A QUICK LOOK AT RENE THOM THROUGH MY EYES AS INFLUENCED BY ROSEN AND OTHERS

 

Don Mikulecky

 

In “Essays on Life Itself” Robert Rosen devotes an entire chapter to Thom’s work.  The subheadings in that chapter span the contributions of Thom which Rosen sees  as going beyond the classification theorem which stands on its own.

 

On Theory In Biology

 

This is a snapshot of the history of the rift between empiricists and theoreticians and the idea that only through experiment can one learn. M The conclusion of this section says “on the other hand, there is only one reason to do either science or mathematics, and that is to understand what is going on.”  It seems then that we might best ask what Thom did to increase our understanding.

 

On Information.

 

Here he explains that he uses information in a semantic sense, not the sense that Shannon did which was purely syntactic.  Thus, here information is found in answers to “why?”.  That of course Rosen answers with Aristotelian causes.  He then identifies Thom’s contribution of the notion of genericity with the notion of surrogacy which is how he deals with the artificial lifers and intelligencers.  The bottom line is the recognition of a necessary semantic component to objectivity.

 

On Nouns and Adjectives

 

Here he develops the very important differences between nouns like “turbulence” and adjectives like “turbulent” water, “turbulent” air, “turbulent”  oil to get deeper into the genericity/surrogacy issue.

 

Of course where this leads is to the comparison of notions of “life” with those of “living”.

 

Genericity

 

Here he examines the role of induction.  He points out that thanks to Thom, what used to be called “robustness” we now deal with in terms of structural stability.

 

A Few Consequences of Genericity

 

Here he defines complexity in a still different way that is totally consistent with his other definitions.  It revolves around the notion of structural stability and what is meant by “a perturbation”.  In complex systems perturbations are a set of entities to be studied in their own right!

 

The Genericity of Catabolic Modes

 

Here he talks about Poston and Stewart among others.  Here he reviews Thom’s argument about the irreversible damage an experimental program does to the living system being studied.  He also introduces a key point in the failure of the empiricist to understand evolution since the focus is always on the idea that system failure and system generation are reverse processes.  He then ties this all to the context-dependent processes that biology is and which are lost when the context is deliberately destroyed.

 

Some Conclusions.

 

He points to surrogacy as it arises from genericity as a concept, as a powerful source of semantic information.  He puts information into this semantic context.  He examines the role of abstraction as it relates to the noun/adjective categorization.  He then states that most of these ideas were implicit in Thom’s book of 1972. 

 

 

THOM’S BOOK

 

The term genericity appears in two places.  The prelude to the  first is in section 2.3 STRUCTURAL STABILITY AND MODELS.  He defines two kinds of models, formal and continuous.  Formal models are those having  a kinematic which is a formal system.  They are not always deterministic and may lead to undecideable questions.  Apparently he saw this as a negative.

 

Continuous models admit a dynamic and are strictly deterministic.  He then says that

as soon as a formal model is realizable, it opens up the way to semantics.  There is the point Rosen saw as so provocative.

 

In the next section  3.1 THE GENERAL PROBLEM  he introduces generic as a synonym for structurally stable.  The counterpart to this comes when there are bifurcations.  He then tells us that by studying the classes of singularities involved in bifurcation we can learn something.

 

The second place he mentions it is in a note which is very technical.  I see nothing added from it to this discussion other than the restrictions Thom self-imposed as mathematician that Rosen seemed able to jump beyond.

 

 

MY CONCLUSION

 

I need to do more work, but at first glance it seems that Rosen saw far more in Thom than anyone else did, at least in this area. Although Thom was interested in applying his ideas to biology, Rosen was interested in biology as his primary drive.  This allowed him to take this seminal passage, that echoed his own writings in some way, and develop the notions on a firmer mathematical groundwork.  What Rosen did with the genericity/surrogacy argument is unique and very valuable.  It is interesting that this is one of the few times he gave credit to anyone for a major idea.