p.468 complexity frequently takes the form of hierarchy... Hierarchy, I
shall argue, is one of the central structural schemes that the architect of complexity uses.
p.469 [footnote] By hierarchy I mean the partitioning in conjunction with
the relations that hold among its parts.
p.469 we propose to identify social hierarchies not by observing who lives
close to whom but by observing who interacts with whom.
p.471 The time required for the evolution of a complex form from
simple elements depends critically on the numbers and distribution of potential intermediate stable forms.
p.472 Let us turn now to... human problem-solving processes.
Consider, for example, the task of discovering the proof for a difficult theorem... The process usually involves a
great deal of trial and error. Various paths are tried; some are abandoned, others are pushed further. Before a solution
is found, a great many paths of the maze may be explored... the trial and error is not completely at random or blind;
it is, in fact, rather highly selective. The new expressions that are obtained by transforming given ones are examined to
see whether they represent progress toward the goal. Indications of progress spur further search in the same direction; lack
of progress signals the abandonment of a line of search.
p.472 Problem solving requires selective trial and error.
p.472 A little reflection reveals that cues signaling
progress play the same role in the problem-solving process that stable intermediate forms [JLJ -
see quote p.471 above] play in the biological evolutionary process... Suppose that the task is to open a safe whose
lock has ten dials, each with one hundred possible settings, numbered from 0 to 99. How long will it take to open the safe
by a blind trial-and-error search for the correct setting? Since there are 100 [to the power of] 10 possible settings,
we may expect to examine about one-half of these, on the average, before finding the correct one-that is, fifty billion billion
settings. Suppose, however, that the safe is defective, so that a click can be heard when any one dial is turned to the correct
setting. Now each dial can be adjusted independently, and does not need to be touched again while the others are being set.
The total number of settings that has to he tried is only 10 X 50, or five hundred. The task of opening the safe has
been altered, by the cues the clicks provide, from a practically impossible one to a trivial one. [JLJ - this has
a direct application to positional strategy in game theory. We can defeat the "horizon effect" with this concept]
p.472-473 human problem solving, from the most blundering to the most
insightful, involves nothing more than varying mixtures of trial and error and selectivity. The selectivity derives
from various rules of thumb, or heuristics, that suggest which paths should be tried first and which leads are promising.
p.473 When we examine the sources from which the problem-solving system,
or the evolving system, as the case may be, derives its selectivity, we discover that selectivity can always be equated
with some kind of feedback of information from the environment.
p.474 in the long run, the behavior of any one of the components depends
in only an aggregate way on the behavior of the other components.
p.477 Apart from requirements of direct interaction, most roles impose
tasks and responsibilities that are time consuming. One cannot, for example, enact the role of "friend" with large numbers
of other people. [JLJ - Simon obviously has not used a Facebook account.]
p.477 From our discussion of the dynamic properties of nearly decomposable
systems, we have seen that comparatively little information is lost by representing them as hierarchies. Subparts belonging
to different parts only interact in an aggregative fashion - the detail of their interaction can be ignored.
p.477 The fact, then, that many complex systems have a nearly decomposable,
hierarchic structure is a major facilitating factor enabling us to understand, to describe, and even to "see" such systems
and their parts.
p.479 The distinction between the world as sensed and the
world as acted upon defines the basic condition for the survival of adaptive organisms. The organism must develop correlations
between goals in the sensed world and actions in the world of process.
p.481 How complex or simple a structure is depends critically
upon the way in which we describe it... My thesis has been that one path to the construction of a nontrivial theory
of complex systems is by way of a theory of hierarchy.
p.482 In their dynamics, hierarchies have a property, near-decomposability,
that greatly simplifies their behavior... In both science and engineering, the study of "systems" is an increasingly
popular activity. Its popularity is more a response to a pressing need for synthesizing and analyzing complexity
than it is to any large development of a body of knowledge and technique for dealing with complexity.
