Explore the second lecture in a graduate course on tame phenomena over the real field, focusing on tameness beyond o-minimality. Delve into Miller's conjecture, examine the first result, and study various concepts including Sigma Sets, metric dimensions, Minkowski dimensions, and Asura dimensions. Analyze dense omega orders through a lemma and engage with an exercise to reinforce understanding. Learn from Professor Philipp Hieronymi of the University of Bonn as he presents this 52-minute lecture at the Fields Institute, part of a comprehensive series on tame phenomena in mathematics.