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I'm familiar with the typical-mind-fallacy posts and glad to see a LW reference on HN. Just the other day, I read Eliezer's article on Algernon's Law [1]. It's

I'm familiar with the typical-mind-fallacy posts and glad to see a LW reference on HN. Just the other day, I read Eliezer's article on Algernon's Law [1]. It's tangentially related. Incidentally, it precedes LW by a decade! His thesis sounds reasonable to me. But I thought MBTI test sounded reasonable too, which I learned doesn't have any empirical backing. So my intuitions may be less than reliable. meh. > According to Galton, people incapable of forming images were overrepresented in math and science. I've since heard that this idea has been challenged, but I can't access the study. So yes, I guess some lack a visual imagination. But I've seen several people enlightened by diagrams, and never seen anyone enlightened via plug-&-chug formulas. So I'd be surprised if a visual imagination did'n confer some kind of advantage in math. I highly doubt that a visual imagination confers a disadvantage, given that Euler had photographic memory. But I concede that the null hypothesis is certainly likely. Yvain says he can't access Galton's study. After a few minutes Googling, I gave up too after I hit a paywal. [1] http://web.archive.org/web/200102021712/http://sysopmind.com/algernon.html http://web.archive.org/web/200102021712/http://sysopmind.com...

dllthomas 13y ago
"But I've seen several people enlightened by diagrams, and never seen anyone enlightened via plug-&-chug formulas." I've personally experienced being enlightened by both, with respect to different things. I probably lean more toward the visual, but don't expect everyone does (without more, carefully gathered, evidence). "I highly doubt that a visual imagination confers a disadvantage" That would surprise me as well, assuming nothing was sacrificed for that visual imagination (and even then I expect a visual imagination to be more useful than many things).
- Double_Cast 13y ago
  I'm sorry to dredge up this thread again, but this boggles my mind. /u/Someone contests that visualizing things like the Monster Group, M-Theory, or 7 Touching Cylinders is practically impossible [1]. I agree. To reason about the Monster Group, I imagine even professional mathematicians manipulate symbols with functions, operations, et al. But, to quote Eliezer, "Does this person [Ph.D economist] really understand expected utility, on a gut level? Or have they just been trained to perform certain algebra tricks?" [2] Clearly, the economist does not understand his craft. Were he able to visualize the substance rather than merely Plug & Chug the symbols [3], then surely he wouldn't have bought the lotto ticket. And since symbols are mere abstractions (lossy compressions) of the substance, Plug & Chugging the symbols will rarely trump visualizing the substance. Therefore, I suspect my inability to visualize the Monster Group reflects the limitations of my brain rather than an intrinsic disadvantage of visualization. I.e. I would prefer visualization of the Monster Group to Plug & Chug if only I were smart enough. (Disclaimer: I have no idea what the Monster Group is. But I do remember seeing an old youtube clip about visualizing 11 dimensions. I still don't get it. If you're interested, [4]) > I've personally experienced being enlightened by both The way I see things, visualization is necessary. However! Here you are saying enlightenment is possible without visualization... So please share with me, exactly how were you enlightened without visualization? Can you give examples? Does it just happen, like that theory about how savants can crunch numbers without knowing what they're doing on a conscious level? Is it akin to weighting parameters according to how strongly they affect a function's output, like in neural networks? Am I missing something that's totally obvious to you, like how some philosophers argued that imagination didn't exist? [1] https://news.ycombinator.com/item?id=7549869 https://news.ycombinator.com/item?id=7549869 [2] http://lesswrong.com/lw/gv/outside_the_laboratory/ http://lesswrong.com/lw/gv/outside_the_laboratory/ [3] http://lesswrong.com/lw/nv/replace_the_symbol_with_the_substance/ http://lesswrong.com/lw/nv/replace_the_symbol_with_the_subst... [4] http://www.youtube.com/watch?v=JkxieS-6WuA#aid=P-eR3HseAzw http://www.youtube.com/watch?v=JkxieS-6WuA#aid=P-eR3HseAzw

dllthomas 13y ago

"But I've seen several people enlightened by diagrams, and never seen anyone enlightened via plug-&-chug formulas." I've personally experienced being enlightened by both, with respect to different things. I probably lean more toward the visual, but don't expect everyone does (without more, carefully gathered, evidence). "I highly doubt that a visual imagination confers a disadvantage" That would surprise me as well, assuming nothing was sacrificed for that visual imagination (and even then I expect a visual imagination to be more useful than many things).

Double_Cast 13y ago
I'm sorry to dredge up this thread again, but this boggles my mind. /u/Someone contests that visualizing things like the Monster Group, M-Theory, or 7 Touching Cylinders is practically impossible [1]. I agree. To reason about the Monster Group, I imagine even professional mathematicians manipulate symbols with functions, operations, et al. But, to quote Eliezer, "Does this person [Ph.D economist] really understand expected utility, on a gut level? Or have they just been trained to perform certain algebra tricks?" [2] Clearly, the economist does not understand his craft. Were he able to visualize the substance rather than merely Plug & Chug the symbols [3], then surely he wouldn't have bought the lotto ticket. And since symbols are mere abstractions (lossy compressions) of the substance, Plug & Chugging the symbols will rarely trump visualizing the substance. Therefore, I suspect my inability to visualize the Monster Group reflects the limitations of my brain rather than an intrinsic disadvantage of visualization. I.e. I would prefer visualization of the Monster Group to Plug & Chug if only I were smart enough. (Disclaimer: I have no idea what the Monster Group is. But I do remember seeing an old youtube clip about visualizing 11 dimensions. I still don't get it. If you're interested, [4]) > I've personally experienced being enlightened by both The way I see things, visualization is necessary. However! Here you are saying enlightenment is possible without visualization... So please share with me, exactly how were you enlightened without visualization? Can you give examples? Does it just happen, like that theory about how savants can crunch numbers without knowing what they're doing on a conscious level? Is it akin to weighting parameters according to how strongly they affect a function's output, like in neural networks? Am I missing something that's totally obvious to you, like how some philosophers argued that imagination didn't exist? [1] https://news.ycombinator.com/item?id=7549869 https://news.ycombinator.com/item?id=7549869 [2] http://lesswrong.com/lw/gv/outside_the_laboratory/ http://lesswrong.com/lw/gv/outside_the_laboratory/ [3] http://lesswrong.com/lw/nv/replace_the_symbol_with_the_substance/ http://lesswrong.com/lw/nv/replace_the_symbol_with_the_subst... [4] http://www.youtube.com/watch?v=JkxieS-6WuA#aid=P-eR3HseAzw http://www.youtube.com/watch?v=JkxieS-6WuA#aid=P-eR3HseAzw