gwern comments on Rationality Quotes August 2013 - Less Wrong
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Besides his letter to Hardy, Wikipedia cites The Man Who Knew Infinity (on Libgen; it also quotes the 'half starving' passage), where the cited section reads:
I can't parse '271" feet', is this an OCR issue? If you loosen the belt by two yards, it can obviously reach at least a yard above the surface, because you can just go from ____ to __|__. And I recall that the actual answer is considerably more than that.
Given that the symbol " is the symbol for inches, and ' is the symbol for feet, I would suspect that there has been a mistyping in the quote.
I think that what was meant to be there was 72" or 72.1" (inches), which is exactly/one-tenth of an inch over two yards (one yard = three feet). That would produce the desired result of a nearly one-foot increase in the radius of the belt; adding 72 inches to the circumference of the belt would produce an increase of 11.46 inches (72 inches / (2 * pi)) in the radius of the belt, which in this case is the height above the ground.