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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Digital infinity | 2/3 | https://en.wikipedia.org/wiki/Digital_infinity | reference | science, encyclopedia | 2026-05-05T15:40:55.677545+00:00 | kb-cron |
The digital computers considered in the last section may be classified amongst the "discrete-state machines." These are the machines which move by sudden jumps or clicks from one quite definite state to another. These states are sufficiently different for the possibility of confusion between them to be ignored. Strictly speaking, there are no such machines. Everything really moves continuously. But there are many kinds of machine which can profitably be thought of as being discrete-state machines. For instance in considering the switches for a lighting system it is a convenient fiction that each switch must be definitely on or definitely off. There must be intermediate positions, but for most purposes we can forget about them. 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. This way, digital computation and communication operates 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's 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.
Information and computation reside in patterns of data and in relations of logic that are independent of the physical medium that carries them. When you telephone your mother in another city, the message stays the same as it goes from your lips to her ears even as it physically changes its form, from vibrating air, to electricity in a wire, to charges in silicon, to flickering light in a fibre optic cable, to electromagnetic waves, and then back again in reverse order. ... Likewise, a given programme can run on computers made of vacuum tubes, electromagnetic switches, transistors, integrated circuits, or well-trained pigeons, and it accomplishes the same things for the same reasons. This insight, first expressed by the mathematician Alan Turing, the computer scientists Alan Newell, Herbert Simon, and Marvin Minsky, and the philosophers Hilary Putnam and Jerry Fodor, is now called the computational theory of mind. It is one of the great ideas in intellectual history, for it solves one of the puzzles that make up the 'mind-body problem', how to connect the ethereal world of meaning and intention, the stuff of our mental lives, with a physical hunk of matter like the brain. ... For millennia this has been a paradox. ... The computational theory of mind resolves the paradox.
== A digital apparatus == Turing did not claim that the human mind really is a digital computer. More modestly, he proposed that digital computers might one day qualify in human eyes as machines endowed with "mind". However, it was not long before philosophers (most notably Hilary Putnam) took what seemed to be the next logical step—arguing that the human mind itself is a digital computer, or at least that certain mental "modules" are best understood that way. Noam Chomsky rose to prominence as one of the most audacious champions of this 'cognitive revolution'. Language, he proposed, is a computational 'module' or 'device' unique to the human brain. Previously, linguists had thought of language as learned cultural behaviour: chaotically variable, inseparable from social life and therefore beyond the remit of natural science. The Swiss linguist Ferdinand de Saussure, for example, had defined linguistics as a branch of 'semiotics', this in turn being inseparable from anthropology, sociology and the study of man-made conventions and institutions. By picturing language instead as the natural mechanism of 'digital infinity', Chomsky promised to bring scientific rigour to linguistics as a branch of strictly natural science.