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

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