On 12/28/2013 4:11 PM, Edgar L. Owen wrote:
Jason and John,
If something is random it can't be computed by any deterministic process. That's the
meaning.
That's one possible meaning, although it can only strictly apply to infinite sets of
something. I think of "random" as just being an instance from a probabilistic set. Here's
what I wrote in another context recently:
Probability has several different meanings and philosophers argue over them as if one must
settle on the real meaning. But this is a mistake. Just like “cost” or “energy”,
“probability” is useful precisely because the same value has different interpretations.
There are four interpretations that commonly come up.
1.It has a mathematical definition that lets us manipulate it and draw inferences
(Kolmogorov).
2.It has a physical interpretation as a symmetry (principle of insufficient
reason).
3.It quantifies a degree of belief that tells us whether to act on it (Bayesian decision
theory).
4.It has an empirical meaning that lets us measure it (frequentist statistics).
The usefulness of probability is that we can start with one of these, we can then
manipulate it mathematically, and then interpret the result in one of the other ways.
Brent
"Probability is never having to say you're certain."
However we have to be careful because there is another kind of non-computability due to
either not enough input data or computing power. The weather would be a combination of
randomness and this type of non-coputability.
Edgar
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