Notes on Godel, Esher, Back XX

Did a naughty thing today and after reading the Overview went straight to the last chapter XX. I really wish I had read this book as a kid since it is amazing how much it relates to many of my own interests... but at the same time I wouldn't have been able to disagree as much as I do with it if I hadn't developed my own ideas.

Just some notes here ... chapter still unfinished. If anyone ever tries to read this blog (apart from myself) apologies it really is a dumping ground and random paper trail of thoughts.
[check the essay you wrote to yourself on this picture, did you get the aufhebung (surprise) of Escher drawing the lower level of the picture?]

> Hofstadter refers to M.C.Eshers hand-drawing-hand picture and to the reality that lies outside the picture; namely that it was drawn by M.C.Esher. As he points out the hand-drawing-hand is possible but only within the picture where a higher reality takes over the construction. Brilliant. This is the SRH very clearly (and seemingly quite different from what I wrote this morning). We could have a drawing of M.C.Esher drawing that famous picture. What would be interesting within that picture would be the explicit reference to "someone doing the drawing". This is isomorphic with the construction of the drawing we are looking at. Now it is that "surprise" (as Hofstadter calls it) of seeing my current level isomorphic with something within that level which is what I used to get a lot as a kid as I explored the world and which brought me to be fascinated with "self" in the first place. This was the insight at seeing the circle of light. So we realise suddenly that M.C.Esher picture was itself drawn by an unseen hand outside the level, just as we get the surprise in seeing the unseen hand that "drew" the universe. Obvious direction for H to go that he doesn't and I don't understand why? But I disagree (sort of) but first the SRH.

The equivalent of drawing a picture in formal systems is applying a transformation rule. So we need to construct a system in which a transformation rule creates a string which is isomorphic with the transformation rule that the string itself encodes. Analogous to "drawing" a picture of a man drawing a picture. That is the system is isomorphic with itself (rather than just strings being self-referential). This is A.I.M.E. that i was so keen to create. The point is that in this system, just as the man drawing a picture (in the picture) suggests to the viewer that this picture itself was drawn, so the transformation rule in the system suggests an "external" transformation rule. Finally a formal system that points outside itself!!!! That would be SRH :-)

It is so odd: reading Hofstadter feels like it has put me back in touch with stuff that somehow I used to know but have forgotten - when I am sure that I never really thought all this stuff before else I would have written it down. He really does get to the point nicely.

What he called levels I have called narratives in this blog. But what I don't get is why he thinks that there is a Grand-Narrative of reality that is somehow "true". G.E.B. is just a narrative. Hofstadter writes it with full consciousness that it is a tangled hierarchy itself and he points outside the narrative quite in accordance with the S.R.H. What I don't get is why he thinks that outside this narrative the narrative of brains and neurons etc holds any more significance than any other? Isn't there something outside that narrative of material reality as well and so on ad infinitum. He doesn't mention God much but he points outside a lot. I don't see why? It is like he is seduced by positivism so deeply that even with such a profound understanding of narratives he still can't escape.

He talks about rules and meta-rules and then notes that at the lowest level it happens automatically. The lowest level rules don't need "permission" to run. Thus a computer runs by itself, although chess in a chess program needs to be executed. Yet isn't this simply because reality is at that level and we can't get outside this narrative? A chess computer thinks that it runs automatically just as H says that we think we run automatically. I don't see at this stage why he holds onto the idea of a "true" level of underlying reality... unless that is his final point.

Basically if that is his final point G.E.B. is a brilliant book on religion far beyond the petty concerns of A.I. that it aims at. A book all religious people need to read because we always think we know God when he is always outside our thoughts!

A1 talk on anarchism.

Don't like the size of this book - it's a bit vain. Does he really expect us to read it all?

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