On Tue, Sep 26, 2006 at 04:10:32PM +0200, Bruno Marchal wrote:
>
>
> Hi Russell,
>
> I got your book. Congratulation for that very nice introduction to the
> subject and to your ideas. It is a very gentle and lovely book.
> Probably because you are to kind to your audience, it seems to me you
> have sacrifice perhaps a bit of rigor. I am still not sure about your
> most basic assumption, but I see we share a big amount of the
> philosophy.
> I am already glad you did take into account 1/5 of my earlier remarks,
> I wish you at least five next editions ;-).
That's a bit like the old chinese curse - "I wish you live in
interesting times"!
> To be honest I don't think you really get the comp idea, and it is a
> good think your work does not really rely on it.
It is true that my work is an independent line of work, but probably
related. I am interested in the connections, however.
> Now I will not hide
> the pleasure I have when seeing the 8 hypostases (even the sixteen
> one!) sum up through their modal logic in table 71 page 129.
> I will neither repeat my olds comments nor make new one, but hope our
> future discussion will give opportunities to clarify the possible
> misunderstandings and relationship between our approaches.
>
Indeed.
> I let you know that I will be very busy from now until end of october,
> so that I will be more slow for the comments' replies (or more grave
> for the spelling mistakes if that is possible).
>
> ==================================
>
> This can make sense only if you tell us how to interpret a string or
> how you interpret the Nothing, I mean formally.
Interpretation is by an observer. Formally, the observer is a map from
a string to an integer. To understand why the observer is such a
formal object requires informal modelling talk, obviously.
> From this I infer that your nothing is an informal theory of infinite
> strings.
It is a mixture of both. The formal part is not so interesting, but
necessary to get some interesting conclusions.
> Also I give only ontological status to object in the scope of an
> arithmetical existential statement. For example I do believe in the
> existence of prime numbers.
>
Whereas I think the whole notion of "existence" is highly dubious. :)
>
>
> > must be inconsistent, of course.
>
>
> Only a theory can be inconsistent. But I don't see a theory.
>
I would say also that interpretations could be inconsistent, but
perhaps there is not much difference between interpretation and
theory. Would you say "There is a red flower" is a theory, or merely
an interpretation of an image?
If it were possible to view the entire "Nothing", it would be
an inconsistent interpretation. However it is not so possible, and
indeed it may be true that it is impossible to have an inconsistent
interpretation (I do not assert this however).
>
>
> > Our
> > reasoning about it need not be, and certainly I would be grateful for
> > anyone pointing out inconsistencies in my writing.
>
>
> That is why I would insist to be as clear as possible so that the
> inconsistencies are more easy to find.
>
Indeed - however we do have a difference in emphasis. Yours is towards
more formal models, but with obscure modeling relations, whereas I
prefer to spend more effort on the modeling relation than with the
formal content (the formal content of my ideas are small, no doubt why
you are disappointed!)
In that respect, I am more the physicist, and you the mathematician. :)
>
>
> >
> >>
> >> Perhaps the exchange is unfair because I react as a "professional
> >> logician", and you try to convey something informally. But I think
> >> that
> >> at some point, in our difficult subject, we need to be entirely clear
> >> on what we assume or not especially if you are using formal objects,
> >> like strings.
> >>
> >
> > I'm not that informal. What I talk about are mathematical objects, and
> > one can use mathematical reasoning.
>
> The formal/informal distinguo has nothing to do with the
> mathematical/non-mathematical distinguo. Nor with
> rigorous/non-rigorous.
>
> 100 % of mathematics, including mathematical logic is informal. Now,
> logicians studied "formal theories" or "machines" because it is what
> they are studying. But they prove things about "formal systems" in an
> informal way like any scientist.
Well, yes - we probably are using the word formal differently
then. For me, a formal system is a mathematical system with the
modelling relation thrown away. Triangles without trangular shaped
paddocks for example.
> In some context formal and informal are relative.
> Of course a description of a formal system looks formal, but we reason
> *about* those formal systems. Now, if your strings are all there is, I
> wait for an explanation of what those strings does "formally", but I am
> not asking to formalize your reasoning in your string-language, unless
> for illustrative purpose in case you want to illustrate how a string
> interprets something. Like we can explain how a brain or more simply
> how a turing machine can interpret some data. To be sure, given that
> your strings are infinite I have no clue how the strings can interpret
> things.
