## Prof. Eduardo R. Caianiello

**Professor Eduardo Renato Caianiello** was born in Naples on June 25, 1921. He obtained his degree of "Dottore in Fisica" at the University of Naples in 1944, and his Ph.D. in physics at the University of Rochester in 1950. He was assistant professor of mathematics at the University of Naples from 1944 to 1948, and successively assistant professor at the University of Rochester and assistant professor of physics at the Universities of Turin and Rome from 1950 to 1955. In 1955 he was "Higgins Visiting Professor" at PrincetonUniversity, holding a course on advanced topics in quantum theory, when he was informed that he had been awarded the Chair in Theoretical Physics at the University of Naples.

He started his academic work there in November 1956, concentrating his research activity on the renormalization of field theory and on the use of Hadamard's part integrals to handle divergencies in relativistic quantum field theories. In 1957 he founded the Institute of Theoretical Physics in Naples, where physicists and mathematicians from all over the world met to exchange ideas and propose new theories in one of the most exciting scientific environments in Italy.

Eduardo Caianiello's interest in cybernetics was indirectly inspired by Enrico Fermi, who in 1954 promoted the establishment at the University of Rome of a seminar on computers and cybernetics of Norbert Wiener. There Eduardo Caianiello became acquainted with Dr. Valentino Braitenberg, a specialist in psychiatry, neurology and neuroanatomy, who eventually joined him at the Institute of Theoretical Physics in Naples and greatly contributed to the establishment of the Division of Cybernetics, sponsored by the Italian National Research Council.

In 1968, Eduardo Caianiello founded the Laboratory of Cybernetics at Arco Felice, which soon became one of the leading institutions in pattern recognition, analysis of form and language, and neural nets. The Laboratory remained under his direction until 1977.

Throughout these many productive years, Eduardo Caianiello's research can well be characterized as avant-garde. A paradigmatic example is his work on the mathematical description of nonlinear binary decision elements and neural nets. This work stemmed from the formulation of neuronic and mnemonic equations laid down in the well-known 1961 paper "An outline of thought processes and thinking machines." The neuronic equations there described account for the behavior of networks with frozen connections, while the mnemonic equations account for the changes of coupling among neurons. Together with his "adiabatic learning hypotheses", they became known as "Caianiello's equations" (*Enciclopaedic Dictionary of Mathematics*, MIT Press, 1974). These were the equations which inspired the formulation of most of the numerous successive approaches to associative memories and learning rules.

From the onset of his interest in cybernetics, Eduardo Caianiello was fascinated by the hierarchical structure of natural languages, a certain manifestation, in his view, of the hierarchical organization of all biological and social systems. He was led to emphasize the essential role played by hierarchical structures in the study of complex systems, and became greatly interested in the general analysis of modular systems and its applications to monetary, urban and other complex systems.

By 1972 Eduardo Caianiello was turning his attention to the nearby University of Salerno. He succeeded in founding a science faculty, a basic curriculum in engineering, and a full curriculum in computer sciences, until then available in Italy only at the University of Pisa. He moved permanently to the newly created Department of Theoretical Physics at the University of Salerno, where he was for many years the dean of the science faculty.

During this period, he opened a new fundamental field of theoretical physics. In the summer of 1979, John Archibald Wheeler wrote to him: "* .... In all of my four trips to Europe in the past months in none was there a more exciting moment than when you told me you had in mind to devote yourself to 'quantum mechanics without quantum mechanics' .... . I hope you will go further. I would think that one should expect in the end to deduce space geometry from quantum theory rather than quantum theory from space geometry; and quantum theory from something about the machinery by which information is acquired. It is exactly on this latter point that you have to make a contribution unique in the world because of your wonderful background in this area ....*".

Hence, a research program on quantum geometry was successfully initiated at Salerno. This program led to the introduction of "maximal proper acceleration" generalizing the relativistic invariance group. The consequences of this theory for cosmology and elementary particle physics are presently the object of further studies in many research groups around the world.

Throughout his impressive career, Eduardo Caianiello sought knowledge tirelessly, not only in the world of science, but also in the world of people. His unceasing commitment to understand different cultures was an essential element of Eduardo Caianiello, who found truth in every nation. For instance, he was a pioneer in establishing relations with the People's Republic of China. He maintained solid friendships throughout Europe, while breaking new ground with the scientists of the former Soviet Union, the Unites States, India, and Japan especially. At the same time, and with the same enthusiasm, he retained his Italian and Neapolitan roots, and opened his home to visiting scholars.

The last institution founded by Eduardo Caianiello was the International Institute for Advanced Scientific Studies (IIASS) in Vietri sul Mare, a picturesque town near Salerno at the beginning of the beautiful Amalfi coast. His last few years were devoted to the development of this Institute, which has already attained a prominent position in the research and application of neural nets. He deserved as president from its 1981 inception until his death.

Eduardo Renato Caianiello suddenly died in his home in Naples on October 22, 1993.