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Discussion
Lederman ( University of Chicago ): I wonder if it is true that in your definition of
order you are really aiming at conditional probabilities rather than just an order in
a given system, because for a given number of elements in your system, under your
definition of order, the order would be higher in a system in which the information
content was actually smaller than for other systems.
von Foerster: Perfectly right. What I tried to do here in setting a measure of order,
was by suggesting redundancy as a measure. It is easy to handle. From this I can
derive two statements with respect to H max and with respect to H . Of course, I don't
mean this is a universal interpretation of order in general. It is only a suggestion
which may be useful or may not be useful.
Lederman: I think it is a good suggestion but it is an especially good suggestion
if you think of it in terms of some sort of conditional probability. It would be more
meaningful if you think of the conditional probabilities as changing so that one of
the elements is singled out for a given environmental state as a high probability.
von Foerster: Yes, if you change H , there are several ways one can do it. One can
change the conditional probability. One can change also the probability distribution
which is perhaps easier. That is perfectly correct.
Now the question is, of course, in which way can this be achieved? It can be
achieved, I think, if there is some internal structure of those entities which are to
be organized.
Lederman: I believe you can achieve that result from your original mathemati-
cal statement of the problem in terms of H and H max , in the sense that you can
increase the order of your system by decreasing the noise in the system which
increases H max .
Won Foerster: That is right. But there is the possibility that we will not be able
to go beyond a certain level. On the other hand, I think it is favorable to have some
noise in the system. If a system is going to freeze into a particular state, it is inadapt-
able and this final state may be altogether wrong. It will be incapable of adjusting
itself to something that is a more appropriate situation.
Lederman: That is right, but I think the parallelism between your mathematical
approach and the model you gave in terms of the magnets organizing themselves,
that in the mathematical approach you can increase the information content of the
system by decreasing the noise and similarly in your system where you saw the
magnets organizing themselves into some sort of structure you were also decreas-
ing the noise in the system before you reached the point where you could say ah
ha, there is order in that system.
von Foerster: Yes, that is right.
Mayo ( Loyola University ): How can noise contribute to human learning? Isn't
noise equivalent to nonsense?