As a followup to my last post, here is the paper that discusses vector subtraction implementation in neurons in detail (the first one in the search):
Before I read it, I want to record what I think is a novel and useful idea, so that if it comes up in the paper I can pat myself on the back (publicly) for having thought of it independently.
Regarding the neural basis of analogy-making, which was the topic of my final paper for Bickle, I have an idea how analogies might be formed using the vector subtraction paradigm. Reference my previous post to get a feel for what I'm talking about.
If you are given two initial points, you can calculate the vector that directly connects them. The connecting vector is the instruction for getting from point A to point B. If you are given a third point C, and asked to "do the same thing," you can move use the instruction from the first set of points to move from point C to an unknown point D. Thus, you've made a simple visual analogy.
If the dimensions involved are properties of things (eg tallness, heavyness, hotness...) the same calculations could be used to make a physical/verbal analogy. Omitting some dimension (or leaving it variable) would be the equivalent of "slipping" in Hofstadter's sense, and would allow the destination point D to fall across a range of values. If one of those values falls within the "conceptual halo" of an existing concept, then that concept can be used to complete the analogy. Otherwise a new concept can be created at the destination point, with a "halo" that's defined by the range of values that were suggested by allowing dimensions in the directional vector to remain variable.
Why is this important? If you give credence to the notion that analogy-is-creativity-is-intelligence, then this account goes a very long way in explaining the neural basis for human intelligence. I note that Jeff Hawkins makes this claim also (on pg 183 of On Intelligence). It could also be used as a a guide to identifying cognition in other systems, and in designing it.
Its such a simple elegant explanation!
Its very deeply rewarding to be able to draw connections between disparate authors (in this case Hofstadter, Baum, Hawkins, and Bickle), especially because I don't see any references to each other in their work. It seems implausible that they'd all be unaware of each other... I wonder if the non-citation is a result of dislike or disagreement?