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I would like to understand why sometimes the indefinite article is used, I thought that the whole name, the concept is "the Turing machine". In texts, I often see it used as a regular noun (the first mention is with "a", then with "the"]. We do not say "a Newton Theory of Gravity",as far as I know. What is the difference then?

We may think of a Turing machine as a...

but

We used Fourier analysis to evaluate the

Why here "analysis" does not need an article?

Can it be because we regarding the machine, can talk about a specific instance? But even then I would say we still talk about the concept, which is still the same.

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  • Great question! However, your title doesn’t seem to match your question. Could you edit it so that it matches?
    – Fivesideddice
    Commented Apr 21, 2020 at 11:14
  • @Fivesideddice Thanks, done. I also clarified in the text so that it matches better.
    – John V
    Commented Apr 21, 2020 at 11:20

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The word "analysis" can be either a countable or an uncountable noun. When used in an uncountable sense, it doesn't require an article.

"Machine" is a countable noun. It's true that "Turing machine" is an abstract concept and a mathematical model of computation. Grammatically, however, "machine" sounds strange without an article. To make it uncountable, we'd have to say "Turing machinery" but no one says that.

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