Date: Sun, 18 Feb 1996 19:25:00 -0400 (EDT) From: DON MIKULECKY Subject: what is coming Date: Thu, 15 Feb 1996 10:28:48 -0400 (EDT) From: DON MIKULECKY A summary of yesterday's meeting for those who missed. Date: Thu, 15 Feb 1996 15:32:02 -0400 (EDT) From: DON MIKULECKY Subject: will the real complexity please stand up? "Jeff Prideaux" 16-FEB-1996 09:23:47.14 Subj: freezing cells Date: Fri, 16 Feb 1996 12:21:17 -0400 (EDT) From: DON MIKULECKY Subject: This a draft...but we'd like your reaction....going to "Nature" From MIKULECKY@gems.vcu.edu Sun Feb 18 17:08:44 1996 From: DON MIKULECKY Subject: a construction about the second law of thermo from Schneider and Kay! From: GEMS::SBROBERTS 18-FEB-1996 18:16:44.08 Subj: RE: a construction about the second law of thermodynamics from Schneider and Kay! Date: Mon, 19 Feb 1996 13:04:05 -0400 (EDT) From: DON MIKULECKY Subject: the frozen cell issue and dynamics!! some dialog Date: Mon, 19 Feb 1996 14:26:48 -0400 (EDT) From: DON MIKULECKY Subject: Thermodynamics raises its ugly head! Date: Mon, 19 Feb 1996 17:53:58 -0400 (EDT) From: DON MIKULECKY Subject: progress! Date: Wed, 21 Feb 1996 08:36:57 -0400 (EDT) From: DON MIKULECKY Subject: Why frozen cells are not machines. Date: Wed, 21 Feb 1996 09:41:52 -0400 (EDT) From: DON MIKULECKY Subject: another comment Date: Wed, 21 Feb 1996 10:38:40 -0400 (EDT) From: DON MIKULECKY Subject: what good is it? From: GEMS::JPRIDEAUX "Jeff Prideaux" 21-FEB-1996 13:12:53.37 Subj: halting problem ----------------------------------------------------------------------------- Date: Sun, 18 Feb 1996 19:25:00 -0400 (EDT) From: DON MIKULECKY Subject: what is coming For those who have not yet invested in the book: The next three chapters in Kampis: 3. From observations to a theory of dynamics 3.1 THE ZENO PARADOXES AND THE SHUTTLE PRINCIPLE 3.2 ON THE NOTION OF STATE 3.3 ANTICIPATION AND THE EXISTENCE PROOF FOR STATES 3.4 MATERIAL AND FORMAL IMPLICATIONS 3.5 CONSTRUCTION OF DYNAMICS AS A TRANSITION FROM MATERIAL TO FORMAL IMPLICATIONS 3.6 STATES AND DYNAMICS BROUGHT TOGETHER 4. THE MECHANISTIC UNIVERSE 4.1 AN ALTERNATIVE VIEW OF DYNAMICS 4.2 DYNAMICS AS STATICS: THE WALLED-IN UNIVERSE 4.3 THE ATOMISTIC PERSPECTIVE 4.4 THE NATURE OF MECHANISTIC SYSTEMS 5. COMPONENT-SYSTEMS: BEYOND ALGORITHMIC DYNAMICS 5.1 THE CONCEPT OF COMPONENT SYSTEM 5.2 ORIGINS OF THE CONCEPT 5.3 PROBLEM PROPERTIES 5.4 COMPONENTS AS DYNAMIC VARIABLES: THE HERMENEUTICS OF LIFE 5.5 THE CONCEPT OF IMMENSITY 5.6 'GENIDENTITY' AND DYNAMICS 5.7 THE MAIN THEOREM 5.8 UNIVERSAL LIBRARIES 5.9 FALSE DYNAMICS 5.10 CREATION AND NON-ALGORITHMIC SELF-MODIFICATION 5.11 A HIDDEN ASSUMPTION ELIMINATED ----------------------------------------------------------------------------- Date: Thu, 15 Feb 1996 10:28:48 -0400 (EDT) From: DON MIKULECKY A summary of yesterday's meeting for those who missed. We began discussing the posting I had sent on equivalence relations. Seth used an example of a shell from a marine critter as compared to a rock. he showed that by many criteria, they fell into the same class, but there were also some by which they were clearly different. It was pointed out that the difference was obvious and rigorous classification schemes were really superfluous. Cindy suggested that as the classification criteria were made more and more refined, there was an initial distinction, but then a unity evolves. We then discussed whether we could encounter situations where classification was of little importance. Norma described the evolution of her research project on spirituality and health. She drew this diagram on the board: POSITIVISM----------->ETHNOGRAPHIC---------------------->CONSTRUCTIVISM (forgive me if I garbled it) And related that the first phase involved developing a scale for "spirituality" while the second involved interviews which were centered around a specific set of questions. The third phase, the constructivist phase, will involve interactions with the subjects which are open ended and allow for the interviewer to change as much as the person being interviewed. In this study, the objective is shifted towards discovery rather than measurement. We also discussed the differences we all bring to the group and the need for patience and openness if we are to nurture the diverseness we have achieved. I also tried to show that the measurement problem in quantum mechanics was indeed a manifestation of the kind of issues that we were discussing. We speculated about whether the hard science/soft science dichotomy is valid or not and whether we would be finding our own answer to the question as we go on. I ask others who were there to add to or modify my account. I also would like to cite some relevant references: First from "Fourth Generation Evaluation" by E.G. Guba and Y. S. Lincoln, Sage Publications, Newbury Park, CA (1989){folks asked for references on constructivism....this is one} From the chapter: "What is this constructivist paradigm?", Under the heading: "Theorems Applying to all Forms of Inquiry" ...... (4) Measurability. Conventional: Whatever exists in some measurable amount. If it cannot be measured, it does not exist. Constructivist: Constructions exist only in the minds of constructors and typically cannot be subdivided into measurable entities. If something can be measured, the measurement MAY FIT into some construction but it is likely, at best, to play a supportive role. Comment: The conventional form of this theorem undergirds all measurement theory. It is often used as rationalization for asserting that data must be quantified to be meaningful. The constructivist form admits a much wider form of information, INCLUDING QUALITATIVE, but does not assign quantitative information the same central position. I will assert that much of biology already, although apologetically, operates in a "closet" constructivist mode. Now let's compare Rosen with this: from: "Drawing the boundary between subject and object: Comments on the mind-brain problem" Theoretical Medicine 14:89-100. "ABSTRACT. Physics says that it cannot deal with the mind-brain problem, because it does not deal in subjectivities, and mind is subjective. However, biologists (among others) still claim to seek a material basis for subjective mental processes, which would thereby render them objective. Something is clearly wrong here. I claim that what is wrong is the adoption of too narrow a view of what constitutes 'objectivity' especially in identifying it with what a 'machine' can do. I approach the problem in the light of two cognate circumstances:(a) the 'measurement problem' in quantum physics, and (b) the objectivity of standard mathematics, even though most of it is beyond the reach of 'machines'. I argue that closed loops obfuscations are 'objective'; i.e. legitimate objects of