Inspired by Scott Aaronson's essay "Who can name the Bigger Number?", we begin the talk with a game - everyone was given 30 seconds and a piece of paper, and asked to write down the biggest number they could. The discussion proceeded to an attempt to discuss some real-life big numbers - the number of cigarettes smoked in the world in a year, the number of letters in the university library, the number of seconds in a human lifetime, the number of elementary particles in the observable universe, etc.
We then went on to discuss some really big numbers - we defined Knuth's Up Arrow Notation, and made an attempt to understand quite how big Graham's number really is. Then we moved onto *really* big numbers. After a (brief) discussion of Turing Machines and the Halting Problem we defined the Busy Beaver, and the Busy Beaver shift function, which provably grows faster than any computable function.