Hi again Günther,

>
> Again a question for Bruno ;-)
>
> There are certain arguments (Deutsch, Wallace, Greaves) that propose
> that they can derive probabilites (and the Born rule) from decision
> theory - although I am not convinced (see for instance Price 2008 -
> http://arxiv.org/abs/0802.1390).


Careful: they derive the Born rule from decision theory AND Everett QM  
= the SWE+comp, mainly).
(but the UDA tells us that with comp we have to derive also QM

>
>
> Criticism notwithstanding, I think that Deutsch Et Al have made
> interesting inroads into the problem of probability and am optimistic
> that it will be solved.

I think so too.


> Everett is at least not worse off than other
> intrepretations concerning probability.


I share with Everett and deWitt the opinion that the SWE provides its  
own internal interpretation. Indeed, I believe Arithmetic provides its  
own internal many interpretations.




>
>
> But I have a question concerning the UDA: here, we don't even have
> intuitive concepts of wave interference, decoherence etc anymore,  
> which
> can account for different branch weights.

The UDA provides an intuition on the weights branch: its terribly  
subtle redundancy on the computations. So the first "intuitive weight"  
is just the measure on the computations going through your state. But  
this is a priori purely additive. So this means that either a  
quantized (digital) version of a UD will win the "measure battles"  
among universal dovetailers, or that we are forgetting to take a data  
into account. And indeed we forget that we have to take into account  
the measure *from the point of view of the machine*. This lead to the  
*intensional* variants of the logics of self-reference G and G*, which  
leads to the material hypostases (for the probability), which leads to  
a quantum Goldblatt -like arithmetical interpretation of quantum logic.
The question is: will this give rise to a sufficiently symmetrical  
base, like in QM?
The material hypostases multiplies themselves into an infinity of  
weaker variants, giving rise to "arithmetical projection" surrounded  
by linear and symmetrical structure, but this is not in my theses. I  
am still hoping for finding sufficiently rich "Temperly Lieb Algebra  
so that I get a notion of space or universal braiding ...




>
>
> In a sense, I don't see how a computation could be "cancelled" by
> another one.

Tricky problem! Sure.



> Do you have intuitions of how to derive the Born rule from
> the measure of all computations?


By the arithmetical quantum logic. We should derive the SWE and the  
projection rules.
Don't expect anything easy here.



> Why should some consistent histories be
> more probable than others?

Because there are more numerous, and handle better the coupling with  
noise and perverse arithmetical histories (white rabbits). If not,  
well, we will *have* reason to doubt comp.



> (there is of course the Quantum Logic and
> Gleason's theorem connection which we have discussed shortly)

Yes. Exactly. We have today just that sign. It is the last thing I  
got, in 1994.



> - but I
> don't see any _intuitive_ connection, of why there should by histories
> with different probabilities?

The intuition is the redundancy of the UD's work, and the way  
histories have to be measure *from the point of view" of the machine.  
In AUDA: the "material pov", which by UDA is given by a probability or  
credibility measure on the consistant extensions, is given by Bp & Dt  
(and their variants B^n d & D^m t, n least of equal to m). With p  
sigma_1 ("comp" in the language of the machine), this gives rise to B  
logics without necessitation rule, it is enough to get an arithmetical  
quantization).

Our intuition is lost here, of course. But we could have expected  
this, no?

Best,

Bruno

http://iridia.ulb.ac.be/~marchal/




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