Continued accumulation of risk of some kind of failure over the years is exponential just like the interest is, and can reach 10^-100 as easily.
A space of correct arguments of N words, and space of invalid but superficially correct arguments of N words, differ in size by factor exponential in N, so improbability of correctness in general too can easily reach googol.
That being said, there is genuinely a problem with description length priors and unbounded utilities. Given a valid theory of everything with length L , a fairly small increase in the length can yield a world with enormous invisible, undetectable consequences. E.g. an enormous (3^^^^3 , or BB(11) ) number of secondary worlds where the fundamental constants depend to the temperature of the coldest 1-gram piece of frozen hydrogen in our universe (something global which we may influence, killing all the aliens in those universes). The perversity is that we don’t know those worlds exist, and we don’t know they don’t exist, and the theory where they do exist is not very much longer than simplest known ToE, and predicts exactly identical observations so it can never be disproved.
Continued accumulation of risk of some kind of failure over the years is exponential just like the interest is, and can reach 10^-100 as easily.
A space of correct arguments of N words, and space of invalid but superficially correct arguments of N words, differ in size by factor exponential in N, so improbability of correctness in general too can easily reach googol.
That being said, there is genuinely a problem with description length priors and unbounded utilities. Given a valid theory of everything with length L , a fairly small increase in the length can yield a world with enormous invisible, undetectable consequences. E.g. an enormous (3^^^^3 , or BB(11) ) number of secondary worlds where the fundamental constants depend to the temperature of the coldest 1-gram piece of frozen hydrogen in our universe (something global which we may influence, killing all the aliens in those universes). The perversity is that we don’t know those worlds exist, and we don’t know they don’t exist, and the theory where they do exist is not very much longer than simplest known ToE, and predicts exactly identical observations so it can never be disproved.