A trip to Geneva
In the middle of this search of the fractals I received a most welcomed invitation from Geneva to discuss a quite different subject: my Brazilian findings about hemispheric laterality and Piagetian operations. In fact, after I recovered from the first shock as a scientist in my beloved but most changed Paris and I decided it was time to publish a long research of mine about cognition and brain lateralization. I met Jacques Mehler, now in Paris and the editor of Cognition, and he recommended I send my paper to professor Henri Hécaen, a master neuropsychologist. Finally this article was accepted in Geneva by the Archives de Psychologie ("Hemispheric lateralization in the development of spatial and logical reasoning in left and right handed children", 1981, 49 83-90). I still think that this was one of my best investigations, but this is another story (VIII). During the Falkland's/Malvinas War (1982) between the Argentine military and the British, a fellow psychologist in London wrote a Ph.D. thesis partly based in those results. I was very happy of this sound intellectual bridge above all political differences. I was strongly against any war between Argentina and the UK as can be verified in another story (IX).
This time I made a détour by train via Pontarlier. My friend Jules Vuillemin, professor of philosophy at the Collège de France, who was once my guest at our home in San Isidro invited me to visit him in his mountain house at the Granges Bérard in the Jura.
Fig. 16. San Isidro, our home (architect Luis F. Benedit, 1971)
Vuillemin is one of the most remarkable european minds I know. I met him during a symposium of Genetic Epistemology in Geneva (David Bohm and Gilles-Gaston Granger were also in that meeting). I travelled this time in first class where I had sufficient leisure and space to write my first notes about fractals and eye movements. I think I worked three hours without interruption. In the train I had the intuition of something to be called "la température du regard". This was a very nice (and sexy) title for a paper and I was very talkative that night chez les Vuillemin. I had Mandelbrot´s book with me and I shared many impressions with my hosts. I even prepared an Argentine barbecue at their fireplace.
The next day I continued my trip to Geneva, but this time I was more relaxed and I enjoyed enormously the marvelous landscape and the arrival to the Lac Léman. Bärbel Inhelder had made for me a reservation at the "Pension Floris", rue de Florissant. A very pleasant and simple place, with a large room and a good desk. I had dinner with the Palás, dear cousins from Uruguay (where my father was born).
Fig. 17. Piaget's desk
My seminar at the Centre International d' Epistémologie Génétique (lundi 28 octobre) was about some new observations concerning the different pathways, left and right, through the brain and their relation with the Piagetian mental operations. As far as I knew this was the first proposal for a neurological discrimination among concrete and formal operations. I remember that for this occasion Piaget invited prof. Assal, a neurologist, to his seminar because -he modestly told me- he wasn't competent in neurosciences. In fact, I remember that in the sixties Piaget gave me the privilege to read and correct the proofs of his Biologie et connaissance (1967). On that occasion I spent an unforgettable whole afternoon with Piaget in his home, discussing a long list of corrections. A description of his indiscribable desk is beyond my capacities. A picture will speak for itself (fig. 17). Biologie et connaissance is a strange book indeed, at least from the neuroscientist's point of view. Only one short chapter was dedicated to the nervous system and it was mostly concerned with McCulloch-Pitts formal neurons. I still remember a rough comment form an expert concerning this lack of brain research in a book about knowledge and cognition! But Piaget knew his own limits, he was a naturalist and epistemologist, not an experimental neurobiologist. His contribution was at a different level. At that time (1968) I was working at the Centre d'Epistémologie Génétique in a neuronal model for the stretch reflex. I was later to obtain a Guggenheim Fellowship, mainly, I think, thanks to Piaget's generous recommendation, in order to continue this research. I moved then to New York, where I was a guest at Roy John's Brain Research Laboratories, New York Medical College. Another story again (VIII). That year at Piaget's Symposium I spoke about two kinds of brain networks: neuronal and glial. Piaget congratulated me after the meeting. But this idea never grew up. Perhaps now with all we know about neuronal nets somebody might find a place for this distinction.
The day after Piaget's seminar I returned to my obsessive search. I spent many hours at the University Library reading about the Zipf Law and making acquaintance with Vilfredo Pareto's powerful insights. Some years earlier the Cahiers Vilfredo Pareto have published a whole issue dedicated to Piaget on his 70th anniversary. It was near all I knew about the famous Italian author of the Cours d'économie politique. I read Zipf (in the French version of the original text published in 1935, Psychobiologie du langage, with an introduction by Georges Miller ) and Pareto's very remarkable Ecrits sur la courbe de la repartition de la richesse. I was curious to learn from all these hyperbolic distributions and log/log transforms for words and money! They proved to be of great help on my way to understanding the hyperbolic distribution of eye movements too, at least from the point of view of rough data processing. I felt commited to try a formula myself following Zipf and Pareto' s examples.
That evening, October the 30th, exactly at 7.30 PM, just before going to have dinner with Bärbel I wrote for the first time "my" formula:
f= K. A-D
f: frequency (number of saccades)
A: amplitude of saccades
K: a constant
D: a fractal dimension
I was so excited that I wrote a letter to my family in Buenos Aires, trying to explain my finding and of course I joked about the new "Battro's Law" with Bärbel at dinner.
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