It occurs to me yesterday that I am embedded in my own thoughts. I mean this is the sense that we get engrossed in a story or film and follow its narrative as it unfolds. Our perspective and horizons are closed down to the limits of the narrative so that it becomes a self contained universe. This is essential in a film for example because we could not accept the film as real and at the same time accept our sitting in an auditorium as real. At the same time we read a text and we either entertain the reality that we are reading a text, or we immerse in the “meaning” of the text, but not both at the same time.
This is identical to the issue of language and meta-language which Godel circumvented by introducing the numbering system so that “texts” could be referred to meaningfully within texts: isomorphism that provide correspondence between the substance of a text and the text itself.
Considering functions the other day I thought about that computing theorem which states that it is always possible to find a new program which takes a certain program as a parameter and computes the same results as that program: in other words an interpreter. This means there are at least 2 versions of every function that we can write. It means that the “result” of a function must be separated from the “implementation”. In that MIT lecture they showed that the Sierpinsky triangle could be generated by Linden-Mayerhoff diagrams as well as by Iterated Function Systems. There is no apparent similarity in method only in result. This means that one cannot explain an emergent property by the (computable) mechanism that created it. This is really why is it called emergent in the first place. So we immerse into the workings of a program or function (become a Turing computer i.e. someone who computes) and we start crunching through the rules of the system. We absorb into the narrative and close our horizons down to the limits of the system. The result and what emerges from our immersion however is quite different from that lower level of detail. To appreciate the result, indeed for a result to be distinguished from the system, for it to output, it must emerge from the system and be distinct from it. This is all present within the ideas of output and result before we even begin. This occurs because of context. A computer object will conceal as private its working and only make available, in accordance with a prescribed interface, certain values of its operation. These are deemed important to the outside. It is the outside which determined what the function outputs. Now this is the essence of one approach of the SRH that the inside cannot determine what it should be available on the outside of a function. Now Godel seems to have put the cat amongst the pigeons here by pointing out that separate the inside from the outside as much as you might try you cannot eliminate isomorphism and meaningful parallels between the two levels… something that the observant Godels among us can pick up on to show how inside and outside are not really separate. My argument here is that we still need the Godels amongst us to see these things: isomorphism don’t come out of the mix by themselves. So the Godels introduce a new level to the in/out systems: a level presumably which has its own in/out. I need to think this through still…
Linking to GEB (Godel, Esher, Bach) the inner message and the outer message are indeed separate. The outer message being the text or the code of the function and the inner message would be the meaning or the working of the function that we find when we immerse into. The pictures on the screen versus the story that is being told by those pictures. Vipassana Meditation in Buddhism specifically trains us not to get into the story being told so that we can see the pictures in their plain outer message way. The outer message is then the Truth and the inner message is the imagination that is an illusion. This I will investigate a bit further: my current understanding of sunyata (emptiness) is that the “form” or outer message is actually the illusion. An example being the bringing the components of a cake together and baking and being amazed at how this now delicious food came from what before was quite odd tasting. It is as though the cake has come out of nothing. We scientifically know the process that created it, like we know the processing of a computer function, but the result is an emergent property of that processing. Cake is not present in the original ingredients because if it was why do we need to make a cake? That refers to the blog on Making a few weeks ago. So the outer message is the illusion because it is quite separate from the ingredients. In Vipassana however it seems to be the other way around: the form is what we are sensing and the process is what we are thinking and so it is the illusion. This is Hegel’s view and that of Phenomenology for reference. Actually I see both views are the same. The point is that Cake is real. We eat it, we know it, we desire it. The process that creates it is something we learn and we imagine that it is happening. We don’t actually see it. Buddha uses cause and effect however to show us that that there is nothing in Cake that is not present in its ingredients to show us Voila! that the fixed form Cake (that we like) is empty and not itself “made” of something called Cake, but rather from things (we don’t like so much) called the ingredients. They are the same and our desires are for things that are ephemeral and substances less.
So returning to the start I realise that I am embedded in my thoughts. I find myself inside the story that my brain creates with all these words. Where I should try at will is outside these thoughts so that I do not take them to be too solid and Cake like!
Maybe this is the SRH. A function cannot identify its own output.