Nobody doubts that you can mechanicize rote human behavior. In fact, that's exactly the point of a universal Turing machine. It is designed to implement any process that can be machanicized that way.
How you get from that to "the brain or the world are a computer/mechanism" is mysterious to me. And it was to Turing and Church who always resisted such an unwarranted extrapolation.
No extended discussion needed, really. There is simply nothing that supports your worldview...