Lee_Corbin comments on Words as Mental Paintbrush Handles - Less Wrong
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I knew a man who was chess champion of California who claimed that neither he nor his father could visualize anything. His father was a taxi driver in London, and long knew that the other drivers had mental maps, whereas he had to memorize lists of street names in just the right order. My friend, by the way, could also play blindfold chess just fine. He'd merely remember that "e7 is attacked on the diagonal from g5", presumably from long practice with the sequence e-f-g, 7-6-5. He lamented that his inability to visualize put an upper limit on his chess ability, and given how hard he worked, I believe it.
Galton was astonished that many scientists of his acquaintance did not visualize. Judging from Galton and other things I've read, the ability to visualize is more common today. TV, maybe. Please try to picture this without thinking of the old joke: "A man walked down the street, and turned into a drugstore". (The joke, of course, is that people do not become drugstores.)
Now did you happen to notice which side of the street he was walking on (left or right), and whether he was walking towards or away from you? The problem for those of us who use visualization for almost all our thinking, is that we must add irrelevant and often distracting information, which can be costly in math and science.
Sometimes it's useful to add "irrelevant" information to better visualize the full implications of something, i.e. fill in the gaps.