I'm <i>trembling with excitement</i> at the prospect that easy-to-use high-performance automatic differentiation looks likely to become a "must have" capability for more and more computer languages. It's going to become easier and easier to specify objective functions and have the computer optimize programs for a wider range of application.
The idea of duality is insane. Its present in linear logic, automatic diff, constructive mathematics, probability, quantum theory, game design, discrete optimization, etc.<p>I wonder if it's related to chirality.