-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Günther 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 Gödel'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 Gödel'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.com The 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.org iD8DBQFHfan8ZeB+vOTnLkoRAj4MAJ9NHNZl1DxVdKdsfRiH5JZ+M2Zb0gCdHGnA 3VQ96KRWOeZptPnpKTPVKMc= =XFiM -----END PGP SIGNATURE----- ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
