L'ERESIA CHE NON SI E' FATTA METODO. SEGNI E FORME NELL'OPERA DI RENE' THOM.

This research is devoted to the study of the work of René Thom. In a way, this research should be regarded as a case study. My intentions, already outlined in my research project, and all my efforts during these years were arranged in an attempt to make a contribution in the epistemological research and history of science. I studied philosophy and I have gratitude to those people, those professors who have taught me, with patience and commitment, in this discipline. Even with regard to these considerations, entirely personal, I have found at least one of the reasons that prompted me to make this Milano, 9 Luglio 2012 1 Dr Massimo Simone Dottorato di ricerca: Scienza e Società Discipline interarea Unimi-SISSA contribution by using the terminology, categories and methods that are widely used in philosophical research. René Thom was a mathematician of great stature: for his scientific contributions, he received the Fields Medal in 1958. He was without doubt an important mathematician but he swam against the tide, he opposed the general trend; he was also a disputed mathematician, one who challenged other scientists. The theory that René Thom proposed in the first half of the seventies is known, for the most part, as “catastrophe theory”: this expression is mainly due to a certain type of journalism and the spreading of Thom’s ideas beyond the strictly specialized areas. Catastrophe theory had, indeed, a significant media exposure in the years just after its birth, and it raised some clamor. It was discussed to the point that it was impossible to avoid some misunderstandings triggered, probably, just by the use of the expression “catastrophe theory”. A large part of social agents, except scientific community and a few others, interpreted the term “catastrophe” using the common sense categories and, thus, creating a very bad association with certain natural events of disastrous proportions: one read the term “catastrophe” and thought, for example, something like the earthquakes and then proceeding along a rather inadequate way of interpretation ended up believing that Thom’s theory was able to predict this type of phenomena. For a time, even the communist ideology took the opportunity to try to find, in Thom’s theory, a scientific – indeed even mathematical – confirmation of the dialectical development of history, that would be accomplished through breakthroughs, which could finally be described with the precision of mathematical language. Well, none of this could be attributed to catastrophe theory, but to realize it, you would have to perform a delicate work of analysis and understanding; a work that, under certain circumstances, was not even started. Nevertheless, Thom’s theory is a very other thing: it cannot meet certain expectations simply because it intercepts other problems, studies other phenomena, contemplates other issues and provides, at most, other answers. In fact, Thom’s theory applied very advanced and recent mathematical concepts – new concepts, which Thom himself had helped to shape – to create models intended to explain the morphogenesis, changes of quality and variations of state. In other words, Thom was working to give rise to new geometric models that could be used beyond the narrow specialized areas and that could prove useful in biology, physics, psychology, linguistics, philosophy and in economics. First of all, Thom had the advantage to guess that even the most abstract mathematics could have non-trivial interaction with the world and could be used in a profitable way to 2 Dr Massimo Simone Dottorato di ricerca: Scienza e Società Discipline interarea Unimi-SISSA solve problems in disciplines that are different and, in some way, distant from mathematics. Part of the charm that this figure of a scientist acts on me lies here: what an opening, what a horizon, what a breathe through the thoughts and the actions of René Thom. But open-mindedness, substantial independence and calling for interdisciplinary interaction wouldn’t been won without efforts, hard work, commitment and, above all, without paying, in a certain way, the penalty to persons and scientific institutions which proposed – and still propose – scientific activity paradigm in a sectoral and specialized manner. In some way, Thom had to break barriers, borders and baffles, and had to find open-minded partners; and finally – and this is no less significant – he had to rediscover the ancient wisdom and the philosophers’ think, in order to draw valuable ideas and important concepts in the works of authors considered quite marginal by most part of scientific community. In my opinion, finding courage and motivation to take a so different point of view, even more after having obtained important results and awards in mathematics, deserves a note of praise rather than censure. According to some authors, however, this part of the scientific career of René Thom isn’t very significant; others have interpreted it as a path that has actually produced mistakes. Well, I cannot share this kind of judgment and, indeed, this study finds its own right in an attempt to critically retrace the path outlined by Thom. The leap, the epistemological break, that René Thom makes in the mid-seventies is significant and requires a redefinition of assumptions and references, because this author provides new answers, and in doing so redefines the problems themselves. On the other hand, the shift of the point of view cannot have different consequences. Again, in the opinion of some critics, Thom would stop dealing with math to deal with philosophical issues. We are