Bruno,
Sometimes gedankenexperiments - or even theoretical
contemplations - include unvoiced/unconsidered
presumptions and biases that a system may not
be self-aware of. Benj Whorf brought this aspect
of systemic nature into consideration, in the 1930's,
when he applied Einstein/Reichenbach notions of
'relativity' to the "subjective" field of language
and linguistics. {Reichenbach called his analysis
of it (1927) vis a vis gravity, Theorem Theta.}
Several years ago, I proposed that attention
should not be paid to the Halting Problem, but
instead be paid to what comes after. Meaning,
not to the effective information production
of the computation run, nor to any activity
resulting from the computation run .. but rather
to this: future re-activation of 'the' or any
computation process.
We exist in a universe that is always 'in process'.
Even if some operations 'halt', the essential nature
of co-present simultaneous systems is that dynamics
are so 'on-going' that the main priority is on
re-enacted/re-established/re-initiated actions.
No systems are 'pure isolates' .. there are always
and importantly: relationships of context, continuity,
and recursion.
Placing the Turing or Church or any other devised
'closed conditioned system' on the table of evaluation,
is to miss THE critical group of parameters, that no
'idealized' parameters group includes.
Current closed-set evaluations are fundamentally:
utilitarian, task-oriented, single assignments/missions.
But the statespace of the universe is open, relative,
re-accessible, and re-instantiable .. WITH .. all
systems being vulnerable to correlary/additional
instructions.
It makes no nevermind if a system or computation
'halts' or not.
The crucial things is whether 1) if a computation
halts .. what are the conditions for re-instantiation?,
and 2) if it never self-halts .. then what parameters
are present to induce halting? (a) sufficient utility of
incomplete data, (b) eradication due to untimely utility,
(c) exhaustion of operational resources, (d) ???? ....
You see Bruno, mathematics carries a self-blinding
presumption: Perfect universal information distribution/access.
"Sequential operations" functions are an attempt to
evaluate non-instantaneous information processing.
And physical reality includes both AND contraints
unique to both - but interactive with the other
domain.
James
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Received on Sat Jun 17 2006 - 14:11:58 PDT