From: Trans Date: 2007-03-23T19:38:28+09:00 Subject: Re: Just for fun... On Mar 23, 5:59 am, Mauricio Fernandez wrote: > On Fri, Mar 23, 2007 at 05:20:36PM +0900, Trans wrote: > > On Mar 22, 11:45 pm, Clifford Heath wrote: > > > This is a very concise statement about what's flawed in your analysis. > > > It's not just about repetition, it's about removing *whatever* is > > > predictable. All's fair when it comes to improving predictability. > > > Of course. When I used the term "repetition" I didn't mean to be so > > narrow as to to suggest nothing more than "a a a a a". A better term > > would have been "patterns". > > (redundancy) > > > > > Predictability is not the whole center piece of > > compression either. If it were, you couldn't get much better a > > compression of Kings James than a file with this in it: > > > "http://patriot.net/~bmcgin/kjv12.txt" > > > Pretty predictable. That may seems silly, but there's a point. This is > > not general compression. It doesn't really matter that the process of > > decompression involves a remote machine -- locality is relative. But > > even better, if I sent you a new algorithm for compressing King James, > > and along with it the file I sent you to uncompress had only one bit > > of data in it, "1", then how can it work? Of course, the algorithm > > itself had the entire content of King James within it. Pretty > > predictable again. But not general compression. When looking at > > general compression its important to take the size of all the elements > > involved as well, including the compression algorithm itself. > > Given that Kolmogorov-Chaitin complexity is not computable, what's wrong with > finding practical algorithms that approximate it? > > I don't see the intention behind your remarks: surely, any practical > compression method we come up with is going to perform worse than the optimum > one (whose performance we can only estimate... using inferior compression > methods!), so what? The existence of an uncomputable lower bound on the length > of the description of a message is no more of a deterrent to research on > better (practical) compression methods than e.g. Shannon's theorem is to > channel coding. When did I say otherwise? I believe my original point was simply one of surprise that BWT improved deflate, which I believe says more about deflate's deficiencies than BWT's use as a means of compression. I've only been trying to explain my reasoning for that thought ever since. > Regarding your remark on the choice of the universal machine and some choices > not being "general compression", you could add that even if descriptive > complexity relative to two different universal machines differs at most by a > constant term, the latter does matter when we're approximating the algorithmic > complexity in practical scenarios... I'm sorry. Would you care to put that in layman's terms? I did not have the good fortunate of academic education in the field (oh, if only!), so I cannot readily address your statement (assuming of course you are using academic terms in good faith, and not just being intentionally obscure). T.