ESP Biography

Are some infinities bigger than others? What does it mean for one infinity to be bigger than another infinity? These may sound like crazy questions. After all, infinity is infinitely big. Nothing could possibly be bigger than it. Or is it so? In this class, we'll explore these questions and some implications that arise from them. It turns out that this question is fundamental to modern mathematics and to knowing the limits of computation!

How would you measure the distance between two things? With a ruler, perhaps. But what if these two things are intangible, like 'cat' and 'rat'? Or the DNA of two humans on earth? Turns out, we can generalize the idea of a 'distance' and it can become super useful! In this class, we'll attempt to motivate the mathematical notion of metric, and look at some interesting applications in information theory, machine learning and social science.