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pragmatist comments on How confident are you in the Atomic Theory of Matter? - Less Wrong
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Like I said in my edit, I can't give you a precise answer, but to narrow it down a bit, I'm comfortable saying that the probability is higher than 1 - 10^(-9).
Really? What's the probability that a human can even be in an epistemic state that would justify 30 bits of belief?
About the same as the probability that a human can be in a physical state that allows them to walk. Winners of a 100 million-to-one lottery overcome a prior improbability of 10^-8, and presumably are at least as certain they have won, once they have collected, as they were previously expecting to lose, so there's somewhere above 10^16 of updating, 160 decibans, 53 bits. And ordinary people do it. If you're so smart you can't, there's something wrong with your smartness.
What strikes you as implausible about 30 bits of belief? It takes more than 30 bits to single out one individual on this planet.
So all we need is an example of a universe without atoms (corresponding to the example of someone who did win the lottery despite the improbability of doing that) for this analogy to work.
I think there are fields of thought in which the best paradigm is that something either is or isn't, and where probabalistic thinking will do no good, and if forced or contrived to seem to work, may do harm (e.g. the models by which Wall Street came up with a plausible -- to some -- argument that CDSs of subprime mortgages could be rated AAA).
And there are fields of thought in which the idea that something simply is or isn't is the thing likely to mislead or do harm (see http://en.wikipedia.org/wiki/Interesting_number where one gets into trouble by thinking a number either is or isn't "interesting").
The "interesting number" business isn't probabalistic either, though there may be some usefulness, in Baysian arguments that treat subjective "levels of certainty" like probabilities.
Note that probabilities like that cannot be estimated because they are at the noise level. For example, the odds are about the same that you are delusional and no one asked this question (i.e., the odds are tiny and hard to evaluate).
What level of confidence is high (or low) enough that you would feel means that something is within the 'noise level'?
Depending on how smart I feel today, anywhere from -10 to 40 decibans.
(edit: I remember how log odds work now.)