

I’m sorry you had to learn this way. Most of us find out when SciShow says something that triggers the Gell-Mann effect. Green’s background is in biochemistry and environmental studies, and he is trained as a science communicator; outside of the narrow arenas of biology and pop science, he isn’t a reliable source. Crash Course is better than the curricula of e.g. Texas, Louisiana, or Florida (and that was the point!) but not better than university-level courses.
I guess that I’m the resident compiler engineer today. Let’s go.
The process will reach a fixed point after three iterations. In fancier language, Glück 2009 shows that the fourth, fifth, and sixth Futamura projections are equivalent to the third Futamura projection for a fixed choice of (compiler-)compiler and optimizer. This has practical import for cross-compiling; when I used to use Gentoo, I would watch GCC build itself exactly three times, and we still use triples in our targets today.
Oh, it’s his lucky day! Yud, you’ve just been Schmidhuber’d! Starting in 2003, Schmidhuber’s lab has published research on Gödel machines, self-improving machines which prove that their self-modifications will always be better than previous iterations. They are named not just after Gödel, but after his First Incompleteness Theorem; Schmidhuber et al proved easily that there will always be at least one speedup theorem which a Gödel machine can never reach (for a given choice of axioms, etc.)
Once again the literature on metaheuristics exists, and it culminates in the discovery of genetic algorithms. As such, we can immediately apply the concept of gene-oriented evolution (“beanbag” or “gene pool” reasoning) and note that, if goals don’t change and new genes don’t enter the pool, then eventually the population stagnates as the possible range of mutated genes is tested and exhausted. It doesn’t matter that some genes are “meta” genes that act on other genes, nor that such actions are indirect. Genes are genes.
I’m gonna close with a sneer from Jay Bellou, who I hope is not a milkshake duck, in the comments: