Maps and Focused Attention
The cause of map formation is important to understand. Interestingly, small maps seems to form by the logic of focused attention, as well as hierarchical maps of a certain nature. A few more comments on this may be of use.
The nature of PLN is that the effectiveness of reasoning is maximized by minimizing the number of independence assumptions. If reasoning on N nodes, the way to minimize independence assumptions is to use the full inclusion-exclusion formula to calculate interdependencies between the N nodes. This involves 2^N terms, one for each subset of the N nodes. Very rarely, in practical cases, will one have significant information about all these subsets. However, the nature of focused attention is that the system seeks to find out about as many of these subsets as possible, so as to be able to make the most accurate possible inferences, hence minimizing the use of unjustified independence assumptions. This implies that focused attention cannot hold too many items within it at one time, because if N is too big, then doing a decent sampling of the subsets of the N items is no longer realistic.
So, suppose that N items have been held within focused attention, meaning that a lot of predicates embodying combinations of N items have been constructed and evaluated and reasoned on. Then, during this extensive process of attentional focus, many of the N items will be useful in combination with each other — because of the existence of predicates joining the items. Hence, many HebbianLinks will grow between the N items — causing the set of N items to form a map.
By this reasoning, it seems that focused attention will implicitly be a map formation process — even though its immediate purpose is not map formation, but rather accurate inference (inference that minimizes independence assumptions by computing as many cross terms as is possible based on available direct and indirect evidence). Furthermore, it will encourage the formation of maps with a small number of elements in them (say, N<10). However, these elements may themselves be ConceptNodes grouping other nodes together, perhaps grouping together nodes that are involved in maps. In this way, one may see the formation of hierarchical maps, formed of clusters of clusters of clusters..., where each cluster has N<10 elements in it. These hierarchical maps manifest the abstract dual network concept that occurs frequently in OCP philosophy.
It is tempting to postulate that any intelligent system must display similar properties — so that focused attention, in general, has a strictly limited scope and causes the formation of maps that have central cores of roughly the same size as its scope. If this is indeed a general principle, it is an important one, because it tells you something about the general structure of derived hypergraphs associated with intelligent systems, based on the computational resource constraints of the systems.
The scope of an intelligent system's attentional focus would seem to generally increase logarithmically with the system's computational power. This follows immediately if one assumes that attentional focus involves free intercombination of the items within it. If attentional focus is the major locus of map formation, then — lapsing into SMEPH-speak — it follows that the bulk of the ConceptVertices in the intelligent system's derived hypergraphs may correspond to maps focused on a fairly small number of other ConceptVertices. In other words, derived hypergraphs may tend to have a fairly localized structure, in which each ConceptVertex has very strong InheritanceLinks pointing from a handful of other ConceptVertices (corresponding to the other things that were in the attentional focus when that ConceptVertex was formed).