Re: [gentoo-user] Re: OT Best way to compress files with digits

[Matti Nykyri <matti.nykyri@iki.fi>]

> On Nov 1, 2014, at 23:56, David W Noon <dwnoon@ntlworld.com> wrote:
> 
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> On Sat, 01 Nov 2014 22:47:15 +0200, Alan Mckinnon
> (alan.mckinnon@gmail.com) wrote about "Re: [gentoo-user] Re: OT Best
> way to compress files with digits" (in <545546D3.3030005@gmail.com>):
> 
>> On 01/11/2014 19:59, meino.cramer@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]
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> dwnoon@ntlworld.com (David W Noon)
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