Re: Rosen & Ashby

["James N Rose" <***>]

Tim Gwinn wrote:

> >
> > FANTASTIC!.  I have been taking-on Godel since day-one of my writings,
> > challenging erroneous premises and pre-set limits which invalidate
> > any attempted generalization of his incompleteness theorems.
> > There have been several "limits to knowledge" conferences, Sci-Am
> > articles and books, and general extrapolations of Godel's
> > theorems, which became the rage of the scientific community.
> > All balderdash, IMO.   To know that Rosen also saw that
> > emperor godel wears no clothes is gratifying.
>
> [TG]
> What do you mean when you say that "emperor godel wears no clothes"?
> That sounds like it dismisses the Godelian results as unimportant.
>
> Rosen takes Godelian noncomputability as a symptom that
> in science it is erroneous to believe that all natural
> systems will have computable models, or that Newtonian-
> style reductionism is a universal physical principle. In
> his view, natural systems with noncomputable models are
> generic, and natural systems with only computable models
> are non-generic.


Tim,

I share Rosen's insight that Godelian noncomputability
signifies a fundamental inherent problem in conventional
science.  But I go a step further, which he might have
taken issue with, but then again, might have seen as
being a worthwhile next-step possibility - in an effort
to integrate things in a holistic way.

Let me re-phrase my almost flippant remark.  The
emperor godel is wearing a set of clothing, but its not
appropriate for all occasion; while all-occasions
is the scope we're going for.




> > > "Exhausted", in his sense, refers to the dictionary sense of
> > > "To treat completely, to cover thoroughly", as in "to exhaust
> > > a topic".  So, there is no vitalism or volition or other
> > > funky things being imputed to mathematical systems or models. :)
> >
> > I never imputed any.  I'm asking about it in consideration
> > of 'actions enactable' within a domain that is larger than,
> > equal to, or smaller than, the whole performance domain,
> > however large they may be individually or relationally.
>
> [TG]
> I know you didn't impute any. :) I thought you were asking
> if Rosen made any such imputations. I do not know what
> "actions enactable" or "performance domain" or "domain"
> mean in your terminology. If you could rephrase or explain
> them, I might be able to respond.


Maybe this.  A specific algorithm could be seen as one
of many possible algorithms available to depict the
activities and relations of a natural system.  Alternative
applications of values in that algorithm poses another
comparative set which is smaller yet.

The 'applications' set will never exceed the group of
all possible instances of the algorithm.  The algorithm
will never exceed/exhaust instantiations of all
possible algorithms.  The application of all possible
algorithms will never exhaust/exceed the relations
that exist and emerge and arise during the natural operations
of a natural system. Ergo, no algorithm/s is/are sufficient to
describe a natural system.

But.

But, the relationship I find most intriguing is that
information of relations and performances of any aspects
of a natural system - can in fact be denoted and identified
in an algorithmic way.  Effectively:  the information
of a natural system is -compatible- with and
transformable in some way, algorithmic expressions;
even, and this is what I personally find seminally important,
even if the information/relations are 'unknown' at some
present moment in time and information awareness.

Consider:  If Godel's incompleteness theorem was
enunciated just after Principia Mathematica, and
some bright student circa ~1735 ruminated about
the possibility of 'what if light travelled at
a fixed velocity, then strange not-quite-exactly
Newtonian mechanics would result', but there was
no advanced enough mathematics to work on the
problem, and no methodology to test the hypothesis,
a godelian would say that such information cannot
be considered because it may or may not be
compatible with the 'already known'.

A trans-godel logician would reason, yes that might
be the case, -however-, whatever information the future
-might- reveal that -does- prove reconcilable with
the currently known, such information IS RIGHT NOW,
_even as unspecifiable 'potential'_, -compatible- with
the currently known.  SO, we can concretely specify
that which godelian logic says we can make -no-
statements about, because in GL it is 'unencountered'
information.

Coming back to 11/2003, the application here is
to draw attention to the fact that information
of any algorithmic specification OR generality,
IS COMPATIBLE AND CONSISTENT AND COHERENT with
any natural system information not currently
mapped with an algorithmic meme.

The domains may seem irreconcilable, but they
share qualia none the less, and -that- is more
important IMO than incomplete mappability.

Now, this is -not- to say that distinguishing
closed vs open systems is not a crucial distinction
to make.  I only identify an additional relation
that seems of importance as well.


> >
> >
> > > He is saying that a complex system cannot be modeled
> > > completely by any finite set of simple models or superposition of those
> > > models. Instead, what is required is either the addition of
> > noncomputable
> > > models, or by regarding a complex system as the limit (in the
> > mathematical
> > > sense) of the set of simple models. [EL 338, LI 247, 280] I do
> > not know of
> > > any place where he elaborates on the latter option, which is
> > too bad, since
> > > it sounds intriguing.
> >
> > Again, I take a different tack.  I deduce that a small
> > number of behavior rules -can- generate performances
> > as we know them, and, can generate 'life' from primordial
> > aspects that wouldn't qualify as 'life' in and of themselves
> > alone.
>
> [TG]
> Are these behavioral rules all computable? Are they all mathematical
> formulas? Does noncomputability enter in anywhere?
>
> Just trying to get a grasp of the nature of these "rules".


Yes, they are.   More to the point, they are interpretable.

Gradients and relative displacements produce behaviors
that relate to endurance and survival and next-engagement
behaviors.  You could categorize the rules as applicable
to many-bodied events, many gradients events, since they
shine light on 'behaviors' of systems more than 'operations'
or 'functions' of systems.

I know Tim, that my use of these terms probably only
conpound your confusion.  Sorry about that, but
my semantics is pretty straight forward.


Jamie
11/23/03