User blog comment:Syst3ms/YAUD/@comment-30754445-20180810132619/@comment-35392788-20180812193234

You didn't totally misunderstand, but you forgot one step.

\(\psi(\psi_M(x))\) first expands to \(\psi(\psi_{\psi_M(x)}(\psi_M(x)))\), which then expands to a fixed point of \(\psi(\alpha \mapsto \psi_{\psi_M(x)}(\alpha))\)