Turing test direction depends upon the preservation of his original vision, which is to say, further, that the promulgation of a "standard interpretation" of the Turing test—i.e., one which focuses on a discursive intelligence only—must be regarded with some caution. Turing did not explicitly state that the Turing test could be used as a measure of intelligence, or any other human quality. He wanted to provide a clear and understandable alternative to the word "think", which he could then use to reply to criticisms of the possibility of "thinking machines" and to suggest ways that research might move forward. Nevertheless, the Turing
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.