Good article. The issue is that his parallel computation isn't itself a Turing machine. If you build a system which can "keep pace with the diagonalization arg

Good article. The issue is that his parallel computation isn't itself a Turing machine. If you build a system which can "keep pace with the diagonalization argument", necessarily, it isnt a computer. No computer can process at the rate real numbers require, this is another way of stating the Cantor result. If you build a computer (here, note, computer = an abstract mathematical formalism over discrete numbers), you cannot compute fast enough. I happen to think reality, esp. spacetime, is geometric (ie., real-valued) though empirical measures of it are, of course, just a discrete approximation.