Dear Stan:
> Replying to Loet -- I wish the case were this simple! Yes,
> vagueness suggests the possibility of variety (informational
> entropy), but in itself it IS not variety, and cannot be
> measured in this way.
I agree that vagueness cannot be considered as variety. However, vagueness
is the opposite of stabilization (which allows for delineation).
Stabilization is the result of two selection mechanisms operating upon one
another in a process of mutual shaping. Selection mechanisms are properties
of structures; structure are properties of matrices. Matrices can be
considered as two-dimensional probability distributions. (Vectors are
one-dimensional probability distributions and can be used to model
variation.)
When two selection mechanisms operate upon one another one can expect a
three-dimensional probability distribution: the first dimension provides the
variation; the second the structure or the first selection; and the third
the selection of some selections for stabilization (and thus less
vagueness). Stabilizations can be further selected for globalization. This
can thus be modeled as four-dimensional probability distribution.
Entropy statistics enables us to compute with probability distributions.
Stabilization annihilates vagueness and can thus be modeled using entropy
statistics. For example, a trajectory can be formed over time. This can be a
gradual process with perhaps phase-transitions (bifurcations, etc.). Because
stabilizations can be plural, they can also be considered as second-order
variations, potentially to be selected for globalization as a second-order
selection mechanism. Note that stabilizations are variations within the
system, while first-order variation can be considered as exogenous
uncertainty.
I hope that you find this helpful for solving the problem of vagueness.
With kind regards,
Loet
________________________________
Loet Leydesdorff
Amsterdam School of Communications Research (ASCoR)
Kloveniersburgwal 48, 1012 CX Amsterdam
Tel.: +31-20-525 6598; fax: +31-20-525 3681
[email protected];
http://www.leydesdorff.net
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Received on Mon Nov 28 00:19:29 2005
