Le 27-sept.-07, à 12:43, Russell Standish a écrit :
>
> 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.
Hmmm.... What could that mean? Darwinism by itself is a fuzzy theory
with a lot of presuppositions. What does mean "all the infinite
strings" + Darwinism?
It seems to me like (exagerating a bit for being clear) I presuppose
string theory + the existence of the moon.
>
> Your problem may be in the lack of formal precision.
No. Conceptual precision. I still don't know what you postulate and
what you consider as derivable from the postulates.
> 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.
Sure.
>>> 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 what if U is a machine? What are the relations with the partitions.
What is an observer (in the all infinite strings context)?
>>> 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.
Me neither. The successor function is just what we need conceptually to
talk about the steps of the Universal Dovetailer. Subjective time is a
much higher level concept related to the 3rd hypostasis (aka first
person, knower).
>>> 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?
I don't see, and I don't think so. UD* is the infinite running of the
UD. Now, what is true is that the UD dovetails on all portion of
generable infinite (even uncountable sets) so that all programs will be
executed relatively of all infinite strings, but also infinite trees,
graph, etc. And all this each time relatively to the execution of a
programs, and this only from the first person point of view. UD* as
seen from a third person perspective never goes to the uncountable.
Eventually UD* endows all the non trivial constraints from computer
science/mathematical logic.
>>> 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.
So now, you assume things like Church thesis. But then there are others
statements which makes no sense (if only like: only the strings).
I understand many of your answer locally, but do not succeed in
relating them coherently, (and thus the problem of conceptual clarity)
except by assuming comp, and correcting a few bit your intuition by
using my own work.
>
> 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.
Sure.
>>> 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? ...
This is an ASSA type of reasoning, and I don't see how this could work
(even without comp). Even a new born baby would experiment the quasi
exact splitting in two of a flux of z-photons send on an x-analyser (to
take the quantum version of the WM iterated duplication).
In the WM iteration, most of the mutiplied baby will be in front of
incompressible WM-strings independently of the fact that they can read
it or not due to the contingent fact that babies cannot read).
> ... 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.
That is a move like "white rabbit does not exist because they make no
sense". But both by UDA and AUDA, all the problems is that white rabbit
does makes sense. They does not entail inconsistency, and they can only
be avoided by a (absolute and/or relative) measure.
>>> 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.
This is a subtle point. Formally you *can* know that you know something
(Know p -> Know Know p). But indeed, you cannot know *for sure* that
you know for sure something. That is why comp prevents us to ever know
we are awake or sound, or things like that, although we can know to be
wrong or dreaming, etc.
The price of attaching knowledge to the (unameable, undefinable) truth,
is that we loose the connection of knowledge with certainty.
But this is like in "real life" where you can still have the memory of
having believe knowing something, and then changing your mind. If not,
we would always say "believe" in place of "know".
>
>> 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?
I will try to come back on this. It is explained in my SANE and
PLOTINUS paper (and the theses (in french)).
>
>> 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.
You did. Perhaps you don't ask enough.
>>> 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.
This is what I explained in 300 pages in "Conscience et Mécanisme", but
has been replaced in the Lille thesis by "see Godel, Lob, Solovay".
It is pure computer science/mathematical logic.
> 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?
It is incorrigible for the reason that it is attached to truth by
definition. But as I said above with the subtle comp point concerning
knowledge, you can be lobian and go to a state where you know something
false, but 'course, you are loosing lobianity there. No problem,
because in "real life" you have a non-monotonic layer making you
capable of recovering lobianity by recognizing your error. But for
deriving physics, you don't have to consider that non-monotonic layer.
(A logic is non-monotonic when adding new axioms can lead to the
suppression of old theorems).
>>> 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.
Thanks.
>> 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?
Yes. To be sure Plotinus use the term "hypostasis" only for the 3
"divine hypostases": that is TRUTH, DIVINE-INTELLECT (arithmetically
interpred through G*), and the UNIVERSAL-SOUL (arithmetically
interpreted through S4Grz*).
Plotinus does not call "hypostase" the material and sensible matter,
but I will not attempt to justify here the extensions of vocabulary,
except by pointing out it makes the whole arithmetical interpretation
of Plotinus much more smooth and symmetrical. Plotinus get some
difficulty in passage where he confuse the "terrestrial" intellect (or
soul) with the divine one, but then Plotinus didn't know about the
precise gap between G and G*.
Same problem with S4Grz, except that S4Grz = S4Grz* (i.e. "terrestrial
soul" = "divine soul"). This is a miracle! (a not obvious theorem at
all).
I think you bought the book by Boolos 1993, so you can take a look on
the chapter 12 on a provability logic preserving S4 (knowledge logic)).
But we are in some advanced part here so I stop.
>
>>
>> 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.
Thanks for your kind patience,
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Fri Sep 28 2007 - 12:57:06 PDT