In the wake of large language models, there has been a resurgence of claims and questions about the Turing test and its value for AI, which are reminiscent of decades of practical "Turing" tests. If AI were quantum physics, by now several "Schr\"odinger's" cats could have been killed. Better late than never, it is time for a historical reconstruction of Turing's beautiful thought experiment. In this paper I present a wealth of evidence, including new archival sources, give original answers to several open questions about Turing's 1950 paper, and address the core question of the value of Turing's test.