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Digital infinity is a technical term in theoretical linguistics. Alternative formulations are "discrete infinity" and "the infinite use of finite means". The idea is that all human languages follow a simple logical principle, according to which a limited set of digits — irreducible atomic sound elements — are combined to produce an infinite range of potentially meaningful expressions. Noam Chomsky cites Galileo as perhaps the first to recognise the significance of digital infinity. This principle, notes Chomsky, is "the core property of human language, and one of its most distinctive properties: the use of finite means to express an unlimited array of thoughts". In his ''Dialogo'', Galileo describes with wonder the discovery of a means to communicate one’s “most secret thoughts to any other person ... with no greater difficulty than the various collocations of twenty-four little characters upon a paper.” This is the greatest of all human inventions, Galileo continues, comparable to the creations of a Michelangelo…〔 == The computational theory of mind == 'Digital infinity' corresponds to Noam Chomsky's 'Universal Grammar' mechanism, conceived as a computational module inserted somehow into ''Homo sapiens otherwise 'messy' (non-digital) brain. This conception of human cognition — central to the so-called 'cognitive revolution' of the 1950s and 1960s — is generally attributed to Alan Turing, who was the first scientist to argue that a man-made machine might truly be said to 'think'. The idea of a thinking machine had previously been considered absurd, having been famously dismissed by René Descartes as ''theoretically'' impossible. Neither animals nor machines can think, insisted Descartes, since they lack a God-given soul.〔Rene Descartes, 1985 (). 'Discourse on the Method.' In ''The Philosophical Writings of Descartes.'' Translated by J. Cottingham, R. Stoothoff and D. Murdoch. Cambridge: Cambridge University Press, Vol. 1, pp. 139-141. 〕 Turing was well aware of this traditional theological objection, and explicitly countered it.〔Alan Turing, 1950. Computing machinery and intelligence. ''Mind'' 59: 433-60.〕 Today's digital computers are instantiations of Turing's theoretical breakthrough in conceiving the possibility of a man-made ''universal thinking machine'' — known nowadays as a 'Turing machine'. No physical mechanism can be intrinsically 'digital', Turing explained, since — examined closely enough — its possible states will vary without limit. But if most of these states can be profitably ignored, leaving only a limited set of relevant distinctions, then ''functionally'' the machine may be considered 'digital':〔 An implication is that 'digits' don't exist: they and their combinations are no more than convenient fictions, operating on a level quite independent of the material, physical world. In the case of a ''binary'' digital machine, the choice at each point is restricted to 'off' versus 'on'. Crucially, the intrinsic properties of the medium used to encode signals then have no effect on the message conveyed. 'Off' (or alternatively 'on') remains unchanged regardless of whether the signal consists of smoke, electricity, sound, light or anything else. In the case of analog (more-versus-less) gradations, this is not so because the range of possible settings is unlimited. Moreover, in the analog case it ''does'' matter which particular medium is being employed: equating a certain intensity of smoke with a corresponding intensity of light, sound or electricity is just not possible. In other words, only in the case of ''digital'' computation and communication can information be truly independent of the physical, chemical or other properties of the materials used to encode and transmit messages. Digital computation and communication operates, then, independently of the physical properties of the computing machine. As scientists and philosophers during the 1950s digested the implications, they exploited the insight to explain why 'mind' apparently operates on so different a level from 'matter'. Descartes' celebrated distinction between immortal 'soul' and mortal 'body' was conceptualised, following Turing, as no more than the distinction between (digitally encoded) ''information'' on the one hand, and, on the other, the particular physical ''medium'' — light, sound, electricity or whatever — chosen to transmit the corresponding signals. Note that the Cartesian assumption of mind's independence of matter implied — in the human case at least — the existence of some kind of digital computer operating inside the human brain. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Digital infinity」の詳細全文を読む スポンサード リンク
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