scientific scrutiny. These are explicitly forbidden in any machine or mechanism. a material system which contains such loops is called 'complex'. Such complex systems thus must possess non-simulable models; i.e. models which contain impredicativities or 'self-references' which cannot be removed, or faithfully mapped into a single coherent syntactic time-frame. I consider the consequences of the above, in the context of thus redrawing the boundaries between subject and object." A reminder: This line of thinking arose with Rashevsky's seminal paper on "Relational Biology" in 1954. Rosen was following this path back then. The issues we are confronting may seem new. They may appear to have such different natures as manifest in quantum physics and social science. I think this is a myopic view. I'd suggest that we are all in the same boat this trip! I close by reminding everyone that Rashevsky first applied relational biology to sociological problems in the 1950's. For this he and his followers were labeled "charlatans"! Charlatans unite! ----------------------------------------------------------------------------- Date: Thu, 15 Feb 1996 15:32:02 -0400 (EDT) From: DON MIKULECKY Subject: will the real complexity please stand up? Sumarry of a Book Review: Reference: "Crichton's Lost World" review by Richard Lewontin in the Feb. 29, 1996 issue of "The New York Review of Books" On Lewontin: He is Alexander Agassiz Professor of Zoology and Professor of Biology at Harvard University. He is the author of "The genetic Basis of Evolutionary Change", "Biology as Ideology: The Doctrine of DNA" and co-author with Levins of "The Dialectical Biologist". The latter I have often used in my Honors courses. He, Levins, the Roses, and Stephen Jay Gould have been instrumental in debunking the racist genetic "theories" about intelligence which recently resurfaced in the book "The Bell Curve". The review starts with the following: "According to Haggadic legend, when God decided to create the world he said to Justice, " Go and rule the earth which I am about to create." But it did not work. God tried seven times to create a world ruled by Justice, but they were all failures and had to be destroyed. Finally, on the eighth try, God called in Mercy and said, "Go, and together with Justice, rule the world that i am about to create, because a world ruled only by justice cannot exist." This time apparently it worked, more or less." Lewontin does not treat Crichton very kindly, IF, what Crichton wants to be is a science fiction writer. This is because Lewontin sees the science fiction writer as a kind of lesser god who creates worlds with specific purposes in mind, the highest of which is the exploration of sociological ideas and sociological experimentation. To use his words: "JURASSIC PARK and THE LOST WORLD use some science in creating a fiction, but they are not Science Fiction." elsewhere he says: " The Buck Rogers space operas,...,and their multimillion dollar equivalent STAR WARS, are just high-speed action stories in which the cops and robbers wear funny suits and drive around in jet-propelled dinner plates. It is to this latter class that Jurassic Park and Lost World belong......" O.K. He isn't a big Chrichton supporter! But the reason I am send ing this is his opinion of the actual science in the book. "The contrast between the behavior of middle-sized, heterogeneous systems like people or thunderstorms, and the body of classical, simplified, law-like science has been profoundly disturbing to scientists for whom Newton and Mendel remain the ideals. Somehow the messiness of the world must be tamed and brought under the aegis of theoretical simplicity. This imperative has given rise, over the last thirty years, to three distinct theoretical developments whose very names reveal the epistemological angst in which they were born: "CATASTROPHE THEORY", "CHAOS THEORY" and "COMPLEXITY THEORY". skipping some ...Finally, complexity theory is as yet only a set of metaphors and a rudimentary sketch in the dreams of some venture capitalists of the mind at the Santa Fe Institute for the Study of Complex Systems. It proposes that sufficiently large systems of parts with enough interactions will generate totally new, but simple, "laws of organization" that will explain, among other things, us." {Jeff Prideaux's comment: "If they are really that good, they should have also predicted that Lewontin would write this article".} "Crichton's invocation of these trendy theories, although in a confused form, is a reaction to the unlimited epistemological optimism of triumphant nineteenth-century science that still marks our world view.......The irony is that the theories he invokes have exactly the opposite intent. They are the latest expression of the belief that all things, no matter how complex they may seem to the surface observer, are simple to those who know the secret.. There are no epistemological barriers. Everything is knowable. " I send this for your comments. I hope this group gets to be more interactive. Anything you send will be distributed unless otherwise marked. We are certainly not alone in believing that these attempts to produce a "science of complexity" are really the death throes of a paradigm! ----------------------------------------------------------------------------- From: GEMS::JPRIDEAUX "Jeff Prideaux" 16-FEB-1996 09:23:47.14 Subj: freezing cells For the complexity group: Kampis (in chapter 5) brought up an interesting (and obvious) point (when you think about it). When formulating a dynamic model, one must have both initial conditions and "equations of motion". These are independent of each other. Likewise, in a mechanistic model, one has a state-space description and the forces (and constraints) that take state to state. In either case, it is necessary to have the information contained in at least one particular state to then generate all future states. Intuitively (if we believed that life falls in the class of mechanisms) we would think that if only we had access (like Maxwell's demon) to the complete state space information of an organism and knew all the laws of nature, we could in theory determine all future states of that organism. The mechanistic view is that life is embedded in process of the immutable laws of nature operating on the state-space information of organisms ....and it is the task of biologists to illuminate (determine) all the state variables (and all the laws of nature). For then (the idea goes), if we knew the state variable information (at any particular time) and we knew the constraints and the laws of nature, we would know life. State variables are typically things like the generalized notions of positions, velocities, and amounts. For example, in particle mechanics, the state