Confidence and inverse relationships

"A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator the smaller the fraction."
-- Leo Tolstoy

I came across this quote and saved it to use this year when my ninth graders and I get to inverse relationships.  I am not sure any of my kids have ever heard of Tolstoy (though maybe they will surprise me...) but I do think some of them will appreciate the comparison to non-math and non-physics concepts.  The idea of having a big ego is certainly something they can relate to, and it's fun that the quote brings in some math vocab.

The quote also makes me think of my current class of AP calculus students.  I've only spent two days with them so I don't know them very well yet, but I got the rundown from their precalc teacher before school started.  Of the eight students, he identified two as the top mathematicians of the group, but noted that they have very different confidence levels.  He says that H is confident almost to the point of cockiness, and he showed this side to me a little already, writing, "I am really good at math" on my first day survey under the question about what does Ms. Pippi need to know about you.  On the other hand is J, who he says is just as bright as H but is constantly doubting herself.  She has already come for help after school with the trig value review we were doing, and she phrases any description of what she did in terms of a question.  She is underconfident to the extreme, and one of my goals this year is to try to change that a bit.

By Tolstoy's definition, J is a "larger fraction" than H, and theoretically a better person, if that's how you interpret the quote.  But I can't help thinking that it's not as simple as an inverse relationship.  Surely a huge ego is a detriment, but there's also a basic floor level of reasonable self esteem.  Constantly bashing yourself isn't helpful.  So, maybe more of a Gaussian shaped curve than an inverse function, Mr. Tolstoy.