>
Nor do I. Observers do the interpretation, the strings are what they
observe. Self-awareness requires some form of mapping between strings
and the observer. Supervenience means this is a map, not a multimap.
>
>
> >>
> >>> I should note that the PROJECTION postulate is implicit in your UDA
> >>> when you come to speak of the 1-3 distinction. I don't think it can
> >>> be
> >>> derived explicitly from the three "legs" of COMP.
> >>
> >>
...
> > Fair enough, the "Yes Doctor" is sufficiently informal that perhaps it
> > contains the seeds of the PROJECTION postulate. When we come to the
> > discussion of the W-M experiment, there are 3 possible outcomes:
> >
> > 1) We no longer experience anything after annihilation at Brussels
> > (contradicts YD)
> > 2) We experience being both in Moscow and Washington simulteously
> > (kinda weird, and we dismiss as a reductio, but could also be seen
> > as contradicting PROJECTION)
> > 3) We experience being in one of Moscow or Washington, but not both,
> > and cannot predict which.
> >
> > I've noticed a few people on this list arguing that 2) is a possible
> > outcome -
> > probably as devil's advocates.
>
>
> Really? I thought only Chalmers does that. Do you know someone else?
> Lee Corbin was apparently doing that, but when I insisted on the 1/3
> distinction, Lee did eventually admit he could not predict its
> immediate future *first person* experience: the comp 1-person
> indeterminacy (casr "3)" above). OK Lee, if you are still there?
>
But is this 1-3 distinction implicit within your statement of COMP?
I'm not sure that it is.
>
>
> > That would certainly be eliminated by
> > something like the PROJECTION postulate.
>
>
> Honestly I feel it not being necessary, for the same reason the
> collapse is not necessary in QM.
>
Collapse is conceived of as a physical process, and as such is
problematic. Nonphysical collapse is just the 1 POV of the
Multiverse. That's all I'm talking about.
>
> What is 1*, is it "1111111111..." why 1/2?
> Is it "1" follow by any strings. Then OK, for some measure.
>
Yes - I'm just using standard regular expressions. The measure will
follow provided we insist on another rule:
m(x_1x_2...x_N*) = m(y_1y_2...y_N*)
\forall x_i, y_i.
>
>
> > Looks like a topological line, but would need to
> > check the axioms.
> >
> > It is "Nothing", because of the modelling relation, and the insistence
> > that all we can know of anything comes in the form of strings.
>
>
> Is that a new postulate? Why "Nothing" ?
>
It is not new, it underlies all of Chapter 2 of my book, and also of
"Why Occams Razor". Perhaps I'm guilty of assuming it without
explicitly stating it, but by way of challenge can you give me a piece
of knowledge that doesn't come in the form of a string? It is
certainly hard, given we live on the opposite sides of a digital world
- a record of a telephone conversation we have will be a a string of
bits, as will any emails we use, any my book left my hands in the form
of a string of bits and so on.
>
> Indeed, but a theory of everything should, in some sense (by definition
> of everything). If you have only infinite string in the ontology, I
> guess you have to modelize the observers by an infinite string, or by
> something you can derive from the set of infinite strings, and you have
> to explain how you make the derivation, and how those observer will
> converge on your theory, or explain why they diverge from it.
>
Perhaps thats why I say my theory is a "theory of nothing"
:). Seriously, all I am interested in an understanding of why the world is
as it appears - theories of everything are of little use.
>
>
> > One
> > can use whatever mode of logical reasoning one is comfortable with -
>
>
> Sure, but in front of unclarity or conceptual problems we should be
> able to say which logic we use, even informally, like with or without
> excluded-middle, or with or without some infinity axiom, etc.
>
I use the usual one (excluded middle), and I don't use any infinity
axiom that I'm aware of.
> I guess you
> presuppose some set theory?
Yes. See page 6 of "Why Occams Razor".
> It is different to say "all strings exist"
> and "the set of all string exists". Again, in some informal reasoning
Yes - I appreciate the ontological difference. I would say that only
"Nothing" exists (in ontological meaning). Strings and sets of strings
only exist in the same sense that the number "1" exists.
> to make that difference explicit would be falling in the 1004 fallacy,
> but if you say the strings are the fundamental object, then if you talk
> on that set you have to explain in which sense that set is a string.
The set of all strings is not a string in itself - there is no need
for self-reference. But there is a need for the string to describe the
observer of that string - this is the supervenience or anthropic
issue. And I note there is still unfinished work here, for those who
sense an element of confusion. I don't have _all_ the answers.
