Example #4: Logarithms. Jeff thinks we have a reference frame for everything! Every word, every idea, every concept, everything you know has its own reference frame, in at least one of your cortical columns and probably thousands of them. Then displacement cells can encode the mathematical transformations of logarithms, and the relations between logarithms and other concepts, or something like that. I tried to sketch out an example of what he might be getting at in the next section below. Still, I found that his discussion of abstract cognition was a bit sketchier and more confusing than other things he talked about. My impression is that this is an aspect of the theory that he’s still working on.
George Lakoff’s whole shtick is this! He’s a linguist, so he frames it in terms of metaphors; “abstract concepts are understood via metaphors to concrete spatial/sensory/movement domains”. His book “Where Mathematics Comes From” is a in depth exploration of trying to show how various mathematical concepts ground out in mashups of physical metaphors.
Jeff’s ideas seem like they would be the neurological backing to Lakoff’s more conceptual analysis. Very cool connection!
Yeah! Somehow I had the memory that the two of them actually wrote a book together on the topic, but I just checked and it looks like that’s not the case.
Great post!
George Lakoff’s whole shtick is this! He’s a linguist, so he frames it in terms of metaphors; “abstract concepts are understood via metaphors to concrete spatial/sensory/movement domains”. His book “Where Mathematics Comes From” is a in depth exploration of trying to show how various mathematical concepts ground out in mashups of physical metaphors.
Jeff’s ideas seem like they would be the neurological backing to Lakoff’s more conceptual analysis. Very cool connection!
Ooh, sounds interesting, thanks for the tip!
Hofstadter also has a thing maybe like that when he talks about “analogical reasoning”.
Yeah! Somehow I had the memory that the two of them actually wrote a book together on the topic, but I just checked and it looks like that’s not the case.