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).
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.
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? Did he not attempt to
make a selection with some flash of light? 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).
Take it easy. Happy holiday!
Bruno
David
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.