variables are position and velocity (or momentum). Now, it is an interesting fact that one can freeze cells, store them, thaw them out and then do experiments on them. The cells can survive the freezing ordeal. There have been reports of freezing (prokaryote) cells down close to absolute zero, warming them back up, and having them still be viable. The significance of this is that all kinetic motion stops in these frozen cells. All molecular motion and reaction rates approach zero. In terms of our mechanistic models, we loose some of the values of the state variables. We have a situation where nature is able to operate without the information of all the state variables....and our mechanistic models are not able to operate without all the state variable information. Something is amiss. Either nature is doing it wrong or we are. As natural scientists, we hopefully should take the position of forcing our theories to fit nature (not visa versa). People like Kampis, Rosen, Pattee, and others are suggesting that we take a hard look at exactly what is assumed in the formation of our mechanistic models...and does nature fit these assumptions. Jeff Prideaux ----------------------------------------------------------------------------- Date: Fri, 16 Feb 1996 12:21:17 -0400 (EDT) From: DON MIKULECKY Subject: This a draft...but we'd like your reaction....going to "Nature" Order for Free? Sir, Ian Stewart's recent review of Stuart Kauffman's book, At Home in the Universe, compounds a major flaw in Kauffman's thesis. Both Stewart and Kauffman tell us "that in adaptive complex systems, a great deal of order is obtained for 'free'". Boltzmann, Lotka, [Onsager] and Schrodinger must be rolling over in their graves and our colleagues in thermodynamics are amazed that such statements make it past the most junior reviewers. The basic tenet of the second law of thermodynamic is that nothing is for free. That is why we don't have perpetual motion machines. Even the much vaulted "spontaneous order" seen in the transition from conduction to convection in Benard Cells has an entropy price (Schneider and Kay). Kauffman seems so enthralled with computer generated models of, chaos, catastrophe and complexity, that he hardly touches real phenomenological systems before taking on the "emerging global civilization" with "strings, eggs, jets and mushrooms". To be sure topologic constraints greatly effect the stability and operation of most systems. Take a television apart and put it back together randomly with the same components, and it will not operate. How things are connected in a system is of vital importance. However, if one is exploring of rules for self organizing systems, the search should begin with the thermodynamics of real systems, like Benard Cells, biochemical reactions, cellular processes and ecosystems, rather than computer generated patterns of nonlinear interactions. As early as Boltzmann and Lotka it has been recognized that thermodynamics held one of the keys toward understanding order and structure in life. Schrodinger's suggested research program, with it's "order from disorder" premise and its now awkward "negentropy" was a key sign post for researchers in this field. In his first chapter Kaufmann gives a brief curtsy toward thermodynamics, noting that "Since all free living systems are non-equilibrium systems...... it would be of deepest importance were it possible to establish general laws predicting the behavior of all non-equilibrium systems. Unfortunately, efforts to find such laws have not yet met with success. Some believe that they may never be discovered." He shrugs off thermodynamics in one half page and then roars off into computer generated complexity hardly touching the messy world of biology. Those of us working at the intersection of non-equilibrium thermodynamic and biology are not as pessimistic about our field as Kaufmann. In non-equilibrium thermodynamics there are two distinct branches. In one branch, the near equilibrium, so called "Onsanger region", where force and fluxes are linear and a minimum entropy production rule is in force, we know quite a lot. Onsanger, Nicolis and Prigogine and Puesner showed that stable dissipative non-equilibrium processes and structures can occur in this linear reciprocal region, Ficks law, Ohms law, (Don give me more ). Biology is rampant with linear near equilibrium processes (Don give me some examples, membranes). Quite frankly we have all the theory and methods to solve many biologic problems in this branch of thermodynamics. In the nonlinear non-equilibrium branch of thermodynamics, many of the problems become more difficult. It is true that parts of complex systems (life) may not be computable (Rosen) and that the relationship between forces and fluxes are non linear, but much can be done with available theory, phenomenology, and methods.. If one looks at the second law as always proceeding in such a way as to reduce imposed gradients; the cooling cup of hot tea in a cold room, or Le Chatlier's Principle in chemistry, a key postulate for non-equilibrium systems is evident. As gradients move or maintain systems away from equilibrium, they will utilize all avenues available to them to counter these applied gradients, and processes can emerge so that the system organizes in a way that reduces or degrades the gradient. As the gradients increase, so does the system's ability to oppose further movement from equilibrium. If dynamic and or kinetic conditions permit, self organization processes are to be expected. The building of organizational structure and associated processes degrades the imposed gradient more effectively than if the dynamic and kinetic pathways for those structures were not available This behavior is not sensible from a classical second law perspective, but it is what is expected given our expanded view of the second law. The outside universe pays the entropy price for the order and processes of the non-equilibrium system. No longer is the emergence of coherent self-organizing structures a surprise, but rather it is an expected response of a system as it attempts to resist and dissipate externally applied gradients which would move the system away from equilibrium. The term dissipative structure takes on new meaning. No longer does it mean just increasing dissipation of matter and energy, but dissipation of gradients as well. We know that all non-equilibrium dissipative systems exhibit cycling . Morowitz calls cycling intrinsic to all non-equilibrium systems, perhaps a fourth law.. Much of this cycling is auto-catalytic, self reinforcing positive feed back (Eigen). When driven by a gradient, the auto-catalytic nature of these systems allows them to go out and gather material and energy into themselves. These systems are the "first