This raises a question: what does it mean to "understand" a proof?
Good question; what does it mean to understand anything?
Biologically, it means a sequence of neural firings in the cerebral cortex have occurred, which result in the mental state associated with "I get it!"
I would try to model this in the sense of Kolmogorov complexity, where the brain constructs a program which generates the same data as the object to be understood.
-- Rich
How do you know there is any specific mental state that constitutes understanding this or that?
Suppose we wish to understand the geography of the United States. What would it mean for the brain to "construct a program which generates the same data as the object to be understood"?
Nearly non-sequitur.
Smokin' ;-)
...Jim Thompson
A 'specific' state? Undoubtedly, there are a large number of such states.
The brain is a dynamical system. It evolves through a sequence of states; mental states = brain states. Some of them correspond to "I don't get it", others correspond to "I get it".
Get it?
It means you could ask the student to draw a map of USA, and he responded, correctly.
-- Rich
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