On 28 Feb 2014, at 15:28, David Nyman wrote:
On 26 February 2014 17:04, Bruno Marchal <marc...@ulb.ac.be> wrote:
Hi David,
On 24 Feb 2014, at 17:32, David Nyman wrote:
On 24 February 2014 15:50, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 24 Feb 2014, at 02:41, David Nyman wrote:
On 24 February 2014 01:04, chris peck <chris_peck...@hotmail.com>
wrote:
>>This is the same as saying that I will experience all possible
futures in the MWI - but by the time I experience them, of course,
the version of me in each branch will be different, and it always
seems to me, retrospectively, as though I only experienced one
outcome.
Each duplicate will only experience one outcome. I don't think
there is any disagreement about that. The problems occur when
considering what the person duplicated will experience and then
what probability he should assign to each outcome and that seems
to me to depend on what identity criterion gets imposed. Its a
consideration I've gone into at length and won't bore you with
again. But I will say that where you think that what Bruno wants
is just recognition that each duplicate sees one outcome, I think
that he actually wants to show that 3p and 1p probability
assignments would be asymmetric from the stand point of the person
duplicated. Certainly for me he doesn't manage that.
Correct me if I'm misremembering Chris, but I seem to recall
proposing to you on a previous occasion that Hoyle's pigeon hole
analogy can be a useful way of tuning intuitions about puzzles of
this sort, although I appear to be the sole fan of the idea around
here. Hoyle's idea is essentially a heuristic for collapsing the
notions of identity, history and continuation onto the perspective
of a single, universal observer. From this perspective, the
situation of being faced with duplication is just a random
selection from the class of all possible observer moments.
Well, the "just" might be not that easy to define.
If the universal observer is the universal machine, the probability
to get a computational history involving windows or MacOS might be
more probable than being me or you.
But how would "you" remember that?
By noting it in my diary, by inquesting my past, and hacking data
banks, or reading book on "my" origin.
Well, I'm not sure if it makes sense to say the Hoyle's universal
observer is the universal machine.
OK, but in this setting, the universal observer was the universal
machine from the "observable" points of view. It is not "just" the
universal machine.
The point is that if we assume comp, it seems there is room only for
the indexical self-ordering leading to rational (or over-rational)
sort of past.
I don't know to what extent his idea is compatible with comp.
OK.
But to be clear, you suggested above that a computational history
involving windows or MacOS might be more probable than being me or
you, so I asked you how Bruno, for example, could remember that,
meaning to suggest that of course you could not. I suppose it would
be some sort of problem for Hoyle's idea if one suspected not simply
that certain classes of non-human observer vastly out-numbered human
ones, but that they were likely to be asking themselves similar
sorts of questions. IOW, what might constitute an appropriate
equivalence class for ourselves?
It is very complex, and I try to make sense first, then see if it make
sense in comp, and from which points of view.
I am not sure that the notion of "observer moment" makes sense,
without a notion of scenario involving a net of computational
relative states.
I think the hypostases describe a universal person, composed from a
universal (self) scientist ([]p), a universal knower ([]p & p), an
observer ([]p & <>p), and a feeler ([]p & <>p & p)).
But I would not say that this universal person (which exist in
arithmetic and is associated with all relatively self-referential
correct löbian number) will select among all "observer moment".
Well, perhaps "eventually" it will select all of them, if we can
give some relevant sense to eventually in this context.
Is this not done by simple 3p arithmetical realism?
Not, I think, in the 1p sense, without a certain amount of
equivocation.
Ah... this I don't know.
There is a sense "God" select them all, but they inter-relations are
indexicals.
Yes, but the inner God cannot select them all simultaneously,
without the equivocation to which I refer.
?
And I suppose Hoyle's point is that if one imagines a logical
serialisation of all such moments, its order must be
inconsequential because of the intrinsic self-ordering of the
moments themselves.
That is the mathematical conception of an order, and there are
dualities between those ways of considering a structure.
You can already see that with the modal logic, where properties of
accessibility will characterize modal formula and theories.
Essentially he is saying that the panoptic bird view is somehow
preserved at the frog level, at the price of breaking the
simultaneity of the momentary views.
I am not sure I understand.
I think he is saying (as did Schroedinger) that the frog must see
every indexical reality, but cannot see them all simultaneously.
But this fits the comp 1p/3p relation, and Everett, etc. This is were
many of us seem to agree.
The "hypostatic" universal person is more like a universal baby,
which can split in a much larger spectrum of future 1p histories,
but from its first person perspective it is like it has still to go
through the histories to get the right relative statistics on his
most probable universal neighbors.
Won't this still be effectively satisfied by Hoyle's heuristic?
ISTM that "going through the histories" is a notion that splits in
the 3p and 1p views.
It splits the 1-p views, as in the 3-1 views, the 1-views themselves
never split.
I meant something different. The 3p view of a history is a matter of
the relations that obtain "eternally" between its elements.
At some level, OK. It is basically the "[]p"
The 1p view however is a matter of the relations that obtain
"momentarily" between discrete sensible contexts,
OK. It will be basically []p & p (in the lucky situation where I will
interview it for deriving physics, in practice, it is far more complex).
if indeed in the end we can make sense of such a conception.
