Yesterday was pi day (3.14) From Tia Ghose at LiveScience:
Pi is definitely weird, but is it normal? Though mathematicians have plumbed many of the mysteries of this irrational number, there are still some unanswered questions.
Mathematicians still don’t know whether pi belongs in the club of so-called normal numbers — or numbers that have the same frequency of all the digits — meaning that 0 through 9 each occur 10 percent of the time, according to Trueb’s website pi2e.ch. In a paper published Nov. 30, 2016, in the preprint journal arXiv, Trueb calculated that, at least based on the first 2.24 trillion digits, the frequency of the numbers 0 through 9 suggest pi is normal. Of course, given that pi has an infinite number of digits, the only way to show this for sure is to create an airtight math proof. So far, proofs for this most famous of irrational numbers has eluded scientists, though they have come up with some bounds on the properties and distribution of its digits. [fact 8] More.
So no. Not normal. And things get worse. Surely this oddity is related in some way to the unreasonable effectiveness of mathematics.
See also: Pi: How did mathematics come to be woven into the fabric of reality?
At PBS: Puzzle of mathematics is more complex than we sometimes think
and
Eugene Wigner: Nobel Prize Winner Promotes ID, Ccirca 1960
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