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S13h. How do probabilities apply in practice?
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If one has a sound probabilistic model of a multitude of independent
events e_i with same assigned probability p one would be surprised
if the frequency of events is not close to p within a small multiple of
sqrt(p(1-p)/N). Rather than just accepting a rare occurence
(e.g., a brick going upwards due to fluctuations) as something within
one's probabilistic model, one would probably rather try to explain
it away by assuming a hidden, unobserved cause (someone throwing it).
The way probabilities are used in practice is always as informative
guides of what to expect, but not as statements with a 100% exact
meaning. I wrote a paper on surprise:
A. Neumaier,
Fuzzy modeling in terms of surprise,
Fuzzy Sets and Systems 135 (2003), 21-38.
http://www.mat.univie.ac.at/~neum/papers.html#fuzzy
that may help understand the fuzziness inherent in our concepts of
reality.