What is Understanding?

What is understanding? What do we mean when we say that we understand someone or something?

Some of my friends' wives would claim that they understand their husbands. They live with their husbands and they see their husbands everyday--of course they understand their husbands best. Maybe they do. They know what their husbands like to eat; they are familiar with their sleeping habits and probably knows what they will say or react in certain situations.

But I am constantly amazed at how much husbands can still conceal from their wives. Many I believe only knows less then fifty percent of their husbands' activities. Husbands too shouldn't assume that they know their wives well. Everyone has secret lives.

Which brings me back to my original question: What is understanding? Does understanding a person means knowing how much he weighs, what is her hobby, what is her star sign, how he spends his day at the office? Or is it something deeper?

In school, when we first studied mathematics, we probably did not grasp the relevance of some of the things we were taught. What was the purpose of solving differential equations? Why did we study set theory? We weren't sure, but yet we studied the rules and techniques for manipulating algebraic symbols and became even quite good at solving equations. We probably did very well in the exams too. Obviously, we understood mathematics. Or did we?

If I remember correctly (I read this somewhere when I was a teenager--I could be wrong), it was the famous mathematician John Von Neumann who once remarked: "In mathematics, we don't understand things. We just get familiar with them".

We claim that we understand our spouses. Check again. Maybe it's just familiarity. Or maybe familiarity is understanding?