A Serendip experience

The Three Doors of Serendip:
"Experimental" Understanding, continued

Door image from http://www.woodstone.com/photoalbum7.html

So ... you've tried out Three Doors of Serendip (Mark II), and persuaded yourself that indeed you're better off switching as opposed to staying? If you've done some serious experimenting, you'll know now that you win twice as often (or collect money twice as fast) by using the strategy of switching as you do using the strategy of staying. And that if you randomly switch and stay on succesive trials you win about half the time, which is better than always staying but less good than always switching.

What you've achieved is what we might call "experimental" understanding, which is to say a kind of understanding which results from having an hypothesis which predicts observations yet to be made and then making those observations to see whether your prediction holds or not. Actually, its a kind of understand which results from doing these things "consciously". If you started with Three Doors of Serendip (Mark 1), you'll know that the process of coming to an understanding based on observations can in fact be done "unconsciously". So, what's the difference between "intuitve" understanding and "experimental" understanding? If they're different, what's the relation between them? "Experimental" understanding is sometimes referred to as "scientific" understanding, implying that it is somehow better. Is it? Always, or only in some cases? If ever, why?

To explore those questions, let's think a bit about what you did to achieve "experimental" understanding. First, you had to have at least some intuition about how best to play the game, at least one "strategy" in mind. Then, you had to have some alternative strategy in mind, so that you could design a new set of observations to compare the results of the two. Then, you had to have made enough observations to be certain that effectively compared the two. Then you had to decide whether there could in principle be some OTHER strategy that might be better than either of the ones you tried. Only after being sure that all possible strategies had been tested could you be sure that you had adequate "experimental" understanding.

Two points follow from this:

Nature of experimentation, have to have intuition, have to analyze, think of possibilities (depends on logic)

Link to reaction.html

Make clear that experimentation can be done unconsciously

get James, "not enough regularity" in here?

be explicit about when expt understandings better (not when want truth/reliability), yes when can be reasonably sure of possible alternatives

note that just as intuitive influences experimental so experimental influences intuitive (will react differently to choice games in future).
"Hands on" understanding
intuitive, unconscious
"Experimental" understanding
conscious, observational
"Rational" understanding
conscious, analytical, logical