Re: Randomness of digits within pi

On 9 Nov, 12:53, "George Marsaglia" <g...@xxxxxxxxxxxx> wrote:
<jonas.thornv...@xxxxxxxxxxx> wrote in message

news:1194606172.590463.231420@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx





On 9 Nov, 11:53, jankri...@xxxxxxxxxxx wrote:
On 9 Nov, 11:41, jonas.thornv...@xxxxxxxxxxx wrote:

When i was playing around at "http://zenwerx.com/pi.phplooking"; for
occurences of my personalnumber within PI i noticed that 333333 and
especially 666666 do not seem to occur as frequent as
111111,222222,444444,555555,777777,888888,999999 or XXXXXX (without
testing all ;)

Is this just a fluke result of to small sample size at the page, could
anyone verify searching in the big file with a program?

If that really the case that 333333 andd 666666 is a lot less frequent
what is the mathematical reason?

J

If there are 4 million digits, that's a sample size that is far too
small to say anything about the frequency of 111111 and the others.
Each of them should only turn up once in one million digits on
average.

---
J K Hauglandhttp://home.no.net/zamunda

Yes i thought the downloadable sample file was bigger but i can see it
is same size now.
But what is known about the distribution of larger digits
(numberstrings?) within pi, is it really randomed distributed?

So i try again is six digit numbers randomly distributed within pi, if
not why?

J

The pdf article

interstat.statjournals.net/YEAR/2005/articles/0510005.pdf

describes results from a number of tests on the randomness
of the digits of pi, as well as e, sqrt(2) and the decimal
expansions of various rationals.

A related article,

interstat.statjournals.net/YEAR/2006/articles/0601001.pdf

refutes claims from Physicists at Purdue that the digits
of pi are not as random as those from other sources.

George Marsaglia- Dölj citerad text -

- Visa citerad text -

Maybe but for sure it is an interesting fact that two strings of
"7777777" turns up in just a sample of 4 million and that "666666"
only occur one time in 4 million digits.

Of course it does not say anything about the big picture, but i can
see while people studying pi historical did find 7 to be a lucky
number and 6 not that lucky.

J

.

Relevant Pages

  • Re: Randomness of digits within pi
    ... do not seem to occur as frequent as ... Each of them should only turn up once in one million digits on ... Lucky number 7 of "7777777" turns up two times in a sample of 4 ... Visa citerad text - ...
    (sci.math)
  • Re: Randomness of digits within pi
    ... do not seem to occur as frequent as ... Each of them should only turn up once in one million digits on ... Visa citerad text - ... Lucky number 7 of "7777777" turns up two times in a sample of 4 ...
    (sci.math)
  • Re: Randomness of digits within pi
    ... occurences of my personalnumber within PI i noticed that ... do not seem to occur as frequent as ... Each of them should only turn up once in one million digits on ... Yes i thought the downloadable sample file was bigger but i can see it ...
    (sci.math)
  • Re: Randomness of digits within pi
    ... occurences of my personalnumber within PI i noticed that ... do not seem to occur as frequent as ... If there are 4 million digits, that's a sample size that is far too ... Yes i thought the downloadable sample file was bigger but i can see it ...
    (sci.math)
  • Re: comparing two randomizers
    ... Galathaea is talking about Kolmogorov complexity, aka algorithmic information content, aka compressibility, where a string is considered random if the shortest program that prints the string is longer than the string itself. ... But programs are known (pseudorandom generators) which produce strings that appear to be random, even though they're not; that is, there's no known general way of detecting that they're compressible unless someone reveals the algorithm+input to you. ... Of course this also casts doubt on the idea that there are any sources of true randomness: maybe radioactive decays would be easy to predict if we just knew the right formula. ... The digits of pi seem to be good pseudorandom numbers. ...
    (sci.math)