On 11 Aug 2017, at 13:40, Bruce Kellett wrote:

On 11/08/2017 7:13 pm, Bruno Marchal wrote:
On 11 Aug 2017, at 02:11, Bruce Kellett wrote:
On 11/08/2017 9:45 am, Stathis Papaioannou wrote:

"What will I see tomorrow?" is meaningful and does not contain any false propositions. Humans who are fully aware that there will be multiple copies understand the question and can use it consistently, and as I have tried to demonstrate even animals have an instinctive understanding of it. Probabilities can be consistently calculated using the assumption that I will experience being one and only one of the multiple future copies, and these probabilities can be used to plan for the future and to run successful business ventures. If you still insist it is gibberish that calls into question your usage of the word "gibberish ".

Not everyone will be successful in this scenario. No matter how mane duplications cycles are gone through, there will always be one individual at the end who has not received any reward at all (he has never seen Washington :-)). This is the problem of "monster sequences" that is so troublesome for understanding probability in Everett QM.


? You might elaborate. It looks like the white rabbit problem.

It has nothing to do with the white rabbit problem. In the duplication model, each iteration gives W and M, each with unit probability.

In the third person view. OK. That is part of the enunciation of the problem which will concerned the first person points of view.





This is a trivial consequence of the fact that there is a person created in W and in M every time, so we know in advance that these occur necessarily.

OK. (assuming mechanism)



So after N iterations of the duplication (each person is re- duplicated on each iteration) so there are 2^N sequences after N iterations.

Indeed.




One of these sequences will be N occurrences of M, and one will be N occurrences of W. So the prediction of the person with N occurrences of M, based on induction from his past experiences, will be M, with p =1.

Not if the person is rational and understand mechanism. Even if you have thrown a perfect coin 1000 times and get head, the probability to get head is still 1/2. If the iteration is continued, most of the copies will confirmed that p = 1 was wrong, and by definition of the first person and mechanism, we have to take their feelings into account.







Similarly, for the person with N occurrences of W, his prediction will be p(W) = 1.

Similarly wrong.



People from other sequences predict W or M with varying probabilities. Very few actually predict p(W) = p(M) = 1/2.


They are incompressible in the limit, which appears quickly. 1/2 is provably the best bet, due to that provable incompressibility of the vast majority of sequences.





In the duplication scenario, the third person view enables one to put a natural measure over these sequences -- just by counting the number of sequences with particular relative frequencies. The low measure (probability) sequences are those known as "monster sequences" in Everett QM, and they can be seen to be of small measure in the classical duplication scenario.

Very good; so you did get the point. That was not apparent from above.





The problem in QM is that no external observer is possible.


That is the problem with Copenhagen QM.





A probabilistic interpretation then becomes problematic because we cannot count over all the sequences: we only have the one sequence that we actually observe, and we can have no way of knowing whether or not what we have observed is a "monster sequence". This gives rise to the question as to whether observation can ever be a reliable guide for determining the underlying probabilities -- how can we use any sequence of observed results as a test of some theory? The sequence we have observed might, for all we know, be some 'monster sequence' of very low probability.

Yes, that is science.

We cannot prove there is a reality, and no experience can prove anything about that possible (or not) reality.

But we have beliefs, some more solid than other, and when we do experiences, either our beliefs are confirmed, and we learn nothing, or our beliefs are refuted, and we learn something. If a very solid belief is refuted, we learn a lot.





The problem is usually circumvented by assuming a probabilistic model from the start, but that is imposed from the outside and does not arise from the theory itself.

Until Everett realized that the probabilities were *first person (plural)*, and relative. But he uses digital mechanism, which "aggravates" the situation, in the sense that now we have to extract the universal wave from a sum on all computations, or explain why the classical aberrant dreams are rare, and, question, are their rare in the near death first person experience.





Deutsch and Wallace get around the problem in this way -- they assume at the outset that small amplitudes correspond to small probabilities, so monster sequences are assumed to be very unlikely, and observed frequencies are assumed to converge towards the true underlying probabilities. But then, this convergence is not uniform, or even necessarily monotonic: the best one can say is that observed frequencies tend to converge only in probability to the true probabilities.

Probably so :)



Hence there is circularity inherent in any such approach to probability in Everett QM, where every outcome occurs with probability equal to one. Deutsch and Wallace do not avoid this circularity in their attempts to derive the Born Rule.

OK, but they try. But if they succeed, they still miss the first person, which is not even called for, and so they miss that for getting right both the physical and the psychological perspective the only way to get it is by studying the "observer" ability to introspect itself, and what, mathematically, can he proves about itself and its consistent or sound continuations.

Everett has just decided that the physical laws applies to the physicists.

Gödel has do the same in math, someone, with the birth of metamathematics: the mathematical study of mathematical theories, and the relation between truth and proofs in general.

In that approach, we can distinguish many ways a universal machinery can look at itself, and isolate from inside the unique measure which has to exist, if digital mechanism is assumed.

The problem of Deutsch and Wallace and many physicists is that they take the brain-mind identity thesis for granted, even Everett did it explicitly. With mechanism, this is corrected, and, to be short, we need to use a the theological structure imposed by the difference between the provable and the true.



