On randomization and discovery

In the first part of this paper, traditional computability theory is extended to prove that the attainable density of knowledge is virtually unbounded. That is, the more bits available for storage, the more information that can be stored, where the density of information per bit cannot be bounded above. In the second part, the paper explains how machine intelligence becomes possible as a result of the capability for creating, storing, and retrieving virtually unlimited information/knowledge. It follows from this theory that there is no such thing as a valid non-trivial proof, which in turn implies the need for heuristic search/proof techniques. Two examples are presented to show how heuristics can be developed, which are randomizations of knowledge – establishing the connection with the first part of the paper. Even more intriguing, it is shown that heuristic proof techniques are to formal proof techniques what fuzzy logic is to classical logic.