Re: Realization of (M,R)-systems, 'Artificial Life' and Dynamical Systems

[Ionel <***>]

Dear Tim:

I think I will just manage a quick reply, and will write to you also
separately an important continuation of this old idea of mine. The computer
people were quite amused by the idea of the categorical computer--on of
them said he "thought in 1971 that it sounded like science-fiction".
Perhaps, that's a reductionist's first reaction to relational biology--as
it is so very different from the reductionists' habits of thinking.
You might say that what started my train of thinking is a paper published
about that time in Michael Arbib's book (The Theory of Automata), in which
only one chapter deals with Topological Semigroups, whereas all the others
are on 'standard' , algebraic semigroup theory. In essence the state-space
of any automaton can be represented by a semigroup, and in effect many of
the machine properties are determined by certain types of semigroups. The
sentence that caught my attention in the Topological Semigroup structure
was speculating about the possibility of building a "topological automaton"
based on such topological semigroups, with quite different 'decomposition'
properties. Whereas the machines and automata we have built so far can be
mathematically and physically decomposed in algebraic group machines and
some simpler small sub- semigroup machines wired either in cascades or in
series, this basic theorem about automata wouldn't apply in the case of
most types of 'topological semigroup machines'. Therefore, such "machines"
that we have not yet built, or we don't know we have, may not be readily
decomposable, and would be somewhat 'complex' in Robert's sense, and could
not be studied in general by 'cutting them up into pieces' and then putting
back together the pieces in any obvious way, just like complex living
systems properties that Robert is discussing in "Life Itself", and also
in "Essays on Life Itself". In fact, if you take the so called 'horse-shoe'
two-dimensional topological space, with a cut and a paste one can get
chaotic behavior as shown by a famous theorem by Smale (?), that made a
very big stirr when it was proven mathematically. As another interesting
example, please imagine a Moebius band that 'has only one face', cut it
across and then it becomes quite a different state-space , the rectangle
with two faces; on the other hand, if you cut it along the length of the
Moebius band, you get two Moebius bands --e.g., it "self- reproduces" its
shape, or state-space, and one gets two identical state-spaces, each with
just one face. i'm sorry I didn't make you drawings of these topological
spaces but you can find them in most introductory topology books, such as
Paul Alexandroff's "Elementary concepts of Topology." (Dover publs., N.Y.)
A very cute one is in his Fig.4, that looks much like an egg's embryo in
cross-section. 3D ones are probably even more attractive and intriguing.
I am leaving the more serious stuff for my follow up email to you.

With best regards,
Ionel



On Fri, 4 Jun 2004 23:38:11 -0400, Tim Gwinn <***> wrote:

>Ionel,
>
>Just a quick reply for the moment. I will try to get the Dejong papers this
>weekend (assuming I can order and download them online) and take a look at
>them, so I am more on the same page with you.
>
>I am intrigued by your "algebraic-topological computer". I'm trying to
>envision how it 'computes'...I have several probably wildy off-base ideas.
>You shall have to say more about this. :)
>
>I hope you feel better - I know when I'm sick I can't put my thoughts
>together well either. :)
>
>Regards,
>Tim
>
>> -----Original Message-----
>> From: ROSEN Forum [mailto:*** Behalf Of Ionel
>> Sent: Friday, June 04, 2004 9:46 PM
>> To: ***
>> Subject: Re: Realization of (M,R)-systems, 'Artificial Life' and
>> Dynamical Systems
>>
>>
>> Dear Tim:
>>
>> I appreciate your thoughtful responses concerning realization problems in
>> terms of dynamics, 'Artificial Life', sequential machines/automata, etc.
>> As a result of our sharper/precise/in focus discussion of the realization
>> aspects, we are now getting to a very interesting part of our ongoing
>> discussion of the realization problem. This lies at the heart of Robert's
>> ideas on biological systems complexity and... 'Life Itself'.
>>
>> ----How is an (M,R)-system being entailed?----
>>
>> In the sections that I cited from Robert's "Essays..." in my previous
>> posting, he addresses in significant detail this very important question,
>> as well as the closely related question of 'AL' implementation based on
>> realization strategies.
>>
>> It is useful to look at the problem of realization from different angles,
>> or points of view, and differences of opinion are therefore naturally
>> occurring; I feel that such differences in viewpoints are quite 'healthy'
>> as they obviously can lead to further developments and deeper
>> understanding
>> of the realization process when rationally pursued. From a relational
>> biology practitioner's viewpoint this as a key step.
