Wednesday, November 6, 2013

Sequences and Analogies, Part II

Part I, II

Abstract

Previously, I wrote about Professor Douglas Hofstadter's claim that analogy is at the core of human intelligence. Although I agree with Hofstadter to a certain extent, I faulted him for focusing on language and symbols instead of investigating the root of the phenomenon. In this post, I argue that there is something that is even more fundamental than analogy: the sequence. I further argue that the neuronal mechanism responsible for discovering analogies can only work while the brain is asleep.

Temporal Proportions

Analogy comes from the Greek ἀναλογία (analogia), a word that means 'proportion' or 'proportionality'. When we think of proportionality, we usually think of geometry. For example, we can say that two triangles of different sizes are analogous if their sides are proportional. I think the ancient Greeks hit the nail right on the head. In this article, I defend the hypothesis that the mechanism used by the brain to make analogies is also based on proportionality. However, in the brain, the proportions are not measured in units of length but units of time.

Proportional Sequences

One of the curious things about analogies is that we have no recollection of learning them. They seem to suddenly materialize into our consciousness out of nowhere. We can safely surmise that the process of recognizing and establishing analogies is automatic. We can further assume that memory is organized in such a way as to make it easy for a neural mechanism to examine two chunks of knowledge and determine whether or not they are analogous, i.e., proportional.

Unlike Hofstadter, I believe that the primary function of intelligence is to make predictions, not analogies. It just so happens that predictions are possible only if recorded events are stored in sequences of patterns. The chunking ability of memory that Hofstadter is so fond of is simply the result of its hierarchical structure. Each branch of the hierarchy corresponds to a chunk. In the Rebel Science model of intelligence, a chunk is a single sequence of up to seven nodes. A node can be either another chunk or a sensory pattern. Sequences do not have fixed timing. The temporal intervals between the nodes in a sequence can vary but their proportions are invariant.
In the figure above, a yellow-filled circle represents a sequence or chunk of knowledge. I hypothesize that the brain can replay the sequences during sleep and determine whether or not any two sequences are proportional. If they are, a link is established between the two to form an analogy. The reason that analogy discovery must be done during sleep is that the sequences must be played back and that would disrupt normal brain function and behavior. During waking hours, the activation or recall of one sequence triggers the recall of another if they are analogous. I believe that all types of analogies are based on sequence timing comparisons.

Note: I am hard at work incorporating all of these principles into the Rebel Science Speech program. I hope to release a demo as soon as it is ready. Hang in there.

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