There seems to be a consensus that art cannot be compressed. A plot summary of Hamlet is not the same as Hamlet. A photo of Picasso’s Guernica is not the same as the actual painting in Madrid. Music is a particulary interesting case. A Bach partita can be written down in a few thousand bits but reading the music is not the same as hearing it played by Heifetz or Menuhin. One could even argue that one performance by the same artist is not the same as a recording or even another performance.
This is in contrast to Science. We all know the theory of evolution but most of us have never read Darwin’s On the Origin of Species. The three volumes of Newton’s Principia Mathematica can now be reduced to F = ma and F = G m1 m2/r^2. Obviously, it takes some concerted study to understand these equations but one doesn’t need to read Newton to do so. It is interesting that scientists tend to worry a lot about priority of a discovery while they are alive but unless their name is directly associated with a concept, theorem or equation, the provenance of many scientific ideas tend to get lost. Quantum mechanics is often taught before classical mechanics now so most starting students have no idea why the energy function is called a Hamiltonian. The concept of the conservation of energy is so natural to scientists now that most people don’t realize how long it took to be established and who were the main players.
If art is not compressible then we can interpret the complexity of the brain in terms of the complexity of art. The complete works of Shakespeare runs a little over 1200 pages. Estimating 5000 characters per page and 8 bits per character leads to a total size of less than 50 million bits, which is not very much compared to the hard drive on your computer. Charles Dickens was much more prolific in terms of words generated. Bleak House alone is over 1000 pages. I haven’t counted all the pages of all twenty plus novels but let’s put his total output at say a billion bits.
If art is incompressible then that means there could not be an algorithm smaller than a billion bits that could have generated the work of Dickens. This would put a lower bound on the complexity of the “word generation” capabilities of the brain. Now perhaps if you are uncharitable (like some famous authors have been), you could argue that Dickens had a formula to generate his stories and so the complexity is actually less. One way to do this would be to take a stock set of themes, plots, characters, phrases and so on and then randomly assemble them. Some supermarket romances are supposedly written this way. However, no one would argue that they compare in anyway to Dickens, much less Shakespeare. Given that the Kolmogorov complexity is uncomputable we can never know for sure if art is compressible. So a challenge to computer scientists is to write a program that can generate literature with a program shorter than the work itself.