A._Denis comments on Entropy, and Short Codes - Less Wrong

36 Post author: Eliezer_Yudkowsky 23 February 2008 03:16AM

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Comment author: A._Denis 24 February 2008 10:00:49PM 0 points [-]

"So these people are frauds?"

To answer your question , I think the card can be one of the better random generator existing, so it is absolutely not a frauds ( and pheraps I will buy one ... thank you for the link ) . But there are many definition of random . The only one theoretical random definition I accept as true is that a bit string S is random only if this string has K(S) >=Len(S) . My strong deterministic opinion is that in the real world these random objects exist only if we take short object , also for quantum field ( like Wolfram think ). I read articles where people reasoning on the quantum field and the relation on exponential or polynomial world , I don't know what is the answer but I don't think that quantum filed open the door for an exponential world. This opinion come to me from many discrepance I find in the mathematical description and what happen in practical . For example for the K function ( Kolmogorov complexity ) there are proof say that for major part of value we have K(X)>=Log(X) and if you watch on the function you can say it is absolutely correct , not only but for very very few case we have K(X)

If you watch this function min( 2^N , M/N ) what happen is this! for small string we have exponential behaviour and this is coherent with mathematical classical view but after a limit M what happen change and the probability to compress for example increase! .

Another important characteristic is that big variation on the parameter M make small variation on the behaviour of the function , so is more important to assume the existence of this behaviour also if we don't know M also if it is impossible to compute M !.

This cause a discrepance in the entropy , in the assumption of Log as function of information measurement , etc ... becouse this theories suppose an exponential world ! a very big world! ( exponential functions are very big and we can not underrate them ! )

There are many consequence of this simple observation and many to be investigate .

I don't know if quantum field will open the exponential door but the world behaviour seem to me polynomial.

Denis.