456
J. Maruani
Work is in progress to specify the best variables, functionals, and optimization
procedures in concrete cases.
4.3 Looking for an Extremum Principle for Biological Evolution
from the Quantum Properties of Living Systems
Now we shall look for an extremum principle for biological evolution similar to those
of Fermat and Hamilton for trajectories of light rays and matter particles.
Figure 2 is intended to illustrate the analogies and differences between the propagation of light through an inhomogeneous medium, which obeys Fermat’s principle
for individual wavelengths, and the progression of life through variable environments during geological eras. Trees of life are mentioned in many traditions [e.g. 1],
but they were first used by Darwin [2] and Haeckel [4] as branching diagrams to
show evolutionary links between biological species. In the sketch shown in Fig. 2b,
based on traditional morphologic criteria, living species appear as emerging all from
a same root, as in the light dispersion pattern of Fig. 2a. However, white light is a
superposition of wavelengths which are dispersed in variable directions, while the
root genome undergoes structural changes while interacting with the environment,
as in the light inelastic scattering expressed in Eq. (9b). Figure 2c displays a more
sophisticated branching diagram, based on modern genetic criteria (but not showing
horizontal gene transfer between unrelated organisms).
The determinist way to proceed would be to identify the original genome, if any,
then to monitor its fractal evolution through the various, extinct or living species, if
they are known. However, in searching for an extremum principle it is, as a first step,
simpler to focus on its evolution to that of a single species, e.g. homo sapiens (which
would clarify the detailed working of the Anthropic principle).
In What is Life [16], Schrödinger showed that a living organism is a kind of aperiodic crystal endowed with quantum properties showing up at the macroscopic level.
Ever since then, starting with the pioneering work of a few quantum scientists [34],
including Löwdin’s team [35], there have been advances on both the trivial (physicochemical) and non-trivial (specific biological) quantum aspects of biological systems
and processes [e.g. 36–38]. An overview of these issues can be found in Ref. [39].
Various attempts have also been made to rationalize biological evolution processes
through modern thermodynamics [40] or quantum mechanics and statistics [41], or
by using information recording, processing, and transfer [42]. Extremum biological
principles involving genidentity, entropy or fitness have been searched by extending
usual thermodynamic concepts [e.g. 43–45]. Although not antinomic, our approach
is somehow different. It rests on the idea that genomes are endowed with ‘quantum waves’ corresponding to ‘higher-order structures’ which may interfere either
directly, due to their internal dynamics, or indirectly, through the organisms undergoing natural and sexual selection, species symbiosis, and ecosystem dynamics. This
would give rise to interference fringes and resulting extremal paths, in a way similar
J. Maruani
Work is in progress to specify the best variables, functionals, and optimization
procedures in concrete cases.
4.3 Looking for an Extremum Principle for Biological Evolution
from the Quantum Properties of Living Systems
Now we shall look for an extremum principle for biological evolution similar to those
of Fermat and Hamilton for trajectories of light rays and matter particles.
Figure 2 is intended to illustrate the analogies and differences between the propagation of light through an inhomogeneous medium, which obeys Fermat’s principle
for individual wavelengths, and the progression of life through variable environments during geological eras. Trees of life are mentioned in many traditions [e.g. 1],
but they were first used by Darwin [2] and Haeckel [4] as branching diagrams to
show evolutionary links between biological species. In the sketch shown in Fig. 2b,
based on traditional morphologic criteria, living species appear as emerging all from
a same root, as in the light dispersion pattern of Fig. 2a. However, white light is a
superposition of wavelengths which are dispersed in variable directions, while the
root genome undergoes structural changes while interacting with the environment,
as in the light inelastic scattering expressed in Eq. (9b). Figure 2c displays a more
sophisticated branching diagram, based on modern genetic criteria (but not showing
horizontal gene transfer between unrelated organisms).
The determinist way to proceed would be to identify the original genome, if any,
then to monitor its fractal evolution through the various, extinct or living species, if
they are known. However, in searching for an extremum principle it is, as a first step,
simpler to focus on its evolution to that of a single species, e.g. homo sapiens (which
would clarify the detailed working of the Anthropic principle).
In What is Life [16], Schrödinger showed that a living organism is a kind of aperiodic crystal endowed with quantum properties showing up at the macroscopic level.
Ever since then, starting with the pioneering work of a few quantum scientists [34],
including Löwdin’s team [35], there have been advances on both the trivial (physicochemical) and non-trivial (specific biological) quantum aspects of biological systems
and processes [e.g. 36–38]. An overview of these issues can be found in Ref. [39].
Various attempts have also been made to rationalize biological evolution processes
through modern thermodynamics [40] or quantum mechanics and statistics [41], or
by using information recording, processing, and transfer [42]. Extremum biological
principles involving genidentity, entropy or fitness have been searched by extending
usual thermodynamic concepts [e.g. 43–45]. Although not antinomic, our approach
is somehow different. It rests on the idea that genomes are endowed with ‘quantum waves’ corresponding to ‘higher-order structures’ which may interfere either
directly, due to their internal dynamics, or indirectly, through the organisms undergoing natural and sexual selection, species symbiosis, and ecosystem dynamics. This
would give rise to interference fringes and resulting extremal paths, in a way similar