Simplicity", 2004)

"All pendulums exhibit such rotation, but for most pendulums this behavior is masked by other more prominent effects. For an ideal Foucault pendulum, the plane of oscillation would be seen as fixed by an observer positioned in the stars. (In this discussion we ignore the rotation of the earth around the sun, and the rotation of the sun around the center of the galaxy, and so forth.) Therefore the earthbound observer sees a slow rotation of the plane of oscillation and it is this remarkable feature of the Foucault pendulum which demonstrates, on a large scale, the rotation of the earth." (Gregory L Baker & Jammes A Blackburn, "The Pendulum: A Case Study in Physics", 2005)

"For very long pendulums the spurious effects are small, and the main concern is the dissipation of energy as the pendulum gradually losses amplitude. However, for short pendulums the spurious effects are, not negligible. After the following literary divertissement, we note some ways that builders of Foucault pendulums have overcome the complicating effects of these limitations and thereby produced workable pendulums that are much smaller than Foucault’s original giant creation." (Gregory L Baker & Jammes A Blackburn, "The Pendulum: A Case Study in Physics", 2005)

"In theory, any earth-based pendulum is a Foucault pendulum. However, a realistic Foucault pendulum is a one that is specially constructed to highlight the rotation of its plane of oscillation due to the earth’s rotation relative to a frame of reference fixed in the stars. That is, the plane of the pendulum’s oscillation is fixed relative to the stars while the earth rotates underneath it." (Gregory L Baker & Jammes A Blackburn, "The Pendulum: A Case Study in Physics", 2005)

 "Pendulum clocks exemplify important physical concepts. The clock needs to have some method of transferring energy to the pendulum to maintain its oscillation. There also needs to be a method whereby the pendulum regulates the motion of the clock. These two requirements are encompassed in one remarkable mechanism called the escapement. The escapement is a marvelous invention in that it makes the pendulum clock one of the first examples of an automaton with self-regulating feedback." (Gregory L Baker & Jammes A Blackburn, "The Pendulum: A Case Study in Physics", 2005)

"A pendulum is simply a small load suspended to a string or to a rod fixed at one end. If left alone it ends up hanging vertically, and if we push it away from the vertical, it starts beating. Galileo found that all beats last the same time, called the period, which depends on the length of the pendulum, but not on the amplitude of the beats or on the weight of the load. It also states that the period varies as the square root of the length: to double its period, one should make the pendulum four times as long. Making it heavier, or pushing it farther away from the vertical, has no effect. This property is known as isochrony, and it is the main reason why we are able to measure time with accuracy." (Ivar Ekeland, "The Best of All Possible Worlds", 2006)

"In this world, there are two times. There is mechanical time and there is body time. The first is as rigid and metallic as a massive pendulum of iron that swings back and forth, back and forth, back and forth. The second squirms and wriggles like a bluefish in a bay. The first is unyielding, predetermined. The second makes up its mind as it goes along." (Alan Lightman, "Einstein's Dreams", 2012)

"Social scientists use the term 'equilibrium' to describe balance between opposing forces, say, supply and demand, so small disturbances or deviations in one direction, like those of a pendulum, would be countered with an adjustment in the opposite direction that would bring things back to stability." (Nassim N Taleb, "Antifragile: Things that gain from disorder", 2012)

"In mathematics, pendulums stimulated the development of calculus through the riddles they posed. In physics and engineering, pendulums became paradigms of oscillation. […] In some cases, the connections between pendulums and other phenomena are so exact that the same equations can be recycled without change. Only the symbols need to be reinterpreted; the syntax stays the same. It’s as if nature keeps returning to the same motif again and again, a pendular repetition of a pendular theme. For example, the equations for the swinging of a pendulum carry over without change to those for the spinning of generators that produce alternating current and send it to our homes and offices. In honor of that pedigree, electrical engineers refer to their generator equations as swing equations." (Steven H Strogatz, "Infinite Powers: The Story of Calculus - The Most Important Discovery in Mathematics", 2019)

On Prediction V (Chaos)

"Chaos is but unperceived order; it is a word indicating the limitations of the human mind and the paucity of observational facts. The words ‘chaos’, ‘accidental’, ‘chance’, ‘unpredictable’ are conveniences behind which we hide our ignorance." (Harlow Shapley, "Of Stars and Men: Human Response to an Expanding Universe", 1958)

"The term chaos is used in a specific sense where it is an inherently random pattern of behaviour generated by fixed inputs into deterministic (that is fixed) rules (relationships). The rules take the form of non-linear feedback loops. Although the specific path followed by the behaviour so generated is random and hence unpredictable in the long-term, it always has an underlying pattern to it, a 'hidden' pattern, a global pattern or rhythm. That pattern is self-similarity, that is a constant degree of variation, consistent variability, regular irregularity, or more precisely, a constant fractal dimension. Chaos is therefore order (a pattern) within disorder (random behaviour)." (Ralph D Stacey, "The Chaos Frontier: Creative Strategic Control for Business", 1991)

