Each year, hundreds of thousands of kids apply1 to New York City’s public school system with a ranking of up to twelve schools. The Department of Education then matches all of these students up with a single offer from one of NYC’s 1,800 public schools,2 ensuring maximum satisfaction for the applicants. How does it work?
At first glance, my intuition was that this was a really complex problem. After watching this fantastic video, I then sketched out the algorithm in a notebook and came to believe that it was pretty simple.
Recently, I came across an intriguing working paper. The goal of the paper is to offer a mathematical formula that describes the emergence of empirical observations of innovation in the world—i.e., how likely innovations are to be observed and how innovations make the observation of further innovations possible. As the authors write, they model how an innovation changes the shape of the “adjacent possible,” faciliting the emergence/discovery/observation of new innovations.