Intuition is the part of your knowledge that you cannot test for correctness. Proving correctness requires deriving a very low dimensional representation, so you can apply analytic operators. Most of the functions that a brain approximates cannot be translated into that form.
A lot of people do. I recommend starting with reading "Quantum Mechanics, the theoretical minimum" and Aaronson's "Quantum Computing since Democritus" to build your intuitions. You need to cut through the formal language to build geometric and graph theoretic intuitions.
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In short, we can only create intuitions that are based on 3D geometric objects. In short, what we call intuitive explanations are what satisfies our intuitive cognition. That is, a warm and fuzzy explanation that appeals to our own physical experience.
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Not true! We can do at least 4D space (i.e. dims with rotational operators), and the tensor that we use to describe our perceptual content has hundreds of partially dependent dims (velocities and their first and second derivates, directions, colors, general distortions etc.).
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