Why is mathematics so spectacularly effective at describing the physical universe?
The answer is that the universe itself is simply a timeless mathematical construct. Of what type, we’re not exactly sure yet; it’s looking like it’ll be some kind of mashup of a 3+1-dimensional pseudo-Riemannian manifold with tensor fields obeying certain partial differential equations, plus operator-valued fields on ℝ4 with certain commutation relations acting on an abstract Hilbert space. But when we do have our theory of everything, plus the initial conditions of the universe, it’s clear to me that within…
Suppose we want a differential operator $T : (\mathbb{R}^n \rightarrow \mathbb{R}^n) \rightarrow (\mathbb{R}^n \rightarrow \mathbb{R})$ such that
\begin{align*}
&T(g) = 0 \Longleftrightarrow g \in G \\
&g \in G \Longrightarrow T(g \circ f) = T(f)
\end{align*}
where $G = \text{Aff}(n, \mathbb{R}...
