I like this q, in the vein of "objective measures of subjective reality" For me: Map colors first: pink-red 2 matches purple 4 (easy), blackish 7 repels eggplant 8 (ugh but ok) Stack em up, 8+7=15, anchor (green) 5, carry (yellow) 1, collapse remaining colors into 7, = 75https://twitter.com/Wparks91/status/1143666051793788928 …
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I'm shocked to read responses like
@michael_nielsen's who just "know" it's 75. This is why I'm terrible at doing math in my head! 7's in particular are troublesome bc it has the least distinct color4 replies 0 retweets 13 likesShow this thread -
Replying to @nayafia
It's not quite "just knowing". More like several half-conscious explanations occur to me at the same time. If the answers conflict I need to think about it carefully, if they're all the same, I'll trust it & feel that I "know" it.
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Replying to @michael_nielsen @nayafia
Looking at what I just wrote... I suspect that me saying more is not helping for demystifying this.
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Replying to @michael_nielsen @nayafia
I wonder if a more complex example would help clarify what happens in your head. E.g. how do you approach 2484+5839? Or 349753+935731?
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Replying to @lpolovets @nayafia
Very differently, though still with some overlap: multiple instinctive approximate models, but then detailed step-by-step models for exact computation. Though the exact model will tend to be somewhat made up on-the-fly.
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The first one, I immediately think 8200 plus the sum of 84 & 39. I then work that out (123), and there we are 8323...
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Which is a long way from the grade-school algorithm, I guess. There's certainly some sense of making the algorithm up on-the-fly, in response to a sense of what will work most easily. (And sometimes messing up and backtracking when I realize a different approach would be easier)
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