selves"; the emergence of the "id". Auto-catalytic processes can be actions of selection, suggesting that natural selection grew out of, and is still today, a auto-catylic process pruning ineffective components, constrained by entrained environments. Because of the auto-catylitic nature of dissipative systems and the stochastic world they inhabit, they exhibit nonlinear behavior, multiple steady states, and catastrophic and chaotic behavior. Punctuated or rapid changes in system states can be endogenous ( self induced ) as well as exogenous to the system. We agree with Kauffman and Stewart that there are some general propensities or rules in biological processes and that evolution is not the end result of random contingencies (Gould). This not the forum to go on at length about the modern advances in thermodynamics, however it must be evident that thermodynamics must have a central role in the discussion of self organization. However we need not turn off our computers, and stop trying to generate simple rules for complex behaviors, as this domain of science may play an important role in translating the gene into the phenotype. Nonetheless if one is looking for "order for free" in thermodynamics, start with a perpetual motion machine. Eric D. Schneider Hawkwood Institute ---------------------------------------------------------------------------- From MIKULECKY@gems.vcu.edu Sun Feb 18 17:08:44 1996 From: DON MIKULECKY Subject: a construction about the second law of thermo from Schneider and Kay! Are Schneider and Kay constructivists? From time to time I speak or write about Schneider and Kay's reformulation of the second law of thermodynamics. The idea is this: As systems are pushed farther from equilibrium they eventually become non-linear. What does this mean besides the fact that their mathematical model must be changed? It has profound meaning. None of that meaning comes from dynamics. The Santa Fe Institue folk see it as "life at the edge of chaos". They get this from their Boolean networks and artificial life simulations. These computer objects tend to "look like" living systems as they are pushed further in their dynamics from an equilibrium. This seems to match reality. Furthermore, pushing them too far does seem to cause a breakdown of all this nice self-organization into chaos. Thus dynamics does mimic life in a way. Rosen shows us why this is, at best, a cute metaphor. Schneider and Kay give us another view. The systems are intrinsically non-linear, but this non-linearity has a semantic meaning that transcends the math and the dynamics! The issue is gradients. Gradients arise from the very act of moving the system from equilibrium. Lets do the causality question: Why do gradients form? They form because some source of energy is impinging on the system. Notice....no dynamics there. Oh sure, implicitly, there will also be a dynamics CAUSED by the gradient...a response. O. K. impinging energy causes the gradient, and the gradient causes a dynamic. Near equilibrium, the dynamic is linear....a relaxation process. It suffices to either dissipate the gradient or at least keep it at a steady state level if the energy source persists. If, however, the energy source becomes stronger, the gradient will increase. This changes the dynamic in some way which is CLEARLY independent of the dynamic since it was linear up to now. The system has in itself an ANTICIPATORY model (its very material nature) which allows it to respond to bigger stress (gradient) by inducing a new dynamic. The new dynamic is more effective in dissipating the gradient. However, it was caused by the increased stress, not by any dynamic process. In fact the transition is generally a destruction of one dynamic to allow the second! Stress the system still further and still another dynamic arises. The last one is chaotic but we know that chaos is also an ordered phenomenon. This new order is the systems final response to a perturbation of great consequence. It will not arise until the previous order (self-organization as we call it) is also gotten out of the way. Some systems do not go through these steps. Beams snap. FLUID systems are more likely to behave this way. Weather cycles, living systems, etc. are the ultimate and involve far more than the simple picture I just painted. Evolution requires long periods during which the system is allowed to explore a variety of dynamics some of which will serve to give a stabilizing result to the impinging disrupting energy source. And all of this is the second law of thermodynamics at work! So how is such an idea proven? Need it be? Is it not the best CONSTRUCTION we have consistent with our experience? I think so. I think that the earth IS an organism in Rosen's sense since it becomes closed under efficient cause in just this way. The formal causes and final causes have their home in the existence of the system. Were they not operative, we would have boiled away the atmosphere a long time ago. Notice that causality always overrides dynamics. That's why the Newtonian/reductionist approach is useless here! It seems that once again, ONLY a constructivist approach works. What do you think? ----------------------------------------------------------------------------- From: GEMS::SBROBERTS 18-FEB-1996 18:16:44.08 Subj: RE: a construction about the second law of thermodynamics from Schneider and Kay! Dr. Mikulecky, please forward this message to the complexity group, and comment if you'd like. (could you save me a copy of this message?--i can't figure out how to print it.) {ok...my comments are in these brackets} ================================= In response to Dr. Mikulecky's message: I liked the way that your message points out the difference between dynamical "explanations" of the behavior of systems versus and causal explanations. In point of fact, describing a system dynamically (e.g. by Newton's laws--say, calculating where a baseball will land if you throw it at such and such a speed and at some trajectory) is nothing more than that...it's only a DESCRIPTION of what you see. It says nothing about the causal events at work in the world around us. {Yes and it also has the same fault as the prisoner in the prisoner's dilemma, namely that all the information is there at once therefore the system must be static as Jeff pointed out a while back. Clearly, stressed real systems are changing with the stress.