I keep criticizing connecting the dots thinking as overly narrow. It’s just now occurred to me that my fundamental objection is that connecting the dots is a finite game when we need to be playing an infinite game.
Finite vs. infinite games is a distinction philosopher James Carse makes in his book Finite and Infinite Games. A finite game is a game with a clear set of rules and boundaries that you play to win. An infinite game, on the other hand, is a game you play with the primary goal of continuing to play. Carse makes a compelling case that infinite games are far more interesting and that we should be looking for opportunities to transform whatever game we are playing from finite to infinite. If you haven’t read it, go find yourself a copy now and read that.
Converting a connecting the dots situation into a solving for pattern exercise is a perfect example of converting a finite game to an infinite game. Rather than seeking the picture cleverly hidden in a series of disconnected dots, solving for pattern opens up the game to the exploration of multiple possibilities and options.
There’s an old joke about baseball umpires discussing calls after a game;
Umpire #1 – I call them as I see them
Umpire #2 – I call them as they are
Umpire #3 – They aren’t anything until I call them
The point about infinite games and about solving for pattern is that you are playing the game and making up the rules as you play.