After having resigned from NPL and moved past the idea of a universal computer, Turing had the idea that a machine could think and act just like a computer as he mentioned in his 1950 paper, Computer Machinery and Intelligence. It was quite a controversial idea at the time, and sparked many debates about if the 'unique' human mind may not be quite so unique. At the time, Turing estimated it would take around 50 years for computers to reach human thinking, although now it is estimated to take until around 2030.
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A discussion took place in Manchester (October 27, 1949) about the human mind and computer intelligence. Turing makes a remark that is both humorous, but also a serious point that intelligence involves the ability to make a joke. Full transcript here.