} Dynamical equations that describe the world can be regarded as recipes for SIMULATING things that we see in the world. But as Rosen points out, a simulation is NOT the same thing as a model. In a simulation, the only thing we have done is MIMICKED the behavior of some system (for example, you could attach a little light sensor to a motor-powered boat, and it could simulate the behavior of an organism that swims toward light). On the other hand, if you have constructed an adequate MODEL of a system, then there is an equivalence causally between the system and the model (that is, not only are the behaviors of the system and its model the same, but the underlying workings which produce those behaviors are the same). {yes, this why artificial life, artificial intelligence are NOT ever going to be anything but a parody. Even a self modifying computer program is ONLY modifying the software. The hardware is constant. And the causal relations are totally different than in what is being simulated!} On another subject, I was reading about Godel's theorem this weekend. I was fascinated by how he was able to prove that you could never completely syntacticize Number Theory--i.e. that Number Theory could not be replaced by just manipulating symbols according to rules. What he did was to represent propositions ABOUT numbers BY numbers. He modeled Number Theory with numbers (interesting that Number Theory contains a model of itself). By doing this, he was able to show the complexity of Number Theory (i.e. that it is more than symbol manipulation, more than any one formalism could capture). What he said with numbers could be roughly translated into English as follows, "You cannot prove this statement in any given formalism." It is a true statement, yet it cannot be included in any formalism! If it were included in a formalism, it would be a false statement. { this is why constructivism seems the only answer. The incomplete system needs constructions from without. Subject/object boundaries must be eliminated and we must become part of a meta-system consciously!} I was wondering if we could come up with a similar proof for other complex systems, say living things. But I can't think of what in organisms is equivalent to "propositions about numbers." If we could think of an analog to this, perhaps we could represent these things by parts or components of the organism itself (just like Godel used numbers to represent propositions about Number Theory). Then we could make a Godelian statement about the organism, thus proving that there is no largest formalistic model of the organism, no syntactic model that includes all there is to know about the organism (i.e. that the Newtonian Paradigm gives us a vastly incomplete picture of the world). We would have used a Newtonian model to show that the Newtonian Paradigm is incomplete, just as Godel used a formalism to show that formalistic representations of Number Theory were incomplete!--Seth {Goedel's proof is formulated in terms of number theory, but IS perfectly general. It applies equally well to living systems} [Dr. Mikulecky--I think that Rosen has already done something similar to this. Rosen's relational diagrams are themselves formalisms (that is, once constructed, they consist of symbols which are manipulated according to rules). But by using this formalism, Rosen shows that no formalism (or equivalently, mechanical model) will ever tell us all there is to know about an organism.] {what are the rules for manipulating a category theoretical diagram? Is it not true that the decision of how to encode and decode as well as whether or not the diagram commutes are all necessarily done from WITHOUT the formalism? There is no escape!} {Nice to get your thoughts. I'm not sure my responses are correct so please take issue if they don't make sense to anyone! Especially thanks for keeping the discussion going!} ----------------------------------------------------------------------------- Date: Mon, 19 Feb 1996 13:04:05 -0400 (EDT) From: DON MIKULECKY Subject: the frozen cell issue and dynamics!! some dialog From: GEMS::JPRIDEAUX "Jeff Prideaux" 19-FEB-1996 11:37:10.66 To: MIKULECKY CC: Subj: comments to Fords comments on freezing and thawing For the complexity discussion group. George Ford wrote: >Without spending a lot of time thinking about it, my initial >reaction to your "frozen cell" model is that it's an ideal way to >perhaps set the initial conditions the so called kinetic models >require (I get very confused by the semantics used to describe >various models, so I hope the term "kinetic" is correct). >The real question, to me anyway, is any "information" lost when the >cell is frozen? If it is, then the initial conditions could be set >and the kinetic theory would argue the cell should evolve to the >same state every time in a series of freeze-thaw cycles. If >information is indeed not lost, the evolution would not be >predictable since we, the outside observer, still would not have >"information" that the system does. In fact, this might be an >experimental test of some of the arguments being made. > > George I would cast the situation as follows: I see two possibilities even if you assume the system is a mechanism. Assume the system is a mechanism. The dynamics is describable by a time evolution function' (that takes state to state) which includes an environmental forcing function (which is the way in which the system is frozen or thawed). Think of one forcing function for the case of freezing the system, and another forcing function for the case of thawing the system. When the freezing forcing function is applied, there is a single attractor (located at the region of phase-space where all the velocity-state variables take the zero value) that has a basin throughout all of the phase space. Assume that when the thawing forcing function is applied, there are multiple wells throughout the phase-space landscape (and, of course, the freezing attractor is not in effect). When the freezing forcing function is applied, the system evolves to a point where the velocity state variables all assume the zero value. Other non-velocity state variables (such as position state variables) will still have non-zero vales at absolute zero. Note that there wouldn't be a unique point in the phase space where all the velocity state variables were zero. There would, in general, be lots of possible absolute zero states for the non-velocity state variables. (For instance, the system could be frozen motionless in different physical positions). When the thawing forcing function is applied, the system will follow a trajectory (according to the time-evolution equation) into one of the wells in the state space landscape (that appear once the thawing forcing function is applied). Which well the system enters depends on where the system was (in state space) at the time the thawing forcing function was applied. Consider a cell operating in one of the wells (in state space landscape) while the thawing forcing function is being applied. Assume that the system takes some kind of periodic trajectory inside this well where a particular state (A) repeats. Now switch over to the freezing forcing function at an instant when the system is in state (A). At this moment the phase-space landscape changes and there is a freezing attractor. The system progresses by its time-evolution equations towards this freezing attractor. It settles to a point "in the ravine" of the freezing basin where all the velocity state-variables equal zero. Now switch over to the thawing forcing function. The phase-space landscape changes to what it was before. Now, if the current state of the system is in the basin of the well that contains state (A), then state (A) will be accessible for the system. In a sense, the system will remember how to get back to state (A). In a sense, no information will have been lost. If, on the other hand, the current state is not in the well that contains state (A)...