Re: [Fis] biological "dynamics"

Colleagues,

To Stan, further discussing the passage by Loet:

>The issue is, in my opinion: under which conditions is the emerging system
>able to develop an additional degree of freedom? If this is the case, the
>situation cannot be contained in the phase space ex ante

We should be very specific about what do we take as a system here. If this is an individual organism, then we cannot talk about evolution and new emerging degrees of freedom.

If, however, we discuss the population, or species, (and only this is, in my opinion, the correct level of discussion here), we surely do have the increase in the degrees of freedom. At biochemical level, as new biochemical reactions are added to metabolism, and the corresponding phase space (for example, the phase space of metabolite concentrations) increases its dimensionality, hence extra degrees of freedom occur. At cell structural level, when new organelles evolve. At morphological level of the whole organism, when new organs appear. At environmental level (new food chains).

            This is a very important paradox. The evolution manifests itself in individual organisms, but happens in the population.

To Alex

"Usually, the image of a system in two-dimensional phase space is some
random cloud. But now imagine a circle in a 2D phase space: we need two
dimensions in the phase space to model it. But in reality, the system
*reduced* the degrees of freedom - through its ability to maintain the
radius from some point it became more predictable, yet the phase space
isn't able to automatically make use of this simplicity. Phase space is
a bad model, because it does not capture the simplicity of the process."

I think that there is a bit of confusion here. The phase space is the space of vectors which contain all the parameters of the system. What you talk about is phase trajectory, which belongs to the phase space and is a subset of it due to constraints enforced by the evolution equations of the system. The phase trajectories range from very simple ones (orbital motion in the coordinate-momentum phase space) to rather involved - here you get "clouds" in the phase space of many-body systems as studied by statistical mechanics. You may also have strange attractors, which are also phase trajectories in the phase space, although such trajectories possess some specific features, like fractional dimensionality.

Igor

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Received on Mon Jan 30 09:14:11 2006