To speak and understand a language well, an ordinary person must learn thousands of words. To learn the proper use of a single word must involve great numbers of connections between the agents for that word and other agents. What could cause such connections to be made, and what might be their physical embodiments?
Any comprehensive theory of the mind must include some ideas about the nature of the connections among agents. Consider that a person can learn to associate virtually any combination of ideas or words. Does this require us to assume that it is possible for a given K-line agent to become connected, directly, to any of thousands or millions of other agents? That seems out of the question, in view of what we know about connections in the human brain. Many brain cells have fibers that branch out enough to approach many thousands of other cells — but few of them branch out enough to reach millions of other cells, and as far as we know, a mature brain cell can only make new connections to other cells that already lie close to the fibers that branch into or out from it. Furthermore, we do not seem to grow many new brain cells after birth; on the contrary, their number actually decreases. To be sure, brain cells continue to mature for several years, and probably their fibers grow extensively. But no one yet knows whether this comes about as a result of learning new connections or whether it must happen first, to make it feasible for those cells to learn new connections.
Even the arrangements of long-distance connections between our brain cells do not permit direct connection between arbitrary pairs of agents, for those long connections are generally arranged in relatively orderly bundles, less regular but otherwise resembling the parallel pathways from skin to brain. Fortunately, direct connections are not really necessary, for the same reasons that every telephone in the world can easily be connected to any other telephone without the need for connecting a billion separate wires to each house. Instead, telephone systems make their connections indirectly, by using agencies called exchanges that require only moderate numbers of wires. I don't mean to suggest that brains use the sorts of switching-schemes found in telephone systems but only to say that it is not necessary for every K-line agent to directly contact every agent to which it might eventually become linked.
There are several factors that reduce the magnitude of the interconnection problem. First, in order to reproduce the major features of a remembered partial state of mind, it should suffice to activate only a representative sample of its agents. Second, according to our theory of knowledge-trees, most K-lines' connections are indirect to begin with, since they connect only to other, nearby K-line trees. A polyneme, too, need be connected only to a single memorizer agent near each agency. And no K-line needs potential connections to all the agents in any agency, since it is enough to make connections only in a certain level-band.