Dear Laurence,
Thank you for taking interest in my essay. The idea is that the quantum vacuum as a set of qubits, say (0, 1) set to a|0> = 0, has a phase structure based on how qubits are transformed into each other. We normally think of the vacuum as invariant under a certain symmetry group, but underneath that it could just be a vast self-referential loop, where there are "accidents" that occur where the vacuum has a symmetrical structure. This means zones exist where there are dynamical structures, where symmetries are aspects of division algebras.
These self-referential qubits, or loops of them, form a strange basis for the universe, or multi-verse, that can't be derived or computed. We can't then know what is not computable. It is similar to Chaitin's halting probability; we can know there are incomputable symbol strings in a set of them of length N, but we can't compute with certainty which are not computable (Turing's halting problem), we can't compute the number of them that are computable or not computable, or the probability for any of them to be incomputable or nonhalting. We are then faced with a bit of a conundrum; this would be a theory that tells us that this state of affairs exists, but we can't compute much of anything with it.
If physics and cosmology reaches this state of knowledge it might be the end of these foundations. The end of scientific foundations might occur this way, though I suspect we have quite a ways to go before progress in physical foundations stops at this point.
Cheers LC