I have to say, I'm not really convinced by this explanation. In
conventional QM, the state vector evolves continuously between
measurements, at which point the state vector appears to collapse to
an eigenvector of the observable. I say "appears" here, because any
Everettian will object that it is the universe or mind splitting or
differentiating at that point.

The 1-OMs correspond to these measurement points, but the timing of
the measurements and choice of observable is entirely first person,
and entirely discrete. Certainly, I can count the bits streaming in
through my senses, but since these arrive at a completely different
rate from the bits received by other people sharing my world, it is of
little use in communication (or doing physics). So what we must do is
refer to external processes that change in predictable ways that
everybody can observe. These we call clocks, and without exception,
are entirely discrete - even the so-called analogue clocks. We model a
hypothetical continuous time that these clocks count out, but it is no
more than that - a convenient fiction allowing us to get on with
discussing physics. Even if that "physical time" is found to be
continuous or not-continuous (the quantized space-time issue), it has
no bearing on the fundamental discreteness of "subjective time", the
discrete nature of which we cannot be aware. 

If you are sceptical about whether one could not be aware of the
discreteness of one's own subjective time - let me refer you to the
saccadal experiments Dan Dennett writes about in "Consiousness
Explained". Here, subjects are wired up to eye trackers. Whenever
their eye performs a scaccadal movement (flicks between points of
view), a computer inserts random rubbish on the computer screen. When
the subject's eye focusses on the screen, meaningful data is displayed
on the screen. To the subject, the computer screen is displaying
normal, continuous data. To everybody else, the computer screen is
randomly jumbled. The discrete nature of the subject's visual stream
is obvious to everybody but the subject erself.

On Tue, Jan 04, 2011 at 06:57:39PM +0100, Bruno Marchal wrote:
> 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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Prof Russell Standish                  Phone 0425 253119 (mobile)
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Australia                                http://www.hpcoders.com.au

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