>> ----------------------
>> You wrote:
>>
>> >>If I understand your remarks, I think you are also considering that any
>> such dynamical models would have to be of the kind (e.g., non-integrable)
>> that are symptomatic of a complex system. I am hesitant, though, that
even
>> inclusion of these kinds of dynamical models will lead to a successful
>> physical realization.>>
>> --------------------------------------------
>> The page numbers that I quoted to you in my previous posting and that
were
>> from Robert Rosen's "Essays on Life Itself", are indeed concerned
>> with both
>> AL and the dynamic realization and entailment of (M,R)-systems. They are
>> very important: they are key to developing specific applications of
>> (M,R)-systems, as well as other relational biology modeling. Robert
>> distinuguishes in several examples he gives in his "Essays..." between
>> microstates and macrostates in a dynamical systems, but he did
>> not identify
>> necessarily microstates with quantum states.
>>
>> I, really, would like to pursue this topic with you further in a specific
>> context. This is why I cited DeJong's papers in BMB (2004) that also deal
>> with the connection between macro- and micro- states. His
>> approach involves
>> not only a computer classification of 'macrostates' in
>> qualitative dynamics
>> but also a relational/functional approach that might become very useful
>> for realization if adequately developed. You can find them on the web at
>> the BMB site (Elsevier's actually).
>>
>> Furthermore, I did provide 33 years ago, as well as in 1987, a third
>> alternative to the 'computability'/ simulation issue for complexity and
>> biological systems. Thus in agreement with Robert Rosen and Otto Rossler
>> I concluded in my review on "Computer Modeling and Automata theory in
>> Biology and Medicine", that despite widespread use of computers
>> for 'simulating' and modeling biological systems, the recursive, or
>> numerical/'digital' simulation with digital computers does not allow for
>> a positive answer, also in agreement with your 'suspicions' and Robert's
>> statements in response to Dr. Michael Arbib' suggestions that biological
>> systems can be completely simulated by automata, or sequential machines,
>> (statements made back in 1967-68 in his BMB paper on the Category of
>> (M,R)-systems). However, when it comes to "computability" in general,
>> things may be quite a bit different, depending on how one
>> defines "computability", as discussed at length in my 1987 review that I
>> cited above. For example, in one of my printed contributions in 1971, I
>> introduced the concept of a symbolic-categorical 'computation' system, or
>> algebraic-topological "computer" -- if you wish a hypothetical system
that
>> would be capable to "compute" either algebraically or
>> categorically adjoint
>> dynamical models of (M,R)-systems and biological systems, and
>> thus 'simulate' in the strict sense of Rosen's Analogous System
>> Dynamics, and my follow up "Adjoint Dynamical Systems", models of
>> biological systems and functional/physiological processes. This
>> concept has
>> been, and still perhaps is, obviously far ahead of its time, but maybe
now
>> on the basis of Robert's notion of realization we might get very close to
>> AL. The most interesting point about such a realization, is that
>> if it were
>> really successful--according to Robert-- there would be no valid
criterion
>> to call such a thing  anything but 'alive', as it would be truly
>> indistinguishable from a relational biology 'viewpoint' from what we
>> perceive as a living system. This is also covered by Robert in the
section
>> that I cited to you from his "Essays on Life Itself." Hope you'd find
this
>> quite interesting, but please also remember Robert's warnings... also in
>> his televised interview. The topic is getting quite 'hot' in real
>> possibilities. Furthermore, it may have some religious and
>> ethical counter-
>> current views upon the problems from a human standpoint: 'Creating life/
>> cloning possibilities... etc'.
>>
>> I wish I could continue and complete my thougths here, but today I am
>> not feeling well at all physically, and I find it very hard to
concentrate
>> because of being temporarily 'out of commission'. Hope to
>> continue this with
>> you when I feel better.  To conclude, according to Robert, realization
>> does not mean neccessarily, or at all, going from complexity to "simple"
>> systems such as sequential machines, etc. Hope you'd find this conclusion
>> much more to your liking than the other possibilities we have discussed
>> before.
