Page - vii - in Differential Geometrical Theory of Statistics

vii Preface to “Differential Geometrical Theory of Statistics” This Special Issue “Differential Geometrical Theory of Statistics” collates selected invited and contributed talks presented during the conference GSI'15 on “Geometric Science of Information” which was held at the Ecole Polytechnique, Paris-Saclay Campus, France, in October 2015 (Conference web site: http://www.see.asso.fr/gsi2015). Let us first start with a short historical review on the birth of the interplay of probability with geometry and computing, which is rooted in the 17th century. 1. Preamble: Aleae Geometria, the Geometry of Chance by Blaise Pascal The “calculation of probabilities” began four years after the death of René Descartes, in 1654, in a correspondence between Blaise Pascal and Pierre Fermat. They exchanged letters on elementary problems of gambling, in this case a problem of dice and a problem of “parties”. Pascal and Fermat were particularly interested by this problem and succeeded in “Party rule” by two different methods. One understands the legitimate pride of Pascal in his address of the same year at the Académie Parisienne created by Mersenne, to which he presented “the ripe fruit of our Geometry” (“les fruits mûrs de notre Géométrie” in French), an entirely new treaty about an absolutely unexplored matter, the distribution of chance in games. In the same way, Pascal, in his introduction to “Les Pensées”, wrote that under the influence of what Méré has given to the game, he throws the bases of the calculation of probabilities and composes the Treatise of the Arithmetical Triangle. If Pascal appears at first sight as the initiator of the calculation of probabilities, looking a little closer, its role in the emergence of this theory is more complex. However, there is no trace of word probabilities in Pascal's work. To designate what might resemble what we now call calculation of probabilities, one does not even find the word in such a context. The only occurrences of probability are found in “Les