Mirror notation: symbol manipulation without inscription manipulation
Tóm tắt
Stereotypically, computation involves intrinsic changes to the medium of representation: writing new symbols, erasing old symbols, turning gears, flipping switches, sliding abacus beads. Perspectival computation leaves the original inscriptions untouched. The problem solver obtains the output by merely alters his orientation toward the input. There is no rewriting or copying of the input inscriptions; the output inscriptions are numerically identical to the input inscriptions. This suggests a loophole through some of the computational limits apparently imposed by physics. There can be symbol manipulation without inscription manipulation because symbols are complex objects that have manipulatable elements besides their inscriptions. Since a written symbol is an ordered pair of consisting of a shape and the reader's orientation to that inscription, the symbol can be changed by changing the orientation rather than inscription. Although there are the usual physical limits associated with reading the answer, the computation is itself instantaneous. This is true even when the sub-calculations are algorithmically complex, exponentially increasing or even infinite.
Tài liệu tham khảo
Cajori, F. (1929) A History of Mathematical Notation, Open Court, Chicago.
Casati, R. and Varzi, A. (1998) “True and False: An Exchange”, typescript.
Clark, A. and Chalmers, D. (1998) The extended mind, Analysis 58(1), 7–19.
Copeland, J. (1998a) Even Turing machines can compute uncomputable functions, in C. S. Calude, J. Casti and M. J. Dinneen (eds), Unconventional Models of Computation, Spinger-Verlag.
Copeland, J. (1998b) Turing's O-machines, Searle, Penrose and the brain, Analysis 58(2), 128–138.
Fodor, J. (1987) Psychosemantics, MIT Press, Cambridge.
Gardner, M. (1990) The New Ambidextrous Universe, W. H. Freeman, New York.
Garey, M. R. and Jonson, D. S. (1979) Computers and Intractibility: A Guide to the Theory of NP-Completeness, W. H. Freeman, New York.
Geach, P. (1969) God and the Soul, Cambridge University Press, Cambridge.
Gregory, R. (1997) Mirrors in Mind, W. H. Freeman, New York.
Horst, S. W. (1996) Symbols, Computation, and Intentionality, University of California Press, Berkeley.
Ittleson, W. H., Mowafy, L. and Magid, D. (1991) The perception of mirror-reflected objects, Perception 20, 567–584.
Kim, S. (1989) Inversions, Byte Books, Peterborough, New Hampshire.
Langton, R. and Lewis, D. (1998) Defining 'Intrinsic', Philosophy and Phenomenological Research 57(2), 333–345.
Manly, P. L. (1991) Unusual Telescopes, Cambridge University Press, Cambridge.
Ramsey, F. (1927) Facts and Propositions, Proceedings of the Aristotelian Society, Supp. vol. 7, 153–170.
Slutz, R. (1976) Taped interview with R. Slutz, in The Pioneers of Computing: an Oral History of Computing (issued by the Science Museum, London), the Turing Archive, University of Canterbury. This information was supplied by Jack Copeland.
Sorensen, R. (1998) How to Subtract with a Mirror, typescript.
Thomas, D. E. (1980) Mirror Images, Scientific American, 206–228.
Zellweger, S. (1997) Untapped potential in Peirce's iconic notation for the sixteen binary connectives, in N. Houser, D. D. Roberts, and J. Van Evra (eds.), Studies in the Logic of Charles Sanders Peirce, Indiana University Press, Bloomington, pp. 334–386.