> On Nov 1, 2014, at 23:56, David W Noon <dwn...@ntlworld.com> wrote: > > -----BEGIN PGP SIGNED MESSAGE----- > Hash: SHA1 > > On Sat, 01 Nov 2014 22:47:15 +0200, Alan Mckinnon > (alan.mckin...@gmail.com) wrote about "Re: [gentoo-user] Re: OT Best > way to compress files with digits" (in <545546d3.3030...@gmail.com>): > >> On 01/11/2014 19:59, meino.cra...@gmx.de wrote: > [snip] >>> Ah! By the way...I was astonished to read, that the digits of PI >>> are called random on the one hand and on the other hand there is >>> a formula [1] to calculate a certain digit of PI without >>> calculation of the previous digits... Calculated random? Are >>> nature constants the purest form of PRNGs ??? ;) (Quantum physics >>> is everywhere... ;;)) >>> >>> [1]: >>> http://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula >> >> >> The sequence of digits that make up pi are a random sequence - you >> can analyze the order any way you want and you'll find no inherent >> pattern. > > Actually, the sequence of digits is most definitely *not* random. If > the sequence of digits is written any other way then the value is not > Pi. Hence the sequence is unique, not random. > > I think what you are grasping for is that the frequency of distinct > digits tends to be uniform: 0's occur as often as 1's as often ... as > 9's. Note that the "as often as" operator is really approximate for > finite sub-sequences, but is asymptotically accurate. > > Moreover, this is the same in any number base: the binary > representation has 0's occurring as often as 1's; the ternary > representation has 0's occurring as often as 1' and as often as 2's; > etc., etc. > > Such numbers are called "normal". It was a poor choice of name, but > we are stuck with it. I would have called them "digit soup" numbers > - -- an oblique reference to alphabet soup.
Well all the digit of pi can be compressed to the following: =pi(); If you have the infinite series that calculates the digits :) >> However, any given digit in the sequence is 100% predictable, as >> you just showed :-) >> >> Randomness has got to be the second most mind-boggling thing out >> there, first being quantumness (that's not a waord, I just made it >> up. You you should get the meaning OK from context ;-) ) > > I would say that probability theory is more mind boggling, as it > underpins much of quantum theory. But, as someone who majored in > probability theory, I might be biased. [Incidentally, there is a small > statistical joke in that last sentence.] > > Getting back to Meino's original request, one of the optimum > compression algorithms for this would be custom Huffman encoding. To > do this the algorithm requires that all the data (i.e. digits) be read > and a frequency table built. The only problem is that to read all the > digits of Pi could take rather a long time. ... :-) That would take infinite time :) > - -- > Regards, > > Dave [RLU #314465] > *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* > dwn...@ntlworld.com (David W Noon) > *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* > > -----BEGIN PGP SIGNATURE----- > Version: GnuPG v2 > Comment: Using GnuPG with Thunderbird - http://www.enigmail.net/ > > iEYEARECAAYFAlRVVyQACgkQRQ2Fs59Psv/9qwCeKwuLz/7RGEV06X+RdDQryDe+ > /xwAoK1qMgb9RZXkQByBUMqB8eqs20bG > =XUPB > -----END PGP SIGNATURE----- >