[that is, the current state is in the basin of another well]...then the system cannot get back to state (A) and in a sense it has forgotten how to get back there. In a sense, information has been lost. I conclude that whether or not a system can get back to a known state after freezing-thawing doesn't discriminate whether or not the system is a mechanism. ------------------ If the cell is not a mechanism The problem with the mechanistic approach is that the concept of an attractor requires knowledge of what state variables will be in use. Included in the attractor's definition is the forcing function used and relations between the state variables used. A cell which makes its own parts is analogous to a cell making its own state variables. Each time a new part is made (and a new state variable introduced), the phase-space landscape (or attractor present) would change. There is a meta level in effect (how to change the phase-space landscape) that comes from outside the dynamic system (or mechanistic) description (for systems that make their own parts). The alternative would be to have a state-space landscape that included all possible state variables that the system could use (or produce)...and at any given time, most of these would simply take a zero value. This alternative would assume that the distinction between zero and non-existence is not important. (FOR ME, THIS IS A KEY POINT TO KAMPIS'S VERSION OF CONSTRUTIVISM ...THE DISTINCTION BETWEEN ZERO AND NON-EXISTENCE). More about this later. In a mechanism, the only thing that changes the phase-space landscape (attractors) is different environmental forcing functions. In a part-making complex component system, the phase-space landscape (as observed by us) will change with each new part made. Of course, with a fixed set of parts, the system will behave mechanistically. But each time a new part is added (or deleted) a meta level (not accessible to a mechanism) is invoked (from our perspective) that changes the phase-space landscape. ----------------------------------------------------------------------------- Date: Mon, 19 Feb 1996 14:26:48 -0400 (EDT) From: DON MIKULECKY Subject: Thermodynamics raises its ugly head! Some definitions and clarification for the group and my own thoghts on the frozen cell problem: Phase-space: [from Rosen:"Dynamical System Theory in Biology,1970, Wiley, p3] "...a single Newtonian particle moving freely in space comprises a system whose instantaneous states may be completely characterized by six independent measurements. The six measurements are canonically taken to determine the three coordinates (x,y,z) of a particle in space.......and the corresponding three coordinates of momentum [mass times velocity, so a velocity variable] (px,py,pz)...Thus we have n=6 state variables for this system. if the system is unconstrained, then any 6-tuple represents a possible state of the system, and the phase space in this case is the full 6-dimensional Euclidean space..." note that for N particles this becomes a 6N dimensional space. The point is that this IS the state space for a Newtonian mechanical system. No other information is required! attractor: In any dynamic system (see previous postings) the system is a mathematical object defined by a set of ordinary differential equations which we often call equations of motion. By standard methods of analysis, there are qualitative methods of analysis which give nice pictorial representations of the dynamics. These are called "Phase-portraits". In the phase portrait lines, curves, and points can represent equilibria or limit cycles(the steady state trajectory of an oscillating system) which eventually the system's dynamics will migrate towards. These lines, curves, or points are called "attractors". landscape: In a phase portrait the regions of the portrait between attractors (or other objects called repellors) divides up much like the contour map of a landscape. These landscapes allow for qualitative predictions about the systems possible behaviors. basin (or basin of attraction): around attractors will be low areas (things move down hill on these landscapes as in the real ones) which are basins. I have some problems with what Jeff said. Let me pose some questions about them. First, I don't understand what a freezing or thawing forcing function is. My picture of the freezing and thawing process is that a new boundary condition is introduced in each case. This does not appear as a forcing function in the particle dynamics. The whole discussion smears out distinctions between dynamic variables and their thermal averages. I thought George was approaching this from the standpoint of kinetic theory. He is visualizing the result of the freezing and thawing process as coming from the usual averaging over particle dynamics. The question of specific basins of attraction and other related arguments seems to go far afield from what Kampis was trying to get across. Let me quote him for those who do not have the book: "...When deeply cooled, all information concerning the motion of the particles gets lost, only structural information remains. Only the spatial positions and types of particles are preserved. Why that is important is the following. The usual assumption is that biological systems can be understood in terms of molecular dynamics or, in the worst case, by the building-block dynamics of atoms. That would mean that all information is of a dynamical nature and is expressible in the form of process states." He goes on to discuss the significance of the choice of a spatio-temporal description. he points out that: "...although there is an infinitude of other possible observables, most systems seem to be approached in this way... Now this assumption is at risk here. The challenge comes from the direction of thermodynamics: dynamical information is process related and cooling destroys it. Cooling switches off all processes - it switches off even the structurally non-programmable processes which