I've been thinking more about the idea that there's no such
thing as a random number. You can have a random /distribution/
over numbers, in which case the randomness in the distribution,
not in any number drawn from the distribution.
This has important implications for how we think about data,
including raw data that we take in the lab. The individual
points don't have error bars. The error bars pertain to the
/distribution/ from which the points were drawn.
Tangential remark: This can be seen as reason #437 why sig
figs are a bad idea, i.e. unhelpful in practical terms, wrong
in conceptual terms, and just plain bad in every way. In this
case, sig figs force you to attribute error bars to every data
point you write down, even though that's conceptually wrong.