On 06 Jul 2012, at 15:07, David Nyman wrote:

On 6 July 2012 10:27, Bruno Marchal <marc...@ulb.ac.be> wrote:

In which structure is that relative-frequency defined, and to whom does it apply? How can we verify it?

The structure, if you like, is the total state of knowledge of the "knower" (as you have characterised it in a post to Brent) which ex hypothesi must embrace all possible occasions of sentience.


This might lead to perhaps interesting question. The knower I described to Brent, was the knower that we might associate to the universal machine. Usually (before salvia!) I would not have been open to that idea, because, well, first the math is lacking, and might not exist or be trivial. I would have said that the knower begin with the Löbian entity. But that might be a detail in our setting: the Löbian machine is basically the same as the universal machine, but having the belief in some induction axioms. This gives the reflexive loop giving them the rich and stable cognitive abilities of the Löbian machine (with the 8 hypostases). Those hypostases will never get change on all computational histories where the machine remains correct (that is enough for the derivation of the physical laws, but is quite too much simple for "real life psychology". Now, such machine (the virgin universal or the Löbian which is slightly less virgin) have basically no knowledge at all, and live in a disconnected conscious state.

I am not sure it makes sense to ask for such a machine if there is a probability that they become suddenly "me". I would say that may be the first person indeterminacy of such a machine might have a indeterminacy domain limited to slightly more complex universal state, perhaps becoming a bacteria, before becoming a mammal, say. The idea, is that you always survived in the most normal (Gaussian) neighborhood available to you, and that normal state is given by the relative proportion of computations going into that state. So in all situations the indterminacy is relative to the actual state of the machine, as brought by the universal dovetailer (or its arithmetical equivalent).

It is not impossible that a rich conscious state, like the one by a Löbian mammals, necessitates a very long computation, so that the probability to become such a Löbian mammals, directly from the universal knower, would be a very rare event (possible, but stochastically impossible).





Each such occasion is here conceived as a set of spatio-temporal relations in the context of a particular personal history. Taken as a whole the structure is of course timeless and eternal. Hoyle's heuristic is then simply a way of thinking about this structure such that occasions are given (i.e. from the pov of the knower) in proportion to their measure, in mutually exclusive succession. Hence the intrinsic spatio-temporal relations of the substrate are conceived as unfolding experientially in the form of the myriad personal histories. It's a way of rationalising the experiential dynamic, if you like, from the pov of a universal knower, which as you yourself point out, cannot be an arithmetical, or indeed a physical, notion.

Indeed. But it is still describable in arithmetical terms, like arithmetical truth, which is not arithmetical, but concerns only arithmetical sentences. I think that here you have a good intuition that the spatiol temporal unfold experentially from the knower, and this is confirmed, as the knower logic, with comp, is given by S4Grz (and the X logics) and this defined indeed a sort of dynamic. In my (old) opinion: this confirmed Brouwer theory of consciousness, which relates intrinsically consciousness and time (and S4Grz has indeed been used as a logic of time by some philosopher). Now, the salvia experience has refuted this for me, as it generates an hallucination which put some doubt on that perspective, and which is why I am willing to attribute a consciousness to the non Löbian universal machine. Indeed, it seems conceivable that we can be conscious in a completely non spatio-temporal way. I thought comp would prevent such possibility, even through an hallucination. Here your thought might be helpful. But I am not sure it needs to postulate an absolute indeterminacy. I am not sure it might make sense to ask: "being a virgin UM, what is the probability of being David in the next instant?".

But the plant salvia, I have to say, provides evidence for your idea that it might make sense, for we can apparently get the virgin state (or be close to it), and yet *it seems* that we survive. It remains possible that actually, I am correct, and that the probability to "become a bacteria" when smoking salvia is close to 1, from the 1-pov. Of course the "third person view will not confirm this. Brrr...


You ask me how this could be tested; since it is a way of thinking, rather than a theory, the only relevant test is whatever power it may possess to reduce confusion and enhance conceptual clarity. I became particularly aware of this when reading some of the posts about jumping and backtracking, etc. When we reason about some divergence of "my future moments" in copying scenarios it is perfectly natural of course to relativise these to my personal history as given, without consideration that the relevant reference class might be any broader. Furthermore, since our reasoning here seems naturally to "follow" the spatio-temporal evolution of some underlying "real system" (as Bitbol calls it),

OK. Comp forces us to derive the spatio-temporal reality from the statistics of the machines experiences, and this is the result of the comp reduction of physics to arithmetic. Everett confirms the existence of first person plural notion (which multiplies collections of interacting universal machine), and if comp derives Everett QM, comp is saved from solipsism, which is still a logical threat for comp.



it does not seem relevant to distinguish the logico-physical relations of next or prior from the bare notion of succession itself.

