Re: Rosen & Ashby

["Tim Gwinn" <***>]

Hi Jamie,

The two Rosen quotes are of decidely different natures. The first statement
comes from personal notes that were not originally intended for publication.
I would take that as such, and not as intended to be a necessarily precise
definition or phrasing. The second statement comes from his published book
"Essays on Life Itself" and is referred to in the Index as "complexity;
defined". So, the latter is the one that constitutes a precise definition.

You are correct that they, in effect, say the same thing. The "subjective
limitation" in the first statement that is codified in the second statement
is the subjective expectation that all models are "simulable".  It was one
of Rosen's great insights that the belief that all systems should be
entirely able to be modeled by algorithmic models was incorrect. So it is
that complex systems are those that sit on the other side of that subjective
limitation, by virtue of their possessing nonsimulable models.

This brings me to discussing the meaning of "simulable" and "simulation",
which you refer to in your paragraph that references Chaitin. Like so many
of Rosen's choices of terms, "simulable" and "simulation" are used in a very
specific way by him and are not always what they might appear to be in
common usage. (How often I wish he had never chosen the word "complexity"
for his central concept!!!) "Simulable" means precisely "evaluable by a
Turing machine", or more concisely, "Turing-computable". So, Rosen's
definition of complexity can be restated with no loss of precision as: "A
system is called complex if it has a non-Turing-computable model."

Similarly, "simulation" refers to a very specific concept for Rosen. It took
him an entire painstaking chapter in "Life Itself" to explain. I'll try to
crudely summarize simulation as: the substitution of algorithmic entailments
in a Turing machine for the entailment structure of the original system. The
upshot is that 'simulation' both invokes the limits of Turing-computability
and also uncouples any necessary relationship between the entailment
structure in the simulation and the entailment structure in the original
system. This makes simulation a very insidious way of superficially
appearing to do modeling, when it fact, the two are generally worlds
apart.I'd probably have to refer anyone to ch. 7 of LI for any more detailed
explanations on these concepts.

I don't make these remarks in order to be nitpicky. Without incorporating
these precise usages of these terms by Rosen, his definition of
"complexity", which invokes this specific concept of "simulable", unravels
completely, as you demonstrate below. This is one of the burdens of his
exactness: the concepts and definitions fit together so carefully and so
precisely that any misunderstanding or wayward rephrasing can bring the
whole edifice tumbling down. And, this is why anyone's remarks that ascribe
to Rosen a concept in a notably alternate rephrasing, or with different
terminology than he used, needs to be able to demonstrate that the statement
can indeed fit back into that precise edifice of his design. Otherwise, I
think it would be improper to ascribe it to Rosen. Ascribing something to
Rosen is, of course, is an entirely different matter than drawing upon Rosen
or others as either an analogical or inspirational source for ideas. In
those cases, the resulting statements and concepts are necessarily ascribed
to the person extracting the ideas and not to the source.

