## Creating a Passion for Learning LO17575

Winfried Dressler (winfried.dressler@voith.de)
Fri, 27 Mar 1998 16:19:14 +0100

Dear At,

I have some questions regarding mathematics.

>Mathematicians distinguish between two basic mathematical
>transformations: functions F and relations R. The difference between
>them is as follows. For every function F each input x leads to a
>unique output F(x). For every relation R each input x leads to two or
>more distinguishable outputs, represented togther by R(x). A function
>is thus deterministic while a relation is indeterministic. Guess
>what? Mathematicians favour functions far more than relations.

In the theory of deterministic chaos, where nonlinear functions are
applied iteratively while parameters are changed, I heard for the first
time the word "bifurcation". Has this bifurcation in chaos theorie
anything in common with your bifurcation at entropy saturation? Sometimes,
iteration or changing the parameter is referred to as "increase in time".
Do you see useful analogies between chaos theory and thermodynamics far
from equilibrium?

Mentioning relations, are you (or any other) familiar with Gottfried
Guenters "proemialrelation", which seems to be a basic concept of second
order cybernetics based on his polycontextural logic. It must be close to
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