posted on 2022-04-30

the uncertainty of 2+2=4

people generally claim "it will rain tomorrow" and "2+2=4" are different kinds of knowledge. not only is one about the world and the other about mathematics, but the former is probabilistic and the latter is certain.

i here would like to dispute this second claim; in fact, 2+2=4 is, as we are now with our brains the way they are, probabilistic knowledge as well. it is possible that, by sheer chance, every time you and every other human and every computer ever calculated what 2+2 would be, they made a mistake by random chance, and happened to make the exact same mistake. it could be that actually 2+2=5. or, for a more systematic example, one could find themself as the mathematician in a lying simulation.

now, that's extremely unlikely, just because of how universally 2+2=4 is claimed to be observed and verified. but it is indeed possible, and this fits into the lack of absolute certainty.

maybe there could be minds and computers that could determine this for sure (although, what about unknown unknowns?); but those aren't what we have now.

once you know this, other probabilistic guarantees like cryptography, or more generally problems that are in computational complexity classes like BPP and BQP, can be percieved as more reasonable relative to exact guarantees: after all, everything we interact with on top of the standard model is probabilistic.

posted on 2022-04-30

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