Within your commentary submitted Friday, April 3 you state:
> Your subsequent phrase "that defines the bifurcation point" is one
> gigantic leap in emergent learning. You have sensed that flux-force
> pairs lead to bifurcations (the "identity" part of sureness), but it
> lacks the "categoricity" part of sureness). The flux-force pairs
> rather define "entropy production" and the latter, if produced fast
> enough, leads to "bifurcations". Thus, between the "flux-force pairs"
> and "bifurcations" you neglected to articulate one of the most
> important becomings of reality, namely "entropy production"
Yes, yes. I should have related this to the flux-force issue from
thermodynamics. But to continue this pursuit.
In your initial submittal, you mentioned each of the seven
essentialities are represented by a dual identification format; first by
a pair of "seminal" names and second by a single "nominal" name.
Proceeding with the thought, in fact, all of the seminal names relate
flux-force pairs. Thus, it is possible to extend your argument to state
each defines a portion of the entropy production. And this is why if
any one of the essentialities is missing, the possibility of emergent
learning becomes critically damaged.
You then comment:
> Then you
> articulate your tacit knowledge that somehow they (have) to do with
> linear-nonlinear. Why did you not persist with this self-learning,
> because it would have brought you deep insight! Instead, you assumed
> that "in the de Lange model for creativity, nonlinearity is implicit
> and he has simply not felt it was a driving requirement".
It appears here there is some confusion over my meaning because I did
not appropriately express myself. To begin, I realize from your
comments, returning to the submittal you quote, that what I missed is
becoming-being and nonlinearity are likely related categories, thus
filling the missing correlation I was attempting to make. Given entropy
production is produced by the flux-force pairs fast enough, the
bifurcation point will be reached and emergent learning will occur.
But now for the issue of linearity. My thinking about
linearity-nonlinearity has evolved into a direction different from
mathematical metaphor because we can play games with nonlinear equations
so they have a linear representation. For example, one of the nonlinear
equations in your note is of the form
Y = 3X^2 + 2.
This can be rearranged to be of the form
(Y - 2) = 3X^2.
If we take the natural logarithm we get the form
ln(Y - 2) = ln3 + 2lnX
Redefining Y' = ln(Y - 2) and X' = lnX, we end up with the equation
Y' = constant + 2X'
Which is linear. In my opinion, we cannot use such constructions in a
constructive manner. Rather, I think of nonlinearity in terms of
irreversibility, which in turn implies entropy production. I believe I
was inherently doing this when I related being to linearity and becoming
to nonlinearity. I did so because to me being is static - equilibrium,
or at no worst near-to-equilibrium. Becoming is nonlinear because it
implies dynamic, changing, irreversible. Using this framework, I can
take each of your other seminal pairs and relate one or another of the
terms, some more obviously than others, to a static condition
(identity, monadicity, connect, limit, quality, paradigm) or a dynamic,
changing condition (categoricity, associativity, beget, quantity,
variety, open)
David
David T. Novick e-mail: david.t.novick@boeing.com
Mail Stop: GE99 Phone: (714)762-5522
The Boeing Company Fax: (714)762-6222
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--"Novick, David T" <David.Novick@West.Boeing.com>
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