Perspex machine III: continuity over the Turing operations
James A. D. W. Anderson · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2005
The perspex machine is a continuous machine that performs perspective transformations. It is a super-Turing machine that contains the Turing machine at discrete locations in perspex space. We show that perspex spaces can be constructed so that all of the operations in a Turing program lie in a continuum of similar operations in the space, except for the Turing halt which is always a discontinuous operation. We then show how to convolve a Turing program to produce an isolinear program that it is robust to missing instructions and degrades gracefully when started incorrectly, sometimes even recovering in performance. We hypothesize that animal brains are similarly robust and graceful because animal neurons share the geometrical properties of the perspex machine. Furthermore, convolution of Turing programs makes possible the band-pass filtering and reconstruction of programs. Global processing can then be obtained by executing the broad bands before the finer ones. Hence, any existing computer program can be compiled on a perspex machine to make it global in operation, robust to damage, and degrade gracefully in the presence of error. The three “Holy Grails” of AI -- globality, robustness, and graceful degradation -- can be supplied by a compiler. They do not require specific programming in individual cases because they are geometrical properties of the perspex machine.