apparently cannot be switched off by any other means. This has energetic reasons. If we switch off a computer, all information about the current content of memory will be lost.... This is because information is stored in the (metastable) states of a dynamic process, and when the process halts, the states will be reset to their trivial values. Exactly the same happens during cooling. It does not matter WHAT are the state variables. The same happens to all of them - that's why cooling, especially strong cooling near to absolute zero, sips out energy from the system up to the point where everything must stop. It provides the basis for a very strong argument. If all process states are emptied, but when you restore the temperature the processes return as if nothing has happened, the conclusion is that the information was not stored in process states." He goes on to point out that position-only information constitutes a nonholonomic restraint in mechanics. Without getting any more technical let me just say that these situations are treated as VERY special examples in physics!!! Yet they are the substance of biology as this experiment demonstrates. This is said another way: NOW ALL WE NEED DO IS PUT EVERYTHING INTO PLACE AT ABSOLUTE ZERO AND WE WILL HAVE A LIVE CELL WHEN WE THAW IT! Ahhh that's the rub! What does it mean to have everything in place? ----------------------------------------------------------------------------- Date: Mon, 19 Feb 1996 17:53:58 -0400 (EDT) From: DON MIKULECKY Subject: progress! Here is a communication from Seth with my comments in brackets: From: GEMS::SBROBERTS 19-FEB-1996 16:06:27.26 To: GEMS::MIKULECKY CC: Subj: RE: Thermodynamics raises its ugly head! Let me see if I am following this discussion correctly. It sounds like that what Kampis is saying is that when we cool something to absolute zero, all the molecules and atoms will stop moving. Thus, we lose one very important piece of Newtonian information: that is, we no longer know the velocities of these particles. Now in the Newtonian world, as Dr. Mikulecky stated, the ONLY meaningful "things to know" about a system are the positions on the x, y, and z axes, the masses, the velocities, and the momenta of all that system's particles (say, atoms and molecules). {That's essentially it as I see it. We've lost half the information! (Clearly there is a lot of information there that the Newtonian dynamics picture simply ignores. Without even needing to get technical, one can imagine all sorts of electrical and magnetic fields which are now only going to depend on position, but still contain an awful lot of information. These are "interactions" of various kinds. They do not need velocities to survive and are "second order" with respect to the dynamics when they are happening.} When we have these bits of info, we can just plug them into a mathematical equation and calculate any future or past state of the system. Additionally, the answers we get out of these calculations represent ALL there is to know about that system. {That's what makes the Newtonian world so attractive. Heck, the living system is JUST those neat variables and nothing more! Sure it is complicated. We are waiting for a bigger computer.} So what Kampis is saying is that, in our thought experiment, we cool the cell to absolute zero, then we thaw it. If it remains organized as a cell after we thaw it, then this is an argument AGAINST the Newtonian Paradigm. {Evidently, this is MORE than a thought experiment! It has actually been done!} The reason this is true is that, by cooling the system, we lose an essential piece of information (the particles' velocity). So, reasoning by the Newtonian Paradigm, the system should be totally changed when you warm it up (because you stopped all the particles' velocities [eliminated this essential information], and then gave them new, different velocities by warming the system back up [introduced a completely different set of information]). So the system shouldn't be a cell any more. It would start out looking like a cell, but then it would "fly apart" because the particles would have the "wrong velocities" [that information changed] to make up a cell. {yes, that's the idea, as I see it!} Using this same line of reasoning, we can conclude that if the system remains as a cell, this is an argument against the Newtonian Paradigm. The reason: we lost the velocity information, and then gave the system new velocity information when we warmed it. Therefore, if the system remains a cell, then this information that we changed WAS NOT THE ESSENTIAL INFORMATION THAT MAKES THAT SYSTEM A CELL. Is this anything close to what you all and Kampis mean? {That is what I mean and, therefore, what I think Kampis means.} I also have a question. Are we in fact justified in rejecting the Newtonian Paradigm based on this thought experiment? Couldn't a Newtonian biologist just say, "well, all that you've shown is that the info important to that system being a cell isn't the VELOCITY variable. It still could be contained in the other newtonian variables--position, mass, etc." {Ah, but he can't have his cake and eat it too! If the information is "in the positions" and NOT in the velocity variables, then there is a real paradox! What is a velocity, but a CHANGE in position? If we let the velocities come back, the positions [WHICH ARE ALL WE HAVE LEFT TO KEEP OUR INFORMATION SAFE!] will necessarily have to change. How could that be? Aren't we looking under the lamppost for the keys we dropped over in the dark because it is lighter under there? There MUST be more involved!} I'm probably completely confused, as usual. seth {I wish my confusion would manifest itself so brilliantly!} DCM ----------------------------------------------------------------------------- Date: Wed, 21 Feb 1996 08:36:57 -0400 (EDT) From: DON MIKULECKY Subject: Why frozen cells are not machines. More on the frozen cells problem: Rosen with great clarity sheds some light on the questions raised by Morowitz's example of the cell which recovers after being brought to absolute zero. The reference is in Kampis, but I'll repeat it here. I realize that we are getting way ahead of ourselves, and much which we have not yet discussed in Kampis bears on this problem. Ref: Rosen, R. (1986) "Causal Structures in brains and machines." Int. J. Gen. Sys. 12:107-126. I will try to summarize with my own thoughts mixed in. Those who want the "pure" treatment will have to make a copy of my copy and struggle through it. The way we go from single particle dynamics to many particle dynamics is a fairly big deal. It is all Newtonian, but depending on what we do, we can arrive at Kinetic Theory of Gases, Fluid Mechanics, or a field more concerned with the motion of rigid bodies such as machines, namely, Analytical