On Heuristics III

"Intelligence has two parts, which we shall call the epistemological and the heuristic. The epistemological part is the representation of the world in such a form that the solution of problems follows from the facts expressed in the representation. The heuristic part is the mechanism that on the basis of the information solves the problem and decides what to do." (John McCarthy & Patrick J Hayes, "Some Philosophical Problems from the Standpoint of Artificial Intelligence", Machine Intelligence 4, 1969)

"Heuristic (it is of Greek origin) means discovery. Heuristic methods are based on experience, rational ideas, and rules of thumb. Heuristics are based more on common sense than on mathematics. Heuristics are useful, for example, when the optimal solution needs an exhaustive search that is not realistic in terms of time. In principle, a heuristic does not guarantee the best solution, but a heuristic solution can provide a tremendous shortcut in cost and time." (Nikola K Kasabov, "Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering", 1996)

"Heuristic methods may aim at local optimization rather than at global optimization, that is, the algorithm optimizes the solution stepwise, finding the best solution at each small step of the solution process and 'hoping' that the global solution, which comprises the local ones, would be satisfactory." (Nikola K Kasabov, "Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering", 1996)

"A proof of a mathematical theorem is a sequence of steps which leads to the desired conclusion. The rules to be followed [...] were made explicit when logic was formalized early in the this century [...] These rules can be used to disprove a putative proof by spotting logical errors; they cannot, however, be used to find the missing proof of a [...] conjecture. [...] Heuristic arguments are a common occurrence in the practice of mathematics. However... The role of heuristic arguments has not been acknowledged in the philosophy of mathematics despite the crucial role they play in mathematical discovery. [...] Our purpose is to bring out some of the features of mathematical thinking which are concealed beneath the apparent mechanics of proof." (Gian-Carlo Rota, "Indiscrete Thoughts", 1997)

"A heuristic is ecologically rational to the degree that it is adapted to the structure of an environment. Thus, simple heuristics and environmental structure can both work hand in hand to provide a realistic alternative to the ideal of optimization, whether unbounded or constrained." (Gerd Gigerenzer & Peter M Todd, "Fast and Frugal Heuristics: The Adaptive Toolbox" [in "Simple Heuristics That Make Us Smart"], 1999)

"Fast and frugal heuristics employ a minimum of time, knowledge, and computation to make adaptive choices in real environments. They can be used to solve problems of sequential search through objects or options, as in satisficing. They can also be used to make choices between simultaneously available objects, where the search for information (in the form of cues, features, consequences, etc.) about the possible options must be limited, rather than the search for the options themselves. Fast and frugal heuristics limit their search of objects or information using easily computable stopping rules, and they make their choices with easily computable decision rules." (Gerd Gigerenzer & Peter M Todd, "Fast and Frugal Heuristics: The Adaptive Toolbox" [in "Simple Heuristics That Make Us Smart"], 1999)

"Theories of choice are at best approximate and incomplete. One reason for this pessimistic assessment is that choice is a constructive and contingent process. When faced with a complex problem, people employ a variety of heuristic procedures in order to simplify the representation and the evaluation of prospects. These procedures include computational shortcuts and editing operations, such as eliminating common components and discarding nonessential differences. The heuristics of choice do not readily lend themselves to formal analysis because their application depends on the formulation of the problem, the method of elicitation, and the context of choice." (Amos Tversky & Daniel Kahneman, "Advances in Prospect Theory: Cumulative Representation of Uncertainty" [in "Choices, Values, and Frames"], 2000)

"A heuristic is a rule applied to an existing solution represented in a perspective that generates a new (and hopefully better) solution or a new set of possible solutions." (Scott E Page, "The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools and Societies", 2008)

"A heuristic is a decision rule that utilizes a subset of the information set. Since in virtually all cases people must economize and cannot analyze all contingencies, we use heuristics without even realizing it." (Lucy F Ackert & Richard Deaves, "Behavioral Finance: Psychology, Decision-Making, and Markets", 2010)