Turing’s paper attempts to answer the question, ‘Can machines think?’ His approach is both philosophical and technical, with even the technical sections seeming more philosophical than truly technical.
Turing opens his investigation by claiming that an answer to the question can be found by subjecting machines to what he calls the “imitation game.” 
Two people and one machine play the game, with one of the persons acting as interrogator. By asking questions of both the machine and the other person, the interrogator attempts to deduce who is machine and who is human. The goal of those being interrogated is to fool the interrogator. Thus, Turing rephrases his initial question: “Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman?” 
[With the goal in this variant being the correct assignment of ‘man’ and ‘woman’.]
Turing moves on to narrow the field of machines that could potentially play the game. Turing argues that only the digital computer should be able to participate. He defines the digital computer to be those machines “intended to carry out any operations which could be done by a human computer. The human computer is supposed to be following fixed rules; he has no authority to deviate from them in any detail.” 
Turing argues that the digital computer, through proper programming, can imitate any other similar ‘discrete state machines.’ It would therefore be unnecessary to use any machine other than the digital computer in the imitation game—i.e., Turing argues that only digital computers have the potential to mirror the human thought process.
Throughout section 6 Turing addresses the various contemporary arguments against the possibility for conscious machines. 
Ultimately, though, Turing believes that such machines will eventually be able to pass (intellectually) for humans . 
In his last (and I believe his most interesting) section, Turing abstractly addresses the problem of creating a thinking machine. Instead of programming into a computer every little nugget of human knowledge and understanding, and the relations between, Turing argues that a program must be written that directs a computer to learn. Thus, a computer will be able to build its own understandings, just as a child does.
Turing’s paper is very much an investigation into the prospects of there ever existing a tool which is able to flawlessly and gracefully function as a brain outside of ourselves—the ultimate spatial extension of the human intellect. Turing defines the digital computer as that machine whose explicit purpose is to mimic, i.e. incrementally become indistinguishable from, the human computer. Consequently, I believe that this text offers a McLuhanistic view of the medium of the computer. 
Furthermore, although this article was written before the “convergence of two separate historical trajectories” 
and the subsequent creation of new media, I believe that in order to understand and appreciate the ways in which we relate to new media, we need to understand the historical precedence of each historical trajectory. Is it significant to new media today that computers were at one point expected to parallel human thought? Is contemporary computer design still attempting to achieve AI? To what extent are contemporary computer programs ‘intelligent’ and what does this mean for the concept of new media? If the computer is meant to at least partially externalize human thought, is it telling that the computer is increasingly absorbing all old media?
Although Turing does not directly address the role of the computer as a medium, I believe his article illustrates the benefit and importance of stepping back from the medium and asking, “How does new media extend and amputate the human sensorium?”
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 Manovich, Lev, What is New Media?