= 27d567bc2d48d9f40e9ccc20ea370b15)
Exploring the Idea Space Efficiently
Simon is writing a calculus textbook. Since there are a lot of textbooks on the market, he wants to make his distinctive by including a lot of original examples. To do this, he decides to first check what sorts of examples are in some of the other books, and then make sure to avoid those. Unfortunately, after skimming through several other books, he finds himself completely unable to think of original examples—his mind keeps returning to the examples he's just read instead of coming up with new ones.
What he's experiencing here is another aspect of priming or anchoring. The way it appears to happen in my brain is that it decides to anchor on the examples it's already seen and explore the idea-space from there, moving from an idea only to ideas that are closely related to it (similarly to a depth-first search)
At first, this search strategy might not seem so bad—in fact, it's ideal if there is one best solution and the closer you get to it the better. For example, if you were shooting arrows at a target, all you'd need to consider is how close to the center you can hit. Where we run into problems, however, is trying to come up with multiple solutions (such as multiple examples of the applications of calculus), or trying to come up with the best solution when there are many plausible solutions. In these cases, our brain's default search algorithm will often grab the first idea it can think of and try to refine it, even if what we really need is a completely different idea.
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Spock's Dirty Little Secret
Related on OB: Priming and Contamination
Related on LW: When Truth Isn't Enough
When I was a kid, I wanted to be like Mr. Spock on Star Trek. He was smart, he could kick ass, and he usually saved the day while Kirk was too busy pontificating or womanizing.
And since Spock loved logic, I tried to learn something about it myself. But by the time I was 13 or 14, grasping the basics of boolean algebra (from borrowed computer science textbooks), and propositional logic (through a game of "Wff'n'Proof" I picked up at a garage sale), I began to get a little dissatisfied with it.
Spock had made it seem like logic was some sort of "formidable" thing, with which you could do all kinds of awesomeness. But real logic didn't seem to work the same way.
I mean, sure, it was neat that you could apply all these algebraic transforms and dissect things in interesting ways, but none of it seemed to go anywhere.
Logic didn't say, "thou shalt perform this sequence of transformations and thereby produce an Answer". Instead, it said something more like, "do whatever you want, as long as it's well-formed"... and left the very real question of what it was you wanted, as an exercise for the logician.
And it was at that point that I realized something that Spock hadn't mentioned (yet): that logic was only the beginning of wisdom, not the end.
Of course, I didn't phrase it exactly that way myself... but I did see that logic could only be used to check things... not to generate them. The ideas to be checked, still had to come from somewhere.
But where?
When I was 17, in college philosophy class, I learned another limitation of logic: or more precisely, of the brains with which we do logic.
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