3.4 The General Structure of Cognitive Dynamics: Analysis and Synthesis 43
metaphor Kampis uses is that of Lego blocks, combining to form bigger Lego structures. Com- pound structures may in turn be combined together to form yet bigger compound structures. A self-generating system is basically the same concept as a component-system, but understood to be computable, whereas Kampis claims that component-systems are uncomputable.
Next, in SGS theory there is also a notion of reduction (not present in the Lego metaphor): sometimes when components are combined in a certain way, a “reaction” happens, which may lead to the elimination of some of the components. One relevant metaphor here is chemistry. Another is abstract algebra: for instance, if we combine a component f with its “inverse” com- ponent f~', both components are eliminated. Thus, we may think about two stages in the interaction of sets of components: combination, and reduction. Reduction may be thought of as algebraic simplification, governed by a set of rules that apply to a newly created compound component, based on the components that are assembled within it.
Formally, suppose C1, C2,... is the set of components present in a discrete-time component- system at time t. Then, the components present at time t+1 are a subset of the set of components of the form
Reduce( Join(C;(1), ...,Ci(r)))
where Join is a joining operation, and Reduce is a reduction operator. The joining operation is assumed to map tuples of components into components, and the reduction operator is assumed to map the space of components into itself. Of course, the specific nature of a component system is totally dependent on the particular definitions of the reduction and joining operators; in following chapters we will specify these for the CogPrime system, but for the purpose of the broader theoretical discussion in this section they may be left general.
What is called the “cognitive equation” in Chaotic Logic [Goe94] is the case of a SGS where the patterns in the system at time ¢ have a tendency to correspond to components of the system at future times t+ s. So, part of the action of the system is to transform implicit knowledge (patterns among system components) into explicit knowledge (specific system components). We will see one version of this phenomenon in Chapter 14 where we model implicit knowledge using mathematical structures called “derived hypergraphs”; and we will also later review several ways in which CogPrime’s dynamics explicitly encourage cognitive-equation type dynamics, e.g.:
e inference, which takes conclusions implicit in the combination of logical relationships, and makes them implicit by deriving new logical relationships from them
e map formation, which takes concepts that have often been active together, and creates new concepts grouping them
e association learning, which creates links representing patterns of association between entities
e probabilistic procedure learning, which creates new models embodying patterns regarding which procedures tend to perform well according to particular fitness functions
3.4.2 Analysis and Synthesis
Now we move on to the main point of this section: the argument that all or nearly all focused cognitive processes are expressible using two general process-schemata we call synthesis and
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