>>
>> With best regards,
>>
>> Ionel
>>
>>
>> On Fri, 4 Jun 2004 11:55:22 -0400, Tim Gwinn <***> wrote:
>>
>> >Hi Ionel,
>> >
>> >Just to clear up any possible confusion, by 'realization' I do mean what
>> >Judith said: "creating a living system using Rosennean models as a
>> >springboard". And, as equally stated by RR in Essays p. 263: "We want to
>> >produce material systems that manifest those general attributes that we
>> >associate uniquely with living organisms."
>> >
>> >In my remarks, I referred specifically to "Rosen's relational models (in
>> his
>> >view of relational models in "Life Itself")". I do not assert
>> that this is
>> >the only way to do relational modeling. (Rosen himself differentiates
his
>> >relational modeling from Rashevsky's.) I do assert that it is a primary
>> >conclusion of "Life Itself" that relational models of this
>> particular class
>> >(such as the (M,R)-system) of a complex system cannot be
>> directly or simply
>> >restated into state-based model(s): "no (finite) concatenation
>> of syntactic
>> >models of an organism yields something which must be an organism",
>> and: "the
>> >abandonment of fractionability , however, means that there is no 1 to 1
>> >relationship between such relational, functional organizations and the
>> >structures which realize them. These are basic differences between
>> organisms
>> >and mechanisms or machines." [LI 280]
>> >
>> >Thus, I assert that the relational modeling he refers to in LI is of a
>> >different formal universe from the formal universe of mechanistic
>> >(state-based) models in which structures would be represented: the one
>> >cannot universally be reduced to, or subsumed by, the other.
>> That is all I
>> >wished to convey.
>> >
>> >Moving to the task of realizing something like an (M,R)-system....I
>> heartily
>> >agree that realization - the creation of a physical specimen - from
>> >something like the (M,R)-system will not simply require a
>> translation from
>> >the functional relational model to a dynamical representation to
>> then using
>> >that dynamical representation as a blueprint for manufacturing the
>> specimen.
>> >Sorry if I gave a wrong impression on that point. That was one of the
>> points
>> >I wanted to make by quoting Rosen's own instructive discussion of his
>> failed
>> >realization attempt in TB&C, where he tried interpreting the (M,R)-
system
>> as
>> >a sequential machine.
>> >
>> >I feel that realization of a complex functional relational model like
the
>> >(M,R)-system is difficult because these universes of discourse are so
>> >fundamentally different. I certainly do not feel that dynamical
>> models are
>> >to be summarily ommitted from the task of realization. I never
>> made such a
>> >suggestion. I do, however, have concerns about the relationship between
>> >dynamical models and functional relational models of a complex system.
>> >According to Life Itself, the class of systems which admit a functional
>> >relational description which is also reducible to a
>> state-description would
>> >be 'machines' (in Rosen's specific sense of the term in LI). Clearly
that
>> is
>> >not what we want to create in our realization, so the
>> relationship between
>> >between the relational and any of its dynamical models must be less
>> obvious.
>> >If I understand your remarks, I think you are also considering that any
>> such
>> >dynamical models would have to be of the kind (e.g., non-integrable)
that
>> >are symptomatic of a complex system. I am hesitant, though, that even
>> >inclusion of these kinds of dynamical models will lead to a successful
>> >physical realization.
>> >
>> >Regards,
>> >Tim
>> >
>> >> -----Original Message-----
>> >> From: ROSEN Forum [mailto:*** Behalf Of Ionel
>> >> Sent: Friday, June 04, 2004 7:11 AM
>> >> To: ***
>> >> Subject: Re: Modern Physics, Newtonian Paradigm, and the
>> notion of State
>> >>
>> >>
>> >> Dear Tim:
>> >>
>> >> Let's look together at some more facts that do not appear to match
your
>> >> proposition: a significant proportion of Robert's book on
>> "Essays on Life
>> >> Itself.",  written much more  recently than 1973, and printed in New
>> York,
>> >> in 2000, i.e. the latest printed work of Robert Rosen contains very
>> >> significant sections and chapters that are exactly along the
>> lines that I
>> >> pointed out to you before about his previous work on dynamical
systems.
>> In
>> >> my view, there is nothing wrong whatsoever with that; this is
>> what Robert
>> >> intended  to do, because this is a reasonable and fruitful way to
>> >> carry out
>> >> the Relational Biology program--through modeling at several levels,
not
>> >> only at ONE level. In a certain sense, such 'too restrictive'
>> an approach
>> >> to just one level of reality would in effect be also
>> 'reductionistic-to-
>> >> abstract-semantics-ONLY' , which in effect would be  exactly on the
>> >> opposite side of the 'reductionistic' coin, e,g. "purely
>> >> abstract 'semantics'--without real meaning", no syntax, no
>> developmental/
>> >> numerical tools, ...and also quite sterile.
