Turing test be answered. The Turing test, even if imperfect, at least provides something that can actually be measured. As such, it is a pragmatic attempt to answer a difficult philosophical question. The format of the test allows the interrogator to give the machine a wide variety of intellectual tasks. Turing wrote that "the question and answer method seems to be suitable for introducing almost any one of the fields of human endeavour that we wish to include." John Haugeland adds that "understanding the words is not enough; you have to understand the "topic" as well." To pass a well-designed Turing test,
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