How real are virtual realities,how virtual is reality?—Constructive re-interpretation of physical undecidability

Throughout the ups and downs of scientific world conception there has been a persistent vision of a world which is understandable by human reasoning. In a contemporary, recursion theoretic, comprehension, the term “reasoning” is interpretable as “constructive” or, more specifically, “mechanically computable.” An expression of this statement is the assumption that our universe is generated by the action of some deterministic computing agent; or, stated pointedly, that we are living in a computer-generated universe. Physics then reduces to the investigation of the intrinsic, “inner view” of a particular virtual reality which happens to be our universe. In this interpretation, formal logic, mathematics and the computer sciences are just the physical sciences of more general “virtual” realities, irrespective of whether they are “really” realized or not. We shall study several aspects of this conception, among them the conjecture that randomness in physics can be constructively reinterpreted to correspond to uncomputability and undecidability in mathematics. We shall also attack the nonconstructive feature of classical physics by showing its inconsistency. Another concern is the modeling of interfaces, i.e., the means and methods of communication between two universes. On a speculative level, this may give some clue on such notorious questions such as the occurrence of “miracles” or on the “mind-body problem.”