Awareness of ignorance

A series of three lectures from David Gross called "The Search for a Fundamental Theory of Reality" [scroll down, April 2006], each about 1hr 40min. There's no math, the guy speaks well, and he won a Nobel prize in physics - three things that rarely come together on the topic.

In the third lecture [1hr 15min in], Gross dismisses the idea of progress in science being like peeling an onion, getting closer and closer to the truth. Instead he sees knowledge as expanding outward, like a growing sphere.

Since ignorance exists at the boundary of knowledge, more knowledge = greater awareness of ignorance. But, thinking in terms of the sphere, we can see that the volume is knowledge and the surface is ignorance, which means there is a net gain, even as ignorance increases. He ends the idea with this formula:

wisdom = knowledge / ignorance.

Now, I have no idea what Gross means by wisdom, but I like that image of learning. It reminds me of Nassim Taleb's point about Umberto Eco's library, which runs like this [lifted from a pdf accompanying a Taleb talk]:

..the interesting thing about Umberto Eco is that he has a library, and he has two kind of visitors. His library has 30,000 books, so two kinds of people come to pay homage to Professor Eco. The first category is people who tell him, "Oh wow, how many of these beautiful books have you read"? And you have a second category of people who realize that the value of a library does not lie in the books you've read, but in the books that you haven't read.

So really there's some people who use a library as a tool for self promotion or to convince themselves that they're very smart and look how much I've read. Basically people focus on what they know. Or, you can use it to humble yourself. Every morning you wake up you go down to your library, you have your cup of coffee and look at it and it reminds you how ignorant you are. So this is the idea of a library.