"anyone can learn to do it"
"Higher than average IQ and passionate interest is all that's needed"

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Yes, because "I can't perform the basic mental operations integral to what x *is*, but I have a passion for x" is incoherent. Passion requires some basic degree of ability. If you're arguing you can leverage a lot from there, I agree. But not everyone has even that to start with.
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Possibly, but they can’t exercise that meta-skill arbitrarily. You cannot just yell at someone “make your brain do the thing that makes you understand this!” and expect magic to happen.
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Translating very direct instructions into a particular syntax is probably something that can be taught to anyone. "Write an if-else statement in Python that..." Sure. "Solve Fizzbuzz without having someone else do it for you" is much trickier, and you don't practice for it.
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Solving FizzBuzz. This is what programmers do. They are not syntax-translators, they are problem-solvers.
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I don't think that's a reasonable comparison. FizzBuzz is a *really* basic programming task that demonstrates only a very basic understanding of how loops & if-else statements work. The comparison I would use is to a "writer" who can copy out a text perfectly but cannot read it.
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