tgb comments on Justifiable Erroneous Scientific Pessimism - Less Wrong Discussion
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Here's an example of the 'opposite' - a case of unjustifiable correct optimism:
Columbus knew the Earth was round but should also have known the radius of the Earth and size of Eurasia well enough to know that the voyage East to Asia was simply impossible with the ships and supplies he went with. It seems to have turned out OK for him, though.
This is probably not a very useful example and I wouldn't be surprised to see that there were plenty more of these examples.