Compression of random binary data

[jonas.thornvall at gmail.com]

Den måndag 11 juli 2016 kl. 20:09:39 UTC+2 skrev Waffle:
> On 11 July 2016 at 20:52,  <jonas.thornvall at gmail.com> wrote:
> > 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?
> 
> Compression relies on some items in the dataset being more frequent
> than others, if you have some dataset that is completely random it
> would be hard to compress as most items have very similar number of
> occurrances.
> 
> > 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.
> 
> A square root may be smaller numerically than a number but it
> definitely is not smaller in terms of entropy.
> 
> lets try to compress the number 2 for instance using square roots.
> sqrt(2) = 1.4142
> the square root actually takes more space in this case even tho it is
> a smaller number. so having the square root would have negative
> compression in this case.
> with some rounding back and forth we can probably get around the fact
> that sqrt(2) would take an infinite amout of memory to accurately
> represent but that neccesarily means restricting the values we are
> possible of encoding.
> 
> for sqrt(2) to not have worse space consumprion than the number 2
> itself we basically have to trow away precision so sqrt(2) ~= 1
> now i challenge you to get that 2 back out of that 1..

Well who it to say different kind of numbers isn't treated differently, i mean all numbers isn't squares. All numbers isn't naturals.