As I point out here (http://news.ycombinator.com/item?id=2302695), there is a difference between a formalized process for expressing computation being Turing complete, and implementing an actual Turing machine. The first is possible, and most general purpose programming languages are Turing complete. The second is impossible, for obvious reason.

Perhaps the confusion comes from the fact that the easiest way to prove a formalized process is Turing complete is to express a simulation of a Turing machine.