"Often, we use the word random loosely to describe something that is disordered, irregular, patternless, or unpredictable. We link it with chance, probability, luck, and coincidence. However, when we examine what we mean by random in various contexts, ambiguities and uncertainties inevitably arise. Tackling the subtleties of randomness allows us to go to the root of what we can understand of the universe we inhabit and helps us to define the limits of what we can know with certainty." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1998)

"We use mathematics and statistics to describe the diverse realms of randomness. From these descriptions, we attempt to glean insights into the workings of chance and to search for hidden causes. With such tools in hand, we seek patterns and relationships and propose predictions that help us make sense of the world." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1998)

"The subject of probability begins by assuming that some mechanism of uncertainty is at work giving rise to what is called randomness, but it is not necessary to distinguish between chance that occurs because of some hidden order that may exist and chance that is the result of blind lawlessness. This mechanism, figuratively speaking, churns out a succession of events, each individually unpredictable, or it conspires to produce an unforeseeable outcome each time a large ensemble of possibilities is sampled."  (Edward Beltrami, "Chaos and Order in Mathematics and Life", 1999)

"A Black Swan is a highly improbable event with three principal characteristics: It is unpredictable; it carries a massive impact; and, after the fact, we concoct an explanation that makes it appear less random, and more predictable, than it was. […] The Black Swan idea is based on the structure of randomness in empirical reality. [...] the Black Swan is what we leave out of simplification." (Nassim N Taleb, "The Black Swan", 2007)

"[...] a high degree of unpredictability is associated with erratic trajectories. This not only because they look random but mostly because infinitesimally small uncertainties on the initial state of the system grow very quickly - actually exponentially fast. In real world, this error amplification translates into our inability to predict the system behavior from the unavoidable imperfect knowledge of its initial state." (Massimo Cencini et al, "Chaos: From Simple Models to Complex Systems", 2010)

"In chaotic deterministic systems, the probabilistic description is not linked to the number of degrees of freedom (which can be just one as for the logistic map) but stems from the intrinsic erraticism of chaotic trajectories and the exponential amplification of small uncertainties, reducing the control on the system behavior." (Massimo Cencini et al, "Chaos: From Simple Models to Complex Systems", 2010)

"Strange attractors, unlike regular ones, are geometrically very complicated, as revealed by the evolution of a small phase-space volume. For instance, if the attractor is a limit cycle, a small two-dimensional volume does not change too much its shape: in a direction it maintains its size, while in the other it shrinks till becoming a 'very thin strand' with an almost constant length. In chaotic systems, instead, the dynamics continuously stretches and folds an initial small volume transforming it into a thinner and thinner 'ribbon' with an exponentially increasing length." (Massimo Cencini et al, "Chaos: From Simple Models to Complex Systems", 2010)

"The Newtonian universe is material in the sense that the world was viewed as being made up of stuff - tangible, real objects. It was argued that even forces like gravity that appear to act across empty stretches of space are conveyed by tiny particles, or corpuscles. Moreover, since the universe is material, its behavior can be predicted or understood. Things are they way they are for a reason or a cause. The Newtonian world is mathematical, in that it was viewed that the regularities or laws that describe or govern the world are mathematical in nature." (David P Feldman,"Chaos and Fractals: An Elementary Introduction", 2012)

On Prediction IV (Theories)

"In scientific thought we adopt the simplest theory which will explain all the facts under consideration and enable us to predict facts of the same kind. The  catch in this criterion lies in the world 'simplest'." (John B S Haldane, "Possible Worlds and Other Essays", 1928)

"It is characteristic of a good scientific theory that it makes no more assumptions than are needed to explain the facts under consideration and predict a few more." (John B S Haldane, "Possible Worlds and Other Essays", 1928)

"One often hears that successive theories grow ever closer to, or approximate more and more closely to, the truth. Apparently, generalizations like that refer not to the puzzle-solutions and the concrete predictions derived from a theory but rather to its ontology, to the match, that is, between the entities with which the theory populates nature and what is ‘really there’." (Thomas S Kuhn, "The Structure of Scientific Revolutions", 1962)

"A theory in its scientific context is not a static museum piece, but is always being extended and modified to account for new phenomena. […] Moreover, without a model, it will be impossible to use a theory for one of the essential purposes we demand of it, namely to make predictions in new domains of phenomena." (Mary B Hesse," Models and Analogies in Science", 1963)

