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Yhaqtera
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21 Aug 2009, 6:50 pm

I know all the digits of pi... just can't tell in which order they come.

Anyway, the digits of pi is random as far as I understand.

If you take the digits and "translate" them into ASCII codes you will eventually end up with every text that's ever been written and everyone that is going to be written. Also every text that never existed and never will exist. Also, these texts will occur an infinite amount of times. Isn't that fascinating?

You could try and generate images (computer images are simply streams of characters) and when you have generated every previously unexisting image you could claim copyright for anyone making that image after you... or you could generate every 4.5 minute MP3-file and do the same. Of course you would need a lot of diskspace and a really powerful computer.



Aoi
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21 Aug 2009, 7:07 pm

Emphasis on "a lot". As has been show in probability theory, it would take a very, very long time (far longer than the current age of the universe) for the famous infinite group of monkeys to produce all of Shakespeare's works.

As always with information, it's the signal versus the noise. So if it's all out there in pi (or the Golden Mean, e, or other transcendental numbers), then we get to interesting topics in information theory.

Then too, how many bits of a song, image, or text have to be changed before said song, image, or text is no longer the same as the original? (Obviously, a reference to the Borges' Library of Babel)



aleclair
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21 Aug 2009, 8:50 pm

A while back I read about a thought experiment where someone asked whether it was possible to create a set of 128*128 pixel GIF/JPG using 8-bit color, creating one file for every possible combination of said 2^8 = 256 colors. They're all small numbers, but because combinatorics involves multiplication and exponentiation, you get something like (128*128)^256 possibilities, assuming the colors are independent events. That's an enormous number and has to be in the petabytes or larger. It's scary to think that, even though all of our data is discrete and thus has a finite amount of permutations and combinations, it's still too much data for us to handle.

Since you bring up pi in the initial premises, are you familiar with the joke that begins "it is illegal to store the digits of pi in binary"? You'd enjoy it.



azulene
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26 Aug 2009, 5:21 am

I sometimes think about this thing. A non-computer example is a glass of water with some soluble dye mixed in. Unfathomable combinations occur every second but we don't notice the difference. It's just coloured water rather than a visible plethora of shapes formed by dye molecules. The dye "unmixing" into something recognisable is never observed if the dye is soluble.

How many coherent words can be formed by the first few hundred digits of pi? How many gramatically correct sentences and in what language are there? It gives you an idea on the success rate of this interesting consideration.


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pakled
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26 Aug 2009, 10:41 am

We tried doing Pi as ascii art, but it made a picture of Cthulhu, who told it wasn't 'time' yet...;)

But then I'm the one who always wondered when monitors said 'reproduces 6.7 million colors', I'd wonder, 'what are the names of all those colors?...;)



ValMikeSmith
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31 Aug 2009, 5:08 am

Wasn't the monkey who wrote Shakespeare named Shakespeare?

It's much easier to find everything in the number 0.123456789101112131415161718192021...

A pattern in Pi has been discovered like the pattern in this number,
because now there is a formula for finding any single digit of Pi or that number
instantly by how far from the decimal point it is. But the next numeral in Pi is
still harder for people to guess.

Quote:
You could try and generate images (computer images are simply streams of characters) and when you have generated every previously unexisting image you could claim copyright for anyone making that image after you... or you could generate every 4.5 minute MP3-file and do the same. Of course you would need a lot of diskspace and a really powerful computer.


When RIAA started suing people I told them that they had no new songs because they are
all in "my" number, and since it can be indexed a digit at a time I don't even need memory
to play it. Since it is NOT RANDOM, there is a 1:1 probability of finding music and even an
equation to do that. The RIAA can't sue me because I sued them and they lost and they
haven't paid me, for literally illegally hacking and stealing and deleting data, and the data
was about this kind of math. No way would they put themselves out of business by funding
automatic digital music generators without any copies needed. You are right on with the
4 minute MP3 idea. There are an incredibly finite number of possible 4 minute DIGITAL sounds, and they are all bunched together between so many 0's and so many 1's,
and they have already been counted. There are very much less than 2^(2^27) of them!