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Is celeb number pi “normal”?

A photograph of the Greek letter pi, created as a large stone mosaic embedded in the ground.
pi in mosaic, Berlin/Holger Motzkau

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


Eugene Wigner: Nobel Prize Winner Promotes ID, Ccirca 1960

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Phinehas, Now, now! You know the tau is 6.283185307179586476925286766559.... and not 1! Stephen SteRusJon
Stephen @11 You are welcome. It hit my geeky-nerve as well. The tau is one! Phinehas
Phinehas @ 7. Thanks for that link. I found the Tau Manifesto to be a geeky-fun and interesting read. I'm a tau-comrade, now. Stephen SteRusJon
How about apple pi day? Take one apple. Divide circumference by diameter. Voila, apple pi. aarceng
Denyse, 'If it bleeds it leads.' Is perhaps amongst the worst of tabloid journalism's absurd pronouncements. Also there is no '22' day because 22 describes the value proceeding from 21, and leading up to 23. Of course all numbers are equal in their main aspect, figuratively showing a value, it's just that, 'some are more equal than others.' Pi, on the otherhand describes the ratio between the diameter of a circle and its circumferance. A fact so amazingly useful, (almost supernatural) in the natural world that it is used in all fields of the natural sciences, and almost made me believe in God. Happy 'Pi' day, sorry I missed Darwin Day. rvb8
I prefer Phi myself. Florabama
More of a Tau guy myself. Phinehas
Here's a little discussion with useful links of the issue from Mathoverflow (question posted by (Sir) Timothy Gowers, a Fields medalist): What is the state of our ignorance about the normality of pi? From one of the responses:
... even the questions like "all decimal digits from some point on are 0s and 1s" cannot be shown unconditionally.
Quite remarkable. daveS
Bob O'H at 4, if it bleeds, it leads, and in a stream of a thousand possible stories, that's not normal. Bet it isn't in math either. Reminds me of the uproars around whether the universe could have an infinite past. News
Denyse - I'm not sure you understand that "normal" is used by mathematicians in a specific way that does not equate to the way it is used by the general public. You specifically say that pi is "[n]ot normal". But in the mathematical sense (in which it is being discussed), we don't know if it is normal or not. Being European I refuse to acknowledge pi day, although I will happily celebrate "better pi approximation day" in July. Bob O'H
DieB, when there is a big uproar around anything, it is never "normal." There is a Pi Day. There is not a No. 22 day (except maybe on Sesame street? Nah, probably not even there). Your contentions about pi might be right but they are contentions. Has anyone ever contended about 22 as a concept? News
Science journalists.... Sigh 1) It isn't sufficient for a normal number that each numbers 0..9 appears with equal probability (see, e.g. the wikipedia article): otherwise, 13717421/1111111111 would be a normal number 2) To make it worse, Denyse O'Leary declares the problem for decided, as the absence of a proof is obviously the proof for the absence... DiEb
So no. Not normal. And things get worse.
I believe most mathematicians expect that π is indeed normal, but no one has proved it yet. It's just a very difficult problem apparently. daveS

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