(originally published: 1993)

Critique of "Chaotic Autocatalysis"

S. Kauffman:  "Origins of Order"

In September of 1993, I happened to watch a Learning Channel/Discovery Channel TV program on the topic of Chaos Theory and anti-chaotic Complexity.

There were several ideas presented in this overview program on chaos/anti-chaos theory which I found disturbing.   One dealt with ideas presented by Stuart Kauffman of the Sante Fe Institute and the University of Pennsylvania.  I had previously started reading Kauffman's book "Origins Of Order" back in May of 1993 and was already pursuing my own evaluation of his work from the perspective of the Integrity Paradigm.  I had been analyzing his intense academicly written presentation, so that when the show aired I was fascinated hearing him discuss his ideas in vernacular summary-presentation for a general audience.

Per Kauffman's book presentation, his cumulative data is quite impressive, as it builds on the theoretical work done by Manfred Eigen, and attempts to formulate a strong mathematical model for genetic behavior (drift and evolution dynamics). Basically, they assigned stable molecular nodes with Cartesian coordinates (to numerically model econiches and genetic configurations ... those indistinctly bounded biological stability locations) and then attempted to formulate a mathematics which would analog and act the same as what is observed in the real world.

This is an interesting technique and has some degree of merit.    It's my opinion, however, that it has led them blithely into an erroneous conclusion, that being : "Autocatalytic sets" as a present and dominating function.   These proposed biochemical "sets" are supposed to have the same qualities as mathematical chaotic-attractors. {A chaotic attractor is a localizable area (or behavior focus) around which special randomizable mathematical functions seem to organize themselves. The mathematical relationships don't reduce to any specific values, yet continue to hover around these regions in consistent but subtly reshaping forms. Bio-complexity is assumed to be similar and to exhibit such process nodes. Autocatalytic sets are envisioned as being real world expressions of this mathematical process.} The principle dynamic they are trying to evaluate is the process by which complex systems arise so naturally and pervasively when thermodynamic laws do not allow for or expect such events. What the processes or rules might be that drive atoms and molecules over the entropy threshold in displays of such strongly organized negentropic activity.

Because catalysis is a reasonable and viable chemical process found in many metabolic reactions, autocatalysis appeared to these researchers to be a reasonable way to get over that wall of thermodynamic entropy. They have apparently found some correspondences that indicate Boolean order vis a vis genetic coding and sequence drift. There is also some relevance with protein production. However, as Kauffman is quick to point out over and over again throughout his text exposition, his models have numerous failings and don't fit in many situations. He continually defers to the need for more investigation to clarify these deficiencies.   Nonetheless, he continues to express with confidence the over all validity of the "autocatalytic" paradigm.

{Aside:    (November, 1993)  : As I continue to polish this document, I review my several decades accumulation of useful and pertinent references.  Back in the 1960's work was done in this exact same area.   Apparently it received little notoriety because it preceded Fractal Math and Chaos Theory by several decades, and was not even referenced in "Origins of Order".    I'm sure this was an oversight rather than intentional omission. H.H.Pattee, Stanford Biophysics Professor, published in 1964 Recognition of Hereditary Order in Primitive Chemical Systems, 8th Ann.Biophys.Soc.Meeting (Chicago, 1964) :

"The new approach to origin of life experiments which I am proposing, is directed at the simplest possible level of hereditary propagation in macromolecules which may arise after a stage of spontaneous chemical evolution, but well before self-replicative biological evolution, which progresses by natural selection. This intermediate level of organization I would call the stage of molecular automata, or to paraphrase Charles Babbage, the stage where polymers begin to "feed on their own tails."

This is exactly identical with "autocatalytic sets", thirty years before becoming institutionally popular, to explain dynamically stable metabolic plateaus that build complexity in opposition to perceived "general entropy". }

 

Throughout Kauffman's book his negatively-expressed asides and cautious disclaimers about the validity of his ideas troubled me as I read him, but I couldn't focus my thoughts to pinpoint exactly what was wrong. While watching the TV presentation though - his vernacular, demeanor and the visual graphics - it came to me. While I don't debate the theoretical correctness of applying catalytic functions to some biochemical processes, his model would require some degree of autocatalysis at nearly every biochemical threshold, which intuitively seems an extraordinary requirement. But, more important, when we evaluate what "autocatalysis" is ... focussing on it strictly as a process of thermodynamic exchange ... it begins to resemble a Carnot Engine! ...a "perpetual motion machine(!)".

