Turing test the world as humans do. Numerous other versions of the Turing test, including those expounded above, have been raised through the years. A modification of the Turing test wherein the objective of one or more of the roles have been reversed between machines and humans is termed a reverse Turing test. An example is implied in the work of psychoanalyst Wilfred Bion, who was particularly fascinated by the "storm" that resulted from the encounter of one mind by another. In his 2000 book, among several other original points with regard to the Turing test, literary scholar Peter Swirski discussed in
Church–Turing thesis three formally-defined classes of computable functions coincide with the "informal" notion of an effectively calculable function. Since, as an informal notion, the concept of effective calculability does not have a formal definition, the thesis, although it has near-universal acceptance, cannot be formally proven. Since its inception, variations on the original thesis have arisen, including statements about what can physically be realized by a computer in our universe (physical Church-Turing thesis) and what can be efficiently computed (Church–Turing thesis (complexity theory)). These variations are not due to Church or Turing, but arise from later work in complexity theory and digital physics.