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see comments on Harry Potter and the Methods of Rationality discussion thread, part 14, chapter 82 - Less Wrong
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Why would I do that rather than simply round correctly for the number of sig figs I'm dealing with?
I don't particularly care how many digits Harry want to go to, just think he should pick 3, or 3.1, or 3.14, or 3.142, or 3.1416, or 3.14159, or 3.141593, or 3.1415927, or 3.14159265 . . . etc.
Obviously Harry should go up to the Feynman point.
It's a risk for a hypothetical person who is bothered by having to round, which isn't precisely the thing you're bothered by. A person who doesn't decide in advance how many digits to use/remember.