I think we have to do that distinction, but I am not sure what you mean by "bare notion of succession". There are many one. The barest is probably the notion of successor of a natural number, axiomatize by the successor axiom of robinson or peano arithmetic (0 ≠ s(x), x ≠ y -> s(x) ≠ s(y), etc.). The semantic of this is the usual function y=x=& from n to N. Then you have the succession of the step of the universal dovetailer. This one will be defined from many application of the axioms of arithmetic. Then you have the succession of steps in particular computation, including for example simulation of galaxies. But comp makes the real galaxies and the real physics a first person (hopefully plural) notion, which means that physical time and subjective time are internal views, which borrows from what the UD does in the limit (which defined the first person domain indeterminacy, by the delay invariance of the first person view). Those notion of time needs to be extracted from some of the machine's hypostases.



Real problems of coherency in this way of thinking emerge, however, when we begin to consider "future moments" of low intrinsic measure, such as in quantum suicide scenarios, or extreme threats to conscious survival. At this point, we seek to avoid cul-de-sacs or occasions of extreme improbability by resorting to notions of jumping or backtracking referred to a particular personal identity, or even in extreme cases the idea of merging with the infant consciousness of a different identity entirely. But here we are no longer following - or at the very least least are forced to undertake highly non-standard excursions within - the real system.

I see what you mean. This is difficult indeed. That is why in the publication I try to avoid, amnesia, but of course, through quantum erasure, we know that "nature" does not avoid this. Here my strategy consists in trying to get QM from arithmetic, instead of trying to figure out intuitively the indeterminacy domain for experience involving amnesia or first person fusion of computational histories. But we can try.



This reaches perhaps its reductio ad absurdum in Saibal Mitra's treatment of memory erasure scenarios. He is forced by this mode of reasoning to speculate, for example, that the "you" that "escapes" disaster by memory erasure has "swapped histories" with another "you" that would otherwise have avoided it! It is interesting to speculate how one would test, or even recognise, this eventuality!

This is without doubt a difficult problem. Normally comp still suggests that you survive in the closest possible computation. But as salvia and even just sleep seems to illustrate, amnesia is always computationally close. Simple switch that can transform a rich computationally deep machine into a virgin baby seems to exist, which make such bactracking available. I wish it is like that, because the next option looks like an infinite agony!



It should, I hope, be obvious that all of the above incoherencies can be resolved quite simply by adopting the heuristic under discussion. The structure under consideration, as I have said, is the total state of knowledge of the knower; all possible occasions of sentience, duly distributed amongst distinguishable personal histories in due measure, exist within it.

I fail to make sense of this, as I fail to see the necessity of this.



All that is required, conceptually, is to make explicit the experiential notion of the mutually-exclusive succession of occasions of sentience; all relativisation of personal identity and past-future relations are referred to those aspects of the substrate associated with a given occasion. There is no suggestion of prior or next in the bare notion of experiential succession; no extrinsic ordering whatsoever is implied. The logical consequence is that all notions of personal history are referred to a singular point-of- view: that of the knower.

But the knower "code" is intrinsic in all universal machine, (or all Löbian one) making all of them in the state of having unique singular experience, with huge, but not totally complete, first pov indeterminacy domain. They become complete if you take all transitive closures on the accessible computational states. The probability of a bacteria becoming you is one, no doubt, but the probability that a bacteria becomes you in one computational step, although non null, is very close to zero. A fortiori this is the case for the universal knower. Somehow, you are "him", but he is not always you. (A good thing for that motivates for the meeting of others).


"I" am fundamentally that knower,

On this I can completely relate.



and the knowledge successively recoverable from occasions of sentience is what informs me of who, where, when, and relative to what, I am on any given occasion.

On this too, but I still don't see why we would need to make the universal "I" being undetermined on all occasion of sentience, in one strike, so to speak, even if salvia seems to agree with this (but salvia is capable of making me doubting on comp too!).

Nor do I see how we can put a distribution probability on all moments. It is not unfrequent that people thought to be able to refute the UDA by pointing on the fact that such a global distribution of probability does not exist, and my usual reply is that all the probabilities are defined in the relative conditional way. To be sure I know now that such global probabilities can exist, if we abandon the "sigma- additivity" axiom in probability theory for example, but this remains rather awkward, and unnecessary, because the universal knower is "directly all of us": it is coded in your actual brain, and even cells (admitting the non Löbian weak notion of knowing). If a computation support knowledge, it automatically "run" the universal knower.

Of course this makes all indexical into a sort of illusion (like "me", "here" and "now"), but the math explains, or should explain if comp is true, why a deep spatio-temporal structure unfold, and why it is stable and lawful. Comp makes somehow consciousness and arithmetic absolutely real, and all the rest are relative opinions and knowledge.

I am sure your analysis might help to better apprehend consciousness, and can perhaps better handle the amnesia situation. But you have not (yet) convinced me that it has to be termed into a new form of *assumed at the outset* indeterminacy. The probability of "being me" is a sort of Dirac distribution: it is one, for "me", and zero for the others. The probability of becoming "me", is perhaps close to one on the transitive closure of the computations, and is complex to compute for particular brain instantiation.

Bruno


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



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