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Note that the Markov chain contains EVERYTHING in the system and OMITS the knowledge state of the observer.
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This Markov Chain idea is new for me - very beautiful. Thank you TinyTree.
So does this idea that the Markov chain contains EVERYTHING bring us directly to decide about infinity? In my view, Infinity is a religious intangible. Infinity means the Markov chain has no closed perimeter.
I think the perimeter is closed and the Markov chain forces us to decide one way or the other. There can be no infinity the moment you make a final perimeter to Everything. And until you do, how can you be sure the markov chain is not somewhere disrupted?
Secondly the sheer duality is breathtaking. The knowledge state of the observer is omitted! Reckless, breathtaking, wonderful. Is this not the duality of consciousness and material form? What else is the ultimate duality - here it is simple and you have to declare this ultimate duality. This is for me like a Goedel axiom - you put something outside the system and say, look, that is unprovable, taken for granted or we cannot get started to even think. And here the single element or axiom said to be outside the system - the knowledge state of the observer. Exactly. Of course there are so many observers, who disagree...
The duality of every linked position ("state") seems to get us to some progress in thinking about things - step by step, this state connects how to that state, exactly the way to proceed. I'd like to expand the word state to consider this process or flow connects to that process or flow - tricky but reality is not cut and dried.
Recursion - YES! I do not see the specific logic used to declare the universe is recursive, and that would tend to indicate it is just taken as an axiom, a just so story. But the question is spot on - once you think of the Universe as a large birthday cake, you wonder how to slice it and how to keep on slicing it and you focus on recursion. Recursion seems so evident in the structure of all there is - which was first - recursion or reality? So many observed fractal patterns, recursion is the basis of biology and the umbilical cord/DNA life stuff - and recursion answers so many aspects of Everything in a very simple and elegant way. If you were some God, or universe designer, would you not say, recursion is essential?
Recursion, duality, fractals and dialectics, contained finite universe, this Markov chain idea pushes all my buttons.
Where I have trouble with this concept is primarily the concept of frozen time in the word "state" as in "state diagram". There is no reality to frozen time, and our challenge is to map fluid dynamics of processes. It is nice to say, remove all the time and just consider states. Nice but not nice enough. However, apart from using the word "state" the method here does not seem to really concern timeless states, the model here seems to apply smoothly to dynamic flows and processes. A major challenge would be explaining turbulence, and the apparent fickleness of "fate", or chaos, the entropy that we observe, and so on. Look:
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So why is there a plural "states" available to the future of the Markov chain rather than a singular "state
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So I am saying, you have INCLUDED knowledge of the observer in presuming a single time origin state: it is surely a matter of opinion and knowledge to say time is assymetrical with multiple futures and a single origin. Maybe there is only a single future and multiple pasts? Again however shocking to consider this as an observer, it is OUR knowledge as observers that tells us one way or the other, and i prefer to omit observer knowledge, why not simply omit conscious awareness and model that separately?
Finally I have to wonder, is the Markov chain for Everything essentially dendritic, or a neural network? That is indirectly a question about time and origins. Again the word "state" presupposes a viewpoint OUTSIDE of time, where frozen time is actually never observed.
Oh one more - if the knowledge state of the observer is omitted, hold on, there are multiple observers ... every fruit fly has it's own observation of reality ... so i am kind of mapping out a hypermarkov chain, a neural or dendritic network of reality to consciousness as many many dual pairs, observer-reality and reality-observer though interactions. Where the idea of any Gods eye view of a single reality is defunct. Why presume a God just to see a single reality, when clearly we all experience things differently. Hypermarkov would mean a network of interconnected but subtly or grossly different realities defined by the observations of the total finite set of observers. Sure humans share and agree on reality, but the elephants knew the tsunami was coming, in their reality...
Some very stimulating ideas here.