Posted by
glen ep ropella on
URL: http://friam.383.s1.nabble.com/Robert-Rosen-tp525527p525542.html
-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1
G?nther Greindl on 01/03/2008 03:29 PM:
> 1) The assertion that the incomputable enters with "life". Rosen seems
> aware that he moves into the range of vitalism here, and tries to defend
> that he says it is not mechanism versus vitalism but simplicity versus
> complexity (=uncomputability in the Rosen sense)
> For my problems with his "uncomputability" see below.
Living systems are just the particular example set of the (possibly very
large) category of complex_rr* systems. It doesn't _start_ with life.
Life just happens to be what RR (Robert Rosen) was interested in.
There is a tinge of vitalism in there. And vitalists of all kinds seem
to be attracted to RR's writings. But, I believe he was not appealing
to any sort of vitalism. There are other, more insidious, assumptions
he makes, though.
> 2) Rosen repeatedly refers to G?del's result and talks about how it
> shows how impoverished formalization are in regard to "real"
> mathematics. This of course leads to the question what "real"
> mathematics is. It seems that Rosen is Platonist (how else would he know
> what "real" mathematics is?), but this is an opinion
> one must not share.
> He also ignores that G?del's results do not place limits on what one can
> formally model (in general), but only with regard to a formal system
> (finitely given, sufficient strenght etc).
>
> The question _if_ physics is completely formalizable/computable is
> indeed an interesting one, but why should this stage only start when
> life is concerned? (see below) Either it applies to the universe as a
> whole or it does not.
RR held that it applied to many systems, not necessarily just living ones.
He does, however, seem to avoid being explicit about the influence of
Goedel's theorems on his own ideas. As far as I can tell, he never even
approaches a technical explanation that extrapolates from Goedel to his
work. His exposition is purely philosophical and others claim to be
able to map what he said directly to Goedel's results. I'm not that
smart, though.
A better exposition comes in Penrose's work, in which tries to argue
that math (as done by humans) regularly involves hopping outside of any
given formal system in order to catch a glimpse of a solution, then
hopping back inside the formal system in order to develop a formal
proof. And in this regard, RR's rhetoric is not inconsistent.
RR's basic claim would be that math is _more_ than computation
(automated inference... formal systems... whatever you want to call it).
Namely, it involves jumping levels of discourse to provide entailment
when none such can be provided inside the formal system. If you take
that to its logical conclusion, you can imagine a _holarchy_ of formal
systems that each patch up the entailments for other formal systems in
the holarchy. In order to avoid an infinite regress or an infinite
progression, however, the level hopping _must_ loop back in on itself.
So, RR's position is that causal loops (a self-justifying rhetorical
holarchy of formal systems), if formalized, might provide the
mathematical infrastructure necessary to more completely capture (model)
living systems.
> 3) In the Kercel paper, we read:
> :START QUOTE:
> Given this, what does the (M,R)-system imply? In this model, the
> inferential entailments, the metabolism map f, the repair map F, and the
> replication map b represent the causal entailments in an organism, i.e.,
> the efficient causes of metabolism, repair, and replication,
> respectively. If the (M,R)-system is actually in a modeling
> relation with the organism, then the same closed-loop hierarchical
> structure of containment of entailment must apply to the efficient
> causes. Just as map F contains map f contains in map b contains map F,
> ad infinitum, the efficient cause of repair contains the efficient cause
> of metabolism contains the efficient cause of replication contains the
> efficient cause of repair, ad infinitum.
>
> This is what it means to say that organisms contain the causal
> counterpart of impredicative loops. Rosen's expression "closed to
> efficient cause" now becomes clear.
>
> A real-world process is "closed to efficient cause" when it contains a
> closed-loop hierarchy of containment of efficient causes. Each efficient
> cause is contained by all the members of the loop that come before it,
> and contains all the members of the loop that come after it.
> :END QUOTE:
>
> What I fail to see that "life" embodies this "infinite" cycle as in his
> (M,R) system: after all, life started around 4 billion years ago - so I
> can _finitely_ list all cycles till some point where we are not
> interested anymore (depending on which theory of origin of life you
> prefer, rna first or metabolism first or whatever).
The part that RR seems to think is not covered is the force or influence
that "guides" a living system in its behaviors. In many contexts,
people tend to make vague claims that "natural selection" or the
"environment" provide such pressure in the form of limited resources or
optimization or even co-evolution. But, those sorts of answers to _why_
a living system assembles and maintains itself are really just question
begging... they put off the question without answering it.
It's this "why" that leads him to consider "final cause". He takes the
most prevalent answer to the why question seriously: living systems do
what they do in order to benefit _themselves_. But how can an organism
at time t_0 know what actions will benefit that organism at time t_100?
The question he asks specifically is: "How can we have organization
without finality?" I.e. How can we say that an activity of an organism
is purposeful without some external _agent_ declaring the purpose of the
organism? In the end, he comes to the idea that effects cause their
causes, which is obviously cyclic.
