Understanding why increasing predictability helps with compression is not the hard part though. What's hard to grasp is why the transform is reversible.
a word can be factored into the set and frequency of letters + the specific permutation. compressable patterns in either channel seem likely when the underlying words are language like.
And in general that set of descriptors provides no compressibility. BWT is much richer that that set in that the way it works performs well for data we care about.
Describing a multiset takes as much information as the multiset contained to begin with, on average. BWT somehow works better on things of use.
