Hypothesis: A cognitive moment consists of
- Consciously posing a problem (as if the conscious mind forms itself into and then holds a certain receptive mould).
- The mind reflexively searching for solutions (other parts of the brain bouncing around, sometimes fitting themselves into the mould).
- Going with one of the best solutions found within a short period of time
Thinking consisting of a series of these searches. Sometimes a less than optimal solution might be chosen, as in simulated annealing, to avoid local minima.
By likeness to what we know of computerized searching (eg best-fit texture synthesis) we would expect:
- The longer the moment, the more possible solutions that can be considered, and the better the best solution found will be.
- The optimal duration would depend on the problem. Short duration would correspond to simple optimization methods such as hill climbing, longer duration would corrsepond to methods such as Newton's method that make brilliant leaps but require a lot of processing per leap.
- We can pose a problem narrowly or widely. A wide pose will catch oddball new ideas, but be less reliable. Too narrow a focus will be more reliable, except when it fails, in which case it fails completely.
- We can pose a problem with fat-tails. Say that mostly we want close matches, but a few curveballs too.
By likeness to best-fit's ability to copy areas of image:
- Sequential recall involves searching for the memory that follows the current memory, then a memory that follows that, and so on. Sequential recall is a result of narrow focus.
I therefore speculate that:
- Attention Deficit/Hyperactivity Disorder is a tendency to pose problems broadly, and thus make large leaps. In the long run this may find better answers, but in the short term it means people with AD/HD answer slowly and are somewhat scatterbrained.
- The Autistic spectrum disorders represent a combination of narrow focus and fat tails. The narrow focus allowing impressive feats of sequential recall, the fat tails causing odd non-sequeteurs. With the best-fit method of texture synthesis, fat-tailed narrow focus searching produced a kind of chunky soup. Pieces of image arranged poorly, and obsessive repetition of some chunks.
I'm also wondering what the different ways people put together jigsaws (like the one I described in earlier posts) would tell us about how they think. Jigsaws involve lots of searching, so we could observe people's search strategy as they construct one.
Clarification, 9 August 2004: By fat-tails I mean the L1 norm, two-tailed exponential distribution. L1 is harder to optimize for than L2 (corresponding to a Gaussian distribution) but, for many types of data, produces better results once the optimum is found. L2 has curved gradients, you can do the Newton's-method thing and find the minima pretty easily. L1 has flat gradients, you can't pick the minima from local curvature. ... Point being i'm not just hand waving, i have *specific* probability distributions in mind. This is something that could be used to make quantitative predictions about behaviour of normal people vs people with AD/HD and Autism specturm disorders.