When we connect two ideas why do we say put two and two together? Why not one and one?

‘Two and two’ is not an accidental turn of phrase. It’s an accurate count: the smallest number of units involved in learning anything.

Pavlov’s classical conditioning is learning at its most basic. Pavlov’s dog learned that the sound of a bell meant food was coming: Bell and food puts one and one together to make two. But how? Through repeated instances in which food and bell arrive together. Two (or more) instances of two (or more) events occurring at the same time caused the dog to make a generalization. (Click here for a Flash animation of the process with me imitating the dog.)

Mind Readers Dictionary: The Podfast : Play in Popup

Mind Readers Dictionary : Play in Popup

Dogs do it, sea slugs do it and of course, even people do it: Yesterday, Sam was nice. Today, Sam was nice. Putting those two (instances) and two (events, attributes or qualities) together, I now have a generalization: Sam co-occurs with niceness. (Click here for a Flash animation of the process). Relying on this new generalization, I have faith that when Sam arrives niceness arrives with him.

The eureka moment in learning is just this turning point, the moment when instead of using instances to build generalizations, we come to rely on the generalization to predict future instances.

The eureka moment is a dividing line between reason and faith. Reason is weighing evidence from instances to make a generalization. Faith is employing the generalization as a reliable predictor of instances.

Eureka (Greek for Aha!) is the root of our word heuristic. A heuristic is a general rule—a generalization that puts two and two together. Eureka moments are exciting. They fill us with optimism. To brighten up the day, nothing compares with discovering a promising new heuristic.

Nothing except losing a heuristic that has outlasted its usefulness. ‘For years I thought Sam was better than me, so I treated him with the utmost deference. But not any more. I’m finally free. . .’ Dismantling a bad generalization can make us sanguine too.

How does one undo a generalization? Through more instances: ‘In the old days, Sam was nice so often that I came to expect it of him. Then, there were a number of instances when Sam wasn’t nice. At first I ignored the change. I gave him the benefit of the doubt. But finally I’d had enough. I realized that Sam was no longer nice.’

Using new instances to correct one’s generalizations is a leap from faith back to reason, from operating on an assumption to refining the assumption. Sometimes it’s just what the doctor ordered. Sometimes it isn’t. When to leap from faith to reason; when to leap from reason to faith—that’s a fundamental question.