> To my knowledge only the UD does that effectively. In a frame with
> infinite objects, some non effective way has been given but it always
> lead toward very difficult mathematics (ZF + axiom of anti-foundation
> like Stephen appreciates, or NF + universal sets (NF = Quine's new
> foundation; nobody know really if NF is consistent).
>
Perhaps - but I think this more correctly touches on the
anthropic/supervenience issue.
>
>
> > When one shows that this
> > leads to Occams razor, one is doing logic, not ontology.
>
>
> Are you really saying that Occam follows from your string "theory"?
> Also you could perhaps use "stream" instead of "string", to prevent
> confusion with the use of string by physicist, and also because for
> many computer scientist strings (of characters) are supposed to be
> finite. Just a little suggestion.
>
Arrrgh! That is why I used "description" in the first place! Now
someone will complain they are confused because stream might mean a river...
At some point we need to pick a word and define it. Something
pronouncable usually helps.
>
> >
> >> To be franc I am
> >> astonished you want already infinite objects at the ontological level.
> >> If *all* infinite strings are in the ontology, that could be a
> >> departure from comp (and that would be interesting because, by UDA,
> >> that would make your theory predicting a different physics and then we
> >> could test it (at least in principle), and only when your theory will
> >> be precise enough.
> >>
> >
> > I'm not convinced it is a departure from COMP, but as you say it would
> > be interesting if true. Can you elaborate further on your reasons,
> > perhaps saying which infinite strings cannot be found in UD* for
> > example?
>
>
> I could elaborate a lot about the vagueness of the notion of "finding"
> something in the UD* (the infinite complete running of the UD).
> I could ask "finding by who?", from inside? from the terrestrial
> (verifiable) view or the divine one (true but non verifiable)?, from
> which x-person point of view? Etc.
> Given that the UD cannot not dovetail on all the reals, there is a
> sense in saying all the infinite strings are generated, but this gives
> a noisy background first person machine have to live with. The UD is
> not equivalent with "all infinite strings", the UD* is a static given
> of all computations. Those computations can be represented by very
> peculiar finite and infinite strings together with a non trivial
> structure inherited from computer science/number theory.
>
About the only difference I see is that the measure might be different...
>
>
> >
> >>
> >> I though your ontic TOE (the strings) was similar to RA, but I guess I
> >> was wrong, so I am less sure I understand what you try to do.
> >>
> >
> > I would say it is more like assuming that UD* exists, whilst remaining
> > silent on the topic of whether a universal dovetailer exists, or even
> > on the prerequisites such as AR or the CT thesis.
>
>
> What could "UD* mean, without CT?
Um - the set of all infinite length strings perhaps?
> If you don't use CT, you have to give
> at least one precise universal machine (or sigma1 complete theory).
>
No - we needn't suppose a builder, just because we see a
cathedral. This is the falacy of Paley's watch.
>
> > or you note as I do that the set of
> > strings is the simplest possible object (by definition of simplicity).
>
>
> An infinite set of infinite objects ? Including obviously some
> structure on it, if only to give sense to your projection postulate, I
> am not sure this is simple.
One can "prove" it. If N is the set of all strings, C(N)=0 for all
observers, where C is the complexity function defined in equation
(2.1) of my book, or equation (2) of "Why Occams Razor".
Of course this is ultimately a metaphysical argument relying on a
modeling relation - if you don't accept it, there is not much I can do
about it. Of course if you arrive at the same position from another
angle (such as from COMP), I don't have a problem with that either.
> So I
> guess your theory is complementary to comp instead.
I more or less always assumed this. Either COMP is more specialised
(you can derive some my postulates from COMP, and others are compatible
with it), or COMP is the only way of deriving these same postulates,
or COMP in some way contradicts these postulates.
I do not know which after 8 years of studying it.
> UD* is a far more
> sophisticate mathematical structure than a real topological line. Its
> sophisticateness, if I may say, comes from the non triviality of
> computer science, of the Fi and the Wi, for example, through the many
> incompleteness phenomena, and it is that highly structured complexity
> which gives rise to highly non trivial internal n-person views (the
> hypostases and their logical multiverses).
>
>
Ideed. And if we think hard enough, these additional structures may be
empirically distinguishable. One can dream...
> Bruno
>
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
--
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A/Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics
UNSW SYDNEY 2052 R.Standish.domain.name.hidden
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Received on Tue Sep 26 2006 - 21:44:45 PDT