Our comforting conviction that the world makes sense rests on a secure foundation: our almost unlimited ability to ignore our ignorance.

That is from Daniel Kahneman, Thinking Fast and Slow, p. 201. The chapter is called “The illusion of understanding.”

I am toying with the following formulation for explaining the significance of ignorance: the policy wonk’s perspective is that he can see everything clearly, from the big picture to the little details; my perspective is that I am groping blindly through a world that is too complex for me to understand.

Also, I am in the process of re-reading the Converse issue of Critical Review, which I first blogged about five years ago. In Jeffrey Friedman’s essay, he raises the issue of how Rush Limbaugh and Paul Krugman could each be sure that he is right.

I think one can model this metaphorically as the outcome of a hill-climbing algorithm where you can get stuck at a local maximum. I will explain this below the fold.A hill-climbing algorithm is a way to solve for the maximum of a function. Imagine that you were plopped down in the middle of some topographically varied terrain and were trying to find the highest mountain peak. Using a hill-climbing algorithm, you would send out small probes in all directions and move in the direction where altitude is increasing. Then repeat, until you get to a point where altitude is declining in every direction.

If there is only one peak in the terrain, this method will find it. But if there are many hills, it is also possible to get stuck at the top of a small hill and never find the peak of the highest mountain.

Think of Limbaugh and Krugman as being stuck on their own hills. Based on where they started, and the paths that their experiences took them, each is at a point where he cannot see any way to improve his understanding of the world by changing his mind. Even though their views are incompatible.

The way to improve a hill-climbing algorithm is to send out distant probes as well as nearby probes. I am not sure how to apply that in this context. Yes, “try to understand the other person’s point of view” is a help. But I don’t think it does the job.