# Re: No(-)Justification Justifies The Everything Ensemble

On Thu, Sep 20, 2007 at 05:05:10PM +0200, Bruno Marchal wrote:
>
>
> Le 19-sept.-07, à 11:56, Russell Standish a écrit :
>
> >
> > On Tue, Sep 18, 2007 at 04:23:58PM +0200, Bruno Marchal wrote:
> >>
> >
> >> OK. You know I like your little book as an introduction to the field,
> >> but, as you have already acknowledge, there is some lack in rigor in
> >> it, and it is not even clear if eventually you are of the ASSA type or
> >> RSSA type, or if you accept comp or not. Use of Bayes and Prior, for
> >
> > I am clearly on the record, both in the book and also in the list
> > archives as an "RSSA type".
>
>
>
> I do not pretend the contrary. Only that it is not clear. (We have a
> problem of communcation I think, not more)
> 

Sure - but on this point I have always been clear :)

>
>
> >
> > As far as comp is concerned, I do not assume it, but accept it as a
> > model of what's going on. See page 79 of my book.
>
>
> This does not help, unless you take some conseq of comp as granted,
> like the reversal physics/number-theology, or a form of
> mathematicalism, etc.
>

I do take the reversal, but not as granted. It is essentially a
consequence of any ensemble theory of everything with a 1-3
distinction. This is most clearly enunciated from within a
computationalist position, which is why I think your UDA is so
important, (to convince the doubters) but in fact the result is much
more general, and computationalism per se is not needed.

> I do consider that the discovery (by Babbage, Post, Church, Turing,
> ...) of the Universal Machine is a major discovery of our time which
> changes almost all what has been thought about machine up to then. This
> is reflected in the computability theory, and I exploit those
> theoretical consequences.
>

Of course. But I also put Darwinian evolution up there with that
(variation/selection is a powerful theory).

>
>
>
>
> >
> >> example, is a symptom of ASSA type reasoning. Distinction between 1
> >> and
> >> 3 person points of view is symptom of the RSSA type of reasoning, (and
> >> favored with comp).
> >
> > Not if the prior were actually given by the observer erself.
>
>
> ?

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.

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.

...

> > Stronger in what sense?
>
>
> In the syntactical, or proof-theoretical sense. A theory A is stronger
> than a theory B if A proves all theorems of B.
> The set of theorems of B is included in the set of theorems of A. For
> example PA is stronger (in that sense) than ROBINSON. (ROBINSON is PA
> without the induction axioms).
> Another example: QM + physical collapse is stronger than pure QM.
> Caution: if a theory A is syntactically stronger than B, then B is
> semantically stronger than A. Given that A has more axioms, it will
> have less models. It is like in algebra: a big set of equations has
> less solution than a little one. Syntax (theory+proof) and Semantics
> (mathematical models) are in a sort of Galois correspondence: the more
> you have axioms (the richer in theorems your theory is), the less you
> have models.
>

As I have said, I have been taking David Deutsch's idea seriously, of
combining a many universes ontology, with information theory and
Darwinian evolution. (David also suggests Popperian epistemology as a
fourth strand, but I consider this to be a special case of evolution).

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.

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. The CT thesis comes into play to justify the use of information
theory. 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
assumed, but your universal dovetailer provides a computationalist
model. It remains to be seen whether computationalism is the only
possible model (I suspect not, but I don't know).

>
>
> > I have only assumed just enough to make sense
> > of the notion of complexity.
>
>
> I still don't know if you take "all the strings" in some first order
> logical setting (in which case it will be not enough for defining a
> notion of complexity) or if you take "all the strings" in some larger
> (second order, mathematical instead of logical, etc.) sense, in which
> case you take far too much.

I don't know either. It will be up to someone else better grounded in
logic theory to work this one out. I suspect it is highly nontrivial.

> Given the relation between "all the strings" and the set of subsets of
> N, sometimes it seems to me you are just formulating (in some awkward
> way, with all my respect) some acceptation of classical logic (boolean
> algbra) pertaining on the natural numbers. In that case, your
> assumption would be arithmetical realism.
>

Perhaps. But it is not clear.

