Over the weekend, I took a trip to North Caronlina to participate in an Undergraduate Mathematics conference put on by this group called SAMSI. I didn’t really know a lot about it when I signed up to go, other than that it was a free trip to North Carolina over spring break, and that math would be involved.
SAMSI is a research group that does mathematical and statistical work on problems like social networking, anomoly detection, and the spread of diseases. Went went to some talks which were frankly quite boring, but while the people were giving their talks, I was doing some work of my own. Back in december or so I started thinking about finite state automata, which are the simplest type of computers. I started thinking about their abilities as compared to other computational frameworks, and my thoughts on these matters left me with a bunch of questions. I wanted to clarify certain things to myself, and so while these guys were giving their talks on things that weren’t interesting to me, i came up with about 20 pages of notes on the topic i was thinking about. I proved some things which I had already sort of known, and came up with some interesting results which are at least new to me.
In addition to computational theory, I did some work on other random problems of mathematical interest. For example, any number that is divisible by three will have the sum of its digits also divisible by three. Why is this? As I figured while scribbling on a napkin at chili’s in the detroit airport, it’s a result of the fact that we use a base 10 number system. Suppose you have some number X, and you add three to it. If the first digit of X is 0-6, you have simply increased the sum of its digits by three. If the first digit is 7, you decrease the sum by 7 (because the first digit goes from 7 to 0) but then you increase the sum by one when you increase the next number, for a net change of -6, which is a multiple of three. Likewise, if the first digit is 8, you decrease the first digit by 7 (from 8 to 1) and increase the second digit by one. In general, if you have a base x number system, the ’sum of the digits’ rule will work for any number y such that x = ky + 1 for some positive integer K. So, in base 16, the divisibility rule works for 3,5, and 15. Cool, huh?
The other cool part of the trip was the socialization. I met some cool peopel from various colleges, and it was neat to hang out and talk with them. I played guitar with a guy named Bob from minnesota, argued politics with a socialist from Dartmouth and a fellow supply sider from Cornell, who told the darthmouth chap to ‘Read some Milton Friedman.’ I even meet some cool UC students, with whom I may hang out some time later.
North Carolina is a pretty place, and I liked it there. I may even go back this may for a week long thing where i’d actually get to solve some problems. The moral of the story is, if you get a chance to go to some thing, even if you don’t know a lot about it, go to it! You just might end up singing a song about the economy of south africa while enjoying a few adult beverages with people you just met.