I have noticed when talking with experts that they cannot wrap their minds around the depths of my ignorance. Mathematicians when I tell them I have a poor track record with math and would like them to start at something simple, inevitably don’t believe me and start with something hard.
I think the answer is that they understand math so well that they have forgotten what it’s like not to understand math and in some sense can’t imagine it, or can’t conceive of it. Obviously they know that there are people who understand math less well than they do — it’s the basis of their livelihood that they possess an uncommon skill, and they, many of them, have the additional job of teaching math to people who are ignorant of it. But in another sense they can’t think it. They cannot look at a mathematical truth that is obvious to them and see it as non-obvious. Just as we, the literate (assuming you are not listening to someone read this blog to you) cannot look at written words and view them as the illiterate do — as meaningless squiggles.
We just can’t.
This wouldn’t be a problem if the moves that led us to our current way of looking at things — our expertise, our competence — were all inevitable and all correct. But some of them aren’t. Some of them, were wrong, either just flat wrong, or wrong in the sense that foreclosed other, better options.
And this is a problem because their wrongness is invisible to us.
We need techniques for unlearning the blindness that comes of expertise, and viewing the world as the ignorant do.