Why is the math of physics so simple? It kind of intuitively feels like the stability of very heavy elements or the breakdown of nice properties in very big algebras. Can this be wholly explained by the obvious natural tendency to just describe the simplest stuff?
Max Tegmark briefly addresses this in an old paper of his I’ve long loved but never finished, “Consciousness as a State of Matter”. The Hamiltonian operator is, um… some big fundamental quantum physics thing corresponding to how the state of a system changes over time? And the Hamiltonian, he concludes,
“is also exceptional in that it contains mainly quadratic, cubic and quartic functions of the fermion and boson fields, which can in turn be expressed linearly or quadratically in terms of qubit raising and lowering operators (see Appendix C). A generic unitary transformation would ruin this simplicity as well, introducing polynomials of enormous degree. What principle might be responsible for this?”