"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)
"The study of infinity is much more than a dry academic game. The intellectual pursuit of the absolute infinity is, as Georg Cantor realized, a form of the soul's quest for God. Whether or not the goal is ever reached, an awareness of the process brings enlightenment." (Rudy Rucker, "Infinity and the Mind: The science and philosophy of the infinite", 1982)
"There are many difficulties in application of [the games] theory to the real world. [...] In general, competitors are not in complete opposition. As a matter of fact often they don't even have the same objectives. This difficulty can often be circumvented by using a different objective, 'games of survival'. Secondly, a decision is seldom made once. This motivated the study of multistage games [...]. Finally, decisions are not usually made simultaneously. Recognition of this fact leads to 'games of protocol' [...]. Games of protocol can also be used to handle processes involving three or more people." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)
"Cybernetics is concerned with scientific investigation of systemic processes of a highly varied nature, including such phenomena as regulation, information processing, information storage, adaptation, self-organization, self-reproduction, and strategic behavior. Within the general cybernetic approach, the following theoretical fields have developed: systems theory" (system), communication theory, game theory, and decision theory." (Fritz B Simon et al, "Language of Family Therapy: A Systemic Vocabulary and Source Book", 1985)
"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)
"Since a point hypothesis is not to be expected in practice to be exactly true, but only approximate, a proper test of significance should almost always show significance for large enough samples. So the whole game of testing point hypotheses, power analysis notwithstanding, is but a mathematical game without empirical importance." (Louis Guttman, "The illogic of statistical inference for cumulative science", Applied Stochastic Models and Data Analysis, 1985)
"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)
"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)
"Mathematics is more than doing calculations, more than solving equations, more than proving theorems, more than doing algebra, geometry or calculus, more than a way of thinking. Mathematics is the design of a snowflake, the curve of a palm frond, the shape of a building, the joy of a game, the frustration of a puzzle, the crest of a wave, the spiral of a spider's web. It is ancient and yet new. Mathematics is linked to so many ideas and aspects of the universe." (Theoni Pappas, "More Joy of Mathematics: Exploring Mathematics All Around You", 1986)
"Science is not a given set of answers but a system for obtaining answers. The method by which the search is conducted is more important than the nature of the solution. Questions need not be answered at all, or answers may be provided and then changed. It does not matter how often or how profoundly our view of the universe alters, as long as these changes take place in a way appropriate to science. For the practice of science, like the game of baseball, is covered by definite rules." (Robert Shapiro, "Origins: A Skeptic’s Guide to the Creation of Life on Earth", 1986)
"That strategic rivalry in a long-term relationship may differ from that of a one-shot game is by now quite a familiar idea. Repeated play allows players to respond to each other’s actions, and so each player must consider the reactions of his opponents in making his decision. The fear of retaliation may thus lead to outcomes that otherwise would not occur. The most dramatic expression of this phenomenon is the celebrated "Folk Theorem." An outcome that Pareto dominates the minimax point is called individually rational. The Folk Theorem asserts that any individually rational outcome can arise as a Nash equilibrium in infinitely repeated games with sufficiently little discounting." (Drew Fudenberg & Eric Maskin, "The folk theorem in repeated games with discounting or with incomplete information", Econometrica: Journal of the Econometric Society, 1986)
"The modern theory of decision making under risk emerged from a logical analysis of games of chance rather than from a psychological analysis of risk and value. The theory was conceived as a normative model of an idealized decision maker, not as a description of the behavior of real people." (Amos Tversky & Daniel Kahneman, "Rational Choice and the Framing of Decisions", The Journal of Business Vol. 59" (4), 1986)
"But the answers provided by the theory of games are sometimes very puzzling and ambiguous. In many situations, no single course of action dominates all the others; instead, a whole set of possible solutions are all equally consistent with the postulates of rationality." (Herbert A Simon et al, "Decision Making and Problem Solving", Interfaces Vol. 17 (5), 1987)
"Linear relationships are easy to think about: the more the merrier. Linear equations are solvable, which makes them suitable for textbooks. Linear systems have an important modular virtue: you can take them apart and put them together again - the pieces add up. Nonlinear systems generally cannot be solved and cannot be added together. [...] Nonlinearity means that the act of playing the game has a way of changing the rules. [...] That twisted changeability makes nonlinearity hard to calculate, but it also creates rich kinds of behavior that never occur in linear systems." (James Gleick, "Chaos: Making a New Science", 1987)
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