> >
> > Its not so much that, but in how you interpret the logical
> > results. Calling G*/G an angel for instance might be colourful
> > rhetoric, but it doesn't really mean much to me.
>
>
> Rhaaaa.... You talk like John, now!

Oh no! Heaven forbid! Sorry, John.

>
> OK I say a bit more. First you are an old participant in the list, so
> you remember surely that I have first presented G and G* as "the
> machine-itself" and "the guardian angel of the machine". This was
> mainly in honor of Judson Webb who is the first to clearly realised
> that Godel's incompleteness results were protecting mechanist
> philosophy against all possible diagonalization à-la LUcas (-Penrose):
> and Judson call Godel's result the guardian angel of mechanism.
>
> But more recently, perhaps because I have introduced the term
> "theology", I have introduced the term "angels, Gods, Supergods ...",
> but then I did define them. By angel I really mean any
> self-refrentially correct entity which is NOT turing emulable. The
> simple angels corresponds to the arithmetical (and analytical)
> hierarchy in computability theory. They are the main object of study of
> computability theory (alias "recursion theory"); Gods, supergods, are
> just higher in such or similar hierachies. They corresponds often (but
> not always) with machine in company of the so-called (by Turing)
> Oracles.
>
> Note: the term "angel" is never used by Plotinus, nor the term
> "theology". Proclus uses the term "theology".
>

I wasn't trying to criticise your use of terms. Mathematics has a long
tradition of borrowing terms from everyday language to label
mathematical concepts. Sometimes the terms might approximate the
everyday term in some sense - eg a "ball" really is a ball in the 3D
case, but other can be quite fanciful, just convenient labels for
remembering stuff that is otherwise a hard to remember formula, and
harder to pronounce. Guardian angel would seem to fit into this latter
category. I have no problem with the use of colourful rhetoric like
this, but I have enough mathematical training to know that it simply
refers to that which is true but not provable, and not something of
greater significance.

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. 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.

But what does any of that have to do with experience? What is the
connection with the dovetailer of the UDA? 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? I can understand that some
of the systems might also be used to model a multiverse of observer
moments, but I don't see the connection between logical statement and
observer moments. So many questions, I know.

>
>
>
> >
> >>
> >>
> >>
> >>> It might seem like such uncountable sets are too much to assume, but
> >>> in fact it is the simplest possible object. It has precisely zero
> >>> information.
> >>
> >> Zero information. Zero justification. Occam razor ... I do agree with
> >> these major motivations for the everything idea, but I disagree with
> >> the proposition saying that the the set of strings needs
> >> zero-information. Why not the infinite strings on both right and left
> >> (coding the integers), or infinite many-dimensional lattices fit with
> >> zero and one on the vertex, or etc. ?
> >
> > Information theory is defined on one-sided strings. It would be
> > possible to redefine complexity to use two-sided strings, or subsets
> > of N, or real numbers, but you just end up with an isometric theory,
> > it wouldn't be saying anything different/
>
>
> ?
>

Sorry a brain-freeze occurred. I meant isomorphic. In the sense of
category theory.

>
>
> >
> >> There is just a lack of enough precise definition so as to verify your
> >> statements that strings needs zero-information, and as I say above,
> >> from some standard and traditional view points, infinite strings needs
> >> a lot of information to be define.
> >>
> >>
> >>> No countable set has this property.
> >>
> >> Why?
> >>
> >
> > For finite sets, one has the objection - why that finite number? For
> > infinite countable sets, can one even define a measure?
>
>
> We can put many measures on all sets, finite, infinite countable,
> infinite uncountable, and beyond.
> Only when there is some extra-structure, making the set a vectorial
> topological space for example, can we find in the lucky case some
> unique measure theorems.
>

I suppose you are right. Consider the rationals - one can impose a
uniform measure on these such that the set of all rationals between
m/n and p/q has measure m=|m/n-p/q|. Then the information content can be
defined by the usual logarithm C=-log m over all subsets of rationals
in [0,1]. It would be interesting to know if this has any affect on
the rest - eg the quantum structure.

