Re: [-empyre-] replying to several posts
On 05.05.03 12:15, "Jim Andrews" <firstname.lastname@example.org> wrote:
> I am not aware of any accepted proof that the computational power of humans
> exceeds that of a
> Turing machine, or the existence of a formal system (that deals within
> finitude) that exceeds
> that of a Turing machine. Are you?
I wasn't really suggesting that human computational skills exceed that of a
Turing machine; rather that they are distinct and that humans can do things
that Turing machines cannot due to their not being formal systems.
Computation is arguably by definition a formal process. People can compute
but they can also do things that are not computable. Computers cannot do
this although what they do do (compute) they do better than people do.
That said, Turing machines do not necessarily compute better than people.
There is no performance specification for a Turing machine. The machine here
is an idea which performs as well as its realisation allows it. If it is
made from matchboxes and paper strips it will be slow and clumsy to operate.
If it is made from VLSI circuits it will be fast and invisible to the
> The diagonal argument guarantees the existence of more 'undecidable
> propositions' regardless of
> how many denumerable axioms we add, Simon, like it does in Cantor's arguments
> transfinite arithmetic, which is where Godel picked up the technique (again,
> gorgeous work).
You are at the limits of my detailed knowledge on this subject at this point
and thus I feel uncomfortable in debating this. What I can say is that you
do not need to analyse and evaluate formal systems from a formal point of
view. Formal systems, as Goedel shows, are only ever partial and thus are
only ever applicable in specific and thus special instances. They can never
be general purpose. If humans only operated formally they would never have
survived as an organism long enough to evolve anywhere near the complexity
to do anything beyond the most basic of operations.
Given this I think it is permissible to critique and analyse formal systems
from an informal point of view and to regard formal systems as part of what
people can do and deal with them within that framework. This was what I was
arguing previously, and clarifying above, when I said that humans can go
beyond formal systems. I would also argue that whilst computers are a formal
instance of writing/language and language is perhaps the defining human
paradigm (as I said elsewhere, I regard people as the products of language)
it does not follow that language is a formal system itself. I would say that
language is very similar to its "other half" (people) in its
inconsistencies, nonlinearities and general chaotic nature.
I am sorry if this argument seems fluffy and informal...but that is where I
will be happiest arguing from. Whilst I am happy to use logic to support my
arguments I am also just as happy to use illogic. If it works that is fine
with me. In many respects my approach is sophist and rhetorical rather than
logical and empirical. Guess I read to much Foucault when I was a kid...
> Apologies. Perhaps we are getting too technical for the list? I would be happy
> to discuss this
> with you backchannel further if you like, Simon, or take it further on the
> list--your call. It's
> great to be able to talk about such things, however, in the context of poetry
> and programming.
No need to go off list. As I say above, my argument will always seek to
avoid technical detail.
Art and Design Research Centre
Sheffield Hallam University, UK
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