Which comes first: maths or the world it describes?

When I should be blogging about politics, I find that I can't stop thinking instead about an article by the brilliant Bryan Appleyard, author of The Brain is as Wide as the Sky and other diatribes aimed at scientism and reductionism.

This is how he describes this revolt at the heart of science:

Unger and Smolin have also just gone into print with a monumental book – The Singular Universe and the Reality of Time – which systematically takes apart contemporary physics and exposes much of it as, in Unger’s words, “an inferno of allegorical fabrication.” The book says it is time to return to real science which is tested against nature rather than constructed out of mathematics. Physics should no longer be seen as the ultimate science, underwriting all others. The true queen of the sciences should be history – the biography of the cosmos.

Appleyard goes on:

Relaying on mathematics is demonstrably absurd because it makes two unprovable assumptions – that maths can accurately describe the universe and, even if that is true, that our maths at this particular moment is good enough to do it.
Two things strike me about this.  The first is that the movement he describes sounds remarkably like the Danish film movement DOGME, a kind of demand for simplicity and authenticity in science and everywhere else.  Just as the authentic film-makers demanded a simple approach to time, telling stories simply and without foreshadowing - so the doyens of authentic science want to return to the point where basic, underlying time is the measure of all things.

My own candidate for a campaign for real science would be to transform the scientific establishment from defenders of consensus to more open-minded seekers after truth, but then I've been dealing with too many dermatologists in my life (I have chronic eczema and am constantly amazed at how unquestioning scientific professionals can be).

The other thing that strikes me is that this very question - whether abstruse mathematics corresponds to the real world - is precisely the same dispute between the great philosopher Ludwig Wittgenstein and the young Alan Turing, which I've described in my book Alan Turing: Understanding the Enigma.

Wittgenstein lectured in his own room in an old lumber jacket and without any notes or preparation, and with copious periods of lengthy silence. When he read from notes, he told his biographer Norman Malcolm, the words “come out like corpses”. Turing was the only mathematician in this particular group and soon the lectures turned into a conversation between the two men, testing Wittgenstein’s assertion that common sense trumped logic. 

For Wittgenstein, the famous Liar’s Paradox - the basis of Turing;s work on computing - was a “useless language game”. Turing claimed it did matter because a practical project could use maths which had been compromised by it. The bridge they were building could fall down.

What is interesting about this is that it isn't quite clear which of the two great men were right.  Which comes first - the maths or the world it describes?

Personally, I would be sorry to lose the parallel universes that so inspired Philip Pullman.  But it may be that we have to return to Wittgensteinian common sense.