438
J. Maruani
1 Introduction
For a long time, in the Western world, it was generally believed that, in accordance
with what was taught in the Holy scriptures, but contrary to what was thought by
Ancient philosophers, the world had a beginning and would also have an end, while
the living species had remained unchanged since they were created ‘after their kind’
[1]. These beliefs prevailed from the early Christian times to the Renaissance.
The idea that the Universe may actually be eternal—and infinite—reappeared at
that time. But it was with later progress in the natural sciences (mainly geology and
paleontology) that one started to realize that the Universe was much older than it
had earlier been surmised. About the end of the 17th century, Whiston suggested
that the six days of the Creation were in fact extended eras. A century later, Cuvier
distinguished several eras which were populated by now extinct, fossile species—the
present, living forms being survivors of geological devastations, supposedly ending
with the Flood.
About the same epoch, ancient beliefs according to which the living forms had
undergone thorough changes through the ages aroused new interest, although interpretations avoided challenging the Holy scriptures. But when Lamarck [2] then
Darwin [3–5] developed their consistent—though competing—theories, the idea of
transformism became definitely established. In §2 we present a short survey of the
developments that occurred in the 19th century and led to the modern theories of
biological evolution [6–13].
Another challenge to the views of the Middle Ages was Copernicus’ proposal that
the Earth was just one of many planets rotating around the Sun, then Galileo’s discovery that the Solar system was more complex than it was thought. Still later, the Sun
itself appeared as being but one of a hundred billion stars in our Galaxy. However,
contrary to what had happened in the biological sciences, modern cosmologies lead
to a revival of the biblical idea that the Universe has a beginning—and a limit [14, 15].
Until Lamarck, biology tended to use a finalist, holistic, teleological language, the
living organisms being viewed as if they were aiming at some goal. After Darwin,
this language started to be proscribed and determinist, reductionist, mechanistic
formulations became the rule in biology. Until the recent prospects on demographic,
climatic, and ecological changes, human history had come to be viewed as a series
of chaotic events ruled by chance and necessity, not by some eschatologic design.
As a result, the scientific interest in biological evolution was focussed on the past,
not on the future, and speculations on intelligent design were discarded. Research
on an encompassing, predictive theory of biological evolution was limited. On the
opposite, modern cosmologies built on the relativistic and quantum theories came to
speculate not only on the past, but also on the future of the Universe, data gathered
from its remote limits being related to its early history [14, 15].
The problem raised in this paper is whether the traditional, finalist, and the modern,
determinist views of biological evolution are compatible, and whether a mathematical
formulation can be derived to reconcile the two viewpoints. In §3.1 we recall how, in
classical mechanics, the Lagrange (or Hamilton) differential equations, derived from
J. Maruani
1 Introduction
For a long time, in the Western world, it was generally believed that, in accordance
with what was taught in the Holy scriptures, but contrary to what was thought by
Ancient philosophers, the world had a beginning and would also have an end, while
the living species had remained unchanged since they were created ‘after their kind’
[1]. These beliefs prevailed from the early Christian times to the Renaissance.
The idea that the Universe may actually be eternal—and infinite—reappeared at
that time. But it was with later progress in the natural sciences (mainly geology and
paleontology) that one started to realize that the Universe was much older than it
had earlier been surmised. About the end of the 17th century, Whiston suggested
that the six days of the Creation were in fact extended eras. A century later, Cuvier
distinguished several eras which were populated by now extinct, fossile species—the
present, living forms being survivors of geological devastations, supposedly ending
with the Flood.
About the same epoch, ancient beliefs according to which the living forms had
undergone thorough changes through the ages aroused new interest, although interpretations avoided challenging the Holy scriptures. But when Lamarck [2] then
Darwin [3–5] developed their consistent—though competing—theories, the idea of
transformism became definitely established. In §2 we present a short survey of the
developments that occurred in the 19th century and led to the modern theories of
biological evolution [6–13].
Another challenge to the views of the Middle Ages was Copernicus’ proposal that
the Earth was just one of many planets rotating around the Sun, then Galileo’s discovery that the Solar system was more complex than it was thought. Still later, the Sun
itself appeared as being but one of a hundred billion stars in our Galaxy. However,
contrary to what had happened in the biological sciences, modern cosmologies lead
to a revival of the biblical idea that the Universe has a beginning—and a limit [14, 15].
Until Lamarck, biology tended to use a finalist, holistic, teleological language, the
living organisms being viewed as if they were aiming at some goal. After Darwin,
this language started to be proscribed and determinist, reductionist, mechanistic
formulations became the rule in biology. Until the recent prospects on demographic,
climatic, and ecological changes, human history had come to be viewed as a series
of chaotic events ruled by chance and necessity, not by some eschatologic design.
As a result, the scientific interest in biological evolution was focussed on the past,
not on the future, and speculations on intelligent design were discarded. Research
on an encompassing, predictive theory of biological evolution was limited. On the
opposite, modern cosmologies built on the relativistic and quantum theories came to
speculate not only on the past, but also on the future of the Universe, data gathered
from its remote limits being related to its early history [14, 15].
The problem raised in this paper is whether the traditional, finalist, and the modern,
determinist views of biological evolution are compatible, and whether a mathematical
formulation can be derived to reconcile the two viewpoints. In §3.1 we recall how, in
classical mechanics, the Lagrange (or Hamilton) differential equations, derived from