The parts I enjoyed most were those related to current AI approaches. Ellenberg describes how one can understand a simple perceptron, a basic neural network, through a familiar decision-making process -- the Electoral College, where electors in each state come together to make a binary decision and the weighted outcomes combine into a national judgment. I wish he had gone further in this discussion, perhaps by exploring how one might compute a loss function in this context and compare it to the popular vote.
I also appreciated his treatment of gerrymandering. He explains the geometric aspects of constructing districts to maximize a political party’s advantage in statewide elections, and he highlights how difficult it is, in geometric terms, to define what a fair or well-shaped district should be. His discussion of simulating districts at random and examining how unlikely a particular enacted map is relative to that baseline was helpful, although I would have preferred a clearer framing in terms of a null process and P-values.
The book also provides a clear description of epidemics, R0, and geometric series. I liked the way it covered historical figures in epidemic research, especially Ronald Ross, the British epidemiologist. In relation to machine learning, I found the explanation of gradient descent, including stochastic gradient descent, intuitive and useful.
Overall, I felt Shape was a good read, offering straightforward explanations of mathematical ideas that can be hard to grasp.
