I took a statistics course at MIT. I would go study and do problems, and have high confidence that I understood the material. Then I’d go to the lecture, and be more confused than I was when I entered the classroom. Thus, I discovered that some teachers were capable of conveying negative knowledge, so that after listening to them, I knew less than I did before.

It was also clear that knowledge varies considerably in quantity among people, and this convinced me that real knowledge varies over a very wide range.

Then I encountered people who either did not know what they were talking about, or were clearly convinced of things that were wrong, and so I learned that there was imaginary knowledge.

Once I understood that there was both real and imaginary knowledge, I concluded that knowledge is truly complex.

– Hillel J. Chiel, Case Western Reserve University

Source: American Mathematical Monthly, Vol. 120, No. 10, p. 923 (December 2013)