(Not really answering your question, just chatting.)
What’s your source for “JVN had ‘the physical intuition of a doorknob’”? Nothing shows up on google. I’m not sure quite what that phrase is supposed to mean, so context would be helpful. I’m also not sure what “extremely poor perceptual abilities” means exactly.
You might have already seen this, but Poincaré writes about “analysts” and “geometers”:
It is impossible to study the works of the great mathematicians, or even those of the lesser, without noticing and distinguishing two opposite tendencies, or rather two entirely different kinds of minds. The one sort are above all preoccupied with logic; to read their works, one is tempted to believe they have advanced only step by step, after the manner of a Vauban who pushes on his trenches against the place besieged, leaving nothing to chance. The other sort are guided by intuition and at the first stroke make quick but sometimes precarious conquests, like bold cavalrymen of the advance guard.
The method is not imposed by the matter treated. Though one often says of the first that they are analysts and calls the others geometers, that does not prevent the one sort from remaining analysts even when they work at geometry, while the others are still geometers even when they occupy themselves with pure analysis. It is the very nature of their mind which makes them logicians or intuitionalists, and they can not lay it aside when they approach a new subject.
Not sure exactly how that relates, if at all. (What category did Poincaré put himself in? It’s probably in the essay somewhere, I didn’t read it that carefully. I think geometer, based on his work? But Tao is extremely analyst, I think, if we buy this categorization in the first place.)
I’m no JVN/Poincaré/Tao, but if anyone cares, I think I’m kinda aphantasia-adjacent, and I think that fact has something to do with why I’m naturally bad at drawing, and why, when I was a kid doing math olympiad problems, I was worse at Euclidean geometry problems than my peers who got similar overall scores.
Oh I was actually hoping you’d reply! I may have hallucinated the exact quote I mentioned but here is something from Ulam: “Ulam on physical intuition and visualization,” it’s on Steve Hsu’s blog. And I might have hallucinated the thing about Poincaré being tested by Binet, that might just be an urban legend I didn’t verify. You can find Poincaré’s struggles with coordination and dexterity in “Men of Mathematics,” but that’s a lot less extreme than the story I passed on. I am confident in Tao’s preference for analysis over visualization. If you have the time look up “Terence Tao” on Gwern’s website.
I’m not very familiar with the field of neuroscience, but it seems to me that we’re probably pretty far from being able to provide a satisfactory answer to these questions. Is that true from your understanding of where the field is at? What sorts of techniques/technology would we need to develop in order for us to start answering these questions?
(Not really answering your question, just chatting.)
What’s your source for “JVN had ‘the physical intuition of a doorknob’”? Nothing shows up on google. I’m not sure quite what that phrase is supposed to mean, so context would be helpful. I’m also not sure what “extremely poor perceptual abilities” means exactly.
You might have already seen this, but Poincaré writes about “analysts” and “geometers”:
Not sure exactly how that relates, if at all. (What category did Poincaré put himself in? It’s probably in the essay somewhere, I didn’t read it that carefully. I think geometer, based on his work? But Tao is extremely analyst, I think, if we buy this categorization in the first place.)
I’m no JVN/Poincaré/Tao, but if anyone cares, I think I’m kinda aphantasia-adjacent, and I think that fact has something to do with why I’m naturally bad at drawing, and why, when I was a kid doing math olympiad problems, I was worse at Euclidean geometry problems than my peers who got similar overall scores.
Oh I was actually hoping you’d reply! I may have hallucinated the exact quote I mentioned but here is something from Ulam: “Ulam on physical intuition and visualization,” it’s on Steve Hsu’s blog. And I might have hallucinated the thing about Poincaré being tested by Binet, that might just be an urban legend I didn’t verify. You can find Poincaré’s struggles with coordination and dexterity in “Men of Mathematics,” but that’s a lot less extreme than the story I passed on. I am confident in Tao’s preference for analysis over visualization. If you have the time look up “Terence Tao” on Gwern’s website.
I’m not very familiar with the field of neuroscience, but it seems to me that we’re probably pretty far from being able to provide a satisfactory answer to these questions. Is that true from your understanding of where the field is at? What sorts of techniques/technology would we need to develop in order for us to start answering these questions?
In case anyone else is going looking, here is the relevant account of Tao as a child and here is a screenshot of the most relevant part: