No. If a Turing machine is executed in a medium depends on public space, then the machine could be extended by adding parts which could use that space to scratch in the sand, put a pen to paper, blow triangular smoke rings, etc.
This means that without such a spatially extended pen, or graphic display such as we have in our monitors, there is no combination of memory settings on the Turing tape which could assume the literal shape of a triangle. Since the Turing machine can, however, continue to process all computations on memory registers *as if* there were a triangle being considered, there would be no possibility of a non-spatially extended logical function (i.e. a program or UD) ever needing to invent such things as space or form. The evidence of our worldly experience as being overwhelmingly filled with forms and spaces should suggest to us then, that computation is not primitive, but rather it must supervene upon a the deeper foundations of the Turing machine which are ignored: The body of the machine, its tape, its read-write head, and the meta-arithmetic physics upon which these depend: sequence, persistence, sensory input and motor output, the possibility of integration and representation, etc. Consider this: A triangle has no smell or sound, no flavor or temperature. There is no experience of triangularity which we can conceive which is independent of visual or tactile presentations. As a Turing machine has no need of eyes or fingers, there is nothing to suggest any basis for the existence of any shape experiences under comp. Of course it is easy to insert such a basis after the fact, since we have eyes and fingers and can imagine a triangle at will, but that's because we aren't Turing machines. We are the recipients of a concretely real human experience, within which other concretely real experiences are presented and re-presented through sense participation. Logic and arithmetic arise a posteriori to sense, as a necessary partitioning protocol among sensory experiences, but it is clear to me that these protocols, like lines between parking spaces, do not create the parking lot, only act as a neutral guide for the drivers of real cars, parking on terrestrial real estate. Craig -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to firstname.lastname@example.org. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.