On 14 Dec 2012, at 22:44, Stephen P. King wrote:

On 12/14/2012 5:09 AM, Bruno Marchal wrote:

On 13 Dec 2012, at 16:50, Richard Ruquist wrote:

On Thu, Dec 13, 2012 at 5:35 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:
My prejudice is that the projection from dreams of the mind is to a
unique physical universe rather than every possible one.

On the contrary. It leads to many-dreams, and it is an open question if this leads to a multiverse, or a multi-multiverse, or a multi-multi- multiverse,

capable of such a projection even if it is not Occam?

CTM predicts it a priori. And it is OCCAM, in the sense that it is the simplest conceptual theory (just addition and multiplication of non negative

Bruno, I presume here you mean that CTM predicts many dreams a priori.

OK. Many dreams, and the feeling to belong to only one dream/reality.

Dear Bruno,

You still do not see that to 'make sense' (yes, Craig's term!) of what you are saying, we have to take a complementary view. On one hand we have the imaginary "god's view" where All is One,

With the CTM, arithmetic is enough. I don't think it is imaginary.

and on the other hand we have the finite observer's actual view of "there are many that I can see".

That is what is made precise in the TOE *derived* from the CTM.

Is the projection to one SWI universe and/or multiple MWI universes
also predicted a priori?

Yes. From the first person perspective. It predicts also the trace of the "many" (dreams/realities/worlds) once we look below our comp substitution level. The projection is no magic: it is like in the Moscow/Washington duplication. Once the copies open the reconstitution boxes, they can only observe Moscow OR Washington---exclusive OR.

My concern is that consciousness is
predicted at the many dreams stage before projection and that
consciousness could decide (a risky term) on a single SWI physical
universe with quantum probability.

Well, CTM predicts this, but with the CTM probabilities, which are not yet well computed. If they differ from the QM probabilities, this would make CTM in difficulties.

Does not this cry out for a discussion of the differences between probabilities and actualities?

Not just a discussion, but an entire mathematical treatment, which has been done.

In other words, the realm of "many dreams" contains all possible
eigenfunctions at various amplitudes. But in my view, if all
eigenfunctions become real in different physical worlds, the amplitude
information is lost despite Deutsch's "measure" argument. That is,
amplitude information is only conserved as frequency of events in a
single physical world integrated over many trials. For Deutsch's
argument to be correct the same "many worlds" eigenfunctions must
exist in every universe of the multiverse, which in my mind makes the
MWI multiverse an illusion.

The "many-worlds" eigenfunctions can be addressed with the frequency operator of Graham, Preskill, and are indeed the same in all universe, even in the Harry Potter universe.

Are not Harry Potter properties, properties that are mutually inconsistent?

Not necessarily.

QM is invariant in the multiverse.

    What does this mean, exactly?

That the SWE and the Born rules applies everywhere, even in the Harry Potter universes, where it seems to not apply.

Even if I find myself in a Harry Potter universe where I saw a billions particle in the 1/sqrt(2)(up + down) all the time being up, I have to bet on 1/2 for the next one.

One thing that I would like to point out. We should not assume 'perfect information' of the ensemble of universes! Statistics are often interpreted as if the sample is a perfect representation of the ensemble. I see this as assuming a 'god's eye view' of all of the members of the ensemble that can: 1) simultaneously access all of the members and 2) compare them to each other instantly. This idea is a complete fantasy!

Not in the CTM where you can use the math to make it precise.

Everett already show that such relative probabilities does not depend on the choice of the basis, nor on my "place" in the multiverse.

I strongly disagree with this statement! Everett showed the exact opposite; that relative probabilities completely depend of the choice of basis and framing.

Prove? This is contrary to what Everett said, and I have try to contradict him on this, eventually he is right. Deustch tought like you but has eventually change its mind. There are no prefer basis, and with the CTM there are not even a prefer ontological theory.

The main message of QM, how ever you may wish to interpret it is that there does not exist a preferred basis.

That's my point. Especially without collapse.

There are very strong number theoretic arguments that the every idea of a relative measure cannot exist in the absence of the selection of a particular basis and framing (aka 'point of view').

Of course, that is why the state is relative, but you can describe the coupling observer+object in any base.


With CTM you can say that the multiverse is an illusion: only (N, +, *) is real, and the multiverse itself is a construct of the mind of numbers to figure out the local arithmetical reality. But then the moon is also an illusion.

Sure, it is an illusion, but it an illusion that we can all agree upon and thus behave as if it where not.

There might also be clusters of different multiverses. We are only at the beginning of the exploration of arithmetic.

Indeed! You need to consider the idea that arithmetic can encode multiverses that are not composable into single Boolean representations. Have you any experience with the work that is required to "debug" a computer program? Given the set of all possible computer programs, how does one consider whether or not a pair of programs are bisimilar?

"In theoretical computer science a bisimulation is a binary relation between state transition systems, associating systems which behave in the same way in the sense that one system simulates the other and vice-versa. Intuitively two systems are bisimilar if they match each other's moves. In this sense, each of the systems cannot be distinguished from the other by an observer."


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