I see the problem with mechanism, (indeed that is the result of the UDA: there is a measure on first person experience problem), but in Everett the problem is solved by Feynman phase randomization, itself justifiable from Gleason theorem. Then the math of self- reference shows that, very possibly, Gleason theorem will probably solve the classical case too, given that we find quantum logics at the place needed.

Everett does not solve the measure problem, or give any non-circular account of probability in QM: Feynman phase randomization is a possible solution to white rabbits, but it has nothing to do with the origin of probabilities.

OK.

You make me think that John Clark is right. The digital mechanist self- duplication explain where the probabilities comes from. Below our substitution level, an infinity of universal numbers compete "the multiverse", above our substitution level, a finite number of universal compete (cosmos, earth, collegues, FORTRAN IV, bacteria, colleagues, family, ...).



Gleason's theorem does not avoid the circularity problem either. All that Gleason's theorem demonstrates is that for space of greater than two dimensions, any viable probabilistic interpretation has to accord with the Born Rule. But that does not demonstrate that one can actually have a probabilistic interpretation in the many worlds case.

With mechanism, you might be right. It is probability only up to some renormalization, but in the big internal picture of any universal machinery (in Post, Turing, Kleene, Church sense), it is a measure of plausibility, and the limit of all renormalization possible of arithmetic is not between 0 and 1, but between 0 and infinity.





Zurek is quite dismissive of Gleason's theorem because, as he says, it assumes the additivity of probabilities, rather than deriving this result from within the theory.

Of course, with mechanism, you got them from the boolean structure, perfectly well determined by the triangle of numbers of Pascal.

I mean in the ultra-simple case of the iterated self-duplication. It is equivalent with a Random Oracle. In that case the computable sequences are among the white rabbit/Monster-sequence.

In the "real" case, in front of the sigma_1 reality, I prefer to tackle the problem by the arithmetical indexicalization of the person. Gödel, Löb and eventually the summing-up theorem of Solovay paved the way, and give a tool to formulate and partially solve the problem, and up to now, the evidence are this might work, and that if this does not work, well, we will learn something.


You have to show that results in QM give a model that satisfies probability axioms, such as those of Kolmogorov --

Let me first get QM. Let us all se if the universal machine get QM.



one can't just assume from the start that these axioms apply.


You are right. But it is very difficult. Sometimes I think that a "proof" in arithmetic of P = 1/2 will require Riemann Hypothesis. the reason is that the infinities of the prime numbers might encode the complete complexity of the relation between addition and multiplication, and reflect the fact addition+multiplication is already Turing universal. Then, the Riemann zero would give the spectrum of a universal quantum system. And the probabilities would be the usually boolean one in the outer picture, and be the standard epistemic one in the many first person, inner, picture.






This is one of the main strengths of Zurek's 'envariance' approach, based as it is on the symmetries of in entanglement -- he does not have to assume a measure (probability) or probability axioms, he derives them from entanglement.

I have heard about it. It seems very interesting.





Are-you defending John Clark? That would be nice! He convinces nobody since years, and some helps might be handy.

I think that John does have a point -- the prediction of probabilities different from unity is possible only in a third person overview of the situation.

?

I do not see the realtion with John Clark idea that there is no first person indeterminacy, which is that if I am asked where I will feel to be after the pushing, the correct (assuming mechanism) answer is that "I don't know".



The prediction p(M) = p(W) = 1 is all that the set up actually allows one to conclude prior to the duplication.

That contradict what you say above. What you say here is correct from a third person description made by someone not doing the experience, or by someone doing the experience and still describing the outcome in the third person way, like John C. did once. The guy in Washington can say "I am in Washington and Moscow", but this means he does not answer the question which is the city seen, not the city seen + the city imagined by hoping the doppelgangers has been well reconstituted too.






Are you telling us that P(W) ≠ P(M) ≠ 1/2. What do *you* expect when pushing the button in Helsinki?

I expect to die, to be 'cut', according to the protocol. The guys in W and M are two new persons, and neither was around in H to make any prediction whatsoever.

Fair enough.

You think the digital mechanism thesis is wrong.

Personally I do not argue on true or wrong. My point is only that it is testable, and that it fits well with the observations until now.


Incidently this provides a rationalist conception of a notion of (universal) person playing the main building block in the appearances. It might help people to learn to listen to themselves, and favors the spiritual on the material, perhaps, for a change. My meta-meta-goal is just to illustrate that it is about time for theology to come back at the academy of science, and allow people to doubt, and be skeptical, in the fundamental field.

The intuition of the mystic is right, we are at the center of the universe, we are the builder of the realities. But "we" is taken in the large sense of "universal Turing machine" or "universal number". Well, the Löbian numbers, or Gödel-Löbian numbers.

The definition is in Gödel 1931 paper, i.e. in Davis Dover book "The Undecidable" from page 17 to 22. It is a simple sequence of 46 definitions starting from division and getting the non computable, but semi-computable Beweisbar. The one later Solovay whose propositional logic is given by G and G*.

God created the Natural Numbers, and looking at them, he said "good".
Then God told the Natural Numbers "add yourselves", and looking at that, he said "good". Then God told the Natural Numbers "multiply yourselves", and looking at the result, he said ... "oops".

Bruno



Bruce


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