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17 January 2005 Perspex machine II: visualization
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The perspex machine is a theoretical computer that arose from the unification of the Turing machine with projective geometry. It is super-Turing because it can operate on any, or all, numbers on the real number line, for example, along a geometrical ray. It can operate on individual Turing-incomputable numbers and on sets of numbers with the cardinality of the continuum (real number line). This exceeds the cardinality of the natural numbers, that is, the number of symbols accessible to a Turing machine. The perspex machine can compute continuous events in addition to discrete ones. We suppose this gives it enough power to describe the operation of the physical universe, including the operation of minds. We review the perspex machine and improve it by reducing its halting conditions to one condition. We introduce a data structure that can accelerate a wide class of perspex programs. We show how the perspex can be visualised as a tetrahedron, artificial neuron, computer program, and as a geometrical transformation. We discuss the temporal properties of the perspex machine, dissolve the famous time travel paradox, and present a hypothetical time machine. Finally, we discuss some mental properties and show how the perspex machine solves the mind-body problem and, specifically, how it provides one physical explanation for the occurrence of paradigm shifts.
© (2005) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
James A. D. W. Anderson "Perspex machine II: visualization", Proc. SPIE 5675, Vision Geometry XIII, (17 January 2005);

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