Explore the intricacies of measuring singularities in this second AMS Colloquium Lecture delivered by Karen E. Smith from the University of Michigan at the Virtual 2022 Joint Mathematics Meetings. Delve into advanced mathematical concepts as Smith presents her insights on this complex topic, offering valuable knowledge for mathematicians and researchers in related fields. Gain a deeper understanding of singularities and their measurement through this 46-minute lecture, which forms part of a three-part colloquium series.