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May 6 at 8:20 comment added Kapil "Mathematicians are better at imagining things that don't exist, while physicists are better at imagining things that do exist!" This is an important point. Counter-examples that show that the proposed theory does not yield what you want are important (in Mathematics) to demarcate the assumptions that are required in order to find the appropriate definitions.
May 3 at 13:30 comment added Richard Erickson I like your comments about imagining things that exist versus those that do not. Also, I you're 're a statistician from your profile. I've read bio of Fisher that say he was great at visualizing and imagining data in higher dimensions because of childhood sickness that left in in bed much of the time.
May 3 at 11:07 history answered Peter Flom CC BY-SA 4.0