Mirror notation: symbol manipulation without inscription manipulation
 Roy A. Sorensen
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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 subcalculations are algorithmically complex, exponentially increasing or even infinite.
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 Title
 Mirror notation: symbol manipulation without inscription manipulation
 Journal

Journal of Philosophical Logic
Volume 28, Issue 2 , pp 141164
 Cover Date
 19990401
 DOI
 10.1023/A:1004307405785
 Print ISSN
 00223611
 Online ISSN
 15730433
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 algorithmic complexity
 computation
 Cambridge event
 duals
 mirror
 NPcompleteness
 symbol manipulation
 Turing machine
 Authors

 Roy A. Sorensen ^{(1)}
 Author Affiliations

 1. Department of Philosophy, New York University, U.S.A.