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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