This is a revised summary of my talk from the November 29, 2012 Theory Lunch. I confess to having made an obnoxious amount of errors during that presentation, for which I apologize to all the listeners. This version is hopefully correct.

There are at least two ways of defining randomness. One is about randomness of *distributions* of objects: this is the subject of the theory of probability. There is another one, which is about randomness of *single objects*, and is the subject of *algorithmic information theory*. Consider the following infinite sequences: Continue reading