Mechanics. What distinguishes these fields from each other is the way we manipulate the basic equations of motion, which are differential equations of first order. For example, a rigid body may have many particles, each with its own dynamics, in principle. But if we are clever enough we recognize that these particles motion has a "constraint" on them....they are all locked together. That's in fact how a rigid body is defined. As Analytical Mechanics developed, it became recognized that all constraints are not equal. There are simple ones, which have a very special mathematical form as they are applied to the manipulation of the equations of motion. A rigid body would have this kind of constraint, called "holonomic". In fact holonomic constraints are very special. The same mathematical requirement is manifest in thermodynamics when we wish to define "states". It requires that differential forms be "exact" or integratable. To make a long story short, the way a system can be made to depend on its structure rather than its phase variables (in this case the velocities) is to apply another, very complicated, form of constraint known as the "nonholonomic" constraint. In short, what such constraints do is force a new, more difficult mathematical form on the dynamics, EXACTLY THE SAME ON WHICH DESTROYS THE ABILITY TO DEFINE STATES IN THERMODYNAMICS! This introduces an absolute situation dependence on the system and a profound form of hysteresis, such as that manifest by the cell, in our discussion. This alone does not prevent us from viewing the cell as a very special sort of machine as Jeff correctly pointed out. However, if we adopt this stance then the degrees of freedom we observe in the cell once back to its normal temperature must be magic! The answer is a simple one. There is more at work here than mere dynamics, even in its most sophisticated form. The way Analytical Mechanics might try to deal with the empirical facts is to introduce strong PARAMETER DEPENDENCE into the equations of motion. But this is the origin of all the modern dilemmas mechanics faces. This is the very root of Catastrophes, Chaos, etc. in the world of nonlinear dynamics. So, in a nutshell, any attempt to rescue the Newtonian paradigm here is doomed from the onset. This is true INDEPENDENT of other problems such as cell division, metabolism and repair, etc. I hope this clarifies a very difficult issue. Your comments are invited. ----------------------------------------------------------------------------- Date: Wed, 21 Feb 1996 09:41:52 -0400 (EDT) From: DON MIKULECKY Subject: another comment Here's another comment: my response in {} From: GEMS::HMARAGH 21-FEB-1996 09:33:06.31 To: MIKULECKY CC: Subj: frozen cells it appears that from the second law: 1) starts at equilibrium 2)perturbation results in dynamic changes in the "SYSTEM" 3)the change that occurs affects the entire system but each component is affected differently and may be we cannot measure some change- does not mean anything is lost . {Clearly if the cell lives after freezing, nothing was lost. However, if the information which it needed to be a living cell was in the velocities, that disappeared at absolute zero. Notice that this is more constrained than "equilibrium". It is very special. Thus the information was somewhere else.} on Dr.Kier's articles: can they be summarized- A mapping that assign a frequency of appearance to the active topology to molecules and macromolecules in a charged hydrated system. {let's leave that for Dr. Kier to answer.} ----------------------------------------------------------------------------- Date: Wed, 21 Feb 1996 10:38:40 -0400 (EDT) From: DON MIKULECKY Subject: what good is it? Just for the record, the thing the halting problem is "good for" is that is a nice demonstration of the fact that there are things brains CAN do that Turing machines can't. Again, this leaves two options, one is to try to say that the brain is a unique machine (whatever that's supposed to mean) or that brains fall in another, entirely different, category, which we now call "complex". ----------------------------------------------------------------------------- From: GEMS::JPRIDEAUX "Jeff Prideaux" 21-FEB-1996 13:12:53.37 To: MIKULECKY CC: Subj: halting problem From: GEMS::MIKULECKY "DON MIKULECKY" 21-FEB-1996 13:02:35.66 To: GEMS::JPRIDEAUX CC: Subj: RE: what good is it? > Well said. As I remember it, the "awkward moment of silence" was > when I had the floor after I had just finished explaining the > halting problem to the group (when the question was asked). After > a few moments, you then spoke up and reminded everyone that the > problem was a demonstration that the brain was complex. My > hesitation to come up with an answer (as to what it was good for) > was because I was thinking along the lines of how you could use > that knowledge to then go out and construct such a complex entity. > I'm optimistic that constructivism may provide clues along that > front. > > Another interesting point is constructivists refusal to incorporate > indirect proof (the exclusive middle). I'm trying to determine if > the halting problem reasoning uses an indirect proof. Penrose (in > discussing the halting problem in SHADOW'S OF THE MIND briefly > referred to the constructivist position (of not using indirect > proof). Penrose claimed that his reasoning didn't violate the > tenants of disciplines such as constructivism because his depiction > of the halting problem hypothesized the existence of something, > then showed a contradiction, then deduced (indirectly) that the > thing didn't exist. Penrose claimed that the problem with indirect > proof is when you hypothesis the non-existence of something, then > show a contradiction, then (indirectly) conclude that the thing > must exist. > > I'm curious if the constructivist position rejects all indirect > proof, or only indirect proof that results in the conclusion of > existence. Kampis may provide the answer in his chapter on the > Turing thesis (in a future information set for me). {As I understand it, the (mathematical) constructivists Kampis refers to have problems in both accepting infinite sets and indirect proof for the same reason, their inability to be experienced directly. In a finite set the elements are, in principle, all knowable by experience. An indirect proof is a way of proving something which might not exist. In the case of the Turing machine, (not the UNIVERSAL Turing machine) we have realizations in our actual computers. Thus the discussion of the halting problem as far as it demonstrates that the machine won't halt is valid to them. However, the leap to what it is saying about brains is still indirect so that they probably reject it. This is just my guess. More to come (I hope).