**Re: Re:Chroot**
*Originally posted by ProCop *

As I thougth it was a cheat and waste of time to read.

You probably didn't understand most of it, knowing you. You indicate in this post that you really don't understand the meaning of probabilities.

They see randomnes as a basically non repetitive number of random elements. If they discover a pattern (eg repeating series wich always present itself in a form (eg (very simplified) 1,2,3, 3,3 ,4,4,1,5,1,2,3) they can replace 1,2,3 pattern with a shorter presentation. Strings which contain 1,2,3 are then not random even if they were randomly produced.

In a random string, (123) is just as likely as (426) or (999). You can't compress a random string by replacing (123) with a smaller representation, because it doesn't occur any more frequently than any other triplet.

In a non-random string, (123) may occur with a greater frequency than other triplets. In such a case, the string may be compressed (represented more simply) by replacing (123) with a shorter representation.

The absence or presence of (123) is not a measure of its randomness --

*it is the frequency of occurence* (as compared to other triplets) that can be a measure of randomness. If the triplet (123) occurs with the same

*frequency* as all other triplets, then the string can be said to be random.

Imagine two containers one with white and the other with blue balloons in a big room. You open the containers and let the ballooons fly, they mingle and mingle. You can with some inteligence sort the baloons so that all the white ones wil come to the right half of the room and blue ones in the other half. But this sorting can also happen by accident, without the inteligence. But your system wil read the inteligence into this happening and declare the situation “not random”.

You're making the same mistake made by millions of high school students everyday -- confusing probability with frequency of measurement. Probability and statistics emerge only over a large sample set or a large amount of time.

This problem is usually expressed by the following fact: it is possible (though very unlikely) that, in the course of their random trajectories, all of the air molecules in a room might find themselves all up in the corners of the room, and you'd suffocate. It's not impossible -- just extremely unlikely.

If all that you tell me is that the air molecules suddenly all wound up in the corners (or that your balloons somehow all found themselves nicely divided) it tells me nothing about the randomness or non-randomness of the system. It's one data point. The statistics of the air molecules or balloons are only realized in the limit as the time reaches infinity. If I come into a room and find all the air in the corners, I can't tell you immediately if it's the result of an intelligence or the result of random motion; if I watch it for some time, I can be more sure. If I watch it forever, I can be precisely sure.

Randomness must include patterns if they were randomly created.

By definition, a random string is one where every symbol is unrelated to all other symbols. This is the mathematical definition of randomness. I have now said this at least three times, but you seem to be ignoring it. In such a random string, there are no global patterns -- because every symbol is entirely independent of all the other symbols. There may be patterns at small scales, but at larger scales (i.e. as the number of symbols approaches infinity) there will be none.

The argument you're making, I believe, is the following one: if you give me the short string 'a,' I cannot tell you if it's random or the product of intelligence -- and you're right. If, however, you give me a long string (the actual numerical meaning of "long" being dependent upon the mechanics of the actual problem), I can tell you immediately if it's a language or a random string, with no knowledge whatsoever of the language. In a random string, every symbol is independent; in any language, symbols are dependent upon each other.

And ProCop, since you don't belive in all this "cheating" and "wasting of time," perhaps you'd like to take up Mike Goldman's challenge?

- Warren