On 20 Apr 2017, at 11:53, David Nyman wrote:
On 20 Apr 2017 10:08 a.m., "Bruno Marchal" <[email protected]> wrote:
On 20 Apr 2017, at 09:23, David Nyman wrote:
On 20 Apr 2017 8:05 a.m., "Bruno Marchal" <[email protected]> wrote:
On 19 Apr 2017, at 19:09, David Nyman wrote:
On 19 April 2017 at 16:48, Bruno Marchal <[email protected]> wrote:
On 19 Apr 2017, at 12:56, David Nyman wrote:
On 19 April 2017 at 08:24, Bruno Marchal <[email protected]> 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.
Could some future bifurcation, perhaps long delayed, really be
regarded as affecting a duplication question at some earlier, not-
yet-differentiated juncture? Interesting question.
(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).
My point to John was just that his proposition would have no
material impact for the restriction I proposed on a plausible 1-
view, from the human perspective at least. My response was agnostic
on the question of measure.
OK.
The
probabilities are plausibly not on 3p-states or 1p-observer moments,
but on distinguishable 1p-histories (memories of sequences of 1p-
observer moments).
Yeah, this is a tricky one without a single "right" answer of course.
Indeed, when we rest on our intuition, but that is why it is nice that
with computationalism, we can handled the problem by using the
(addmitedly counter-intuitive) Gödel-Löbian logics of self-reference.
First things which is given by the machine: the difference between
what we can justify and what we cannot justify, but still know, and
then the non knowable, etc.
Of course, we can continue on the intuitive level, but we are warned:
with computationalism, the intuition ([]p & p) is in a sort of tension/
conflict with what we can justify. It is here that the scientist ([]p)
want to eliminate the first person and god ([]p & p). But this is
exactly the eroor of Penrose: to take for granted his own equivalence
between []p and []p & p. that belongs to G* minus G. It is a "machine-
theological" blasphem.
Hoyle's pigeon hole notion seems to encourage us to think in a
Bayesian way about both absolute and relative measures of classes of
observer moments. In an Everettian context, we are encouraged to
conceive more probable immediate continuations as being represented
in larger measure in the evolving relative wave function - i.e. with
respect to the Born rule. Indeed this is necessary to give any
meaning to the notion of probability in a context where every
possible continuation is conceived as being represented in some
measure. And this would appear to apply over spectra of
continuations that may be distinguishable in some limit but are not
so very different.
So again one should perhaps rationally predict any of such similar
continuations as more or less equally probable and hence summing to
a higher total measure as a class.
That is a bit unclear to me.
Hence we should rationally expect typically to encounter
continuations of this general sort. So what does this mean for
actually indistinguishable continuations (whatever we can take that
to mean in principle)?
It means that the M guy is in exactly the same states. At some point
this means same life and after-life. Clark is plausibly right on this:
having to identical brain will not change your relative measure
(normally: this has not yet been extracted from the Z1* logic,
although it is very close, just to abstract even for me).
(It saves us also of the idea that a brain with big axons and big
neurons, like if fusing the two identical brain in your head, would
have a bigger measure, which would threatened computationalism, as you
would need to ask non digital functional question to the doctor like
the thin-ness of the basic logical components).
Still unsure, but I can't completely shift the intuition that you
couldn't expect to clone even indistinguishable continuations
indefinitely without rationally impacting the prediction scenario.
Could you?
I don't see the difficulty, even if I agree this is difficult to
realize in practice. But this occurs in arithmetic, many infinite
computations are undistinguishable from the 1p views. I have good
reason to think that they don't add up. Yet, if they differentiate,
they "retroact" on the measure. That is not more astonishing that the
invariance of the 1p for the reconstitution delays, even when the
delay are very big. It gives a similar apparent "retroaction". QM have
those too, like in the temporal Bell's inequalities.
If we add fusion and amnesia, the "not-counting-of similar 1p
histories" is closer to explain the negative "amplitude of
probability" interference of QM, but the intuition get tricky, and, as
I said, I prefer to switch to math, given that computationalism gives
us computer science and mathematical logic to get the logic of measure
one, even if this is without really answering the question, at least
not yet (even the quantum extracted from arithmetics remains weird and
counter-intuitive. It is an intrinsically difficult subject).
Bruno
David
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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