What does it mean to extend the manipulability of differentials?

In an interesting paper called Extending the Manipulability of Differentials, the authors Jonathan Bartlett and Asatur Zh. Khurshudyan describe an interesting proposal for representing higher-order derivatives. The argument is basically this: As is well-known, the chain rule for first derivatives seems to follow algebraically if you use Leibniz notation for the derivatives: However, there’s a […]

Hoping for Lane Closures

Two lanes of a four lane highway are closed and you’re stuck in a traffic jam. If there are no on- or off-ramps, what should you hope to see on the road ahead of you: the other two lanes re-open or one of the two open lanes close? I think you should hope to see […]

The CGP Grey Sheaf of Continents

CGP Grey is a youtuber with a variety of interesting videos, often about the quirks of geography and political boundaries.  In this video, he asks the question “How many continents are there?”, discusses a variety of subtleties in the notion of “continent”, and concludes that it is not well-defined enough to provide an answer. Let’s […]