A system is said to be self-organizing if, after observing the input
and output of an unknown phenomenon (transfer relation), the system
organizes itself into a simulation of the unknown phenomenon.
Implicit in this definition is the requirement that the self-organizing
machine (SOM) not possess a preassigned coordinate system. In fact it
is just this ability to acquire that coordinate system implicit in the
input-output spaces which define the phenomenon that we designate as
self-organization. Thus any a priori information programmed into the
SOM by means of, for example, stored or wired programs, constrains
the SOM and limits its ability to adapt. We do not mean to suggest
that such preprogramming is not useful or desirable; merely that it is
inconsistent with the requirement for self-organization. As shown in
Figure 2, it is the given portion of the environment which the SOM is
to simulate, which via the defining end spaces, furnishes the SOM with
all the data it needs to construct the coordinate system intrinsic to
those spaces.
The motivation for requiring the ability to simulate as a feature of
self-organization stems from the following examples.
Consider the operation of driving an automobile. Figure 3 depicts the
relation characterized by a set of inputs; steering, throttle, brakes,
transmission, and a set of outputs; the trajectory. Operation of the
automobile requires a device (SOM) which for a desired trajectory can
furnish those inputs which realize the desired trajectory. In order to
provide the proper inputs to the automobile, the SOM must contain a
simulation of ⨍⁻¹(x).
[Illustration: Figure 2—Simulation of (a portion of) the environment]
[Illustration: Figure 3—Simulation of a relation]
Since ⨍(x) is completely defined in terms of the inputs and the
resulting trajectories, exposure to them provide the SOM with all the
information necessary to simulate ⨍⁻¹(x). And if the SOM possesses
internal processes which cause rearrangement of the input-output
relation of the SOM to correspond to ⨍⁻¹(x) in accordance with the
observed data, the SOM can operate an automobile. It is this internal
change which is implied by the term “self-organizing,” but note that
the instructions which specify the desired organization have their
source in the environment.
As a second example consider adaptation to the environment. Adapt
(from Webster) means: “to change (oneself) so that one’s behavior,
attitudes, _etc._, will conform to new or changed circumstances.
Adaptation in biology means a change in structure, function or form
that produces better adjustment to the environment.” These statements
suggest a simulation because adjustment to the environment implies
survival by exposing the organism to the beneficial rather than the
inimical effects of the environment. If we represent the environment
(or portion thereof) as a relation as shown in Figure 2, we note that
the ability to predict what effect a given disturbance will have is due
to a simulation of the cause-effect relation which characterizes the
environment.
It would be a mistake to infer from these examples that simulation
preserves the appearance of the causes and effects which characterize
a relation. We clarify this situation by examining a relation and its
simulation.
Consider the relation between two mothers and their sons as pictured
in Figure 4. Observe that if symbols (points) are substituted for the
actual physical objects (mothers and sons), the relation is not altered
in any way. This is what we mean by simulation and this is how a SOM
simulates. It is not even necessary that the objects, used to display
the relation, be defined; _i.e._, these objects may be primitive.
(If this were not so, no mathematical or physical theory could model
the environment.) The main prerequisite is sufficient resolution to
distinguish the objects from each other.
[Illustration: Figure 4—A relation of objects—displayed and simulated]