I was chatting with Sylvain today and we ended up discussing about problems, gurus and modesty. He introduced me to the circle of knowledge metaphor, who he originally got from Tom Klaasen:

Imagine to draw a circle and put everything you know and “everything you know you don’t know” into it. Outside the circle remains what “you don’t even know it exists”.

As you learn something new, the area of the circle increases. But this also means that as you increase the stuff you know, you also increase the stuff you know you don’t know, and, usually, the second one grows faster than the first.

This is the reason why wise and knowledge people usually say (and truly believe!) they don’t know much at all, because their “know/know I don’t know” ratio decreases as their learning progresses.

Ultimately, as your circle increases, you end up learning the Socratic lesson:

I know I don’t know

which, using the circle of knowledge, means that your “know/know I don’t know” ratio dropped to zero as your knowledge reached infinite.

Food for thought.

Update: Sylvain also points me to this very interesting paper about the opposite of the above: Inflated Self-Assessments.

Another Update: Tom writes me privately to say that in the original metaphor he used, the “everything you know you don’t know” is actually the border of the circle, which grows as the circle grows. He also believes in a fractal nature of that border since he believes that its dimension grows more than linearly with the circle radius. Well, the math goes short here, but the idea is cool and appealing, very visual.