I think so. Incompleteness forces the machine to have different logic
for []p and []p & p.
I'm pretty sure that this is how Hoyle saw it, because he took pains
to pick out the internal self-ordering of mutually-exclusive
observer moments as predominating in the spatial-temporal
perspective of a universalised "frog" . And there can be no doubt
that he was suggesting, in his analogy, that this frog is the unique
proxy for all of us and that its perspective is, for each moment,
the universal one.
OK. I let you judge and compare, and see if comp, comp + theaetetus,
are coherent with Hoyle's intuition.
I suppose this is equivalent to conceiving observer moments as self-
ordering monads in terms of which any random serialisation over the
entire class must eventually preserve the right relative statistics.
Eventually I use only s, 0, +, *, and classical logic.
May be you will get the tools to make this enough precise so that I
see what you are talking about.
This is "my" problem, I have to unravel things in term of numbers
relations. The 8 "hypostases", and their multimodal combinations
provides means to take into account many nuances.
I am not sure about "observer moment", although for the 1p I guided
myself through possible semantics for the S4Grz logics.
"Eventually" here relies on a similar opacity to delays in
continuation as you argue in the UDA, plus the reliance on prior
relativisation to some specific spatial-temporal orientation, to
get a 1p notion of temporal order.
We must derive the spatiotemporal order by the sum of the
computations below our substitution level.
It is a problem for the "classical computationalist" (by which I
mean accepting the classical theory of knowledge, which is mainly
that know(p) -> p. By definition. A more "introspective axiom" would
be know(p) -> know(know(p)). And that are the main part of the modal
logic S4, in the classical or boolean context.
But perhaps this formulation of a discrete observer moment is
incompatible with comp?
I think it is premature to decide if the 1p can have a discrete
structure. I would say that I am agnostic on this, but that the
evidences are more that the arithmetical knowable and feel-able are
associated with the continuum. Both the evidences coming from the
"arithmetical", and the empirical evidence.
It is an open problem.
Well, of course I don't insist on this. I just find the idea to have
interesting consequences (which we've hardly touched on). But it may
just be misconceived.
Of course it is the point where I switch to technic, and I am aware of
the difficulty of the questions.
Of course, in the arithmetical reality, it don't get it, it is an
indexical internal point of view.
Perhaps it gets it "eventually", in the sense I outline above?
Hmm... I think it gets it at the start. The question, sometimes,
seems to me more why did it lost it?
I think you ask difficult theological question, it might be still
very hard to translate them in arithmetic or in arithmetical,
computer-science theoretical terms.
I suspect so.
The situations of having been duplicated one or more times are
then just non-simultaneous selections from the same class. This
gives us a consistent way of considering the 3p and 1p (or bird
and frog) probabilities symmetrically. That is, it is now certain
that I will confront each and every 3p continuation from a unique
1p perspective, just not simultaneously.
That said, this approach retains a quasi-frequency interpretation
of probability in the case that there are fungible or equivalent
continuations. For example, if the protocol mandates that I will
be duplicated 100 times and 99 of my copies will be sent to a red
room and one to a blue room, it would be rational to anticipate a
higher "probability" of continuation associated with the larger
class, even though each continuation is individually certain in a
different underlying sense. This is just to say that subjective
uncertainty (or the expectation of probabilistic outcomes) is a
function of incomplete knowledge at any given point in the sequence.
OK.
I know that Bruno quarrels with Hoyle's idea as being superfluous
to, or possibly even incompatible with, comp
I think about it. I try to make sense of it. That might have sense,
but then it remains to look at it in arithmetic.
I mean the relations between a person and the universal person "in
her" is complex, and the splitting between []p and []p & p is part
of it.
but personally I still find it a neat heuristic for pumping one's
intuition on the indeterminacy of first-personal expectations.
OK.
It is just that I expect platonism to be counter-intuitive and so
intuition pump must be handled with care. But you know that. I just
try to understand the point.
Absolutely. I appreciate your interest.
The problem with comp is that between the "terrestrial" level, of
the effective and creative sigma_1 complete machine or relative
numbers, and Arithmetical truth, there are many intermediates
"divine" structure (in a weak sense of divine, with divine = non
Turing emulable, but possibly sense-full, arithmetical relations.
With comp, the math is there, but that might not be a so nice news
for a philosopher, especially if he get through some math teaching
trauma.
I am against death penalty, but I am willing to make exception for
the mathematicians which disgusts kids from mathematics for sadistic
purpose.
Yeah, my high school maths teacher used to throw wooden blackboard
erasers at the heads of his students. Perhaps he thought that would
give his instruction more impact. Fortunately it was apparent to me
even then that he was just a foul-tempered old time-server rather
than the embodiment of the spirit of his subject. Nevertheless he
wasn't able to stimulate much appreciation for mathematical enquiry,
which revived independently only somewhat later in life.
OK.
I hope I will succeed to provide the main line of the role of self-
reference in the rise of physics, and we can mediate on the universal
observer and its link with the universal machine.
Sometimes I am embarrassed to have a mathematical theory, but that's
what comp makes possible.
Bruno
David
Bruno
http://iridia.ulb.ac.be/~marchal/
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