Software 259 Let us start by substituting the notes of the musical scale for the letters of the alphabet to create a piece of ‘music. Since it is a direct analogue of the word problem, we have created a non-computable piece of music. It is definitely non-computable, but is it music? If it just looked like a random jumble of notes it would be unconvincing, but luckily there are many forms of music that look exactly like a word substitution puzzle. Bach's Art of Fugue, the canons of Tudor composers such as William Byrd and Thomas Tallis, and the works of Grieg all use sequences of chords that move from one to the next using substitution rules. If you were to listen to the steps in our word substitution music, they would definitely sound musical. I think they should pass the main artistic criticism — that they should not sound formulaic. But is any actual human composition non-computable? Unfortunately, we cannot prove whether a particular piece of Bach, Tallis or Grieg is non-computable because we don't know the specific rules used to compose it. All we know are the general musical principles of harmony and counterpoint that applied at the time. We don’t have these composers personal rule sets because they were held in their brain and they are, of course, long since dead. It is statistically likely that most pieces are non-computable because there are an uncountably infinite number of them, whereas computable pieces are merely countably infinite. But that’s just probability; it is no proof. I puzzled for some time whether there is a way to prove it but had to conclude it is impossible. However, and this is how creativity works, once I had given up on the problem, my brain continued to work on it. I was not conscious of this, I was only aware that failing to solve the problem annoyed me. I then had a Eureka moment. Although I couldn't prove a piece of music was non-computational, I could make one! - a piece that could not have been created using computation alone. T