The Berry paradox

In early 1974, I was visiting the Watson Research Center and I got the idea of calling GSdel on the phone. I picked up the phone and called and GSdel answered the phone. I said, "Professor GSdel, I 'm fascinated by your incompleteness theorem. I have a new proof based on the Berry paradox that I 'd like to tell you about." GSdel said, "It doesn't mat ter which paradox you use." He had used a paradox called the liar paradox. I said, "Yes, but this suggests to me an information-theoretic view of incompleteness that I would very much like to tell you about and get your reaction." So GSdel said, "Send me one of your papers. I'll take a look at it. Call me again in a few weeks and I'll see if I give you an appointment." I had had this idea in 1970, and it was 1974. So far I had only published brief abstracts. Fortunately I had just gotten the galley proofs of my first substantial paper on this subject. I put these in an envelope and mailed them to GSdel. I called GSdel again and he gave me an appointment! As you can imagine I was delighted. I figured out how to go to Princeton by train. The day arrived and it had snowed and there were a few inches of snow everywhere. This was certainly not going to stop me from visiting GSdel! I was about to leave for the train when the phone rang. It was GSdel's secretary, who said that Giidel was very careful about his health and because of the snow he wasn't coming to the Institute that day. Therefore, my appointment was canceled. And that 's how I had two phone conversations with GSdel bu t never met him. I never tried again. I 'd like to tell you what I would have told GSdel. What I wanted to tell GSdel is the difference between what you get when you study the limits of mathematics the way G6del did, using the paradox of the liar, and what I get using the Berry paradox instead. What is the paradox of the liar? Well, the paradox of the liar is