Reading through old correspondence I read (Name redacted) talking about visualising the discrete spaces of the compound of three cubes. I can't do it myself. He can do it partially.* I thought his observation about what our limits are is valuable.
Even though I have an overall sense of what it looks like, I have never been able to visualize the entire compound at once. It is kind of like trying to mentally multiply three ten-digit numbers: I can fathom how someone with more ability than I have could do it, but actually doing it is totally beyond me. (Psalm 139:6) I can imagine how someone could instantly intuit what the right compound is and easily identify all the volumes, but that someone is not me. Intelligence does not work like a lever. Spending twice as much time and effort will not give you the same results as someone who is twice as smart.
Update: "Redacted" tells me he has aphantasia and cannot actually visualise at all. I mentioned my own limitations of visualisation 8 years ago and several of you had interesting comments about brains and pictures. This pops up often in discussions of narrow exceptional abilities - it is often paired with lack of some other ability, such as Idiot Savants or left-handedness, a type of brain damage that results in clumsiness in some domains, yet urns out to be a significant advantage in some sports, and is correlated with full ambidexterity. Some things get stronger at the broken places, which we may all hope is true of psychology and character as well.
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"This pops up often in discussions of narrow exceptional abilities - it is often paired with lack of some other ability, such as Idiot Savants or left-handedness, a type of brain damage that results in clumsiness in some domains, yet urns out to be a significant advantage in some sports, and is correlated with full ambidexterity. Some things get stronger at the broken places, which we may all hope is true of psychology and character as well."
"Sickness will surely take the mind where minds can't usually go" - The Who, "Tommy"
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