# Strategies, Counter-examples and the UnAha! Experience

I stopped for coffee and a chat with Peter Lambert-Cole at Highland Coffee in Baton Rouge. Peter is a mathematics graduate student at LSU and works on low-dimensional topology problems (knots, doughnuts and such). So naturally our conversation took a mathematical turn.

It is funny how a conversation with the right person will sometimes help me connect dots in my own thinking. Talking with Peter helped me figure out something about anti-strategies.

I had completely forgotten about a post I did a long time about the use of counter-examples in mathematics, called the UnAha! Experience (the post has no equations, just pictures, so don’t be afraid to click).  The subject of counter-examples came up naturally in our chat, but the connection struck me as I was driving away from Baton Rouge: counter-examples are anti-strategies. The evil twins of strategies if you will.

Here’s why. A strategy (or cheap trick, to use Tempo terminology) is a flash of insight that helps you organize your muddy thoughts around an ambiguous situation.  The details of the fleshed out concept of cheap trick are in the book, but the key is the flash of insight, an Aha! experience.

The UnAha! experience is nearly identical. It too is a flash of insight that helps you organize your muddy thoughts around an ambiguous situation.  But unlike the cheap trick at the core of a strategy, that helps you organize a course of action, the UnAha! experience allows you to comprehensively scuttle a course of action. Mathematical counter-examples are the clearest instances of this phenomenon. Russell’s “set of all sets that contain themselves” scuttled Frege’s grand program to organize set-theoretic mathematics. Godel’s related manufacture of a true-but-unprovable statement within an axiomatic system scuttled (a significant part of) Hilbert’s program.

The UnAha! is an act of pure destruction masquerading as an act of creation (since counter-examples must be carefully constructed).

If you like the idea that everything we do is simultaneously an act of creation and destruction, the distinction vanishes. The Aha! and UnAha! become exactly the same thing. In an adversarial situation, your Aha! is somebody else’s UnAha! and vice-versa.

Though the first edition of Tempo doesn’t venture too deeply into adversarial decision-making, beyond a couple of passing comments, recent conversations like this one and an earlier one in Atlanta with Hosh Hsiao have helped me clarify my thoughts significantly, and I suspect I’ll be able to include a chapter on adversarial decision-making in the next edition, whenever I get around to that.

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