[extropy-chat] what is probability?
Jef Allbright
jef at jefallbright.net
Thu Jan 18 02:12:47 UTC 2007
The Avantguardian
> I don't know what Scooby would do but I have a third
> solution. Unlike some problems involving the PoI, this one is
> actually a physics problem. Whereas I am unaware of any
> experimental verification of PoI in terms of time or space, I
> do know that there is a verifiable principle in statistical
> thermodynamics that seems somewhat similar to PoI only it is
> defined objectively instead of epistemologically. This
> principle is called Boltzman's equipartition theorem.
> This theorem is only defined for classical systems but as a
> train is a classical system, it should apply.
<snip>
> In order to arrive before 2pm the least amount of kinetic
> energy the train can have is 22,500 (km/hr)^2.
> To determine a probability one has merely to look at what
> proportion of possible kinetic energies allow the train to
> arrive before 2pm versus the total range.
> Thus the probability that the train will arrive at or before
> 2pm is P(<=pm) = (90,000 - 22,500)/(90,000 -
> 10,000) = 0.84375 which is different from either one of the
> answers given above.
>
> So does this help? *wicked grin*
Thanks Stuart for helping to make my point that there's no end to the
variety of dimensions that could be applied to this ambiguously
specified problem.
People get stuck on it because they think of probability as distribution
of "true" values rather probability as distribution of uncertainty.
- Jef
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