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Software
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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. This
requires me to inoculate your
brain.

Take either Andrew
Wiles proof of Fermat’s Last
Theorem or Alan Turing’s proof
of the Halting Problem; both
proofs are non-computable.
Each document is made up of
symbols, the Roman alphabet
and some special Greek symbols
such as α, β, ζ, and so on. Let us

[Graphic: Circular logo containing a syringe with text wrapping around it reading "Creative Inoculation"]
Creative Inoculation

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