Compression of random binary data

[jonas.thornvall at gmail.com]

What kind of statistic law or mathematical conjecture  or is it even a physical law is violated by compression of random binary data? 

I only know that Shanon theorised it could not be done, but were there any proof? 

What is to say that you can not do it if the symbolic representation is richer than the symbolic represenatation of the dataset. 

Isn't it a fact that the set of squareroots actually depict numbers in a shorter way than their actual representation. 

Now the inpretator or program must know the rules. And i have very good rules to make it happen.