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 […]

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 […]