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Laplace, the mathematician who is the symbol of deterministic perspective in sci-
ence, is also the same scientist who grasped the importance and generality of the
normal distribution, as the most extraordinary law of chance. At a first glance, this
seems to be a paradox. In fact, if chance is the absence of rules, how is it possible to
discover a law for phenomena which are outside of any law? Maybe, just this appar-
ent paradox can provide a sort of reconciliation between determinism and chance.
In fact, a way of considering the laws of chance, is that of rules for passing from
the nondeterminism, at level of individuals, to a collective determinism. Namely,
chance is not the pure absence of causes, but rather it is a population of (small)
causes such that we cannot distinguish them singularly [230], but in their collective
combination. Probability enlarged the power of mathematical analyses and expla-
nations, by replacing the rigid Newtonian model of an exact predictability with a
conceptual framework where complex phenomena going beyond any kind of New-
tonian explanation can be mathematically framed for discovering mutual influence
and causal relations. For this reason, presently, probabilistic and statistic methods
are applied everywhere. The discovery, in the second part of the last century, of
deterministic chaos reinforces the limitations of a rigid determinism in science. In
fact, even in simple systems, under suitable conditions, it happens that there is no
way of predicting the behavior of the system even if it is completely deterministic,
because the system is so sensible to the determination of its initial state that only
an (impossible) infinite precision could avoid an error of its future states which will
exponentially amplify with time.
Since the 19th century, statistics begins to be recognized as a discipline, firstly
related to the quantitative analysis of population phenomena interesting for soci-
ological and economical analyses (birth and death rates, richness distribution, mi-
gration fluxes, and so on). Adolphe Quetelet (1796-1874) played a crucial role in
the connection between statistics and probability. He tried to apply the Laplace dis-
covery about the central role of normal distribution in the context of sociological
disciplines. His program was very ambitious (defining a quantitative analysis of so-
ciology based on normal distribution), but his ideas had a strong influence through
the publication of a volume of Henry Thomas Buckle, who reported, in detailed
terms, the theories of Quetelet. This volume had great success, and it was certainly
read by Darwin, Maxwell, and Boltzmann, suggesting to them the power of statis-
tics in the analysis of natural phenomena. If the theory of probability, starting from
a given space of events, provides methods for assigning probabilities to complex
events, statistics plays the inverse game, because it provides methods for inferring
the right probabilities which underlie some statistical observation. This idea had
been emerging since Laplace, but became a crucial aspect of the statistical studies
of 20th century when mathematically advanced methods were developed, in two
complementary directions: i) inferring probabilities from statistical data, ii) discov-
ering the probabilistic laws of statistical parameters. This second trend provided one
of the most powerful tools in the causal analysis of population phenomena, namely,
the methods for testing hypotheses about cause/effect relations. Galton (Darwin's
cousin), who tried to apply Quetelet's approach to biology, introduced the important
notion of
correlation
, better formalized by Karl Pearson [229], who discovered the