>> >> This is the point that Robert
>> >> makes repeatedly throughout the 346 pages of his recent book
>> >> on "Essays ...".  A particularly clear example of this is presented in
>> his
>> >> several chapters in this book on:  Morphogenesis in Networks
>> (Ch.15, pp.
>> >> 224-, especially pp.232-241), Genericity and especially the section
>> >> on "Dynamical Degeneracy" (Ch.12, pp. 175-186), Chapter 14
>> "Optimality in
>> >> Biology and Medicine (pp.201-223), Ch.16 on Order and Disorder in
>> >> Biological Control Systems (pp.246-253), and so on, and on.
>> >>
>> >> Should one decide to ommit/take out such VERY important aspects as the
>> >> dynamical behavior and treatments that Robert specifically
>> >> illustrates with
>> >> differential eqns., and the specific solutions of such eqns., phase
>> >> portraits, trajectories of states, etc., one would look at a much
>> >> impoverished and much less attractive book than Robert's exciting,
>> >> interesting and very readable "Essays...", the new book. The
>> >> selected, 'simple'  and complex dynamical examples that Robert
>> >> provides are
>> >> really crucial to an in depth understanding of his very
>> important work on
>> >> relational biology, with both its inter-connected aspects--
>> abstract and
>> >> dynamics. I do hope that you will give these points the serious
>> >> consideration that certainly Robert's "Essays..." deserve,(without
>> >> attempting to over-simplify the problem of realization to the one
>> intended
>> >> in your paragraph cited below), which as shown in the
>> "Essays..." is very
>> >> important indeed and cannot be/ should not be quickly "pushed under
the
>> >> carpet."--  merely as :
>> >>
>> >> >>>realization of these relational models, whether via
>> sequential machine
>> >> models or via kinetic models, as attempts at interpretation/
>> >> translation/mapping from the universe of state-less atemporal
>> relational
>> >> models into the universe of state-based models.>>
>> >>
>> >> REALIZATION is much more than that: please note specifically pp.
>> >> 263-269 in
>> >> Robert Rosen's "Essays... " concerning the essential need for the
>> >> realization steps, and the importance of the realization steps for
>> >> Entailment, such as in the case of (M,R)-systems. It is a key process,
>> >> connecting the 'abstract' world of relational biology to the real
world
>> in
>> >> which such models are being REALIZED! It is NOT merely
a 'translation',
>> >> as the "traduttore--traditore" saying would make it to be.
>> >> It is much more than that: it's the trully complementary part that one
>> >> needs to see as a 'measure of reality' of the relational models
>> >> considered.
>> >> Faithful realizations are exceedingly important for modeling in
>> relational
>> >> biology, and practice does help, as Robert demonstrates it vividly and
>> >> clearly in his "Essays ...", many times over. Without REALIZATION,
>> >> a pseudo-'relational biology' might simply float into the
>> abstract vacuum
>> >> of a "dolce far niente", totally remote from biological reality,
>> >> a "semantic theory" but without either real meaning or any syntax!
>> >>
>> >> The realization strengthens, and is part of the relational
>> >> biology theories-
>> >> -instead of detracting from them.
>> >>
>> >> As Nicolas Rashevsky--the founder of relational biology--
>> himself pointed
>> >> out: relations in biology are quite 'general' in character:
>> they contain
>> >> BOTH qualitative and quantitative aspects. As also he was fond
>> of saying:
>> >> "Mathematics has been long considered the Queen of Sciences, but...
she
>> is
>> >> a democratic queen!"
>> >>
>> >> In my own Qualitative Dynamics paper of 1971, (and later work) that I
>> >> posted earlier ,I have made the same points that Nicolas Rashevsky and
>> >> Robert Rosen did about the need to use both qualitative and
>> quantitative
>> >> approaches to model dynamics in relational biology. For a more recent
>> >> reference along the same lines-- there are two substantial papers
>> >> by DeJong
>> >> on Qualitative Dynamics in Biology published in BMB in 2004, one
>> providing
>> >> the broader framework, and the other providing the application to a
>> >> specific case in great detail.
