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“The measurement outputs contain at the 99% confidence level 42 new random bits. This is a much stronger statement than passing or not passing statistical tests, which merely indicate that no obvious non-random patterns are present.”arXiv:0911.3427

**A**s often, I bought ** La Recherche** in the station newsagent for the wrong reason! The cover of the December issue was about “God and Science” and I thought this issue would bring some interesting and deep arguments in connection with my math and realism post. The debate is very short, does not go in any depth. reproduces the Hawking’s quote that started the earlier post, and recycles the same graph about cosmology I used last summer in Vancouver! However, there are alternative interesting entries about probabilistic proof checking in Mathematics and truly random numbers… The first part is on an ACM paper on the PCP theorem by Irit Dinur, but is too terse as is (while the theory behind presumably escapes my abilities!). The second part is about a paper in

**published by Pironio et al. and arXived as well. It is entitled**

*Nature**“Random numbers certified by Bell’s Theorem”*and also is one of the laureates of the

**prize this year. I was first annoyed by the French coverage of the paper, mentioning that “a number was random with a probability of 99%” (?!) and that “a sequence of numbers is perfectly random” (re-?!). The original paper is however stating the same thing, hence stressing the different meaning associated to randomness by those physicists, “the unpredictable character of the outcomes” and “universally-composable security”. The above “probability of randomness” is actually a p-value (associated with the null hypothesis that Bell’s inequality is not violated) that is equal to 0.00077. (So the above quote is somehow paradoxical!) The huge apparatus used to produce those random events is not very efficient: on average, 7 binary random numbers are detected per hour… A far cry from the “truly random” generator produced by Intel!**

*La Recherche***Ps-A**s a concidence, Julien Cornebise pointed out to me that there is a supplement in the journal about ** “Le Savoir du Corps”** which is in fact handled by the pharmaceutical company Servier, currently under investigation for its drug Mediator… A very annoying breach of basic journalistic ethics in my opinion!

Filed under: Books, R, Statistics, University life Tagged: Bell’s theorem, La Recherche, Nature, p-value, PCP theorem, quantum mechanics, realism, statistical tests, Stephen Hawking

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