pouët.net

but 1337 must be in the 201th million digits!

I had a math exam today: STFU!
:)
"An excellent mathematical sci-fi thriller."
An excerpt from the film:
"My god! I have to calculate de Jacobian matrix of this R^1235->R^2435 function, to be able to calculate fºg(v), so I can resolve a matrix to decode a wave function, and then aply to it a fourier transform... and then... I HATE MATH... during exams, at least.

I have no idea how to call some things, if you know math and that doesnt't sound right it's not really suposed. I guess I would be nice to know how to call those things in english.

some additional comment on gragas original idea: actually there's another problem aswell: just because a number is irrational doesn't mean it contains all finite sequences of digits in whatever base (binary, decimal, hexidecimal, ...) you use.

nice example is 0.010110111011110111110111111...

and to my knowledge it hasn't been proven (yet) that pi has this property.

in other news, none of the "magic function" compressors work. even ignoring the fact that you just can't beat entropy, you still have the problem that basically all easy to compute functions do NOT have patterns that are likely to occur in data you want to compress.

maali: if you mean 1337 is such a 1337 number that it should always be beyond reach, i agree. technically, it was just a counter-example about the index idea.

ryg: i don't know any 'real' proof, but pi was shown to be random "enough" to be compared to a random number generator [A study on the randomness of the digits of π, Shu-Ju Tu and Ephraim Fischbach]

Ryg: In your comment, you may even exchange "irrational" by "transcendental".

But I think every finite string of integers accours at least once in the decimal expansion of \pi. However, it is an open question (I beleive) to show that \pi is normal.

(and I think you should switch 0's and 1's if you are thinking of the Morse-Thue-number anyway.)

and what about having a function that generates random shapes, but different shapes according to "parameters". then the problem change: you search for an approximation shape that match a region,like the initial problem, but you know you can find it into one or other "configuration of the generator". Then , before searching your pattern, first create an index that register different "results" of the generator, which ease the search for a given pattern...

... OK, we said wicked and lame, right ?

i'll use ogg-vorbis to compress my demo!

makc: i know, but just because it doesn't score too bad in a randomness test doesn't mean it there are no patterns in the digits of pi that preclude certain sequences from ever occuring in its decimal expansion.

hyde: no, i may not. what i said holds for all irrational numbers, not just transcendentals. and i wasn't thinking of the morse-thue number, i just wanted an arbitrary irrational number that doesn't even have all digits in them :)

There is a contest in some american university to create a compressor that can compress a really big random number, and decode it.

could you please share a link ?
cause either they have no clue in math or the compressor will only be capable of compressing some limited number of such numbers ( if not only one ). to do such a compressor which compresses one number you just have to output random sequence of digits and pretend it a decimal expansion, thats it :D
well if they do discover a real one i'll stick my words back cause it'd be for much good then ( read : sooner civilization death :DDD )

ryg: You can not expect the decimal expansion (or some other expansion) of an irrational number to contain any finite string of digits. This is what you say and it is correct as your example shows.

I'm only mentioning that it is still not the case even if you restrict yourself to the subset of transcendental numbers. (A subset that contains \pi and the Morse-Thue number.) Since this statement is stronger and almost verbatim what you said, I thought it would be worthwhile to comment on it.

ryg: of course, and i didn't claim so indeed :) i just pointed out a fact that may explain why it can be easier to think pi might contain any sequence.

fadeout: maybe because they know they don't risk paying the million dollars they for sure promised?