- As an undergrad I learned mostly from taking courses. Hence I could say things like I Know Group theory from a course I had in Abstract Algebra in the Fall of 1978 (Side Note- I know why I should care about groups from reading the algorithm for graph isom for graphs of bounded degree---in 1988). I learned a few things on my own- I learned that a graph is Eulerian iff every vertex has even degree from a Martin Gardner article. But since most of my knowledge was from courses I knew how I knew what I knew.
- As a grad students I still took courses but more routes to knowledge emerged. Papers! I could say things like
I know the oracle constructions about P vs NP because I read the Baker Gill Solovay paper on October 23, 1981. It helps that Oct 23 is Weird Al's birthday. But even here things get a bit murky- someone TOLD ME about the paper which lead me to read it, but I don't recall who. So one more route to knowledge emerged- people telling you stuff in the hallways.
- I saw Anil Nerode give a talk on Recursive Mathematics and that day went to the library (ask your grandmother what a library is) and read some articles on it. This was well timed- I knew enough recursion theory and combinatorics to read up on recursive combinatorics. In this case I know exactly how I know what I know. Might be the last time.
- As a professor I read papers, hear talks, hear things in hallways, and learn stuff. Its getting harder to know how I know things, but to some extend I still could. Until...
- THE WEB. The Web is the main reason I don't know how I know things. I sometimes tell Darling I read it on the web which is (a) prob true, and (b) prob not very insightful.
On Jeopardy recently the final Jeopardy question was as follows.
TOPIC: Island Countries.
ANSWER: No longer Western, this one-word nation has moved to the west side of the international Date Line to join Asia and Australia.
BILL: What is SAMOA!?Darling wondered how I know that:
DARLING: How did you know that? Is there a Ramsey Theorist in Samoa?
BILL: Not that I know if, but that's a good guess as to how I knew that. Actually Lance had a blog post Those Happy Samoans about Samoa going over the international dateline and losing the advantage of having more time to work on their conference submissions.
DARLING: Too bad there isn't a Ramsey Theorist there to take advantage of that!
Thanks Lance!- In this one case I know how I know what I know!