On Self-Organizing Systems and Their Environments - Understanding Understanding: Essays on Cybernetics and Cognition - page 9

( b ) H = const.
If the entropy of the system is supposed to remain constant, its time deriv-
ative will vanish and we will have from eq. (5)

d
d

H
t

d H

t

m

for (7)

= 0 LL > 0

d

Thus, we obtain the peculiar result that, according to our previous defin-
ition of order, we may have a self-organizing system before us, if its possi-
ble maximum disorder is increasing. At first glance, it seems that to achieve
this may turn out to be a rather trivial affair, because one can easily imagine
simple processes where this condition is fulfilled. Take as a simple example
a system composed of N elements which are capable of assuming certain
observable states. In most cases a probability distribution for the number
of elements in these states can be worked out such that H is maximized and
an expression for H m is obtained. Due to the fact that entropy (or, amount
of information) is linked with the logarithm of the probabilities, it is not too
difficult to show that expressions for H m usually follow the general form*:

HCC

m =+

log N .

1 2 2

This suggests immediately a way of increasing H m , namely, by just increas-
ing the number of elements constituting the system; in other words a system
that grows by incorporating new elements will increase its maximum en-
tropy and, since this fulfills the criterion for a system to be self-organizing
(eq. 7), we must, by all fairness, recognize this system as a member of the
distinguished family of self-organizing systems.
It may be argued that if just adding elements to a system makes this a
self-organizing system, pouring sand into a bucket would make the bucket
a self-organizing system. Somehow—to put it mildly—this does not seem
to comply with our intuitive esteem for members of our distinguished
family. And rightly so, because this argument ignores the premise under
which this statement was derived, namely, that during the process of adding
new elements to the system the entropy H of the system is to be kept con-
stant. In the case of the bucket full of sand, this might be a ticklish task,
which may conceivably be accomplished, e.g. by placing the newly admit-
ted particles precisely in the same order with respect to some distinguish-
able states, say position, direction, etc. as those present at the instant of
admission of the newcomers. Clearly, this task of increasing H m by keeping
H constant asks for superhuman skills and thus we may employ another
demon whom I shall call the “external demon,” and whose business it is to
admit to the system only those elements, the state of which complies with
the conditions of, at least, constant internal entropy. As you certainly have
noticed, this demon is a close relative of Maxwell's demon, only that to-day

* See also Appendix.