On 20 Apr 2017, at 09:23, David Nyman wrote:
On 20 Apr 2017 8:05 a.m., "Bruno Marchal" <marc...@ulb.ac.be> wrote:
On 19 Apr 2017, at 19:09, David Nyman wrote:
On 19 April 2017 at 16:48, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 19 Apr 2017, at 12:56, David Nyman wrote:
On 19 April 2017 at 08:24, Bruno Marchal <marc...@ulb.ac.be> wrote:
John has never write one clear post refuting the step-3 which
would make it possible to answer by one post. There is no need for
this, as the answer is in the publications, which makes clear the
1-3 distinction, so the ambiguity that John dreams for cannot occur.
I've often wondered whether Hoyle's heuristic could be a way of
short-cutting this dispute. Hoyle gives us a way to think about
every subjective moment as if it occurred within the 1-view of a
common agent. Essentially the heuristic invites us to think of all
subjective experiences, aka observer moments, as a single logical
serialisation in which relative spatial and temporal orientation
is internal to each moment. In comp terms this conceptual agent
might perhaps be the virgin (unprogrammed) machine, on the basis
that all such machines are effectively computationally equivalent.
Exactly. With comp you have to fix one universal base to name all
the other number/program/machine, and their relative states
relatively to the universal numbers which implements them. The
universal numbers are what define the relative computations. A
computation is only a sequence of elementary local deformation, and
once a universal sequence of phi_i is given, they are parametrised
by four numbers some u, and its own sequence of phi_u(i,j)^s =
phi_i(j)^s (the sth step of the computation by u of the program i
on the input j).
But Hoyle heuristic does not seem to solve the "prediction"
problem, for each 1p-views there is an infinity of universal
competing universal numbers (and thus computations) below the
substitution level (and worst: it is impossible for the 1p to know
its substitution level).
Sure, but I believe the idea is that after the metaphorical
"selection" (i.e. not a real process - more below) of any given 1-
view, the "agent" finds itself immediately 1-relativised to a
particular psychological history. Hence ISTM that, from each 1-
view, relative predictions would be the same as in the usual comp
situation. Of course, there is always the issue of differential
measure over the entire class of 1-views. Hoyle's heuristic imposes
a quasi-frequency interpretation of probability for any finite
segment of the serialisation and, in terms of histories, we do
indeed find ourselves (at least psychologically) bounded within
some quasi-finite segment. So I imagine Hoyle would want us to
think in terms of the "most probable" continuations being selected
more frequently, whether these are considered absolutely pre-
selection, or relatively post. Of course the agent is bound to
"encounter" 1-views of lower probability, but then this is
ultimately a matter to be resolved in the struggle between
consistent remembering (hardly ever) and inconsistent forgetting
(almost always). One could say that the former are perhaps
analogous to the in-phase, least-action part of Feynman's path
integral approach and the latter with the out-of-phase part.
That looks nice. So now, I ask to you, and to everybody a question,
which is important, and still open although I do have some opinion/
hint.
You are in Helsinki, and you are scanned and annihilate as usual,
and (3p)-duplicate in three exemplars: one is reconstituted in W and
two in Moscow. You are told before, in Helsinki, that in Moscow, the
two exemplaries are in the exact same state and environment, and
that this will last forever (they will never 1p differentiate). The
question is asked when you are still in Helsinki. What is P(W) and
P(M) ?
Then, I ask the same question, but in Helsinki we are told that some
differentiation will occur between the two copies in Moscow, at some
later time.
You mean what is the effective differential measure of the states
representing P and M, and should any subsequent question of the
divergence or otherwise of the two examplars of M affect our view of
this? Good question. Not sure. I'm tempted to answer, in terms of
Hoyle, that a larger measure of any particular class of pigeon
holes should always increase the "probability" of encountering
exemplars of that class in any given finite traversal of the
serialisation. So in that case from a Bayesian perspective I ought
to say that P(M) is twice P(W). What's your view?
My view is that the measure is on the distinguishable first person
views sequences. So it is P(W) = P(M) = 1/2 in the first case where we
are told in Helsinki that the copies in M remains forever similar
(assuming this possible, which it can be in virtual rendering of that
duplication, say), and it is P(W) = P(M) = 1/3 in the case the
experiences of the M-reconstituted persons diverge, even if it
diverges only after a long time, by the Y = II rules. A bifurcation in
the future is, subjectively equivalent to a duplication in the path.
(This answers also a question raised by John Clark in his recent
comment to you, and I think we have discussed this also with respect
to the unionist/fusionist problem raised by Bostrom, a long time ago).
The probabilities are plausibly not on 3p-states or 1p-observer
moments, but on distinguishable 1p-histories (memories of sequences of
1p-observer moments).
Bruno
David
Bruno
Anyway, in this way of thinking, after my 3-duplication there are
of course two 3-copies; so in the 3-view it can make perfect sense
to say that each copy is me (i.e. one of my continuations). Hence
my expectation in that same 3-sense is that I will be present in
both locations. However, again in terms of the heuristic, it is
equally the case that each 1-view is occupied serially and
exclusively by the single agent: i.e. *at one time and in one
place*. Hence in that sense only a single 1-view can possibly
represent me *at that one time and that one place*. Hoyle shows us
how all the copies can indeed come to occupy each of their
relative spatio-temporal locations in the logical serialisation,
but also that *these cannot occur simultaneously*.
