I have a compression issue much closer to my heart that is not being properly addresses: AES-256 encrypted plaintext files. Seriously! If you just figure out the 256-bit key, it would compress well with any compressor - there&#x27;s a <i>huge</i> class of files which would only need 256 additional bits! Why isn&#x27;t there any advance on this front? &#x2F;s<p>Entropy is not a broken measurement - in fact, it&#x27;s the perfect measurement (proof: Shannon&#x27;s source coding theorem and its converse), its only downside is that it is only defined with respect to a model.<p>If you measure it on the output of one model (permutations) with respect to another model (i.i.d) then, duh, it&#x27;s wrong. And general permutations are so rare, that they might bug the author but there&#x27;s no incentive to consider them. Non general permutations - e.g., addition-modulo permutations, often ARE reasonably well compressed by markov&#x2F;tree&#x2F;fsmx model algorithms and their delta counterparts. (And they&#x27;re still too rare to consider on their own).<p>Kolmogorov complexity is interesting, but it is too vast and complicated to consider as a whole (proof: equivalence of computing Chaitin&#x27;s omega to the halting problem), other than as a very useful reasoning device. Therefore, like with the halting problem, we focus on specific subsets that seem interesting.<p>Frankly, this rant reads like &quot;But I don&#x27;t understand why they don&#x27;t yet have a car that runs on water&quot;. Compression is math, and it&#x27;s a part of math we understand quite well. BWT, for example, is an amazing algorithm - but if you take a step back, it&#x27;s just an efficient implementation of a compression scheme that was known before. (IIRC, the last gap in understanding the equivalence was closed by Effros et al in 2002)