The chaotic complexity of natural numbers | Data structures in Mathematics Math Foundations 175

This is a sobering and perhaps disorienting introduction to the fact that arithmetic with bigger numbers starts to look quite different from the familiar arithmetic that we do with the small numbers we are used to. The notion of complexity is key in our treatment of this. We talk about both exponential and triangular complexity. Complexity rests on our ability to be able to utilize powers. So this video also gives a rather novel overview of a lot of powers that are usually somewhat beyond our view. It is, I believe, instructive to roll up one’s sleaves occasionally and descend to specific examination of the arithmetic of our mathematics. The disruptive aspect of this topic arises when we inquire into the large-scale behaviour of this complexity. Note: Mike Dupont reports that Wolfram Alpha gives some information related to complexity. For example at we see that 6973568807=2 x 3^20 5. Readers might like to explore this capability (altho