Related, but this reminds me of the story by Richard Feynman [1] when he practices counting up to 60 seconds in his head, and after many experiments around
what he can do simultaneously conclude that he can simultaneously count and read but not speak. Later sharing this to John Tukey, he's told that Tukey can't read while counting but could speak while counting.
Turns out Tukey is visualizing looking at a tape, while he counts, while Feynman imagined himself talking to himself, so he couldn't speak while counting but Tukey couldn't read while counting
>By that experience Tukey and I discovered that what goes on in different people's heads. when they think they're doing the same thing - something as simple as counting - is different for
different people. And we discovered that you
can externally and objectively test how the brain works: you don't have to ask a person how he
counts and rely on his ownobservations of him-self; instead, you observe what he can and can't do while he counts. The test is absolute.
There's no way to beat it; no way to fake it.
>It's natural to explain an idea in terms of
what you already have in your head. Concepts
are piled on top of each other; this idea is taught
in terms of that idea, and that idea is taught in
terms of another idea, which comes from count-
ing, which can be so different for different
people!
>I often think about that, especially when I'm
teaching some esoteric technique such as integrat-
ing Bessel functions. When I see equations, I
see the letters in colors-I don't know why. As
I'm talking, I see vague pictures of Bessel func-
tions from Jahnke and Emde's book, with light-
tan j's, slightly violet-bluish n's, and dark brown
x's flying around. And I wonder what the hell it
must look like to the students.
[1] https://calteches.library.caltech.edu/3591/1/Feynman.pdf