Intuitively, though to restrict the set of strings according to some
pattern (bit expansions of rationals, computable sequences, etc.)
seems like adding information (not quite zero information), but this
may be prejudice.

>
>
>
>
> >>>>> Obviously I'm departing from
> >>>>> Schmidhuber at that point, and whilst in "Why Occam's Razor" I use
> >>>>> the
> >>>>> term Schmidhuber ensemble to refer to this, in my book I
> >>>>> distinguish
> >>>>> between Schmidhuber's Great Programmer idea
> >>>>
> >>>>
> >>>> (which you confuse some time with the UD, I think).
> >>>>
> >>>
> >>> He does actually dovetail,
> >>
> >>
> >> We have discuss this. In the first paper the "great programmer" is not
> >> a dovetailer, and indeed there is nothing in the ASSA approach for
> >> which dovetailing could play a role.
> >>
> >
> > No the great programmer writes and runs a dovetailer on er great
> > computer.
>
>
>
> ? (what is a great computer? A Macintosh, a PC?, a concrete machine, an
> abstract one ??)
>

In Schmidhuber's case, it appears to be concrete. At least that is how
I read it. Obviously by CT, it matters not whether it is a Mac, PC or
Univac 1100.

>
>
>
>
> >
> > I missed the dovetailer on my first reading, as indeed it doesn't seem
> > too important. I suspect the Scvmidhuber intended the dovetailer to
> > "breathe fire" into the ensemble.
>
>
> ?
>
>
>
> > I'm not sure that Schmidhuber accepts arithmetical realism.
>
>
> ? (I have no doubt he accepts it; for example he studies computation in
> the limit, he accepts Church thesis, etc.)
>

AR is not necessary for this. One can manipulate symbols without
believing they stand for anything. I can use real numbers without
believing that real numbers actually exist in the world.

Anyway - if Juergen is still lurking, maybe he can comment. Its too
hard to suppose exactly what other people implicitly assume.

>
>
>
> > His
> > ontology is that the great programmer exists, whatever e may be.
> > The
> > GP is not necessarily a machine, or an arithmetical formula.
>
>
> That's correct, and that is why the notion of dovetailing does not
> apply to his way of working (and this is a major departure between us).
>
>
>
>
> >> Well, I hope you are not referring to the notion of "ensemble" as it
> >> occurs in physical statistics.
> >
> > Not at all! Ensemble is usually used in mathematical terms to refer to
> > a collection that need not satisfy set axioms.
>
>
> You mean a set from naïve set theory? Given that we have never
> mentionned even just one axiom of set theory, distinguishing set and
> ensemble would be a 1004 fallacy.
>

We started the ensemble "habit" back when someone pointed out that
Russell's paradox would apply to a collection of everything, that must
indeed include itself and all subcollections. Tegmark uses ensemble in
his '97 paper for instance. I was merely pointing out that my ensemble
was actually a true set, and the only significance of this is that
sets are required to apply information theory as it is currently
formulated.

...
>
>
> Is it a good idea? Should you not say something like "Nothing
> Physical"? Saying that "all the strings = nothing" looks like a play
> with words.
> There are as many theories of nothing than there are theories of
> things. The quantum nothing, to take a famous example, is everything
> but nothing, but can be called a (quantum) nothingness because it has
> an average energy value of zero (well, this is typically false but I
> guess you see my point).
>

That idea is more correctly called a vacuum. I agree partially that
the way I use Nothing is a play on words. One could more accurately
say say it is a "no-information-thing", but I would argue that since
the only things we can sense are "information-things", dropping the
the "information" part is justifiable.

The only other nothing idea I'm aware of is the empty set, which is
actually related by a dual relationship.

Of course there are plenty of nonscientific ideas of nothing - but I'd
prefer to leave those to literature.

