Thursday, June 23, 2005

Andy Angry

This just in: Supreme Court makes 22 year old college student's head explode from raw anger. Read about it here:

One of the sane justices:
"Any property may now be taken for the benefit of another private party, but the fallout from this decision will not be random," O'Connor wrote. "The beneficiaries are likely to be those citizens with disproportionate influence and power in the political process, including large corporations and development firms."

Wednesday, June 22, 2005


Can Tic-Tac-Toe be thought of as a dynamic programming problem? I think so. Let the board be numbered from the top left corner with numbers 1-9. Let the state vector of variables be a 9x1 vector such that:

If your symbol is in square i, a 1 is in the i'th row of vector x
If no symbol is in square i, a 0 is in the i'th row of vector x
If your opponent's symbol is in square i, a -1 is in the ith row of vector x

Now, x(0) is simply <0,0....>. Let the choice vector, u, be such that if you want to put your symbol in the j'th position, there is a 1 in the j'th column of a vector of zeroes. Then the transition function is simply:

x(s+1) = x(s) + u(s) + p(s)

the p(s) is what I am not sure about. It would be your opponent's play... as a baseline, this could be just a random placement of a -1 in an open row in a vector of zeroes, so that you are playing against an opponent with no strategy.

I think this would work... but I'm not sure. And I am not even trying to come up with how to describe the function which a player would wish to optimize or how this would be done, just if the game could be thought of as a DP problem.

Tuesday, June 21, 2005

Principle of Optimality

I was working on writing the theorems from De La Fuente's dynamic programming chapter. I noticed after a few minutes that my acronym for the Principle of Optimality was P.o.O. I found this funny, Kat... not so much.

Sunday, June 12, 2005

"Fatness" of a Number

My girlfriend was being goofy and said that prime numbers were fat. I got to thinking and decided that she is wrong. Let an integer n be fatter than an integer m mean that n has more factors than m. Furthermore, let a number's "weight" or "fatness" be the number of positive factors of that number. For example:

30 is fatter than 15 since 30 has 8 factors and 15 only has 4. So:

1. What is the fattest number? How fat is it?
2. What is the skinniest number? How fat is it?

Ok, time to watch basketball.

Saturday, June 11, 2005

Primal Economics

I got this link from Marginal Revolution. I love this kind of stuff. My friend and I were talking and we would like to see some more experiments:

1. Build a machine that has some sort of task attached. Whenever a monkey completes the task, a coin is dispensed. Some interesting things might happen:
I. We could get an idea of their consumption/liesure tradeoff
II. We might see the beginnings of monkey income disparity and see what happens.
III. More inter-monkey commerce, like the monkey prostitution, might take place.

2. Run a centipede experiment with the monkeys. Start with one coin, give two monkeys buzzers, double the amount of coins ever n seconds. You get the idea.

3. Inflation shocks, if 1. is effective... lots of things could be done if 1 above is effective.

This is really interesting stuff.

Tuesday, June 07, 2005

The Most Confusing Question To Ask Your Algebra Student

You know that both pi and the square root of two are irrational, but which one is more irrational?

I almost asked this the other day while tutoring just to see if the client really understood what irrational meant, but I decided it wasn't worth seeming like a total nerd. On here, however, I have no worries about my nerdiness.

Monday, June 06, 2005

Calc II Tutoring

I just tutored two people at calc II for the first time in forever. I love tutoring that class. Every integral is like a little puzzle to be solved! Seriously, after figuring out little tricks to problems like x^5*e^(x^3)dx I get an adrenaline rush. I love it.

In other news, I have had some interesting experience with music recently. Kat got an Ipod and we've been downloading Itunes songs right and left. Having Itunes has increased my music consumption ten-fold. It isn't only the fact that music is more readily available, I actually feel like I have started to enjoy it more. Why? I think it is because finding new bands has become a sort of hobby, something that I have always enjoyed (I can be a bit of a music snob) that has become much more rewarding since I got the pod.

Newest group that I like: Art Brut, a neo-art-punk band from London. Coolest track: "My Little Brother" with lyrics like: "My little brother just discovered rock and roll, he's got a noise in his head and he's out of control!" Great, irreverent punk music!