Post 2

I met with my professor's grad student, Eva, last week and we discussed some possible ideas for a project. The conclusion of the meeting was that I still need to do more readings. The paper I am reading now is "The Wire-Tap Channel" by Wyner. It is a very old paper (from 1975), and since it has survived until today, it clearly is very influential. I'm guessing my project can relate to this paper in some way. 

Something I found exciting this week was that in my probability class, we proved the law of large numbers and followed up with a corollary about entropy. The corollary was the asymptotic equipartition property. I had learned about this before, but it was cool to see it presented in another class. 

Another thing I learned which I thought was interesting was how the information theory notion of entropy related with the notion of entropy defined in the second law of thermodynamics. The second law of thermodynamics states that entropy always increases, but when using Markov chains to analyze a physical system, the information theory entropy of the distribution over time can actually decrease. This was surprising. 

Last week, I posted a trivia question. It would make sense for me to post the answer to the question this week, but I don't think anyone has actually read this blog yet. So I will postpone posting the answer.

In the meantime, here is another question which I thought was cute. It is not super difficult, but the idea is nice.

Suppose you have a box with N pieces of string. You reach into the box and randomly take out two ends and tie them together. These two ends can come from the same string or from different strings. You repeat this action until there are not more string ends to tie. What is the expected number of loops?