-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 On Sat, 01 Nov 2014 22:47:15 +0200, Alan Mckinnon ([email protected]) wrote about "Re: [gentoo-user] Re: OT Best way to compress files with digits" (in <[email protected]>):
> On 01/11/2014 19:59, [email protected] 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. > 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. ... :-) - -- Regards, Dave [RLU #314465] *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* [email protected] (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-----
