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
Characteristic class Characteristic class In mathematics, a characteristic class is a way of associating to each principal bundle "X" a cohomology class of "X". The cohomology class measures the extent the bundle is "twisted" — and whether it possesses sections. Characteristic classes are global invariants that measure the deviation of a local product structure from a global product structure. They are one of the unifying geometric concepts in algebraic topology, differential geometry, and algebraic geometry. The notion of characteristic class arose in 1935 in the work of Eduard Stiefel and Hassler Whitney about vector fields on manifolds. Let "G" be a topological