On Wed, Sep 26, 2007 at 05:24:33PM +0200, Bruno Marchal wrote:
> >
> > Of course. But I also put Darwinian evolution up there with that
> > (variation/selection is a powerful theory).
> >
>
>
> This to vague for me. I have no (big) conceptual problem with Darwinian
> Evolution, but this is not something fundamental at all. This has to be
> derived from a more fundamental theory, as even today's Darwinist would
> say (thinking about physics but we know that is wrong).
>
It may well be that Darwinism is some marriage of information theory
with a multiverse idea, but it is not obvious how this works. I'd take
it as a fairly fundamental building block at this stage.
Your problem may be in the lack of formal precision. The real problem
is that there are too many formal models of evolution (eg any Genetic
Algorithm is a formal model of evolution), and not enough is known
about what features unite evolutionary processes.
>
>
>
> > As is stated in "Why Occams Razor", and made more explicit in
> > "Importance of the Observer" and "Theory of Nothing", what is the U
> > used in computing the universal prior? It can be nothing other than
> > the observer. U needn't even be a machine, any partition of the
> > strings into measurable subsets suffices.
> >
>
>
> ?
Which part didn't you understand? The partition bit? If S is the set
of strings, with a measure mu such that mu(S)=1, then a function
f:S->N such that
mu( f^{-1}(N) ) = 1
defines a partition { S_i = { x\in S| f(x)=i } | i \in N} of S.
>
>
> > And this identification turns an essentially 3rd person account
> > into a
> > 1st person account. To talk about ASSA or RSSA one has to introduce
> > some notion of time, or at least successor states.
> >
>
>
> Which we have without ay physical time notion, nor subjective time
> notion with comp. Successor states are definable by use of numbers and
> successor of numbers. This can be important given that everybody agrees
> on numbers (except ultrafinitist, but I know only one in Russia), but
> nobody agrees on what "time" could be (even the third person physical
> one, or first person plural).
>
Well I, for one, have not made the connection between the successor of
a number, and subjective time in COMP.
>
>
> > In order to do this, I need to assume whatever is needed to even
> > make
> > sense of these concepts. At a minimum it would seem to include some
> > of
> > set theory, of measure theory and classical logic, but maybe it can
> > pared down to a more spartan set of axioms. The point is I
> > don't really care what is involved, but someone else will bother
> > themselves
> > with these details. That is why I say I'm acting like a physicist.
> >
>
>
>
> Yes. A problem (at least for communicating) in a non necessarily
> physical context.
>
Its all about covering as much territory as possible to work out if
there's anything interesting there.
>
>
> > One way of connecting with what you do is to say that I assume the
> > existence of UD*, without concerning myself about the existence of
> > the
> > UD.
> >
>
>
> This does not make sense at all for me, given that the UD is
> interesting only through the UD*. UD is just a rigorous definition
> (logical name) of the UD*.
>
Don't you see that the UD* is just the set of infinite strings?
>
>
> > The CT thesis comes into play to justify the use of information
> > theory
> >
>
>
> Why? Actually information theory use CT only when it becomes
> "Algorithmic Information Theory". CT is needed to give "scientific"
> meaning to expression like "computable" and above all expression like
> "NON computable". And with comp this is important given that comp makes
> reality, whatver it is, partially but fundamentally NOT computable.
>
And I get tired of typing algorithmic every time I mention information
theory.
Sure, the complexity measure I use is more general than the
algorithmic prefix complexity on which it is based. But it still needs
the concept of universal machine to get the link to Kolmogorv complexity.
>
>
> > Regardless of what is really out there, all that we can know
> > about it must come to us in the form of strings, and so we can just
> > start with considering sets of strings.
> >
>
>
> This reminds me the particular case of the iterated Washington-Moscow
> self-duplication. But in this case comp predicts random noise (even no
> white rabbits).
Are you really sure of this? What if it is a newborn child placed
inside the W-M duplication experiment, that repeats (100 times a
second might be fast enough). Don't you think the child might end up
distilling some sort of reality from what it observes? Perhaps most
don't, but only those that manage to build up some kind of coherent
reality from the random sequences of W's and M's ever become conscious.
...
>
> > Let's consider a non-Brunotheological case. Your hypostases for
> > instance. I don't understand what makes some of them 1st person,
> > and
> > others 3rd person.
> >
>
>
> Good questions. It seems to me I have answered them, but don't hesitate
> to ask, or wait that I am going through again, and again ...
> Here the real answer has to be long, so I will just say the key idea.
> In science, we never know and we always believe. That gives the third
> person objective frame. It is because it is objective that it can be
> shown to be wrong. But knowledge, by definition, is always directly in
> touch with the (already unameable truth): it is incorrigible. To go
> from third person scientific opinion, to knowledge, Godel's theorem
> shows that the only way to do that (this is proved in detail in
> "conscience et mecanisme") consists in using the Theatetical definition
> of knowledge (By prove p and p is (serendipitously perhaps) true (the
> Bp & p).
OK - but then you can never know that you know something.
