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.


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