On Self-Organizing Systems and Their Environments - Understanding Understanding: Essays on Cybernetics and Cognition - page 10

these fellows don't come as good as they used to come, because before
1927 4 they could watch an arbitrary small hole through which the newcomer
had to pass and could test with arbitrary high accuracy his momentum.
Today, however, demons watching closely a given hole would be unable
to make a reliable momentum test, and vice versa. They are, alas, restricted
by Heisenberg's uncertainty principle.
Having discussed the two special cases where in each case only one
demon is at work while the other one is chained, I shall now briefly describe
the general situation where both demons are free to move, thus turning to
our general eq. (5) which expressed the criterion for a system to be self-
organizing in terms of the two entropies H and H m . For convenience this
equation may be repeated here, indicating at the same time the assignments
for the two demons D i and D e :

d H

t

d
d

H
t

m

H

¥ > H ¥ (5)

m

d

Internal
demon's
results

Internal
demon's
efforts

External
demon's
efforts

External
demon's
results

From this equation we can now easily see that, if the two demons are per-
mitted to work together, they will have a disproportionately easier life com-
pared to when they were forced to work alone. First, it is not necessary that
D i is always decreasing the instantaneous entropy H ,or D e is always increas-
ing the maximum possible entropy H m ; it is only necessary that the product
of D i 's results with D e 's efforts is larger than the product of D e 's results with
D i 's efforts. Second, if either H or H m is large, D e or D i respectively can take
it easy, because their efforts will be multiplied by the appropriate factors.
This shows, in a relevant way, the interdependence of these demons.
Because, if D i was very busy in building up a large H , D e can afford to be
lazy, because his efforts will be multiplied by D i 's results, and vice versa. On
the other hand, if D e remains lazy too long, D i will have nothing to build
on and his output will diminish, forcing D e to resume his activity lest the
system ceases to be a self-organizing system.
In addition to this entropic coupling of the two demons, there is also an
energetic interaction between the two which is caused by the energy
requirements of the internal demon who is supposed to accomplish the
shifts in the probability distribution of the elements comprising the system.
This requires some energy, as we may remember from our previous
example, where somebody has to blow up the little balloons. Since this