One-to-one

Reversible computation is a great metaphor for the foundations of physics. General discussion A reversible computation is a computation which can be reversed completely. That is, after insertion of the input into a reversible computer, the reversible computer generates some output (if ever). In such a case one may run the entire computation backward by inserting the output as new input, thereby obtaining the input one started with. The computation can flow back and forth an arbitrary number of times. The implicit time symmetry spoils the very notion of “result,” since what is a valuable output is purely determined by the subjective meaning the observer associates with it and is devoid of any syntactic relevance. In more formal terms, reversible computation can be characterized by one-to-one operations, by a reversible, bijective evolution of the computer states onto themselves [Lan61, Ben73, FT82, Ben82, Lan94, LR90]. If only a finite number of such states are involved, this amounts to their permutation. In such a scheme, not a single bit gets lost, and any piece of information (including the trash) remains in the computer forever. That may be good