"It is easy to obtain confirmations, or verifications, for nearly every theory - if we look for confirmations. Confirmations should count only if they are the result of risky predictions. […] A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice. Every genuine test of a theory is an attempt to falsify it, or refute it." (Karl R Popper, "Conjectures and Refutations: The Growth of Scientific Knowledge", 1963)

"One often hears that successive theories grow ever closer to, or approximate more and more closely to, the truth. Apparently, generalizations like that refer not to the puzzle-solutions and the concrete predictions derived from a theory but rather to its ontology, to the match, that is, between the entities with which the theory populates nature and what is ‘really there’." (Thomas S Kuhn, "The Structure of Scientific Revolutions", 1970)

"But a theory is not like an airline or bus timetable. We are not interested simply in the accuracy of its predictions. A theory also serves as a base for thinking. It helps us to understand what is going on by enabling us to organize our thoughts. Faced with a choice between a theory which predicts well but gives us little insight into how the system works and one which gives us this insight but predicts badly, I would choose the latter, and I am inclined to think that most economists would do the same." (Ronald Coase, "How should economists choose?", 1981)

"The ability of a scientific theory to be refuted is the key criterion that distinguishes science from metaphysics. If a theory cannot be refuted, if there is no observation that will disprove it, then nothing can prove it - it cannot predict anything, it is a worthless myth." (Eric Lerner, "The Big Bang Never Happened", 1991)

"Good theories are the ones that get those predictions right; the best theories enable us to 'get right' the calculation of how the Universe came into being and then exploded into its present form. But that doesn’t mean that they convey ultimate truth, or that there ‘really are’ little hard particles rattling around against each other inside the atom. Such truth as there is in any of this work lies in the mathematics; the particle concept is simply a crutch ordinary mortals can use to help them towards an understanding of the mathematical laws." (John R Gribbin, "The Search of Superstrings, Symmetry, and the Theory of Everything", 1998)

"[...] the definitive property of good theory is predictiveness. Those theories endure that are precise in the predictions they make across many phenomena and whose predictions are easiest to test by observation and experiment." (Edward O Wilson, "Consilience: The Unity of Knowledge", 1998)

"A theory is a set of deductively closed propositions that explain and predict empirical phenomena, and a model is a theory that is idealized." (Jay Odenbaugh, "True Lies: Realism, Robustness, and Models", Philosophy of Science, Vol. 78, No. 5, 2011 

On Prediction VIII (Systems II)

"Computation offers a new means of describing and investigating scientific and mathematical systems. Simulation by computer may be the only way to predict how certain complicated systems evolve." (Stephen Wolfram, "Computer Software in Science and Mathematics", 1984)

"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)

"Complexity arises when emergent system-level phenomena are characterized by patterns in time or a given state space that have neither too much nor too little form. Neither in stasis nor changing randomly, these emergent phenomena are interesting, due to the coupling of individual and global behaviours as well as the difficulties they pose for prediction. Broad patterns of system behaviour may be predictable, but the system's specific path through a space of possible states is not." (Steve Maguire et al, "Complexity Science and Organization Studies", 2006)

"The only way to look into the future is use theories since conclusive data is only available about the past." (Clayton Christensen et al, "Seeing What’s Next: Using the Theories of Innovation to Predict Industry Change", 2004)

"A scientific theory is a concise and coherent set of concepts, claims, and laws (frequently expressed mathematically) that can be used to precisely and accurately explain and predict natural phenomena." (Mordechai Ben-Ari, "Just a Theory: Exploring the Nature of Science", 2005)

"Complexity carries with it a lack of predictability different to that of chaotic systems, i.e. sensitivity to initial conditions. In the case of complexity, the lack of predictability is due to relevant interactions and novel information created by them." (Carlos Gershenson, "Understanding Complex Systems", 2011)

"Complexity scientists concluded that there are just too many factors - both concordant and contrarian - to understand. And with so many potential gaps in information, almost nobody can see the whole picture. Complex systems have severe limits, not only to predictability but also to measurability. Some complexity theorists argue that modelling, while useful for thinking and for studying the complexities of the world, is a particularly poor tool for predicting what will happen." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"Without precise predictability, control is impotent and almost meaningless. In other words, the lesser the predictability, the harder the entity or system is to control, and vice versa. If our universe actually operated on linear causality, with no surprises, uncertainty, or abrupt changes, all future events would be absolutely predictable in a sort of waveless orderliness." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"The problem of complexity is at the heart of mankind’s inability to predict future events with any accuracy. Complexity science has demonstrated that the more factors found within a complex system, the more chances of unpredictable behavior. And without predictability, any meaningful control is nearly impossible. Obviously, this means that you cannot control what you cannot predict. The ability ever to predict long-term events is a pipedream. Mankind has little to do with changing climate; complexity does." (Lawrence K Samuels, "The Real Science Behind Changing Climate", 2014)

