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civilizations. This scenario is so familiar to all of us, that it can hardly be surprising
for the layman.
However, from a scientific point of view the same scenario raises a paradox so
difficult to analyze and explain, that the most well versed minds of all times were
very often lost in the enormous logical difficulties related to
time's arrow
.This
paradox links two scientists who enormously influenced their disciplines, biology
and physics, between the mid 19th and 20th centuries: Charles Darwin and Ludwig
Boltzmann. The first chapter of Wiener's famous topic,
Cybernetics
, is entitled
New-
tonian and Bergsonian time
and a problematic conciliation is discussed between the
two opposite notions of time in biology and physics. A conciliation which surely
exists, because biology cannot falsify physics on which it is surely based.
The time of classical physics, which successfully explained star and planet mo-
tions, and which is the basis of the modern science inaugurated by Galileo, is a time
where laws are expressed by equations, and therefore where no privileged verse can
be chosen. But people are getting older, and no reliable method has been discov-
ered, so far, for stopping or inverting the aging process. A notion of irreversibility
appeared in physical phenomena concerning thermodynamics. The second princi-
ple of thermodynamics establishes an energy degradation principle pushing isolated
systems, toward states where thermic energy is uniformly distributed. This raised
the problem of relating this principle with classical Newtonian physics, where no
time arrow is postulated. Boltzmann, surely influenced by Darwin, dedicated his
life to the explanation of the thermodynamical arrow of time. Boltzmann's research
was greatly opposed by the leading scientific culture of his time, and the mathemat-
ical proof he presented was criticized in a very aggressive way, surely because of
some technical inadequacies, but essentially because of its revolutionary scientific
meaning. The intrinsic logical difficulty of Boltzmann's theory was put in evidence
by Henry Poincar´e(
we cannot accept an argument where the conclusion is in a
clear contradiction with its premises
). Surely, Boltzmann was on the edge of the
paradox, but he was right, as the following science confirmed his intuition. More-
over, the physical theory that he founded, statistical mechanics, is a masterpiece of
all the physics of the 20th century.
A more subtle paradox is related to the two kinds of time of classical mechanics
and of biology. In fact, even if the Boltzmann theory is accepted and thermody-
namics is conciliated within Newtonian mechanics, even in this case, how can we
explain the dichotomy between the thermodynamic arrow and the time of biologi-
cal evolution, where living organisms evolve, against the order degradation required
by the second principle of thermodynamics? In other words, even if time's arrow is
explained, two opposite arrows rule inorganic and organic phenomena, respectively.
Prigogine's theory of non-equilibrium thermodynamics tries to explain this appar-
ent contradiction, but no definitive explanation seems to be clearly settled. In the
following, we will try to explain the relationship between time and complexity. We
will develop arguments and (numerical) experiments showing that time's arrow is a
consequence of statistical complexity. In the analysis that we develop some crucial
interactions appear among time, complexity, chance, and information.