So, placing it on the 4 billion year timeline, each tiny process obtains
because the effect of that process will be more processes like the prior
tiny process. In layman's terms, "use it or lose it" or "practice
makes perfect". These positive feedback loops where the effect of a
process is to reinforce the process are the heart of RR's idea.
The trouble is that they are not _simply_ self-reinforcing. Each
iteration through the cycle _changes_ the system. So, you cannot
_finitely_ list all cycles up until some point UNLESS you actually do
it. I.e. the end result of the 4 billion years of iteration is not
analytically predictable from the very first set of axioms we started
with 4 billion years ago. It's incompressible because each iteration
changes the building blocks. (And as our discussion about "informal"
formal systems covers, consistency is not necessarily preserved when new
axioms are added or when the axioms are changed, which means that formal
systems can't accurately model these self-modifying systems.)
True, if hindsight were 20/20, we could finitely list everything that
has already happened; but, we (probably) wouldn't be able to finitely
list everything that will happen from now until, say, 100 years from now
_because_ the underlying ontology changes at each iteration.
Of course, we _simulants_ are familiar with this argument because we
have to use it when we argue against those that put full faith in the
power of analytic solutions. But most of us only have to use the form
of the argument that has a _fixed_ ontology. The outcome of a chess
game is relatively easy to predict because the chess pieces, board, and
repertoire don't change with each move.
> 4) An ultrafinitistic view would generally rule out noncomputable models
> anyway (see for instance the nice essay by Doron Zeilberger:
>
http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/real.pdf)
> Or:
>
http://en.wikipedia.org/wiki/Ultrafinitism>
> So Rosen's model's also make some mathematical assumptions (which,
> admittedly, are widely shared - but may change, of course)
I don't understand how ultrafinitism rules out noncomputable models. It
seems to me that even in ultrafinitism, the halting problem is still
noncomputable (as Marcus mentioned).
> 5) What I also find strange is the opposedness to computation: after
> all, with computers we are just beginning to find an "embarassment of
> riches"; fine to explore other avenues (Rosen), but I think it is much
> to early to dismiss the computational approach. So why his radical
> assertion that computational approaches to describe life must fail?
Because he'd bought into the idea that effects cause their causes in
living systems and he believed computation (as we know it today) cannot
represent these causal cycles.
And many people seem to agree. But, it's not clear how much math RR was
aware of. For example, did he know about non-well-founded set theory?
Did he know of quantum computation? Etc. It's entirely possible that
if he were in his prime today, he would not have come to the same
pessimistic conclusions about "computation". You have to remember that
he did much of this work in the 70s and 80s, perhaps even earlier. You
also have to remember that he rarely got a fair hearing from his
contemporaries for whatever reason. Science is full of pompous idiotic
"experts" (probably including RR as well) who destructively criticize
anything they don't immediately understand or agree with. It's entirely
possible that if he'd had a more receptive group of people to work with,
he might have made better progress and/or changed his mind. This
continual rejection also gave him quite an attitude, understandably.
> 6) A point addressed in the Kercel paper: The ambiguity of language and
> the definiteness of computation: this is of import for the AI/Alife
> community, and it is indeed a problem, but is I think addressed if one
> can control the symbol grounding problem(Harnad,
>
http://citeseer.ist.psu.edu/harnad90symbol.html).
>
> If one can let an AI/Alife really learn symbols (instead of programming
> them or assigning meaning to symbols by specification of the prog.
> language; the "learned" symbols would not make sense to us then, of
> course) they would inherently have the same ambiguity as our concepts
> have for us (because they would be learned in an ambiguous world).
I agree. In fact, I don't think ALife will achieve it's ultimate goals
until we develop ambiguous computing (which is more than soft computing,
by the way).
> Conclusion: I think Rosen's ideas are valuable contributions in that
> they sensitivize us to certain problems, especially in modelling life.
>
> But the case against computatability is unconcinving.
I agree... though I would not say "the case against computability"...
I'd say "the case against the expressive power of computation" is
unconvincing. I do believe that there are certain processes in reality
that are noncomputable in terms of what we now call "computation".
And please remember that I'm not an expert on RR. I've done just enough
digging to satisfy my initial curiosity... And I'm LAZY! (I'm only up
to page 166 in "The Road to Reality"... and I bought it when it first
came out. ;-) So, you can rest assured that others are far more
credible and correct.
* I'll try to use "complex_rr" when talking specifically about RR's
definition of complexity.
- --
glen e. p. ropella, 971-219-3846,
http://tempusdictum.comThe only good is knowledge and the only evil is ignorance. -- Socrates
-----BEGIN PGP SIGNATURE-----
Version: GnuPG v1.4.6 (GNU/Linux)
Comment: Using GnuPG with Mozilla -
http://enigmail.mozdev.orgiD8DBQFHfan8ZeB+vOTnLkoRAj4MAJ9NHNZl1DxVdKdsfRiH5JZ+M2Zb0gCdHGnA
3VQ96KRWOeZptPnpKTPVKMc=
=XFiM
-----END PGP SIGNATURE-----