Loet Leydesdorff wrote:
> 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.
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.
The simplicity of the reality manifests itself as complexity of the
default phase space models: it is 2 degrees of freedom *and* the radius.
Of course, you need to see two dimensions simultaneously to even
perceive the simplicity. The projections of the circle in either
dimension are just the usual impenetrable clouds - one would not be able
to spot the pattern.
To summarize:
complexity in the model =
simplicity/order in the reality
It's perhaps interesting to note that a circle would have the fractal
dimension of 1 - not of 2.
So, the physical view is that there are just reductions in the degrees
of freedom. But One can distinguish the agent from the environment. One
can be writing from the point of view of the agent: it is interesting if
an agent has a greater variety of actions it can take. Usually, however,
scientists write from the point of an observer of the environment: it is
interesting if the environment has patterns we can model (reductions in
degrees of freedom - as compared to the maximum degrees of freedom of gas).
> The configuration within the
> system can (by chance?) develop into one which reduces the uncertainty
when
> three subsystems operate upon one another. This reduction of the
uncertainty
> can be considered as a variant within the phase space or as selection by
an
> hypothesized next-order (emergent?) system. Since this system would have
the
> status of a hypothesis, it would all depend on the model and not on the
> system under study. This external referent ("the phase space")
would remain
> tangential.
Yes, an example of this is the circle. The "degrees of freedom" of the
phase space is 2. But the "degrees of freedom" of the process is 1.
Mutual information is a tool to decide about the number of degrees of
freedom of the process - but not a measure of the degrees of freedom.
Aleks
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Received on Mon Jan 30 01:10:40 2006