Regards,
Tim


> -----Original Message-----
> From: ROSEN Forum [mailto:*** Behalf Of James N
> Rose
> Sent: Wednesday, November 19, 2003 5:31 AM
> To: ***
> Subject: Re: Rosen & Ashby
>
>
> Tim,
>
> You kindly cited two explicit statements by Rosen:
>
> > .. Rosen's  "This is essentially what I have called complexity;
> > a system (mathematical or physical) is complex to the extent
> > it does not let itself be exhausted within a given set of
> > (subjective) limitations." [p. 45]"
>
> > Consider the precise definition of complexity from "Essays":
> > "A system is called complex if it has a nonsimulable model."
> > [EL 306]
>
> The first thing I ask you to appreciate is that I'm an
> autodidact, as I visit this haven of Robert Rosen's
> ideas.  John K. cross-posted to this list from Complex-M
> and because I respect and esteem Rosen - among many General
> Systems original thinkers - I signed on to learn here and
> to continue conversation threads John K. felt compelled to
> share here.
>
> People stimulate and cross-fertilize concepts when they
> encounter one another.  Many things I've written about
> are ideas original to me, even while they ring similar
> to other creative people's ideas.  Can't help that.  It's
> one of the things humans do best .. have the capacity to
> independently encounter similar events and relationships
> and come to like-conclusions.  Even like-inventions.
> Witness Wallace and Darwin, Leibnitz and Newton, to name
> a few.
>
> You might call the technique I've used all my life,
> 'essentialism'.  A kind of reductionist approach,
> I evaluate relations depicted in peoples words and ideas,
> then glean the pith and essential memes they speak about
> and have attempted to convey.  Then I compare the memes
> and dynamics among them .. from many people's works.
>
> Analogies, metaphors, homeomorphisms .. shine forth
> as actual commonalities.  The correlations that underscore
> the reality of the meme: "general systems".
>
> And that takes, not an inexactness or corruption of
> 'definitions', but a flexibility to identify and extract
> meanings that come packaged in different ways.  Which
> requires openness.
>
> I love you.
> I you love.
> I l-ve you.
> You, I love.
> Love. Me (to) you.
> XOXOXOXOXOXOXOXO
> Je t'adore.
> ( ) Love you!
>       and so on
>
> The memes take priority for me.  Because that
> way I can converse competently with many people
> about many diverse subjects.  And across
> changes of nuance even within one speaker's
> set of ideas.
>
> The two quotes of Rosen's you cited "defining"
> complexity, is one of them 'wrong'?  And how does
> an information set (a mathematical statement)
> 'not let itself be exhausted'?  Does the mathematics
> have intentional volition of some sort?  Do you
> think that's part of what Rosen was trying to convey?
>
> What I wrote a few posts back, characterizing memes
> of Rosen and of Ashby, were understandings based upon
> my paradigm, which I have struggled long and hard to
> keep in line with memes of other thinkers.
>
> Look, I had no intention of joining the list to
> challenge or to rotely avow Rosen's ideas.  They
> are alive and resilient and open to exploration,
> as are my own.  I am sorry if my evaluations don't
> allign with yours, I seek like-ness and interpretive
> commonalities, not some special purity in one person's
> ideas.
>
> The two quotes, IMO, are identical, by the way.  With
> the warning that even such graspings at 'best definitions'
> face potential challenges. For example, current math
> cosmology, ala Chaitin and others, is now coming to the
> conclusion that, algorithmically speaking, 'a (natural) system
> is the single best 'model' of that system' .. in order
> for there to be completeness and non-exclusion of
> any qualia or content or potential that 'a natural
> system' may have. Reading here for 'natural system', the
> words 'complex system' or 'complexity'(noun).
>
> By extension, a system IS its 'simulation' and therefore
> by being so, negates the above attempted definitions.
> Even the ultimate open system we call 'universe' could
> no longer qualify as 'complex' by the Rosen requirements.
>
> But that is absurd.  Of course all this universe is 'complex'.
>
> Rosen attempted a complete and universally true meme that
> would make, in the tradition of Georg Cantor, 'infinity' an
> openness of special proportions, in regard to dynamics, processing,
> thriving, and performance.
>
> Conventional and extant definitions aren't always up to coping
> with such scope and grandeur.  Words carry subtly different,
> but importantly different meanings that are sometimes hard to corral.
>
> And sometimes, these deeper understanding lead to questions
> that no conventional thinker, no matter how smart or creative,
> can easily answer.
>
> For example, mathematicians have to make a choice when building proofs.
> They have to pick one or the other: commutivity or non-commutivity.
>
> So I've taken to asking this challenging question:
> What would our math look like?, which operations
> are applicable and when?, if we require (per any
> "truly open" environment) that equation operations
> be optionally commutative AND non-commutative
> at every step??!
>
> To a person, mathematicians flee from facing that
> situation, and sevaral like it.
>
> Anyway, back on focus, I apologize for not being
> a purist to Robert Rosen's texts.  I will try to
> avoid gone-stray interpretations.  I thought I had
> a handle on his memes and intentions.
>
> I know you asked for certain of my own definitions, Tim.
> Remind me next week (am distracted by certain obligations
> in my life at the moment) and I'll do my best to comply
> for you.
>
> Jamie