More generally, a string that contains regularities or patterns-of any form that can be expressed in the computer language-can be faithfully reproduced by a short program that takes advantages of these patterns, while a relatively complex or “random” string cannot be similarly compressed. “ 39383827262226…”) can’t be compressed in this way, although it can be expressed by a program that is itself about 1000 characters long (e.g. By contrast a “typical” random string of 1000 characters (e.g. For example, the loop (in pseudocode) “ for i=1 to 1000: print '1'” prints a string of 1000 characters, but the program itself contains only 26 this string is highly compressible. The idea is usually formalized by considering a string S (a sequence of symbols), and then considering the length (in symbols) of the shortest computer program capable of generating it S. Simple strings are those that can be expressed by brief computer programs, and complex datasets are those that cannot. Introduced in slightly different forms by Solomonoff (1964), Kolmogorov (1965), and Chaitin (1966), the main idea is that the complexity of a string of characters reflects the degree of incompressibility, as measured by the length of a computer program required to faithfully express the string (see M. This all changed in the 1960s with the introduction of a principled and convincing mathematical definition of complexity now known as Kolmogorov complexity or algorithmic complexity. Such a definition only arrived in the last few decades. To understand the connection, we need at the very least a more precise definition of simplicity. Quine, 1965 Jeffreys, 1939/1961) began to argue that simpler theories were, in fact, more likely to be true, but until recently the precise connection between simplicity and truth remained, at best, extremely unclear. In the twentieth century some authors (e.g. Simpler theories were seen as more manageable, more comprehensible, and more testable ( Popper, 1934/1959), but not necessarily more truthful. Conversely, some philosophers have assumed that the bias towards simplicity is an essentially aesthetic preference, akin to elegance or beauty that mathematicians prize in theorems, conveying no particular claim to correctness (see Sober, 1975). Hume’s principle of “Uniformity of Nature” suggests that simpler theories are preferable because they make a good match for a highly regular, lawful world. But it has never been clear exactly why this should be so.
1 Since then philosophers of science have adopted a bias towards simpler explanations as a foundational principle of inference, guiding the selection of hypotheses whenever multiple hypothesis are consistent with data-as is nearly always the case.īut why should simpler theories be preferred? Practicing scientists have generally assumed it is because they are actually more likely to be correct. The principle of simplicity or parsimony-broadly, the idea that simpler explanations of observations should be preferred to more complex ones-is conventionally attributed to William of Occam, after whom it is traditionally referred to as Occam’s razor. This brief tutorial surveys some of the uses of the simplicity principle across cognitive science, emphasizing how complexity minimization in a number of forms has been incorporated into probabilistic models of inference. In all these areas, the common idea is that the mind seeks the simplest available interpretation of observations- or, more precisely, that it balances a bias towards simplicity with a somewhat opposed constraint to choose models consistent with perceptual or cognitive observations. The simplicity principle has found many applications in modern cognitive science, in contexts as diverse as perception, categorization, reasoning, and neuroscience. In recent decades the principle has been clarified via the incorporation of modern notions of computation and probability, allowing a more precise understanding of how exactly complexity minimization facilitates inference. The simplicity principle, traditionally referred to as Occam’s razor, is the idea that simpler explanations of observations should be preferred to more complex ones.
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