> >
> > Sure there is a lot of confusion on the subject of emergence, so it is
> > not surprising if there are people "reaching for the gun" when hearing
> > the term. However, the term actually is quite well defined, and the
> > way I use it is pretty consistent with what other recent thinkers have
> > written, such as Bedau, or Ronald, or Fromm.
>
>
> Yes. And personally I prefer when you use "emergence" instead of
> semantiics, which is more involved and has more pecise connatation in
> mathematical logic or computer science.
>

Does the term "semantic level" (or "semantic layer") have a meaning in
semantics? I wasn't aware of one, but I haven't studied semantic
analysis too much.

...

>
>
> >
> > I have actually read quite a lot of literature on the subject, and
> > there aren't any accepted terms for describing the levels of
> > description in emergence. I'm trying to propose the semantic/syntactic
> > level labels, but you know its a market of ideas out there.
>
>
> Yes. Instead of using already known terms, in front of new ideas,
> please  just create your own new terms. Or just use periphrase like

The point is that the idea is still new enough that there aren't any
well-known terms.

> "the levels of description of emergence". In fine, if you define
> clearly your terms, then you can use any terms you want, in principle.
> It helps the outside reader if those terms have some known
> connotations.
>

Indeed. I do define the terms, and use them consistently. If there
were well-known terms for the concepts, I would use those instead.

> If your theory is 100% scientifically clean, it should work with *any*
> etc.
> I can do that for string theory (oops, not your strings, but those of
> superstring theory by the physicists), or "my theory" (I mean the
> theory of the lobian machine, etc. OK this is hard to get, so take this
> remark with a grain of salt .... for a while .... (you can ask me to
> explain how to do that in the case of "my theory" or in the case of a
> mathematical physical theory (like strings).
>
> Now that I am thinking about that the term "string" in the search of a
> TOE is also a quasi copyright type of problem given that you string
> have nothing to do (a priori) with the "bosonic string" or the
> superstring physical theories ....

Indeed. However, my preferred term "description" seemed to cause even
more problems :(.

>
> >
> >>
> >> Another point where your fuzziness does not help is that you are not
> >> clear on the comp hyp.
> >
> > I never assume the comp hyp. I believe comp is consistent with what
> > I've developed, and note that you can pretty much get the consequences
> > of the UDA from a more general functionalist position.
>
>
> This can be made clear with the UDA and after with the AUDA, where the
> reasoning extends to a vast class of non turing emulable (non machine)
> entities. The real key here is the notion of self-referential
> correctness. To derive physics from functionalism is an interesting
> idea, but this is different from deriving the necessity of
> immaterialism from an hypothesis in the cognitive science. I do suspect
> you have something interesting to say (which makes more frustrating
> your incautious use of vocabulary).
>
>
>
> >
> >> Schmidhuber is clear on comp, even if he has
> >> disagreed when discussing online in the list with the consequences I
> >> derive from it. But the disagreement comes not from what comp means,
> >> but from the 1/3 distinction, which Schmidhuber does not consider.
> >> Tegmark does introduce an embryo of 1/3 distinction (but quite
> >> different from mines (see below)), but Tegmark still uses some
> >> identity
> >> thesis implicitly for making observer belonging to universe, and minds
> >> to brain. Such identities have just no meaning at all once you
> >> postulate the comp hyp (or even strong weakening of it btw). OK? (by
> >> UDA). Yes?
> >
> > Yes, but there is still some reason tying the observer to the
> > universe.
>
>
> In this context "universe" has no non ambiguous meaning at all.
>

True, but I usually use it to refer to "what-is-observed". It would be
a sequence of observer moments, or a history in other contexts.

>
>
>
> > Otherwise you get the Occam catastrophe. (again my term, and
> > others have called it differently) I do not know what that reason is,
> > but suspect self-awareness has something to do with it.
>
>
> You really should elaborate.

