I know people who see things in a lot of visual detail, with objects having colors and positions. Yet there are others (like me) where it's more symbolic and abstract. So maybe you don't get corrected, and we end up using the same word for different things.
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Replying to @luqui
Exactly. But this makes me somewhat skeptical of all claims about level of ability to visualize because there is no interpersonal calibration of the word and the language around it.
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The people who claim they can visualize well sometimes claim they *need* to visualize things to understand them. I used to be like that.
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I'm still like that. I can follow a train of logical arguments, but I only feel I understand if I've taken the time to construct a stand-in visualization of them (even if they be poor visual analogies). Did you lose this "need" deliberately (and did you replace it w something)?
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Yes, I lost this need deliberately, because a friend convinced me that it's limiting: there are kinds of imagination and reasoning that don't fit well into images. I improved my powers of verbal reasoning and analogy. I still visualize when it helps to do so.
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Replying to @johncarlosbaez @farkf and
Interesting. I always felt frustrated when college math teachers didn't seem to realize that a visualization was necessary for me to understand (for example, proof-heavy courses). I would like to take a course on how to understand without visualizing.
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Replying to @summerstay1 @farkf and
I disliked my abstract algebra course as an undergrad because I couldn't attach a mental image to a normal subgroup, an ideal in a ring, etc. I loved analysis and topology because I could visualize spaces and functions. Later I learned to visualize algebra and loved it.
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Replying to @johncarlosbaez @summerstay1 and
Much later, when I got seriously into category theory, I outgrew my need to visualize everything. This came from many years of conversations with James Dolan, who argued me out of it and gave me many new tools for thinking verbally - like category theory.
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Replying to @johncarlosbaez @summerstay1 and
It seems like there is a unique satisfaction that comes with visual understanding—maybe a more immediate sense of parts being integrated. But I suppose that feeling may just be a kind of comfort/security, and not the be-all end-all.
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Replying to @Westoncb @summerstay1 and
The visual cortex has a lot of processing power and special ways of processing data - it's good to take advantage of it. But the human specialty is language, and we should develop that to its full extent too. We can use both - relying too heavily on either one is a weakness.
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[aside]: for strange reasons, I'm trying to learn the vocabularies of geomorphology, vasculatury, some anatomy, lightning terminology, and botanical terms before striking out in some complex dynamics directions because those terminologies occasionally have words like `anastomose`
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