Remember back in math class when the professor was talking about Eigenvectors and you thought that it was kind of pointless? Well check out the 25 billion dollar Eigenvector. (Yes, it’s about Google …).

I enjoyed this short talk by famous physicist Murray Gell Mann about “beauty and truth in physics”:

The basic idea is that physics theories that turn out to be correct are often ‘beautiful’ in a mathematical sense. This means that the equations describing the theory are simple, or symmetric, or otherwise elegant in some sense.

I’m no Gell Mann, but I’ve had the same feeling once or twice in economics. Once my coauthor and I were working on a microeconomic search model. Basically, buyers have to find sellers, but buyers are uncoordinated with each other, so some sellers end up with more buyers than they can supply, and some sellers end up with no buyers, so some potential trades don’t take place due to the search frictions. We were looking at how supplying information to buyers about seller qualities can help reduce these frictions. The nice part was that, in one case, the efficiency losses due to search frictions were proportional to a freakin Cobb Douglas function of the information that was provided to buyers. Nowhere did we have any Cobb Douglas functions in our model, but it popped out somehow, so we figured it must be right.

Please don’t call me a nerd, but I think this video is fun … This guy can do complicated arithmetic in his head. I guess he’s using some kind of trick to simplify things but it’s still cool. It’s worth watching to the end where he squares a random 5-digit number in his head …

One thing freaked me out though … how come so many audience members are carrying calculators around with them? (Or were they using their cellphones?).

My father thinks this problem explains life, the universe, and everything:

Suppose you have an ipod with 100 songs. It plays songs at random without regard for what songs were played before. On average, how many songs will you hear before it repeats a previous song?

Real ipods don’t work like this, in random mode they randomise the playlist and play through it in order, so there’s no possibility of repeats. But the answer to the problem is interesting.

UPDATE: I think the answer is 13.21. Click here to see how I worked it out, although it’s not pretty. I’m sure there must be a cute way to apply some clever trick to get the answer more easily. The interesting thing is how low the number is. 100 songs and on average you only get about 13 chosen at random before you hear a repeat.