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.

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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