Week 236 of John Baez’ This Week’s Finds in Mathematical Physics is up. The bulk of this week’s entry is about large countable ordinals. (Something I’ve always wanted to understand is in what sense the Feferman-SchÃ¼tte ordinal captures the idea of an impredicative definition.
John explains how the spaces between interesting ordinals grows large in terms of driving through South Dakota. If you ever drive I-90 the length of South Dakota, you’ll see prairie occasionally interrupted by billboards. Unfortunately, there’s not that much worth advertising, but since there’s a law of conservation of the number of billboards, fake tourist attractions have sprung up simply to catch bored travellers. After seeing billboards for Wall Drug for 400 miles (and the first one travelling west really says “Wall Drug — 400 miles”), you’ll be tempted to stop too.