You are putting words in my mouth. I didn't say "analogue system," I said "physical system." The uncomputable reals don't have any known physical application,

You are putting words in my mouth. I didn't say "analogue system," I said "physical system." The uncomputable reals don't have any known physical application, but the computable reals like sqrt(2) and pi, which do have physical application, can be perfectly well simulated to arbitrary precision by a Turing machine (edit: in particular, the computable reals form a countable set, though there isn't an algorithm to find the bijection). And when I said "simulate any physical system." I very specifically did not say "perfectly simulate," I meant "to arbitrarily high accuracy." What I said is undeniably true according to modern science, and not especially deep: - the human brain can be described as a massive system of Schrodinger equations. I strongly doubt you actually need the full machinery of quantum mechanics to describe it, but certainly quantum mechanics is sufficient. - a Turing machine can solve any arbitrarily large system of Schrodinger equations - therefore a Turing machine can emulate a human brain