English
Remembering Professor Takeyuki Hida
Professor Takeyuki Hida, Professor Emeritus of Nagoya University, died on 29 December 2017. His research on stochastic processes had close connections with this institute. This feature brings together his writings, joint research, and reflections on their significance for Socio-Infonomics.
Space-Time and Chance
With permission from Fumikazu Hida and the editors of Sugaku Seminar (Nippon Hyoron Sha), we make available the complete four-part series by Takeyuki Hida.
Takeyuki Hida: Space-Time and Chance (Japanese PDF)
Takeyuki Hida and the Stochastic Turn in Socio-Infonomics
Yasuhide Yamanouchi — 30 March 2018
Professor Hida was a leading mathematician who served as president of the Bernoulli Society. To a non-specialist, his work seemed to seek a direct understanding of the underlying mechanisms that generate common patterns across the world’s phenomena. For him, probability theory was a way of grasping the world at a fundamental level. This helps explain his appreciation of Tamito Yoshida’s informational turn in the philosophy of science and Shumpei Kumon’s analysis of historical S-curves.
We had taken relatively simple analytical methods, including the differential-equation systems of chaos theory, as a natural approach to such patterns. Professor Hida rejected that assumption as inappropriate and introduced us to stochastic processes and algebraic methods. Rather than applying equations developed in the natural sciences to social phenomena, these approaches offered a more fundamental understanding shared by both fields.
When events are understood through infinitely divisible distributions and functional spaces arising from independent-increment processes in time and space—the area Hida called white-noise analysis (Mathematics Subject Classification 60H40)—the boundary between natural and social sciences is no longer fundamental.
Models based on stochastic processes and independent increments support a historical-constructionist account of changes in social structure. The growing availability of large social datasets and computational analysis created a particularly productive setting for the joint research of Professors Hida and Kumon. Their work helped resolve many questions about mathematical methods in the social sciences.
One topic was how to understand Benoît Mandelbrot’s work. His investigations of non-Gaussian distributions in the 1960s led directly back to Paul Lévi; Norbert Wiener had also studied with Lévi. Professor Hida had discussed these questions with Lévi himself, and repeatedly returned to Lévi’s original writings. Turning to stochastic-process theory was a decisive change in the institute’s approach—a paradigm shift in Socio-Infonomics.