On Dec 13, 1:25 pm, "Stephen P. King" <stephe...@charter.net> wrote:
> On 12/13/2011 10:47 AM, Craig Weinberg wrote:> 4. Computation is not 
> primitive. It is a higher order sensorimotive
> > experience which intellectually abstracts lower order sensorimotive
> > qualities of repetition, novelty, symmetry, and sequence. When we
> > project arithmetic on the cosmos, we tokenize functional aspects of it
> > and arbitrarily privilege specific human perception channels.
>
> Hi Craig,
>
>      No. A computation is by definition not abstracting novelty. Novelty
> is the essence of not-computable. The Halting theorem is an illustration
> of this. Computations are about repetition and sequence and perhaps
> symmetry, yes, but repetition and sequencing of physical states is what
> memory is all about, without the invariance over time there is nothing
> to define a repetition on.

I was thinking of novelty in the sense of the experience of counting,
that it's not just rhythm, but actually progresses with a sense of
unveiling the next integer. Even though you know what it's going to
be, there is a sense of realizing that knowledge in expression - the
next digit of Pi, the solution of a problem, etc. All arithmetic is
fueled by a desire not merely to repeat but to make an unknown
quantity known or verify a known quantity. The motive of solving or
verifying I think requires the preexistence of a novelty concept.

Also, couldn't arithmetic be based on names instead of numbers though
and have no repetition? It could be all novelty. Meaningless novelty,
but novelty. I don't think humans would like it very much but a
computer should be able to function that way I would think. One giant
byte, addressable by name search algorithms.

Craig

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