Godel Esher Bach – Final lecture – mega-summary of a my own interests from 1990 onwards

 

Referring to Lecture 6 of this series: http://ocw.mit.edu/OcwWeb/hs/geb/VideoLectures/index.htm

A load of notes here about different related things.

 

 

First: The Sierpinski Triangle has an area of 0: that is the limit of 3/4^n as n->inf. But this means that within each pixel in the normal rendering (like above) there is another complete Sierpinski Triangle with an empty triangle (1/4 of the area) in the middle. The blank area is 1/4 * (0.75^n – 1)/(n-1) which approaches 1 as n->inf. There are no pixels in the true triangle!! It has no area. So what does the Sierpinski triangle look like if it has no area? And the approximation that is rendered approximates to a shape of 0 area how?

The MIT course is excellent and has refocused my eyes on some important concepts. Isomorphism was previously present in what I knew as Hermaneutics – the idea in text interpretation that a text has many layers of interpretation. My favourite film ‘Betty Blue’ is of interest because of an interpretation that I have of it. Isomorphism simply being a word for things having parallel structures that can be superimposed like football and rugby, or music and poetry.

What I question however is to what extent the structures that are recreated in the isomorphism are “really” present in the original? Does my interpretation of the film really represent something “in” the structure of the film? If we say that there is an underlying structure in the film then apart from the film itself which isomorphic interpretation shall we use to represent that structure. Another way to see that question is to ask what links isomorphisms, or what makes analogous things similar? What makes things different or the same. There is some dialectic involved in thinghood itself which gives a mixture of similarity and difference between things.

How is the rendering of the Sierpinski triangle then isomorphic with the real triangle? Mystery! In fact this is the age old problem which leads very fast to the Third Man Fallacy if we are not careful. That is to say we create a new entity to represent isomorphism (an arrow for example). But then we have a new problem how this arrow relates to the two isomorphic parts. It forms an infinite regress and a chain of infinite number of entities each relying on the next to explain isomorphism. Sooner or later we just have to accept some form of relation as an axiom… and why? Isn’t this the SRH that to explain a relation in terms of a relation creates an infinite regress…

The other big issue from the course is Emergent Property. Up until today I didn’t believe in it. I have played around on the computer for decades and been hopelessly disappointed by the uninspiring creativity of my ants or genetic algorithms. If anything such agent simulations have turned me off the subject and made we realise how remarkable the diversity of the real world and even make me doubt evolution! I am always left with the unremarkable “so what” of a magician who knows how the trick is done. Alan Turing getting excited about his self organising black and white splodges or even Kieran’s computer simulations on the computer screen are “so what” – you are getting out what you put in: a load of rules which effectively transform (in a lose interpretation of the word) the Euclidian plane to create the shapes. Put those ants in a line and suddenly their creativity is less etc etc. The “plane” while featureless and boring enables remarkable transformations to occur – that is what amazes us most I have thought. Odd also that the lecturer should have been put off Biology by realising that it was all the logical implication of Evolution and not been put of everything else by the same thought! This is what puts me off automata.

However, that said, I do understand now what they are going on about. The point is that whatever shapes are created they are not “explicitly” coded into the computer at start time. The same occurs to a pot of paint being spilled. There final splatter is not explicitly encoded into the pot of uniform paint before the accident – it emerges from the complex interaction of paint under gravity, the air moving into chaotic vortexes as the paint falls through and catastrophic release of energy through the paint as it hits the floor. That final “splatter” is an emergent property of a paint spill.

That doesn’t explain the issue of Emergent Property though. The most important thing is to realise that Emergent Property points to “levels of description”: that is what I have missed. It is true that a “splatter” is a short hand way of describing the unimaginably complex interaction of lower order things that creates the splatter. There are 2 levels of description. Now I understand at last why people (especially in MIT that has championed this Revolution since the 1960s) get so excited by this idea. This I believe is the revolution that gives us writers like Fritjof Kapra. This links with the fractal work that it creates “levels of description”. While fractals repeat in a simple way they illustrate the issue of Scale and Level of description that is a profound feature of the world. Which comes first: Scale or Fractal? Does the universe have scale BECAUSE of its self-creating iterative nature or is it the other way around? That was the interesting message I took home in a recent previous post.