again at odds, at least for reasons of degree if not of merit, against these trenchant positions. Among the results of this study there is in fact an attempt to confute so radical statements: René Thom, in our opinion, has not ceased to deal with mathematics, rather he resolved to apply mathematical concepts and tools in different ways and in others contexts. Thom chose not to make too many worries as regards the sectoral origin of a concept or idea and demonstrated, through his work, how fruitful may be an attitude that welcomes the contributions from different disciplines and very distant traditions. The declination and the use, in the work of René Thom, of the concept of shape seem to be very meaningful. A well-known concept, but born in an ancient philosophical tradition, is received, understood, used and redefined by Thom – considering the fruitful developments coming from a certain tradition of twentieth-century research in psychology – with the aim of producing geometric models able to account for morphogenetic development of a living organism. 3 Dr Massimo Simone Dottorato di ricerca: Scienza e Società Discipline interarea Unimi-SISSA An ambitious project and already pregnant with consequences for the epistemic level: in the end, Thom acknowledges that we can describe and, in a sense, give an order to the world but he chooses to do so in a different way. Thom has the ambition to study the order and the change using the concept of shape: the changes in shape, the ruptures of the equilibrium, and the transition from one shape to another become legitimate objects of study, precisely because they can be intercepted, framed and defined through the concepts and tools provided by the catastrophe theory. In other words, the aim of René Thom is to give, by the “refinement of our geometric intuition”, the scientific community a complex of images and patterns that may provide more refined qualitative representations of partial phenomena. Thom’s awareness lies in the knowledge of those mathematical tools that he himself helped to develop: he can certainly say, with knowledge of the facts, that “following the developments in topology and differential analysis is now possible to access a rigorous qualitative thinking”. Now, according to Thom, a rupture of equilibrium, the transition from one shape to another, do not occur in a chaotic way: it is possible to account for them in geometrical terms because we are able to study the geometry of the break or, if preferred, the shape changing. Thom’s attempt is to provide models that are useful to describe, in simple cases, the ruptures of equilibrium and the transformations of one shape into another. The effect of the setting in which Thom wishes to frame this sort of thing certainly produced a paradigm shifting, but maybe it could be argued, not without running the risk of a gamble, that Thom somehow triggers a unique event, opens a new page even on the epistemological landscape. Thom is therefore in the position of having to define an entire context in which to give meaning to objects, problems, tools and answers that he will provide. In this dimension – almost by necessity, we would say – René Thom is in the position of having to draw on the philosophical tradition: in an attempt to define its new proposal chooses to move along the marginal and secondary pathways, draws from unusual sources, deals with authors that may seem quite distant from a mathematician’s acquaintances. The poiesis, started by Thom, sinks in the tradition, and therefore, the movement and the dynamic of his thought are in some way cyclical because he recognizes – in the sense of knowing again – and reinterprets and renews settled, even though forgotten, parts of knowledge. Our task was to go back, arguing and focusing the stages of the intellectual journey of Thom. In this sense, the categories and tools of historical and philosophical research have proved to be useful. In this context thinking in terms of genealogy and considering the dynamics of production and processing of Thom’s theory seemed to be worthwhile. It is about to investigating how Thom’s scientific ideas formed and have been argued, with the 4 Dr Massimo Simone Dottorato di ricerca: Scienza e Società Discipline interarea Unimi-SISSA support of – or despite – what other complex of theories. If the proposal of René Thom is the expression of a novelty, then it is worth trying to identify its source: our work, in other words, is based on, and moves from, the concept of “origin”, bearing in mind the meaning indicated by the German word “Entstehung”, to be understood as provenance rather than in the sense of metaphysic essence (Ursprung). The scope of René Thom’s scientific enterprise imposed a thorough job on this front: Thom soon found himself in the position of having to define the status of the objects described by the catastrophe theory, working both on the semiotic both on the semantic ground. Thom had the audacity to even question the concept of cause, as the scientific community generally understands it. Not without reason, in our mind, even taking into account the fact that a richer notion of cause was required especially in biological theories and disciplines. Given these assumptions about the concept of cause, it is easy to understand the reasons of the critical reactions from his contemporaries. Our impression is that all this was, in a sense, predictable and maybe inevitable. It’s been more than thirty years since the publication of Thom’s most significant works concerning catastrophe theory: both from historical and epistemological point of view it is time for a critical revision of Thom’s perspective.