The sources

Quia minor error in principio magnum est in fine.

Thomas Aquinas, "De ente et essentia".

My interest in the study of eye movements started as a medical student during my military service in Buenos Aires (1956). I was enrolled as an assistant to the Department of Electro-encephalography of the "Hospital Militar Central" under the direction of Dr. Abraham Mosovich. He taught me how to register ocular movements using common skin electrodes around the eye. The eye works as a dipole (the retina having a negative electric potential of about 1 mV in relation to the cornea) and any ocular movement produces a shift in the electric field of the eye that can be registered by two channels of an EEG. The eye movement angle is a linear function of the potential. Figure 2 shows the electrode setting and a sample of an electro-oculagram.

Figure 2. Electro-oculagram

Fig. 3. With my "deux chevaux" in Paris, 1960.

After my graduation as a physician (I was then 21 years old and perhaps "the youngest physician" of my country) I got a French scholarship (and the next year a fellowship from the University of Buenos Aires) to work with Paul Fraisse at the celebrated Laboratoire de Psychologie Expérimentale et Comparée de la Sorbonne. I worked with Fraisse two full and exciting years in the field of visual perception and I finally presented my thesis for a Doctorat de l' Université de Paris with the title L'étendue du champ perceptif en fonction du temps d'excitation. (Paris, 1960, 193 pages, unpublished manuscript). I used in Paris the same technology in electro-oculography that I had learnt in Buenos Aires. I think that the simplicity of the apparatus helped a lot in my research. I published with Fraisse my first paper "Y a-t-il une relation entre la capacité d'appréhension visuelle et les mouvements des yeux?", on eye movements and short visual memory in L'Année Psychologique (1961), quoted some thirty year later in his book Des choses et des mots (Paris,1991). I understand this trace of an old research as a mark of some genuine scientific interest. I must add that, on behalf of this essay, only now, I reread my thesis some 34 years later with some reluctance. Scientific standard research ages badly, only major intellectual contributions or good wines improve with time. But I must say that I was writing there a proto-history of my later fractal search.

Unexpectedly Jean Piaget made some references to my work in an article related to visual perception in children and adults, published with Vinh Bang in the Archives de Psychologie ("Comparaison des mouvements oculaires et des centrations du regard chez l'enfant et chez l' adulte", 1961). This was my first academic contact with the great man and it certainly reinforced my enthusiasm with Genetic Epistemology that was already ellicited by the study of Logique et équilibre (1957), quoted in my thesis. This book was written by Jean Piaget, Léo Apostel and Benoît Mandelbrot. This was my first contact with Mandelbrot's thinking. In retrospect, Mandelbrot's co-authorship of Logique et équilibre is perhaps the most remote source of my microdiscovery of the power function on saccadic eye movements, because he gave me the right motivation to pursue this research. A year later I was invited by Piaget to attend his weekly seminar on Mondays at the Centre International d' Epistémologie Génétique in Geneva in 1962. I was then in Switzerland as a student of mathematical logic at the University of Fribourg. (I became a fellow of the Centre from 1966 to 1968). In Paris my theoretical interest was centered in phenomenology, and I had the privilege to attend the seminars of Maurice Merlau-Ponty, on Husserl's Krisis der europäischen Wissenschaften at the Collège de France, just accross the rue Sant Jacques from the old lab in Sorbonne. My interest in philosophy, logic and epistemology is another story (II).

Figure 4. Rue des Granges, Genève

I met several young scientist in Geneva, as Jacques Vonèche and Ariane Etienne, who became close friends and distinguished colleagues of the University of Geneva later. Other fellows and visitors like Seymour Papert, Marvin Minsky, Howard Gruber, Gilles-Gaston Granger, Jules Vuillemin, played a role in my scientific life later. The place of Bärbel Inhelder, la grande dame de la psychologie génétique, continued to grow in my heart since then. Since those young years Geneva became, in many aspects, my second home.

During my thesis my only contacts with "Information Theory" were George Miller's famous "Magic Number Seven" (Psychological Review, 1956) and G. Sperling's remarkable "The information available in brief visual presentations" (Psychological Monographs, 1960). I must say that I was truly impressed by Miller's speech at the International Congress of Psychology held in Bonn in 1960 and I confess that Sperling's paper came close to provoking a catastrophe in the writing of my thesis.

Fig. 5. AMB, and members of the Laboratoire de Fraisse at the XXX International Congress of Psychology, Bonn 1960

Sperling's informational way of attacking the problem of brief visual presentations was a real breakthrough in the field and I strongly felt the need to remake my whole research. Fortunately Fraisse came to my rescue in extremis and I could arrive to my "soutenance de thèse" in Sorbonne in time (le 6 janvier 1961, Salle Louis Liard, 9h.30, jury: Fraisse, Oléron, Soulairac).

In Paris I began to read Piaget systematically, who at that time published his important volume on perception Les mécanismes perceptifs (1961) -too late to be analysed in my thesis- and back again in Buenos Aires I wrote a Dictionnaire d'Épistémologie Génetique (with a preface of Piaget himself, published in Paris and Dordrecht in 1966 and translated in English as Piaget Dictionary of Terms , Oxford, 1972). I wrote this Dictionnaire at the "Facultad de Ciencias Exactas y Naturales" of the University of Buenos Aires, in French in 1963.

For this Dictionnaire I read the whole published work of Piaget's and consulted the big corpus of the Etudes d'Epistémologie Génétique (the long series of Etudes reached 37 volumes in 1980 and even now some "inédits" continue to appear). The third volume was written by Léo Apostel, Benoît Mandelbrot and Albert Morf with the title: Logique, langage et théorie de l' information (1957). In his text Linguistique statistique macroscopique , Mandelbrot introduces a "fraction" 1/B as the index of the "informational temperature of a text" (page 30, to be exact). It was long before Mandelbrot's impressive breakthrough in Fractal Theory but the idea of measuring the"temperature" of a collection of discrete events with the help of a fraction became important to me some sixteen years later when I made intensive use of the mathematical tools at work in the log-log transform of the Zipf-(Mandelbrot) power law of rank/frequency of words! I don't remember having studied this fundamental article before, during my stay in Paris, in any case it wasn't included in the references of my thesis.

Fig. 6. Campus of the University of Buenos Aires, where I wrote my Dictionnaire d' Epistémologie Génétique

A long period of latency, seems to be a characteristic of many discoveries in science, small or big (see H. Gruber, Darwin on Man,1974). I must say that I never met Mandelbrot in Geneva although I was invited to many Symposia until Piaget's death in 1980. The first time I had the pleasure of meeting Mandelbrot personally was at Harvard during a visit as an Eisenhower Fellow in 1986. During my work in the search of the fractal model for saccadic movements I kept in contact with him only by letter.

Fig. 7. Benoît Mandelbrot

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