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Pentashagon comments on Pascal's Muggle: Infinitesimal Priors and Strong Evidence - Less Wrong
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Imagine someone makes the following claims:
Then they threaten, unless you give them $5, to kidnap you, give you the immortality drug, stick you in the spaceship, launch it at near-light speed, and have you stuck (presumably bound in an uncomfortable position) in the spaceship for the 3^^^3 years the universe will last.
(okay, there are lots of contingent features of the universe that will make this not work, but imagine something better. Pocket dimension, maybe?)
If their claims are true, then their threat seems credible even though it involves a large amount of suffering. Can you explain what you mean by life-centuries being instantiated by causal nodes, and how that makes the madman's threat less credible?
That requires a MTTF of 3^^^3 years, or a per-year probability of failure of roughly 1/3^^^3.
This implies that physical properties like the cosmological constant and the half-life of protons can be measured to a precision of roughly 1/3^^^3 relative error.
To me it seems like both of those claims have prior probability ~ 1/3^^^3. (How many spaceships would you have to build and how long would you have to test them to get an MTTF estimate as large as 3^^^3? How many measurements do you have to make to get the standard deviation below 1/3^^^3?)