Iain Cameron's Diary
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2005-10-10 - 11:18 a.m.
Early on in the book he introduces chaos theory and in particular the Mandlebrot Set – the intricate pattern which has become the icon of chaos and fractals. His point is the Mset is an amazingly intricate object which is generated by following a very simple rule – you can get the rule in about ten minutes even with a base of GCSE O Level. Penrose thinks that the intricacy and self-replication within the Mset strongly suggests that it exists as an independent entity – out there – apart from the thoughts of the mathematical community. For what its worth this sounds right to me.
Part of the fascination of chaos theory is that it has brought to our awareness things which have an amazingly intricate and beautiful make-up. Before that theory was developed we had no idea that such things existed and if asked even people with a fair amount of background knowledge might have dismissed the description as a fantasy. After chaos theory the world is quite simply a more intricate place.
However that is an over-simplification because the world in question is not just the universe of physics – its something over and above that – by giving precise effect to that ‘over and above’ is the tricky part. My guess is that Penrose will be arguing that this other world (sometimes called the third world) is the world that the intuition that is foregrounded by the Godel proof connects with – that mathematical intuition explores the third world. (And of course computer algorithms don’t or can’t.)
One of the newsletter that I subscribe to has thrown up the following article
The author tries to pull together indicators from different sources as to how social life and culture are evolving and may continue to evolve in the medium term. In particular how the model of consumer-choice may be beginning to wear out – also the emerging importance of friendship as a stable and stabilising feature of people’s lives.
I have always found harmony quite stable. Sometimes it seems to be too stable in that there are no new ideas to be had but I am finding Scriabin Magic Chord a good stimulus. For a long while I have liked the dominant extension which involves putting together two dominant chords which are a minor third apart – for example playing C7 in the left hand and an A7 in the right hand. Essentially this means adding a C# and and A to the C7 as the E and G are common. In the SCM it is the D7 that is added to the C7 (the G is omitted from from the C7) – both these chords have an agreeable character to my ears.
It is a common trick in bebop to substitute dominant 7ths which are a tritone apart – and so you can substitute a Gb7 for a C7 and the relevant extensions become Eb7 and Ab7.
I have been thinking about the chord which can be made from the notes not in the SCM – if the SCM is based on C7 then the notSCM chord is a Db9 with a sharp 11th – its easy to work out how this chord is played if it is dropped a semitone. In fact it is close to C-SCM – there is only one note different – the C-SCM contains an A whereas the notSCM chord down a semitone contains a G (as well as a Gb) . It’s the tension between the G and Gb that give the notSCM chord its bite.
Anyway I have been practising some standard jazz-turnarounds with these various chords inserted and they bring a freshness to what can be rather tired sequences.
Anyway I went looking for some late Scriabin piano music on cheap labels to see if I could hear anything of the SCM but I didnt manage to find any. So I bought the Penrose book instead.