Measuring Time with Fuses: What You Can and Cannot Prove

This talk was given at AMS Student Chapter Seminar (Donut Seminar), UW-Madison, on March 14, 2024.

Abstract

You have a candle that burns for a minute. How can you measure half a minute with it? Answer: Light both ends. If you light one end of another candle and light the other end in half a minute, you get 45 seconds. Now if you have an infinite supply of candles (unfortunately not provided), what are all the times that can be measured exactly? These are called the “fusible numbers.” In this talk, we will explore what these numbers look like on the real line and, more importantly, when such facts are not provable.