Splash Biography

How do ideas spread in a society? How do people agree to cooperate when they are incentivized not to? Why are some societies more segregated than others? Society around us is not a mathematics problem, but branches of math (such as game theory and graph theory) can help understand s lot of complex phenomena such as various societal patterns and behaviors of financial institutions. This class will explore some of the societal phenomena through Nicky Case's interactive simulations (which can be found on ncase.me). If we have time, we will also simulate some of the situations amongst each other to see the emergence of some of this behavior.

Suppose we give three people black and white hats by tossing a fair coin; then we ask individually what their hat color is. They can either guess it or pass. Now, how can you maximize your chances that one person gets the correct answer if we need to make sure that noone is wrong? One caveat: noone hears the other peoples' answer. What if we had 7 people? 255? How about the following: 10 people are lined up tallest the shortest on a line, and we ask from back to front what their hat color is; how can you ensure that at most one person gets their hat color incorrectly? What if we had 100 people? 1000? Maybe this puzzle? We have n people, and m possible colors for hats, and m < n; how can you make sure that at least one person guesses their hat color correctly? There are loads more puzzles (Alice and Bob are sending a suitcase to each other with padlocks; 100 prisoners in a room opening 50 boxes to find their number; the classic blue eyes-green eyes puzzle; the checkerboard puzzle; the last card trick of the game of SET), and each of these relies on various interesting branches of mathematics and computer science! (Abstract algebra, combinatorics, algorithms, information theory, probability, logic, random graph theory etc.) While we cannot hope to explore all of these puzzles to a sufficient depth (and the associated mathematical fields) in an hour, we can do a few of these to get a taste of some of the puzzles!