Magic... Or... Math

just some fun today....

Last weekend I linked to this post from Keith Devlin talking about "breakthroughs" happening when disparate mental parts make certain connections (producing the so-called "Eureka" moment); in his case, he related it to mountain biking:

http://devlinsangle.blogspot.com/2014/03/how-mountain-biking-can-provide-key-to.html

I thought back to Dr. Devlin's piece the other day, when I experienced my own simple "Aha" moment in a different context:

Fawn Nguyen tweeted a link to a really fun puzzle on the Web:

http://www.cs.nyu.edu/~dodis/magic-ball.swf

It's called the "Flash Mind Reader" and if you're not familiar with it, go play with it RIGHT NOW, so I don't spoil it for you with what follows.
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I can usually figure out puzzles fairly quickly from having seen so many and being familiar with them… when I'm NOT familiar with a given puzzle, then I'm as big a sucker as anyone! And this puzzle initially stumped me (even though it was just a variation off some other tricks I've seen). In frustration I put it aside, did some other things, and then went to take a shower, the puzzle cast from my mind.
My shower-head spews forth a broad stream of droplets… somehow my mind suddenly flashed with the image of those droplets being the array of right-hand number choices given for the puzzle… in a moment (which I still can't well-explain) the thought occurred that if some subset of those droplets, which looked random, was actually always identical to one another, and, if my attention could somehow be consistently drawn to THAT subset, than this would solve the puzzle. Stepping out of the shower I needed only think about it for another 60 seconds to realize how the problem worked. (If you don't know how it works even after this hint I've given, you can always just google "flash mind reader" to find the solution somewhere; I won't spell it out here.)

Decades ago, Arthur Koestler promoted his notion of "bisociation" between two autonomous mental constructs as being the key to not only scientific and artistic creativity, but to humor as well. Some of the best jokes, in short, result from a comedian weaving together an analogy that the audience never saw coming! (as a complete sidelight, perhaps worth noting that Douglas Hofstadter's latest tome, Surfaces and Essences, also focuses on the central role of analogies in our thinking processes; not just for creativity but for all thought).
Interesting too, that the mathematician-writers of the animated Simpsons TV show, likewise discern a strong link between their senses of humor and their mathematical ability. As author Simon Singh noted of the jokes/math-puzzle linkage: "Both have carefully constructed setups, both rely on a surprise twist, and both effectively have punch lines. Indeed, the best puzzles and jokes make you think and smile at the moment of realization." So who says that underlying mathematics there isn't a lot of fun to be had... be it mountain biking, writing jokes for Homer Simpson, working out puzzles, or showering!