452
J. Maruani
4.2 Hints and Criteria for a Biological Extremum Principle
from Concepts of Former Evolution Theories
It was recalled in §2 that Lamarck was the first to propose a consistent theory of
biological evolution [2]. During medical studies in Paris, he was interested in meteorology and alchemy, then turned to botanics and zoology. His theory can be summarized in four main principles. (1) Life naturally tends to increase the volume and
complexity of organisms and of their parts. (2) New needs generate new functions,
which in turn create new organs. (3) The development or atrophy of organs depends
on their use or nonuse. (4) Acquired characters are hereditary.
Point 1 simply describes the development of ordered structures in the living world
and could also, in Gould’s scheme [12], be applied to whole species. It is compatible
with Carnot’s principle, because living systems are submitted to energy flows as
sunlight. The teleological flavor of Point 2 is discarded in modern evolution theory.
Point 3 simply expresses the adaptative character of living structures and has no
explaining value. As to Point 4, which was then current belief among biologists
(including Darwin and Haeckel), it lead to hard controversies between neodarwinists
and neolamarckists and came to be identified with the whole of Lamarck’s theory.
Newton was inspired by astrology and alchemy when he unified the antique lower
and upper worlds and postulated the action at a distance, which was then unexplained.
Similarly, Lamarck was inspired by meteorology and alchemy when he elaborated
his theory. Newton’s gravitational force was later understood as resulting from space
curvature in Einstein’s relativity theory, while Lamarck’s first law found a justification in Prigogine’s thermodynamics of dissipative systems [30]. One could thus
consider using concepts introduced in Lamarck’s theory in the search for a biological
equivalent to the ‘action integral’ or optical path’.
Lamarck’s first three laws would apply to single individuals in a given species
during their growing period as well as to long-lived ecosystems, while the fourth law
can only apply to specific species, or to a whole phylum if interspecific mutation is
recognized. The second and third laws can be seen as modes of realization of the
first law under the influence of an internal structure q and dynamics v of a system
and its interactions with the environment, defining a kind of ‘biological Lagrangian
operator’ G. One may then consider choosing as a ‘biological Hamilton principle’
that of maximizing a ‘complexity’ C to be defined, possibly using the entropy concept,
either in its statistical (Clausius) or algorithmic (Kolmogorov) form, both in extensive
(size) and intensive (variety) terms, over a given period of time:
C[q] ≡
G(q, v, t)dt(t a → t b ); δC/δq = 0.
(12)
Note that in Hamilton’s principle, Eq. (5), the stationary property, the action
functional S, has dimensions: S ~ ML
2 T
−1 , while in Fermat’s principle, Eq. (8), the
optical path S has dimension: S ~ L. In Eq. (12), the complexity functional C may
be defined as dimensionless, as in the statistical interpretation of negentropy. Here
J. Maruani
4.2 Hints and Criteria for a Biological Extremum Principle
from Concepts of Former Evolution Theories
It was recalled in §2 that Lamarck was the first to propose a consistent theory of
biological evolution [2]. During medical studies in Paris, he was interested in meteorology and alchemy, then turned to botanics and zoology. His theory can be summarized in four main principles. (1) Life naturally tends to increase the volume and
complexity of organisms and of their parts. (2) New needs generate new functions,
which in turn create new organs. (3) The development or atrophy of organs depends
on their use or nonuse. (4) Acquired characters are hereditary.
Point 1 simply describes the development of ordered structures in the living world
and could also, in Gould’s scheme [12], be applied to whole species. It is compatible
with Carnot’s principle, because living systems are submitted to energy flows as
sunlight. The teleological flavor of Point 2 is discarded in modern evolution theory.
Point 3 simply expresses the adaptative character of living structures and has no
explaining value. As to Point 4, which was then current belief among biologists
(including Darwin and Haeckel), it lead to hard controversies between neodarwinists
and neolamarckists and came to be identified with the whole of Lamarck’s theory.
Newton was inspired by astrology and alchemy when he unified the antique lower
and upper worlds and postulated the action at a distance, which was then unexplained.
Similarly, Lamarck was inspired by meteorology and alchemy when he elaborated
his theory. Newton’s gravitational force was later understood as resulting from space
curvature in Einstein’s relativity theory, while Lamarck’s first law found a justification in Prigogine’s thermodynamics of dissipative systems [30]. One could thus
consider using concepts introduced in Lamarck’s theory in the search for a biological
equivalent to the ‘action integral’ or optical path’.
Lamarck’s first three laws would apply to single individuals in a given species
during their growing period as well as to long-lived ecosystems, while the fourth law
can only apply to specific species, or to a whole phylum if interspecific mutation is
recognized. The second and third laws can be seen as modes of realization of the
first law under the influence of an internal structure q and dynamics v of a system
and its interactions with the environment, defining a kind of ‘biological Lagrangian
operator’ G. One may then consider choosing as a ‘biological Hamilton principle’
that of maximizing a ‘complexity’ C to be defined, possibly using the entropy concept,
either in its statistical (Clausius) or algorithmic (Kolmogorov) form, both in extensive
(size) and intensive (variety) terms, over a given period of time:
C[q] ≡
G(q, v, t)dt(t a → t b ); δC/δq = 0.
(12)
Note that in Hamilton’s principle, Eq. (5), the stationary property, the action
functional S, has dimensions: S ~ ML
2 T
−1 , while in Fermat’s principle, Eq. (8), the
optical path S has dimension: S ~ L. In Eq. (12), the complexity functional C may
be defined as dimensionless, as in the statistical interpretation of negentropy. Here