Iain Cameron's Diary
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2007-01-29 - 8:29 a.m.
Rosen says that Mozart engages with sensuous surface of grief and sorrow while also evoking the depths. This was evident on Saturday night in Holy Trinity Gfd when the Gfd Philharmonia had a crack at the Cm Adagio and Fugue and the Gm Symphony. Yersterday I ordered a 2nd hand copy of part 2 of the Moz string 5tets which has the AnF. The anniversary edition of Grace with various extras is also on order.
I stumbled across some disciplines in the last week – morphological analysis is one such – a general problem-solving method which came out of astrophysics. It claims to be able to reduce a mess to a problem which can be broken down into puzzles. The comparison is made with Triz. Another is social simulation which involves trying to get a computer model to impersonate a collection of active entities – firms, peoples or organisms for example. This seems to have come of our evolutionary biology. Paul Omerod who has had quite a big hit with his book about failure is part of the community. Then there’s algorithmic information theory, which is probably best left alone as far as I am concerned although its hard to ignore anything which comes out of Turing’s halting problem. Anyway there they are and if there is a theme threading through it would be using computers to manage and understand complexity.
Behind the AIT stuff are some issues which seem to have got hold of me. There is a chain from Mill to Frege to Russell to Wittgenstein to Turing. I have been dipping into David Bloor’s famous book – the one he was writing in the office next door when I was in Edinburgh for a year. He goes back to the link between Mill and Frege and then further back to unpick the famous Greek proof that the square root of two can’t be expressed as a faction. The Edinburgh School makes a lot of the point that any bit of argumentation has more than one consequence and Bloor illustrates this with the Greek proof. There is a whiff of empowerment about this style of argument – the reader is invited to think more creatively about the proof – almost as if it was a poem.
I have lost Bloor’s book on Wittgenstein – I bought it as an e-book – and somehow a change of laptop has locked it up. In the late 30s lectures on the foundations of mathematics LW looks back on his earlier engagement with the Russell-Frege programme in a quizzical way. Its useful that his statement of the latter is so concise in the Tractatus. I have ordered a book from what’s called ‘The New Wittgenstein’ school of criticism which apparently works on the continuities between the early and later LW. The philosophy of maths has to be part of this.
If one goes back to Mill – as Bloor does – back to the point before Frege laid the foundations of a view of the relationship between maths, logic and philosophy which has been very influential, it seems to be that one is opening up the possibility of a different view of what maths is. And this is why AIT looks attractive – this crew seem to be arguing that the relationship between maths and physics is much closer than had hitherto been supposed. This strain of thought made me go back to Mary Hesse – a Cambridge philosopher of science who was active and influential in the 60s. I am not sure I its that easy to get hold of her book on models and analogies. My memory is that it has a lot about the use of mathematics in physics.
My inclination is to believe that there is an analogical echo in mathematical symbolism – in how people develop new results by moving signs around on the page.