Let S be any system, as above. Let it and ot denote the input to and output of S at time t,
respectively. That is, ot is that part of St which, if it were changed, could in certain circumstances cause an immediate change in Et+1; and it is that part of Et which, if it were changed, could in certain circumstances cause an immediate change in St+1.
Then we may define the behavioral structure of an entity S over the interval (r,s) as the fuzzy
set B[S;(ir,…,is)] = {Em(ir,or+1),Em(ir+1,or+2),…,Em(is,os+1), St[Em(ir,or+1),Em(ir+1,or+2),…,Em(is,os+1)]}. This is a complete record of all the patterns in the behavior of S over the interval (r,s).
Then what is a model of S, on the interval (r,s)? It is a function MS so that B[MS;(ir,…,is)] is as close to B(S;(ir,…,is)] as possible. In other words, a good model is a simple function of which one can say "If S worked like this, it would have behaved very much the same as it actually did."
In order to specify what is meant by "close", one might define the magnitude of a fuzzy set Z,
%%Z%%, as the sum over all z of the degree to which z is an element of z. Then, %%Y-Z%%
will be a measure of the size of the total difference between two fuzzy sets Y and Z.
For instance, assume MS is a Turing machine program; then the best model of S might be
defined as the function MS which minimized %MS%*%%B[MS;(ir,…,is)]-B[S,(ir,…,is)]%%, where
%MS% denotes the size of MS(perhaps (Ms)=%L(Ms)%T).
In general, one good way to go about finding models is to look for functions Y so that
%Y%*%%[Y(S(ip)),…,Y(S(iq))]-[S(op+1),…,S(oq+1)]%% is small on some interval (p,q). Such
functions — simple models of the structures of particular behaviors — are the building blocks out of which models are made. Combining various such functions can be a serious problem, so that it may not be easy to find the best model, but it is a well-defined problem.
That takes care of behavior. Now, what about mind? Let us define the structure St[S;(r,s)] of
a system S on the interval (r,s) as the set of patterns in the ordered set [Sr,…,Ss], where St, as above, denotes the state of S at time t. This is the actual structure of the system, as opposed to B[S;(r,s)], which is the structure of the system’s behavior. In the case where S is a human or some other organism, through psychology we only have access to B[S;(r,s)], but through biology we can also study St[S;(r,s)].
We may define a mind as the structure of an intelligent system. This means that a mind is not
a physical entity but rather a Platonic, mathematical form: a system of functions. Mind is made
of patterns rather than particles.
The central claim of this book is that a certain structure, the master network, is part of the
mind of every intelligent entity. One might make this more precise in many ways. For instance,
define the general intelligence of a system to be the average of its R.S.-intelligence, its S.-
intelligence, and its L.-intelligence. Then I propose that:
Hypothesis 4.1: There is a high correlation coefficient between 1) the degree with which the
master network is an element of St[S;(r,s)], and 2) general intelligence.
If this is too much to believe, the reader may prefer a weaker statement:
Hypothesis 4.2: If A is more L.-, S.- and R.S.-intelligent than B, the master network is almost never less prominent in A than in B.
These hypotheses will be considered again in Chapter 12, once the master network has been
described in detail.
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