Finally in this post the questions that were being discussed at the end are exactly what this blog has ended up focussing on. It is mentioned a few times that such questions are not good for our “survival” but this blog is a question about Life in is broadest understanding of which survival has proven to be a rather trivial aspect. Maslow’s hierarchy of needs (which appears in the lecture) seems more and more inadequate every times I see it now. Does he really mean that the more you eat then the more security you will be able to get and the more self-realised you will get? Self-realisation starts even while you are building the pyramid as does esteem, love, friendship, etc. In economics you even get paid and food for building the pyramid so its hopelessly confused. I think I’ve completed a more realistic understanding of "needs” in this blog so won’t revisit.

The one issue that occurs again and again in the lectures and which makes me cringe is also quite strange because we are all talking about Holism and trying to get away from Reductionism but in a Reductionism mind set. I even realised I was doing the same. Here are my thoughts…

I disagree with Emergent Properties because you can’t get something from nothing. But I had to agree that the emergent property level of description couldn’t be described within the terms of the simple agent rules – a new term had to be introduced to describe what was going on. The problem to solve is how to describe the properties of a simple system – how much more complex is the new system. That was my quest since 1995 and I’m back on course altho its low down on the 2do list. The idea then is that self-consciousness is a very high level new-term to explain what is going on as a system becomes more able to refer to itself. (Altho I reject this now that is the idea that i reject). But from my Buddhism training I am aware that all “things” are nothing but their components. So I suddenly realised that I have been holding two completely opposed positions. When Buddha says that “things” are illusions what he is saying is isomorphic with saying that higher levels of description are Emergent from lower levels. That is to say that a “chair” is an emergent property of its components – this I have examined at length in this blog many, many, many times before. So why am I against emergent properties then? They are the same concept I already hold!!!

What emerges from this is my issue with the whole class and the lecturers: none of them realises that everything is an emergent property of something else. When the lecture says again and again atoms/brains/neurons etc as the building blocks of the body and the mind he doesn’t seem to show awareness that these are just emergent from lower levels (quarks etc). But worse than that it is a strange loop and the lower things are affected by the higher levels of description. The point is that you can start anywhere, take that level of description as your axiom and then see higher levels as emergent properties of that level. Computer science is one place to start but it is no more “fundamental” than politics or anything else. This links with logic because we can chose any axioms we like – that choice lies outside the system.

The error made by everyone is to hold onto the idea that for something “exist” it must have some “existing” thing inside it – some homunculus like thing that renders it “existing” in isomorphism with the error in thinking that there is a person inside our heads looking at the world through our sense… how does this explain “looking” since it uses “looking” in the definition. This is the problem of self-reference again and worth investigating…

Reductionism thinks that this “emergent property” emerges from real agents that underlie the emergent property. The discussion of how software runs on a computer assumes that the computer is somehow more real than the software. But the computer is an emergent property itself as are the atoms and the quarks etc. Every”thing" is an illusion as Buddha discovered a miraculous emergence from suitable conditions (suitable being circularly defined - tautological): just levels of description. Interesting that no-one in that lecture seems to even suspect this – this is the problem of Materialist doctrine and Self which plagues the West. The existince of reductionist and hollistic thinking in the West is the result of this error in our thinking and this is why I personally dislike Fritjof Kapra’s books because as far as I know they don’t acknowledge that they themselves are only a product of the sickness that they seek to reflect upon. As I suppose is Zen and the Art of Motor Cycle Maintenance and their ilk.

Returning to the the Sierpinski triangle quickly we have to chose to stop out of the recursion and create a pixel otherwise it would never render anything since its area is zero. Isn’t this the problems of axioms. We have to chose some fixed level of description as a starting place else we can’t see anything at all. Maybe this is how something comes from nothing – it’s in the fixing of a level of description.  An “attachment” is ignorance that things only look this way because of the fixed level of description we have got. Now I must be careful not to get too stuck in this way of thinking, but have a long way to go until I get some satisfactory proof that self-reference is impossible. Some useful quotes from the lecture:

>A book “Programming the Universe” is mentioned. The universe needs another universe to model itself. One direction I was looking at lat year was using Turing machines to show that there are limits to self-computation: need to pick up this.

(Student) Latiffe - “I am the one being observed” - [my thought, yes so I can't be the observer in SRH]
”When you start talking about yourself you are talking nonsense” … “Self reference is not a well formed thought.” END.1.22

[basically how does reference work? What level of description is necessary for reference? This is the new approach to the SRH]

(Assistant) Kieran: "This structure cannot introspect upon what it is made from because then it wouldn't be itself anymore". 1:31:31
That is the essence of the proof I’m looking for. However I do accept now that a stable situation may arise through iteration – and may have some fractal structure.