On 04 Jan 2011, at 12:03, Kim Jones wrote:


On 04/01/2011, at 9:11 PM, Bruno Marchal wrote:


3-OM are discrete (assuming mechanism)
1-OM does not need to be. The measure bears on the 1-OM, and is related to the measure on all infinite computational histories (including oracles), and this is a set of cardinality 2^aleph_0, and the topology is unknown, but it is more plausible that the set of 1-OM is a non discrete structure, like most possible notion of subjective and physical time.

So the experience of the continuous, the analog experience of time is subjective - an 'interpretation' that my mind supplies(?).

That is right at some level of description. It is similar with the feeling that a movie is showing us continuous deformations, when we know that it is digital. In that case the continuum can be said to be created by your mind.

But if the "ultimate reality" is arithmetical truth, or just the tiny part of it constituting the deployment of the universal dovetailing, there is a sense to say that the continuum you are confronted with "really exist" independently of yourself, as far as you allow a reality for the conscious first person experience. This is a consequence of your global indeterminacy with respect of *all* computations.

Imagine the work of the UD.
It is a working execution of one program: the UD. (be it emulated in arithmetical truth or in a physical universe: this does not matter for the present point). The UD gives a first notion of universal discrete time: the steps of the UD. Let us call that the UD-time. (Or second if you take the first to be 0, 1, 2, 3, ... (the succession of the natural numbers itself)). Now, remember what the UD is doing. It generates the first program P_0 (in some universal language, or in RA, or PA, of fortran or lisp, etc.), then the first input, 0, and then it executes one step of that program. Then, unlike a universal interpreter or machine, instead of computing P_0 applied on 0, it generates the second program. Then it comes back on the first program, and generates a second step of it, then it generates a step of the second program, and then it generates the third program, and so forth, dovetailing also on the inputs. In that way, it will generates all programs step execution on all inputs. But *you* cannot be aware of the execution steps of the UD. No conscious creature generated by the UD can be aware of the UD-time. Now each program P_0, P_1, P_2, P_3, on any input, generates its own time, by its own steps of execution. But some P_i are themselves dovetailers and can generate still other time. All those times are entirely third person describable. But the first person time, like the physical time (which is first person plural, or should be, assuming comp, and no error in the reasoning, ...) cannot be related to any of those particular P_i times. The reason is that your "next 1-OM" is given by a measure on all the P_i computations going through your current 3-OM (your brain state, which you is digital, by the DM assumption). That is what shows the UD Argument. But there are infinitely many such 3-OM. For example, the UD will generate all the quantum histories described by the quantum state of a gas nebula, or of our galaxy, dovetailing on the complex number initial segments, leading already, from the 1-view, to a continuum of Kim Jones and Bruno Marchal, etc.). Our consciousness is not attached to any particular implementation of a computation, but to all of them. This follows from UDA-1-4 mainly.




In fact, "I" don't experience 'observer moments' at all.

You are right. 3-OM is just the computational state. But the 1-OMs are given by the distribution of all the upper level equivalent 3-OMs computations, and the distribution is given by ALL the 3-OMs and their computations, including the infinitely and continuously infinite 3-OM of the sub level of substitution. You are in a (comp) superposition state of all what you ignore (or are isolated from) below your level of substitution. And you are right. One 1-OM has no successors 1-OM. It is more like a point on a surface or on a line. Each 1-OM has a neighborhood of a continuous set of 1-OMs. The natural third person topology can be given by a relation of distance defined by the length of the similar part of the computations involved, but the topology is "derived" by the logic of Bp & p (the link between the computation and the truth, defining the knower). This makes the subjective time "very real", not just a construction of my mind, but also a construction of the universal mind, or the UD, or that tiny part of arithmetical truth. We participate both if I can say.


I experience a 'river of time' or a paved walkway with a continuous border over which I seem to glide.

Well said. And in computer land, like in the country, rivers bifurcate, fuse, and all go to the sea.



The 3rd person version is where I get to watch 'you' do various discrete things (moving your limbs) that I will perhaps agree lead to a similar experience of continuity for you. Actually, I only notice 'you' when you tread on each paver. You disappear as you move between them. This is because when I 'notice you' - the duration of my noticing you (my focussed, conscious attention) forms the duration of the 3-OM.

Betting on some high level of substitution, like the 'neurophilosopher' that is correct, I think. But you can never see completely my body, given that once you look at the detail, you will cross our (hopefully common) substitution level, making what constitute myself relatively to you rather cloudy. Indeed you will see the trace of the parallel computations on which the UD dovetails.



1-OM = analog experience of time

Yes. Typically an indexical (like "me", "I", now, here, there, etc.). And as an experience it is not a point, but an interval, or an open set in a topological space. This is coherent with the different kind of semantics needed for each person points of view (S4Grz1, X1*).




3-OM = digital experience of time

Not so much an experience than the use of the natural numbers successor order for describing digital or arithmetical relation between computational (or not) states. The teacher says that the lesson will finish in 15 minutes (digital), but if the lesson is boring (subjective experience) that can seem very long and continuous (subjective experience).



Ca va un peu? Tu me dira...

Ouais c'est très bien :)

Bruno

http://iridia.ulb.ac.be/~marchal/



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