On 11 Mar 2011, at 13:07, Andrew Soltau wrote:

On 10/03/11 14:10, Bruno Marchal wrote:

On 10 Mar 2011, at 13:47, Andrew Soltau wrote:

All the moments exist, and as Deutsch points out, as you summarise, 'The appearance of change is already explained by the fact that there are different frames that have an implicit sequence and in which the observers state is different', but for change to actually happen, the magic finger must move. Otherwise reality would be like a movie film sitting in the can in storage.


The change in the "working program" is brought by the "universal machine" which interprets it.
Yes, but you still require an explanation of how the machine actually runs. All possible states of the machine exist 'already' in an arithmetical universe.

States "alone" do not make sense. What makes a state a machine's state is that there is a universal number, or the "initial" universal system itself (elemantary arithmetic, say), which includes it in a computation. It is a bit similar to Rovelli's relational idea, but in the context of arithmetic. It is standard to define states and (universal) machines, and pieces of computations in arithmetic. What makes a computation emulated in arithmetic is an infinity of true relations between numbers, and in this case most are provable in a tiny part of any formal arithmetic (like RA, that is Robinson arithmetic, which I use to fix the idea).



All you need is an initial universal "machine". It happens that addition and multiplication, with first order logic is enough to define such an initial universal system, and the UDA+MGA shows that the laws of mind, including the laws of matter, does not depend on the choice of the initial universal system.

So elementary arithmetic does emulate, in the mathematical sense, computations.
Naturally. But you still require an explanation of how such arithmetic, or how such computations, are carried out. This is where you need an 'external' time.

Why? The internal time defined by the basic sequence of the natural numbers is enough. It can be used to define the notion of computational steps, and of sequence of computational steps. Assuming comp, you are "here and now" because it exists a sequence of computational steps leading to your current computational state, at the right level. Of course, there is an infinity of such sequences, and we will have to develop a relative uncertainty calculus on them (or prove that they cannot exist and refute comp).




Arithmetic does not just describe all those computations: it literally emulate them. This is not trivial to show, although computer science gives the insight. Computations in arithmetic are not like movie, they are like a observer line universe in a block universe.
Ok. And you still require an explanation of how something moves along the line. This is what is missing from physics. It is inherently absent in any concept of straightforward existence.

Nothing moves in the "block-universe", be it arithmetical or primary physical. But we can explain why machines will develop discourse about moving things, and, in the case of comp, we can even explain why a part of that moving will be considered as incommunicable by the machine from its first person point of view.




To add an external time reintroduces a mystery where it is not needed.
Provided you can explain how we come to be experiencing change, in other words, how it comes to be that the computation is running, as opposed to simply existing.

"Running" is defined in term of sequence of steps. For all universal number, there will be a notion of steps associated with it, and a notion of running, which will be defined by reference to the successor relation.




That use of time is like the use of "God" as gap explanation by the pseudo-religious (authoritative) people. You will end up with a primitive time, a primitive matter, and why not a primitive "god" responsible for all this.

That is, in my opinion, the correct insight of Deutsch.
In which case you have to accept that the passage of time is an illusion.

I would not call it an illusion. It is only an illusion from the point of view of "God" (arithmetical truth, say). I would call it a personal (first person plural or not) subjective reality. Bergson's subjective duration is retrieved in the "Bp & p" hypostase, and physical time is, or should be, retrieved in the material hypostase Bp & Dp (& p). Physical time (and physical space) appears as first person plural sharable propositions. All we need is a good theory of self-reference, but this is provided by theoretical computer science/ mathematical logic.

(The consequence of UDA are admittedly "unbelievable". That is why the original name of the Universal Dovetailer Argument was "Universal Dovetailer Paradox". But AUDA explains the paradox. The "divine intellect", that is the modal logic G*, proves the equivalence, with respect to arithmetical proposition, between all hypostases, but explains why machine cannot see that equivalence, and why such hypostases (definition of person's view) are all different and obeys different logics (intuitionist temporal logic for the first person, quantum logic for the material views).)

This is also why in none of my papers I separate UDA from AUDA, because UDA is too much unbelievable in the Aristotelian era, but AUDA explains why it has to be like that. The genuine Gödel's bomb is not that machine are limited, it is that machine can study their own limitation, up to the geometry/topology of their relative consistent extensions.

In this case, you are not a being which witnesses change.

Er ... you confuse me with God I'm afraid.
Once I develop special memories, by virtue of being in a state belonging to a computation, I will have the feeling of witnessing change. For many computations, if the measure problem admits a solution, that change will have a referent in term of locally stable physical reality.
If the measure problem does not admit a solution, then comp is false.


You are simply, at each moment in time, that which exists at that moment in time, and has the illusion, at that moment in time, that you have existed at other moments in time. Objectively this is unassailable. Subjectively I personally, for one, consider that it does not account for my experience.

Up to now, no theory account for experience, except perhaps the classical theory of knowledge. This is made transparent in the comp frame, where we can see that the machine is unable to be aware of that "illusion" aspect of its experience. When the machine refers to its subjective experience, it refers to its knowledge, defined by Bp & p (By Plato in the Theaetetus). But the machine can explain that IF she is a correct machine, then she has to make that distinction, between Bp (what she can communicate in a third person scientific way) and (Bp & p), what she knows, and cannot prove to know as such. This entails that machine will not find more easier than us that they are machine, and for them too, "saying" yes to the doctor will need a leap of faith.




I don't really think that there is a lot more one can say about it.
Except that he mentions an "implicit sequence", which is typically made explicit by the universal machine which emulates, albeit statically or arithmetically-realistically, the computation. All computations in that setting are ultimately based on the explicit sequence 0, s(0), s(s(0)), ... (or the equivalent in the combinators, etc.).
How the sequence is defined, and whether it is fundamentally physical or arithmetical, is of no consequence to this - admittedly highly philosophical - point.

What about step 4?

At the seventh step, in the case your remark could be developed as making comp and its 8th conclusion false, the seventh step would still prove that the primary physical universe has to be "little" (non- robust). No Tipler omega-point! In the whole possible multi-multi ... verse, there would be no universal dovetailing, because this one does entail a global indeterminacy (unpredictability) similar to arithmetic. That would already refute the MWI applied to the quantum vacuum, because it provides a universal dovetailing in the multiverse.

Bruno

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



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