Tuesday, May 21, 2013

Do you KNOW how you KNOW what you KNOW? I don't KNOW.

When watching Jeopardy with Darling if I get a question correct that is NOT in my usual store of knowledge (that is NOT Ramsey Theory, NOT Vice Presidents, NOT Satires of Bob Dylan) Darling asks me How did you know that? I usually reply I do not know how I knew that. Recently I DID know and I'll get to that later, but for now the question arises: Do you know how you know what you know?
  1. 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.
  2. 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.
  3. 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.
  4. 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...
  5. 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.
So- do you know how you know what you know?

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!


  1. This is the power of the human brain, it abstracts (somehow?) knowledge so that the relevant parts come up in a fuzzy query in a matter of milliseconds. What's important for you (and your brain) is to know, and clearly to know how you know it not as much (unless you are the person who studies how you know what you know, but then you don't have to know for each specific instance but you can abstract).

    Note that there are subfields of AI (I believe called Knowledge Representation) which precisely treat the somehow part above. However, it is clear that our current abilities are far from that of a human.

  2. is darling her real name or is darling=sweetheart ?

  3. I call her darling. I've heard she has a real first name
    but from lack of use I forget what it is.

  4. If maggie were her real name, i'd rather you use maggie. It's pretty nice, so is jessica ... but you are right, you may run into problems of using these popular names, as they might run into one-to-one correspondence issues.

    so, wifey, seems to be also a decent synonym.

    Just saying.