Had a chat with someone the other day who put forward a good analogy for people. In this view, there are two axes (i.e. plural of axis) - ignorance and arrogance.
No arrogance, no ignorance: a wise person.
Arrogance, no ignorance: well, is a pain, but at least the arrogance is somewhat justified.
No arrogance, ignorance: can cause a compassionate person
Arrogance, ignorance: the worst combination - a fool who is unwilling to be corrected.
We talked about it in the context of a particular group of people fitting the last category, but it would not illumine to go into which group or to whom I was conversing - if anything, it would probably engender the second category ^_^