Can Quantum Theory Concepts Shed Light on Biological Evolution Processes?
453
it may be recalled that in a 1973 Note [22], de Broglie came to the conclusion that
‘the principle of least action would only be an aspect of the second principle of
thermodynamics’.
For a biopolymer, complexity can be defined as a function of both size (total number of monomers) and variety (numbers of different monomers and combinations).
At the higher level of a cell, complexity can be defined as a function of the numbers of genes in the nucleus and of organelles in the cytosol (eukaryotes being more
complex than prokaryotes). For an organism, one could again use both size (the total
number of cells) and variety (the numbers of different cells and connections): thus
an elephant is ‘more complex’ (in terms of size) than a mouse; and a human is ‘more
complex’ (in terms of variety) than a chimpanzee.
For an ecological area, complexity may again involve size (total number of living
organisms) and variety (numbers of different species and interplays, whether competitive or cooperative). In Eq. (12), the time-dependent, extended coordinates q and
associated velocities v would express the structure and dynamics with respect to both
size and variety at each level of organization. The overall complexity functional C(a,
b) between two states q a and q b , reached at times t a and t b , is the integral of the
function G between these two states.
In §2 it was recalled that Darwin’s theory came to prevail over Lamarck’s theory.
Darwin had studied medicine at Edimbourg and theology at Cambridge, and was
influenced by ideas from Malthus and Spencer, which had developed at an epoch of
free capitalism, as well as by the artificial selection commonly practiced by farmers
and breeders. But it was during his five-year journey on the Beagle around the world
that he became fully aware of the Nature wilderness and developed his theory, which
he published twenty years later [3]. In other works, he expressed novel views on
geological, biological, and even psychological evolution, in which he uncovered
homologic and symbiotic links between the mineral, vegetal, animal, and human
realms (e.g. the fertilizing role of earthworms or the symbiosis between flowers and
insects).
Regarding the philosophy of science, Darwin introduced existential and populational approaches which replaced the platonician essences and aristotelician categories that underlined Linné’s and Cuvier’s classifications. By reintroducing the concept of chance in biology, which had been extirped from physics par Descartes’ and
Newton’s rationalism and determinism, Darwin was a precursor of the epistemologic
revolution provoked by the advent of quantum mechanics.
The expressions ‘struggle for life’ and ‘survival of the fittest’ are titles of chapters
of the first volume. In the second volume he conjectured that ‘man is a codescendant,
with other species, of some extinct inferior form’. His theory, as it took form over
the years, can also be summarized in four main points.
(1) Individual variability: organisms of a same species show individual differences.
Darwin attributed these small variations partly to direct effects of the environment
‘on the whole organisation or on certain parts only’ of the adult or the embryo, and
partly to indirect effects of the environment ‘on the reproductive system’.
453
it may be recalled that in a 1973 Note [22], de Broglie came to the conclusion that
‘the principle of least action would only be an aspect of the second principle of
thermodynamics’.
For a biopolymer, complexity can be defined as a function of both size (total number of monomers) and variety (numbers of different monomers and combinations).
At the higher level of a cell, complexity can be defined as a function of the numbers of genes in the nucleus and of organelles in the cytosol (eukaryotes being more
complex than prokaryotes). For an organism, one could again use both size (the total
number of cells) and variety (the numbers of different cells and connections): thus
an elephant is ‘more complex’ (in terms of size) than a mouse; and a human is ‘more
complex’ (in terms of variety) than a chimpanzee.
For an ecological area, complexity may again involve size (total number of living
organisms) and variety (numbers of different species and interplays, whether competitive or cooperative). In Eq. (12), the time-dependent, extended coordinates q and
associated velocities v would express the structure and dynamics with respect to both
size and variety at each level of organization. The overall complexity functional C(a,
b) between two states q a and q b , reached at times t a and t b , is the integral of the
function G between these two states.
In §2 it was recalled that Darwin’s theory came to prevail over Lamarck’s theory.
Darwin had studied medicine at Edimbourg and theology at Cambridge, and was
influenced by ideas from Malthus and Spencer, which had developed at an epoch of
free capitalism, as well as by the artificial selection commonly practiced by farmers
and breeders. But it was during his five-year journey on the Beagle around the world
that he became fully aware of the Nature wilderness and developed his theory, which
he published twenty years later [3]. In other works, he expressed novel views on
geological, biological, and even psychological evolution, in which he uncovered
homologic and symbiotic links between the mineral, vegetal, animal, and human
realms (e.g. the fertilizing role of earthworms or the symbiosis between flowers and
insects).
Regarding the philosophy of science, Darwin introduced existential and populational approaches which replaced the platonician essences and aristotelician categories that underlined Linné’s and Cuvier’s classifications. By reintroducing the concept of chance in biology, which had been extirped from physics par Descartes’ and
Newton’s rationalism and determinism, Darwin was a precursor of the epistemologic
revolution provoked by the advent of quantum mechanics.
The expressions ‘struggle for life’ and ‘survival of the fittest’ are titles of chapters
of the first volume. In the second volume he conjectured that ‘man is a codescendant,
with other species, of some extinct inferior form’. His theory, as it took form over
the years, can also be summarized in four main points.
(1) Individual variability: organisms of a same species show individual differences.
Darwin attributed these small variations partly to direct effects of the environment
‘on the whole organisation or on certain parts only’ of the adult or the embryo, and
partly to indirect effects of the environment ‘on the reproductive system’.