> Confirmation is provided by the fact that that doing this
> gives an unameable (by itself) self quite similar to Brouwer's theory
> of consciousness (which has given birth to intutionnist math and
> philo). Much much more can be said here.
This I've never really understood. What is this unnameable self, if
not a logic statement, or a system of logic statements?
> Another good question nobody seems to ask is: what is the relation
> between this theatetical definition of knowledge/first person and the
> definition of first person used in the UDA? (I let this as exercice or
> subject of reflexion for now).
>
Indeed. Maybe I haven't asked this particular question, but I've
certainly asked similar ones.
>
>
>
> > As I understand it, they're axioms for systems of
> > logical statements. The axioms proscribe what can and can't be
> > stated
> > for the given system.
> >
>
>
> Careful. Those are "axioms" of some modal logic. But those modal logic
> describe the discourse of self-observing machine.
Where is the justification of this? I'm not trying to be
argumentative, but I missed seeing this justification in both your
Lille thesis and your SANE paper. It would go a long way towards
understanding what you've done.
> But this is a
> theorem. nobody has choose those axioms. The main axiom of G is Lob
> formula, for example. But the arithmetical interpretation of Lob
> formula is a theorem (Lob's theorem), capable of being proved by PA (as
> Lob shows). All precise correspondance are given in most of may papers
> (but the complete proof are in the theses).
>
>
>
>
> > But what does any of that have to do with experience?
> >
>
>
> Experiences are the roots of incorrigible knowledge.
>
It seems one can be wrong about one's experiences. How is this
incorrigible knowledge then?
>
>
>
>
> > What is the
> > connection with the dovetailer of the UDA?
> >
>
>
> Again a very good question. Please wait I explain this again when I
> will be convinced most people grasp what is needed to go through this
> without leaving the list in hurry for reason of math anxiety. Actually,
> I was close to make this point as clear as possible until I realize I
> need to use Church Thesis, but also the seven first step of UDA, etc.
>
Of course, I'm happy to wait.
>
>
>
> > I understand that some of
> > the systems admit a representation in terms of Kripke frames, but
> > again what does that have to do with time?
> >
>
>
> The cute reason is that the knower extract from the lobian interview
> gives a temporal logic of evolving states of knowledge (S4Grz). Indeed
> the Kripke frame is a temporal structure. This gives an arithmetical
> transparent interpretation of the theory of time by Bergson/Brouwer
> (and it clarifies the misunderstanding between "scientist" and Bergson
> (or even the one between Brouwer and Cantor, and the one between Goethe
> and Newton, and the one between Parmenides and Heraclite. That is the
> optimistic view of the lobian machine. The pessimist will say that it
> just show that lobian machine will develop the similar
> misunderstanding. They are true, for a while. But in the limit (= some
> day) lobian machine got the root of that misunderstanding too).
>
> (The knower is, again, the one defined by the logic of "Bp and p" like
> in Plato's Theatetus), B is the arithmetical Beweisbar of Godel, p is
> for arbitrary arithmetical proposition, (or other for those who does
> not like the numbers, but my attempt to use the combinators instead, in
> this list, has failed: this is another reason why I keep the numbers:
> people know them).
>
>
>
>
>
> > I can understand that some
> > of the systems might also be used to model a multiverse of observer
> > moments,
> >
>
>
> What you say here corresponds to my old idea (in this list) to model
> the OM by the Kripke worlds. But as you know (I think), the fourth and
> fifth hypostases have no Kripke semantics (or quite deformed one). And
Yes, I remember you mentioned this.
> also, OMs can vary themselves as you change the hypostases. So that you
> can have first person OM, third person OM, first person plural OM, etc.
> (for all the 8 hypostases).
> That is why I have proposed to model the OM by the Sigma_1 sentence,
> and this is the subject of the current "Observer Moment =
> Sigma1-Sentences" thread (or the same with some amount of "Rép : Rép :"
> in front. I will come back on this. The importance of the Sigma_1
> sentences stems from the importance of Church thesis (even if we weaken
> the comp hyp). Roughly speaking the Sigma_1 sentences will classify the
> histories generated by the UD.
>
>
>
>
>
> > but I don't see the connection between logical statement and
> > observer moments.
> >
>
>
> This is just because I interview a machine which makes (logical, and
> arithmetical) statements, and then I interview her on the OMs. More
This would make them statements about OMs, which is not the same thing
at all, surely.
> exactly, for getting physics I restrict the interview of the machine
> (which gives the 8 hypostases) on the sigma_1 sentences. (cf: you refer
> to this in your book page 128-129, if we have the same edition ;)
> We will come back on this.
I tried to figure out what your hypostases were - searching the Google Groups
archive, I found a post of yours that listed 5, which roughly
corresponds to the 4 columns of the table on page 129, as well as
absolute truth. Do you get 8 by counting the G,G*, Z,Z* and X,X* as
two hypostases each?
>
> Must go. Will be rather more busy now. No time to reread (could this
> entails less spelling mistakes ...
>
> Bruno
>
I understand. I've formulating this reply since about 4:30 pm (It is
now 8:30) - many interruptions in between.
--
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Mathematics
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Received on Thu Sep 27 2007 - 06:45:15 PDT