On 5/1/2011 7:08 AM, smi...@zonnet.nl wrote:
I think that in this discussion one is assuming that the classical picture of an OM applies and that then leads to the false notion that you need to look at a sequence of states. But this is completely false. Obviously the brain is effectively classical, but classicality from quantum dynamics is only achived because of decoherence, so the brain gets entangled with the environment. The same is true, of course, if you run any classical machine, like your PC.


Now, the computational state of your brain, represented as an entangled state with the environment, can be written in the suggestive form:

sum over input of |input, corresponding output>

In fact, the entire computational history will be present in the state, as it exist at any moment.

I don't see how that can be. Simply from an informational perspective, the computational history can have a lot more bits than the digitized brain can store as a state - at least as a classical system. I think you must be including all the information that exists in the environment due to interaction with the brain. This of course has been spreading out from the brain at the speed of light; so it's not clear to me where this history starts. With birth? At the big bang? At the last Everett split? At the last Everett split that corresponds to a different quasi-classical "thought??

Brent



This is why I think that in Bruno's program, which apart from the technical details, involves deriving physics from the theory of computation, one can jump to quantum mechanics much more straightforwardly. Also, since decoherence happens in the position bases, one should be able to derive space-time from first principles as well. Simply put, if you have well defined computational states, you should get quantum mechanics plus general relativity free of charge.

Saibal

Citeren Bruno Marchal <marc...@ulb.ac.be>:


On 30 Apr 2011, at 09:09, meekerdb wrote:

On 4/29/2011 8:45 AM, Bruno Marchal wrote:


On 29 Apr 2011, at 02:42, Stephen Paul King wrote:

Please allow me to ask another question. Is the notion of an “observer moment” corresponding to “the smallest possible conscious experience” related to Bruno’s concept of substitution level? ISTM that both act like the idea of a coarse graining on an ensemble that is used to define the entropy of a system in that all of the members of the ensemble that are indistinguishable from a macroscopic point of view.

You can easily relate them.

Let us distinguish the 1-OMs from the 3-OMs. The 1-OM are experiences of an individual when his brain is in some computational state S.

I have reservations about this casual identification of "observer moments" and "brain states". I can accept that a brain can digitally simulated and hence be realized by a succession of states. But I find it very doubtful that each state corresponds to different "thought" or "observation" much less conscious "thoughts".

I was identifying the 3-OM with the brain state. The 1-OM, with consciousness, are in Platonia, and are related with the whole structure of the computations, notably through the measure space. Locally we can still associate consciousness with some open interval, but comp attaches consciousness (and matter) to something much more sophisticated than a "sequence of states". It is the counter-intuitive part of computationalism: the failure of the identity thesis.




Such thoughts are slow things that unfold over time and must be realized by many successive digital-brain states in terms of which they overlap with other thoughts both temporally and spatially. So digitizing brains doesn't imply that consciousness occurs in discrete time slices.

You are completely right on this. I did simplify my talk a little bit on purpose, so as not being too much technical. With comp we can associate a consciousness to a third person event (like "my sleeping friend"). But my friend's consciousness is realized only through an infinity of number relations.

Bruno





Brent

We assume comp, of course, so we can attribute a 1-OM to some such state. The 3-OMs are given by all the equivalent computational states S, S', S'', ... obtained in the universal dovetailing. For example the state of your brain emulated by a program computing the Heisenberg evolution of the Milky Way at the level of strings, or the state of your brain obtained by another program simulating the quantum fluctuation of the void, or the state of your brain obtained by a fortran program emulating a lisp program emulating a prolog program emulating ... emulating the search of the solution of some universal diophantine polynomial, etc. All those programs are emulated by the universal dovetailer, and all the finite pieces of computations obtained by such emulation can be proved to exist in a tiny part of arithmetic. There are aleph_0 such finite piece of computations, and they are all "run" by the UD. The first person glue them into a priori 2^aleph_0 infinite computations. For each of them, you can always find in arithmetic a computation which is more fine grained. But you, by the first person indeterminacy, cannot know in which computation you are. Actually you can be said belonging to all of them, and your physical laws are determined by the measure on your continuations of such computations. From this you can see that the highest level of substitution defines the measure on the possible lowest one, which you cannot distinguish, by definition. That is why, if we look at ourselves below that level, we have to be confronted with a strong form of indeterminacy. Boltzman's idea cannot be used at this stage, though, without having a measure on the relative computations, and this prevents a direct use of the notion of entropy. We need more physics for that, but, as I have already explained we have to derive that physics from the numbers and self- reference if we don't want to miss the relationship between the quanta and the qualia offered by the splitting between provable self-reference and true self-reference (G and G* and their intensional variants).

Bruno

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



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