I think it is the indexical view, that Saunders attributes to
Everett.
Well, it's clear from the narrative of the novel that Hoyle meant
the 1-view.
It is also implicit in Galileo and Einstein relativity theory. With
the discovery of the universal number in arithmetic, and their
executions and interaction are described by elementary reasoning,
although tedious like I have try to give you a gist lately :)
The crucial point to bear in mind is that according to Hoyle, both
of these understandings are equally true and *do not contradict
each other*.
Mechanism would be inconsistent. But even arithmetic and computer
science would be inconsistent. It would be like the discovery of a
program capable to predict in advance the specific answer to where
its backup will be upload in a cut and double paste operation.
In "real life" that is made precise and simple, I think, by the
temporary definition of the first person by the owner of the
personal diary, which enter the teleportation box.
In the math, that will be be featured by the difference between
"[]p", and "[]p & p", with other nuances. They do not contradict
each other, as G* proves them equivalent on arithmetic, but they
obey quite different logic. A logic of communicable beliefs about
oneself, and a logic of informal non communicable personal
intuition/knowledge, here limited to the rational. "[]p & p" cannot
be captured by one box definable in arithmetic, we can only meta-
define it on simpler machine than us that we trust. here you have
to introspect yourself if you agree or not with the usual axioms I
have given (which is really the question, did you take your kids
back from school when a teacher dares to tell them that 2+2=4.
Furthermore, comp or no comp, they are surely consistent with
anything we would reasonably expect to experience: namely, that
whenever sufficiently accurate copies of our bodies could be made,
using whatever method, our expectation would nevertheless be to
find ourselves occupying a single 1-view, representing a
subjectively exclusive spatio-temporal location. Indeed it is that
very 1-view which effectively defines the relative boundaries of
any given time and place. Subjective experiences are temporally
and spatially bounded by definition; it is therefore inescapable
that they are mutually exclusive in the 1-view.
Assuredly.
So what Hoyle's method achieves here is a clear and important
distinction between the notion of 3-synchronisation (i.e. temporal
co-location with respect to a publicly available clock) and that
of 1-simultaneity (i.e. the co-occurrence of two spatio-temporally
distinct perspectives within a single, momentary 1-view). Whereas
the former is commonplace and hence to be expected, the latter is
entirely inconsistent with normal experience and hence should not
be.
But did Hoyle accepted the pure indexical view?
Yes, that he meant the 1-view is quite clear from the narrative
of October the First.
Did he not attempt to make a selection with some flash of light?
But remember it's only meant to be a metaphor. So the flash of
light (or the guy wandering among the pigeon holes) in effect plays
the role of stepping through the computational continuations, when
considered relative to any point of origin within a history.
Otherwise the metaphor would have been static.
It is tempting to select a computation among the infinities, like
when adding hidden variables and special initial condition in QM,
or like when invoking irrationality like Roland Omnès still in QM
(sic), or, no less irrational, like invoking God in QM again (like
Belinfante), or like invoking Primary Matter in Arithmetic (like,
I'm afraid many of us do unconsciously, by a sort of innate
extrapolation, which has its role in helping us to not confuse the
prey and the predator.
With computationalism, what is important is to understand that this
leads to a difficult mathematical problem, basically: finding a
measure on the (true) sigma_1 sentences. This is made possible only
if we get the right logic on the intensional variants of
provability imposed by incompleteness.
I should explain better this: there are three incompleteness
theorems:
1) PA (and its consistent extensions) is (are) undecidable (there
is a true arithmetical proposition not provable by PA, which is
assumed consistent).
2) If PA is consistent, then PA cannot prove its consistency.
3) (which is the major thing) PA proves 2 above. That if: PA proves
(~beweisbar('f') -> ~beweisbar('~beweisbar('f')').
Many people ignores that Gödel discovered (without proving it) that
PA already knew (in the theaetetus sense) Gödel's theorem. That
will be proven in all details by Hilbert and Bernays, and
embellished by the crazy Löb contribution. More on this more later.
My scheduling tight up exponentially up to June I'm afraid.
By the way, I shall be on holiday in Sicily from April 20th until
May 12th (one of me only, I trust) so I probably won't be
appearing much in the list during that period.
Meanwhile I think about the intermediate level, but it is
difficult, if not perilous, to give an informal account of the
formal and informal differences between the formal and informal,
and this without going through a minimum of formality, ... well
don't mind too much.
May be you can meditate on the Plotinus - arithmetic lexicon,
keeping in mind we talk about a simple machine we trust to be
arithmetically correct, the machine will be able to "live" the
difference between
truth (the One, p)
rationally justifiable (the man (G), the Noùs (G*) []p
knowable (the universal soul, the first person, S4Grz) []p & p
(Theaetetus)
====
Observable (Intelligible matter, Z1*) []p & <>t
Feelable (Sensible matter, X1*) []p & <>t & p. (Plotinus might
be a good intermediate level, somehow, Smullyan too perhaps)
Just one truth, but viewed according to many different type of
views (the hypostases above), and different "observer moment"
defined by the many universal numbers in arithmetic (the box are
parametrized by the four numbers above, in a first simple
description).
I will dream on this.
Take it easy. Happy holiday!
I'll do my best!
David
Bruno
David
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