>> >>
>> >> With best regards,
>> >>
>> >> Ionel
>> >>
>> >>
>> >>
>> >> On Thu, 3 Jun 2004 22:27:26 -0400, Tim Gwinn <***> wrote:
>> >>
>> >> >Hi Ionel,
>> >> >
>> >> >Adding the following thoughts to my prior response to this post....
>> >> >
>> >> >>From my perspective, I draw a distinction between Rosen's relational
>> >> models
>> >> >(in his view of relational models in "Life Itself"), and the
>> attempts at
>> >> >*realization* of such models. I consider that these
>> relational models do
>> >> sit
>> >> >in an entirely different formal universe of discourse (for lack
>> >> of a better
>> >> >phrase) from the Newtonian-paradigm formal universe of
>> discourse; it is
>> a
>> >> >formal universe of discourse where "systems are assigned no states,
no
>> >> >environments, and there is no recursion".
>> >> >
>> >> >Generating a physical realization *from* these relational
>> models is the
>> >> >conundrum. Certainly, it would seem likely (or at least, it seemed
>> likely
>> >> to
>> >> >him back then (1964, 1971, 1973) that the process of realization must
>> >> >include some way to interpret/translate/map from these models to
>> >> some kind
>> >> >of state-based model(s) which would tell us, among other
>> things, how to
>> >> >physically put the parts together. I see Rosen's attempts at
>> >> realization of
>> >> >these relational models, whether via sequential machine models or via
>> >> >kinetic models, as attempts at
>> >> interpretation/translation/mapping from the
>> >> >universe of state-less atemporal relational models into the
>> universe of
>> >> >state-based models.
>> >> >
>> >> >Regards,
>> >> >Tim
>> >> >
>> >> >> -----Original Message-----
>> >> >> From: ROSEN Forum [mailto:***
>> Behalf Of Ionel
>> >> >> Sent: Wednesday, June 02, 2004 5:33 AM
>> >> >> To: ***
>> >> >> Subject: Re: Modern Physics, Newtonian Paradigm, and the
>> >> notion of State
>> >> >>
>> >> >>
>> >> >> Hi, Tim:
>> >> >>
>> >> >> I'd go along with most of your comments about
>> (M,R)-systems, but there
>> >> are
>> >> >> some important facts that are running contrary to your
>> sentence cited
>> >> >> below, if I understood your argumentation correctly:
>> >> >>
>> >> >> >>These functional relational models are in an entirely
>> >> different formal
>> >> >> universe of discourse than a formal universe of discourse
>> built around
>> >> >> spatiotemporal relations.>> It is, metaphorically speaking, like
>> >> >> a parallel
>> >> >> formal universe - a rather alien one to the one in which we are
used
>> to
>> >> >> doing physics in. >>....Of course, the opposite is also true: these
>> >> >> relational models have abstracted away state information
>> >> entirely - they
>> >> >> have "thrown away the physics".) >>
>> >> >>
>> >> >> ---------------
>> >> >> FACTS: Both in 1971 and 1973, Robert published in BMB two
>> substantial
>> >> >> papers in which he developed dynamic representations of
>> (M,R)-systems
>> >> that
>> >> >> appear to be aimed at linking the Abstract (M,R)-systems
>> >> approach to the
>> >> >> physical representation of such systems in terms of kinetic or
>> dynamics
>> >> >> eqs.,etc,  e.g. attempting to avoid to "throw away the
>> >> physics", such as
>> >> >> the dynamics in terms of states and state-spaces. It is clear
>> >> >> that Roberts'
>> >> >> states are not quantum states.
>> >> >> -------------
>> >> >> Regards,
>> >> >>
>> >> >> Ionel
>> >> >>
>> >> >> ...>>In TQFT, the relations represented are still between
>> >> spatiotemporal
>> >> >> quantum states: the encoding has gone from the natural system to a
>> >> >> spatiotemporal encoding and then to a topological one. In Rosen's
>> >> >> relational models, the encoding goes directly from the natural
>> >> system to
>> >> >> the functional relational model. This allows for representations of
>> >> >> organizational qualities that cannot be encoded into the
>> spatiotemporal
>> >> >> encodings of the Newtonian paradigm. (Of course, the opposite is
>> >> >> also true:
>> >> >> these relational models have abstracted away state information
>> >> entirely -
>> >> >> they have "thrown away the physics".)