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Provinciales” where he referred to the doctrine of the Jesuits, or in “Les Pensées”. In Pascal’s
writings, we do not find the words of “Doctrine des chances” or “Calcul des chances”, but only
“Géométrie du hasard” (geometry of chance). In 1654, Blaise Pascal submitted a short paper to
“Celeberrimae matheseos Academiae Parisiensi” (ancestor of the French Royal Academy of Sciences
founded in 1666), with the title “Aleae Geometria” (Geometry of Chance) or “De compositione aleae in
ludis ipsi subjectis”, which was the seminal paper founding Probability as a new discipline in
Science. In this paper, Pascal said “… et sic matheseos demonstrationes cum aleae incertitudine
jugendo, et quae contraria videntur conciliando, ab utraque nominationem suam accipiens,
stupendum hunc titulum jure sibi arrogat: Aleae Geometria” that we can translate as “By the union
thus realized between the demonstrations of mathematics and the uncertainty of chance, and by the
conciliation of apparent contradictions, it can derive its name from both sides and arrogate to itself this
astonishing title: Geometry of Chance” (« … par l’union ainsi réalisée entre les démonstrations des
mathématiques et l’incertitude du hasard, et par la conciliation entre les contraires apparents, elle peut tirer
son nom de part et d’autre et s’arroger à bon droit ce titre étonnant: Géométrie du Hasard ». We can observe
that Blaise Pascal attached a geometrical sense to probabilities in this seminal paper. Like Jacques
Bernoulli, we can also provide references to another Blaise Pascal document entitled “Art de penser”
(the “Logique” of Port-Royal), published the year of his death (1662), the last chapters of which
contain elements on the calculus of probabilities applied to history, medicine, miracles, literary
criticism, and life events, etc.
Figure 1. Blaise Pascal and His Seminal Text on « Aleae Geometria »
In “De l'esprit géométrique », the use of reason for knowledge is thought on a geometric
model. In geometry, the first principles are given by the natural lights common to all men, and there
is no need to define them. Other principles are clearly defined by definitions of names such that it is
always possible to mentally substitute the definition for the defined. These definitions of names are
completely free, the only condition to be respected is univocity and invariability. Judging his
solution as one of his most important contributions to science, Pascal envisioned the drafting of a
small treatise entitled “Géométrie du Hasard” (Geometry of Chance). He would never write it.
Inspired by this, Christian Huygens wrote the first treatise on the calculation of chances, the “De
ratiociniis in ludo aleae” (“On calculation in games of chance”, 1657). We can conclude this preamble
by observing that Blaise Pascal’s seminal work on Probability was inspired by Geometry. The
Differential Geometrical Theory of Statistics
- Title
- Differential Geometrical Theory of Statistics
- Authors
- Frédéric Barbaresco
- Frank Nielsen
- Editor
- MDPI
- Location
- Basel
- Date
- 2017
- Language
- English
- License
- CC BY-NC-ND 4.0
- ISBN
- 978-3-03842-425-3
- Size
- 17.0 x 24.4 cm
- Pages
- 476
- Keywords
- Entropy, Coding Theory, Maximum entropy, Information geometry, Computational Information Geometry, Hessian Geometry, Divergence Geometry, Information topology, Cohomology, Shape Space, Statistical physics, Thermodynamics
- Categories
- Naturwissenschaften Physik