I'm watching Andrey who is trying to reach across a small table to grab his toy car. The car is too far and while the table is small he keeps trying even though he can't reach it and it would be very easy for him to go around the table and take the car. Still, he persists in using his (not working) method even after I tell him about the alternative.
This reminded me about what Douglas Hofstadter called a difference between physical distance and problem distance (Godel, Escher, Bach: an Eternal Golden Braid, p.612). When a dog wants to get his favorite bone that is just few feet away, but on another side of a fence with a gate not too far away he has two choices: 1) run up to the fence, stand next to it and bark; or 2) get to the open gate and double back to the bone. While the second options seems to be counter-intuitive (as it increases the distance to the bone), it actually brings the dog closer to it.
What needs to "click" in dog's brain for this to happen? What's that new level of abstraction that allows to solve this problem? What does this solution in some abstract "problem space" have to do with the real material world, where this problem is being solved in a similar way?
Last time this happened six weeks ago. After brief one-time experience with a real fence Andrey knows how to fetch a toy he wants even though he may need initially to move away from his target. I continue being amazed how quickly he learns even from one-time experiences.