I went googling into the Godel Proof and found a version of it which provoked some metaphysical speculation.

Suppose I have a machine which only generates truths � its been built so that if it starts with truths then it will only yield truths.Godel found a sentence G which causes the machine a problem. G is the sentence,�This machine will never say G is true�. A longer version of G is:

�This machine will never say �This machine will never say G is true� is true�

Its got that tricksy recursive thing which features in chaos.

So I ask the machine, �Is G true?� If G is true then the machine can�t say so � suppose the machine said that G was true then the sentence would be false � and the machine is built only to speak truths. The sentence predicts that G won�t be endorsed by the machine and the machine will be able to see that it can�t endorse the sentence. So the machine can�t answer the question.

So the machine will never say that G is true � and indeed this is a true sentence � it is true that the machine will never endorse G. The machine can never know that its true, but we do. So there is at least one truth which we know that the machine doesn�t and so the machine isn�t complete.

Suppose the machine is our brain � or our brain engineered so that it only comes up with true statements. Then the statement becomes �My brain will never say that �my brain will never say that this sentence is true� is true�. This threatens us with the possibility that even if our brains were infallible there might be a sentence which we as individuals knew but which our brains didn�t. So if our brains were infallible then our minds would still know something which our brains didn�t. So we might deduce that our minds are more than our brains � at least they would be if our brains were infallible. ( Maybe our minds can be the same as our brains if both are fallible. )

Two extensions. The first is to do with David Cunninghams CD-ROM artwork which asks us to consider whether various sentences in the screen are true, false, well formed etc. Did he he conceive of this work as a Godel artwork � about our trust in our PCs|. Maybe it�s the first Godel conceptual CD-ROM artwork.

This Godel problem (apparently) crops up in the mathematics of rational and irrational numbers. The problem is to do with the completeness of some theories of these number sets.

This means that it crops up in the mathematics of microtones. Its easy to show that a perfect tritone is irrational eg in terms of the ratio of string lengths required to articulate it. The number of rational pitches � ratios of real numbers is infinite. But the tritone belongs outside this infinity as do all the well tempered intervals.

Apparently � and I have only just read this � mathematicians tried to prove that the number of irrationals was the number of rationals squared. Someone showed that this conjecture was Godel undecidable � a statement beyond the scope of formal proof on some definition.

And so the proposition about the size of the set of irrational numbers in comparison with the set of rational numbers had to be adopted as an axiom.

So in the universe of tuning there is simple infinity of intervals which can be produced by ratios of real numbers. But the only way to scope the larger number of tunings from which the well tempered set is selected is to make an assumption about how big it is.

I bought a 3CD set of Tamla in Tescos � made me think about the Beatles cover of Mr Postman.

I emailed Gilbert about my CD plans.