Spinoza, Leibniz, Kant, and Weyl

I walk into a House of Worship and the guy up front is in the middle of an oration. I don’t expect to stay but catch a few words, “… so my friends, reach down and uplift thy less fortunate neighbor—to the $\frac{1}{2}$-power, for so it is written, and so may it be derived.” Startled, I take a seat; this sounds like theology on a wavelength I can receive. This was my experience meeting (virtually) Glen Weyl and reading his paper with Buterin and Hitzig [BHW19]^{[1] (opens in new tab)}. The paper describes a funding mechanism called Quadratic Finance (QF) and deploys a bit of calculus to show that within a very clean and simple linear model QF maximizes social utility. They differentiate the social utility function. The mathematical content of this note is that by taking one further derivative, one may also deduce that QF is the unique solution. But what drew me into this house of worship, is a line of reasoning in [BHW19]^{[1:1] (opens in new tab)}, made explicit in a phone call with Glen, that Kant’s categorical imperative (CI), properly interpreted, becomes a differential equation uniquely solved by QF. It was this second derivation from Kant’s “axiom” that caused me to take a seat, and for a very personal reason.