Turing Completeness and CAs

Emma Byrne and I should that a big enough net of CAs is Turing complete.
That's not too surprising as a net of continuous valued neurons is super Turing complete (Siegelmann 91).
We did it with CAs and no binding.
If you add binding, you get rules, and you get Turing completeness another way.
So the question now becomes not can you program a brain, but how does the brain program it.
It's pretty clear that people use at least context free rules.
So, to parse (or understand) natural language, you need to use CF rules.
You need binding (or a finite set of sentences) to use CF rules.