observations. Previously the idea of a thinking machine was famously dismissed by René Descartes as theoretically impossible. Neither animals nor machines can think, insisted Descartes, since they lack a God-given soul. Turing was well aware of this traditional theological objection, and explicitly countered it. 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'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. A digital apparatus