The Kauffman model becomes a "perpetual motion machine" reduced to the level of bio-chemical activity! A perpetually functioning looped sequence. In chapter 7 of his book, under the heading, "Main Idea", Kauffman states: "We reach a new and fundamental conclusion: For any fixed probability of catalysis P, autocatalytic sets must become possible at some fixed complexity level of numbers of kinds of polymers. The achievement of the catalytic closure required for self-reproduction is an emergent collective property in any sufficiently complex set of catalytic polymers."

Albeit that continual solar infusion of energy into earth's chemical soup can always be championed as the obvious source of externally derived energy ... so that the autocatalysis is a local event loop still driven by larger energy flows, the fact remains that dynamically, we are still required to recognize some self referencing quality that keeps the bio-chemical reactions looped in consistently regenerating cycles.

The interpretation of that previous statement is that Kauffman et al., are saying that autocatalytic biochemistry establishes the environment and the force to arise complexity. Yet, they fall back on a tautological dynamic ... that "complexity" of some sort is a pre-requisite for autocatalysis(!). Is "complexity" a result, or is it a criteria? I am assuming that this is a very reasonable state of affairs for those researchers, as this is exactly the "quality" of the process and the argument proposition. I.e., why choose which came first, the chicken or the egg; just express that each "causes" the other, and let it go at that.      I find this unsettling and unsatisfactory.

 

"Autocatalysis" ignores basic Physics

I made margin notes as I read his text. This one is dated 6.16.93:  "He does not deal with the prime reality of electro-magnetic functionings for all extants on this level of behaviors. The interconnected Integrity activities are a function of the EM field strengths and domains for each molecular configuration. Conformal spatiality is a "symptom" (a result) of electron shelling variances. It is the differences in the comparative shells which "define" energetics pathways. As I said back in the late 1960's and early 1970's...it is these values which must be determined and mapped, in order to make sense of the patterns at work ... not just gene mapping. The protein paths are built on interactions of EM quantum states." Not just their value differences, but the gradients generated by those values.

First, I should clarify that I do not conclude from this seeming paradox that all of their work is worthless or wrong. Quite the contrary. I just feel that they have yet to establish an overall encompassing paradigm that would embrace the activities they are looking at.   The Integrity Paradigm, however, can be appropriately applied as the more general dynamic, which can locally account for what is perceived as "autocatalysis" but is something quite different.

In support of this you may recall my reasonings re the Universe as a holistic information-process.  I examined the quality, states and dynamics of information transference, and proposed that "dimensions" are a progression of Nested Cantorian Infinities, each being in exponential relation to other infinities, relationally bounded above and below. They correspond with each other per Euler complex-number relations. That is, they are transcriptions of additive-operations linked with multiplicative functions, depending on whether expression is along a domain number-line or along its exponent. In this regard, Logic and function relationships become Boolean.

This idea and other Integrity Paradigm notions in general were deductions already drawn in 1973, even at the outset of formulating a model that coordinates the behavioral diversity of even broader ranges of energetics phenomenon.    I champion using simple known dynamics... in particular a subtle variant of Entropy ... in order to recognize a pan-general source for negentropic phenomena. Integrity is the simpler and better paradigm. It can embrace such programs as Kauffman's concepts and Etzioni's inter-social dynamics, whereas neither of those, for example, can find mutual correspondences in the other, even though "correspondence" is the fundamental criteria for a Unified Theory of Everything that would mesh chaos with anti-chaos, simplicity with complexity, entropy with negentropy, physics with biology, and biology with sociology, etc.

 

Autocatalysis as "Artifact" not Essence

Here is an example of something predicted by the Integrity Paradigm, that shows up in Kauffman's work. To wit, Kauffman expresses in chapter 7:

"Stringent Criterion for Autocatalytic Set Using Exchange Plus Cleavage and Ligation Reactions, such that almost all 2M+1 members of the set have a last-step in their formation catalyzed by at least one other member of the set

"BarP" is designated as the a priori probability of catalysis of any specific reaction.

M+2         M+1    
barP e ^{-P(M-1)     (1+2 )          (2 )}           =      1/e 8 < 0.001"

(value table 7.2 is then presented).

 

As you can see, Kauffman/Eigen express the dynamics in a standard mathematical form that would otherwise be known as "superpowers" or "super-exponents" as they mathematically describe the observed behavior patterns relevant to polymer ligation and cleavage.  Please note that the mathematics categorizes alternating positive and negative "values" in the alternating exponential domains...a relationship predicted in 1972/3 by the Integrity Paradigm as indicative of alternating entropies for nested Cantorian domains.    Ergo, "autocatalytic sets" - as possible biochemical processes - are "attractor functions", subject to energy/exchange behaviors enunciated under Integrity domains. A coordination of oppositely directed entropy gradients. "Autocatalysis" is thus most probably an artifact or qualitative-describer of metabolic loops, rather than a singularly-actual function.

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