"[...] perhaps one of the most important features of complex systems, which is a key differentiator when comparing with chaotic systems, is the concept of emergence. Emergence 'breaks' the notion of determinism and linearity because it means that the outcome of these interactions is naturally unpredictable. In large systems, macro features often emerge in ways that cannot be traced back to any particular event or agent. Therefore, complexity theory is based on interaction, emergence and iterations." (Luis Tomé & Şuay Nilhan Açıkalın, "Complexity Theory as a New Lens in IR: System and Change" [in "Chaos, Complexity and Leadership 2017", Şefika Şule Erçetin & Nihan Potas], 2019)

🆂Walter A Shewhart - Collected Quotes

"Every sentence in order to have definite scientific meaning must be practically or at least theoretically verifiable as either true or false upon the basis of experimental measurements either practically or theoretically obtainable by carrying out a definite and previously specified operation in the future. The meaning of such a sentence is the method of its verification." (Walter A Shewhart, "Economic Control of Quality of Manufactured Product", 1931)

"Postulate 1. All chance systems of causes are not alike in the sense that they enable us to predict the future in terms of the past. Postulate 2. Constant systems of chance causes do exist in nature. Postulate 3. Assignable causes of variation may be found and eliminated."(Walter A Shewhart, "Economic Control of Quality of Manufactured Product", 1931)

"Progress in modifying our concept of control has been and will be comparatively slow. In the first place, it requires the application of certain modern physical concepts; and in the second place it requires the application of statistical methods which up to the present time have been for the most part left undisturbed in the journal in which they appeared." (Walter A Shewhart, "Economic Control of Quality of Manufactured Product", 1931)

"Rule 1. Original data should be presented in a way that will preserve the evidence in the original data for all the predictions assumed to be useful." (Walter A Shewhart, "Economic Control of Quality of Manufactured Product", 1931)

"Rule 2. Any summary of a distribution of numbers in terms of symmetric functions should not give an objective degree of belief in any one of the inferences or predictions to be made therefrom that would cause human action significantly different from what this action would be if the original distributions had been taken as evidence."  (Walter A Shewhart, "Economic Control of Quality of Manufactured Product", 1931)

"The definition of random in terms of a physical operation is notoriously without effect on the mathematical operations of statistical theory because so far as these mathematical operations are concerned random is purely and simply an undefined term. The formal and abstract mathematical theory has an independent and sometimes lonely existence of its own. But when an undefined mathematical term such as random is given a definite operational meaning in physical terms, it takes on empirical and practical significance. Every mathematical theorem involving this mathematically undefined concept can then be given the following predictive form: If you do so and so, then such and such will happen."(Walter A Shewhart, "Economic Control of Quality of Manufactured Product", 1931)

On Prediction XII (Behavior)

"Engage people with what they expect; it is what they are able to discern and confirms their projections. It settles them into predictable patterns of response, occupying their minds while you wait for the extraordinary moment - that which they cannot anticipate." (Sun Tzu, "The Art of War")

"What is big is easy to perceive: what is small is difficult to perceive. In short, it is difficult for large numbers of men to change position, so their movements can be easily predicted. An individual can easily change his mind, so his movements are difficult to predict."(Miyamoto Musashi, "The Book of Five Rings" , 1645)

"The doctrine called Philosophical Necessity is simply this: that, given the motives which are present to an individual's mind, and given likewise the character and disposition of the individual, the manner in which he will act might be unerringly inferred: that if we knew the person thoroughly, and knew all the inducements which are acting upon him, we could foretell his conduct with as much certainty as we can predict any physical event." (John S Mill, "A System of Logic, Ratiocinative and Inductive", 1843)

"How can we dare to predict the behavior of man? We may predict the movements of a machine, of an automaton; more than this, we many even try to predict the mechanisms or 'dynamisms' of the human psyche as well. But man is more than psyche." (Viktor E Frankl, "Man's Search for Meaning", 1984) 

"To assume you know someone well enough that you can and do predict their behavior and mental perspective is a gross and often tragic mistake, for it eliminates that person's freedom to create his or her own opinion and drastically affects the emerging picture of the relationship." (Meredith L Young-Sowers, "Agartha: a journey to the stars", 1984) 

"The challenge for individuals in primate societies is to be able to predict the behavior of others. One way would be for individuals to have a huge mental bank in their brains, which stored every possible action of their fellow troop members and their own appropriate actions." (Richard Leakey, "The Origin of Humankind", 1994)

"Even if someone knew the entire physical history of the world, and every mental event were identical with a physical, it would notfollow that he could predict or explain a single mental event (so described, of course)."(Donald Davidson, "Essays on Actions and Events", 2001)

"We need to stop, and admit it: we have a prediction problem. We love to predict things—and we aren't very good at it." (Nate Silver, "The Signal and the Noise", 2012)