From my book:

Whilst in one sense the Anthropic Principle seems obvious, it is
actually profoundly mysterious. There is no doubt that the Anthropic
Principle works, and it has passed all experimental tests to date.
However, one could imagine being born into a virtual reality
simulator,\index{virtual reality} in the style of the movie {\em
Matrix},\index{Matrix (the movie)} such that you had no knowledge
whatsoever of the outside world containing your body\footnote{We might
imagine that a shunt'' was placed in your spinal column so that no
being any representation of your body within the reality simulated by
the simulator. In this case, observed reality is not constrained to be
compatible with your existence. The Anthropic Principle will not apply
in such worlds.

By reason of the Occam's razor\index{Occam!razor} theorem
\S\ref{occam}, we should be born into the simplest possible world, a
world that would be utterly boring and lifeless. The Anthropic
Principle prevents this catastrophe (which I call the {\em Occam
catastrophe})\index{Occam!catastrophe} by requiring that the world
be sufficiently complex to support conscious life. Clearly the
Anthropic Principle is necessary, but why?

\begin{sloppypar}
David Deutsch\cite{Deutsch97}\index{Deutsch, David} argues an
observer\index{observer} trapped within such a virtual
reality\index{virtual reality} would eventually notice inconsistencies
in how that reality operates, and thus deduce the existence of a
larger reality within which the observer is actually situated. John
Barrow\index{Barrow, John} makes a similar point in his New Scientist
article {\em Glitch!}\cite{Barrow03}, as does Daniel
Dennett\index{Dennett, Daniel} in {\em Consciousness
Explained}\cite{Dennett91}. Considering the case of a virtual
reality which does not contain the observer, one in which there is no
supervenience\index{supervenience} of the mind on any physical thing,
just how might the observer deduce the e was really in a larger
invisible external reality?

The only answer it seems to me is self awareness. Descartes said I
think, therefore I am''.\index{Descartes, Ren\'e}\index{I think, therefore I
am}\index{Cogito ergo sum} From being aware of one's own mind, one
can deduce the existence of something outside of the impoverished
virtual reality of one's experience, be it an immaterial mind, or an
actual brain for that mind to supervene, assuming supervenience.
\end{sloppypar}

We may therefore postulate that self-awareness\index{self-awareness|emph}
is a necessary property of consciousness.\index{consciousness} This is
a prediction, potentially falsifiable in the event of a fuller theory
of consciousness being developed.
\index{anthropic!principle|)}

>
> Russell, I am just mentioning "vocabulary problems" which could prevent
> progress for those who want to take computer science /mathematical
> logic as a tools, like we have to do once we postulate explicitly comp.
> But I have realised in Siena that even such a thing as the mundane
> classical "Church thesis" is not so easy even for logicians, so I know
> that I have to explain that (and probably to write some more papers
> ...).
>
> I am just telling that your use of vocabulary will not help to bridge
> the gap between the physicist (not the "physician" 'course (thanks to
> Brent)) and the logicians. I hope you manage my short and frank but
> undiplomatical way of being direct.
>
>
> Bruno
>

I do appreciate your comments, and I'm not in the slightest offended
by your frankness. Vocabulary differences are indeed a problem,
particularly when many of the concepts are still new, or not well
known. Inevitably my terms are flavoured by physics, blending into
maths and computer science. I do try to be clear in my definitions,
but if I accidently pick a term that has a well-known meaning in a
subject I know little about then that can cause problems. I had hoped
that the wiki project might sort some of these out.

However, be thankful we're all on the science side of the 2 cultures
divide. I found it virtually impossible to discuss these ideas with
someone steeped in the humanties.

Plus - my main motivation in life is not the "theory of everything" at
all, but artificial creative processes. In essence I believe in  hard
ALife and work towards making it a reality. Some of these issues spin
off into the everything ensemble idea, and so I try to communicate
them.

Cheers

--

----------------------------------------------------------------------------
A/Prof Russell Standish                  Phone 0425 253119 (mobile)
Mathematics
UNSW SYDNEY 2052                         [EMAIL PROTECTED]
Australia                                http://www.hpcoders.com.au
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