Archive for Fashionable Nonsense

On randomness

Posted in Books, pictures, Statistics, University life with tags , , , , , on February 6, 2011 by xi'an

A while ago, I posted how strangely people seem to be attracted by re- and re-explaining Bayes’ theorem when I see it as a tautological consequence of the definition of conditional probability (and hence of limited interest per se, although with immense consequences for conducting inference). Through the “spam” book mentioned earlier this week, I noticed that the same (or even worse) fatal attraction holds for randomness! (Although I had already posted on the “truly random” generators…) Having access only to one chapter, I read with a sense of growing puzzlement through Tommaso Toffoli’s chapter and came with the following comments, which are nothing but a Saturday afternoon idle thoughts!

Measure theory, and much of the axiomatic apparatus that goes into what is often called the “foundations” of probability, is just about developing more refined accounting techniques for when the outcome space becomes so large (viz., uncountably infinite) that simple minded techniques lead to paradoxes: “If a line consists of points, and a point has no length, how come a line has length?”

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