Re: No(-)Justification Justifies The Everything Ensemble
On Fri, Sep 28, 2007 at 06:56:43PM +0200, Bruno Marchal wrote:
>
>
> Le 27-sept.-07, à 12:43, Russell Standish a écrit :
>
> >
> > 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.
>
Sure - the theories exist at different ontological levels. But a
fairly major point of my book is that it is essential to take this
into account, and is also fundamental to the 1-3 distinction.
Not that I think that string theory + lunar existence will get you
anywhere, of course (but you never know!).
Where evolutionary process come into the picture is generating
information.
In the Multiverse, all irreversible processes look like
evolution: branching of worlds gives variation, differing measure and
anthropic selection gives the selection part and determinism of the
Schroedinger equation gives heritability.
What is more, even without considering the Multiverse, all creative
processes we know about (ones generating information) appear to be
evolutionary. So it is not too much of a stretch to conclude that all
creative processes must be evolutionary.
Having established Occam's razor as a theorem in the Multiverse, there
is the immediate problem of the Occam catastrophe. This is resolved by
requiring a minimal complexity of the observed universe. The simplest
(and most probable by Occam) scheme for generating this complexity is
a creative process operating within a simple universe, and is far
simpler than an ab initio complex universe (a Boltzmann brain).
So the assumption that all creative processes are evolutionary (which
one might hope will be better established than that in the future)
endows evolution with a pivotal role in these grand theories of
everything. Its particularly interesting that the evolutionary
concepts map directly to the fundamental postulates of QM.
>
>
>
>
> >
> > 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.
>
Well obviously, I cannot at this stage explain more clearly than in
my book. However, feel free to ask questions, as in asking questions I
understand better your conceptual framework, and may well be able to
connect to it.
As for results, I would list them as:
Zero information principle
Occams razor
Elimination of white rabbits (these are 1st person white rabbits - I
have no idea what a 3rd person white rabbit could be).
Necessity of self awareness for consciousness
3 out of 4 postulates of QM, namely:
1) Hilbert state space
2) Schroedinger equation
3) Born rule
>
>
> >>> 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?
It works if f is a machine, although not all machines satisfy the
above partitioning requirements, in particular non-halting machines.
> What are the relations with the partitions.
> What is an observer (in the all infinite strings context)?
>
Whatever else an observer is, it does map strings to interpretations.
>
>
>
>
> >>> 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
Re: No(-)Justification Justifies The Everything Ensemble
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
Re: No(-)Justification Justifies The Everything Ensemble
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 under
Re: No(-)Justification Justifies The Everything Ensemble
Le 21-sept.-07, à 02:30, Russell Standish a écrit : > 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 agree. I do propose this as subject research, but it is full of (technical) traps. > >> 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). 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). > 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. 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). > 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). ... like I consider "evolution" as a special case of distributed interacting computations. > 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. > 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*. > 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. > 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). And this is completely different from the guy who is in front of a universal dovetailer (running in his reality to makes things straight). This leads to a infinitely subtle prediction. CT is a strong postulate, despite or because it admits deep weakening. > Hence computationalism is not > 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 proved and I have insisted that if COMP is true then COMP is either refutable, or unprovable, in which case comp justifies (and even more: comp classifies) all other possible model. The point here is that the logic G and G* (on which physics and theology eventually reduce) still apply. Only the big unnameable can be thought as escaping the laws of G and G*. > Guardian angel would see
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 start with considering sets of strings. Hence computationalism is not 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
Re: No(-)Justification Justifies The Everything Ensemble
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)
>
> 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 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.
>
>> 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.
?
> This is
> the main point of departure between Schmidhuber's and my approach.
>
>>>
>>> Not equivalent. Equivalent status. Assumption of the set of all
>>> infinite strings plays the same role as your assumption of
>>> arithmetical realism, and that is of the ontological background.
>>
>>
>> I don't know. Let us fix a simple alphabet: {0, 1}. Then an infinite
>> string like
>>010001001110001010010111101001 . (infinite on the
>> right) can be seen as the chracteristic function of a subset of N (the
>> first 1 in the string means then that 0 is in the set,, the second one
>> that 1 is in the set etc. The resulting set is
>> {0, 1, 2, 3, 5, 9, 12, 13, 14, 22, 24, 27, 29, 34, 35, 37, 40, ...}
>> So there is a bijection between the set of infinite strings on the
>> {0,1} alphabet, and the subset of N. So without putting any
>> extra-stcruture on the set of infinite strings, you could as well have
>> taken as basic in your ontology the set of subset of N, written P(N).
>> Now, such a set is not even nameable in any first order theory. In a
>> first order theory of those strings you will get something equivalent
>> to Tarski theory of Real: very nice but below the turing world: the
>> theory is complete and decidable and cannot be used for a theory of
>> everything (there is no natural numbers definable in such theories).
>> From this I can deduce that your intuition relies on second order
>> arithmetic or analysis (and this is confirmed by the way you introduce
>> time). But then this again is really a strong assumption, far stronger
>> than arithmetical realism.
>
> 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.
> 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.
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.
>
>> To be sure, I still don't know if your ontic base is just "nothing"
>> (but then in which theory?) or the infinite strings (again, in which
>> theory and as I said you will to use rich mathematics for that), etc.
>> As you know, I am trying to go a little beyond the UDA result so as to
>> give a little smell of the real thing. The trouble is that the basic
>> tools of logic and
Re: No(-)Justification Justifies The Everything Ensemble
Bruno Marchal skrev: Le 19-sept.-07, à 09:59, Youness Ayaita wrote (in two posts): Probably, we won't find the set of natural numbers within this universe, the number of identical particles (as far as we can talk about that) of any kind is finite. Not in all "models" (cf type 1 multi-realty of Tegmark). The type 1 multi-reality of Tegmark does not require infinity. The type 1 multi-reality is true also in a finite universe, that is *enough* big... -- Torgny Tholerus --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
Le 19-sept.-07, à 09:59, Youness Ayaita wrote (in two posts): > You mentioned the ASSA. Yesterday, motivdated by your hint, I have > read about the ASSA/RSSA debate that is said to have divided the list > into two camps. Since I have trouble with the reasoning I read, I will > probably send a new message hoping for leaving the misunderstanding > behind. > Searching for the Universal Dovetailer Argument, I found a quite > formal demonstration that you wrote in the list, and an even more > formal demonstration that you published in the original work. I do see > the advantage to have such a formal demonstration when it comes to > detailed discussions, but sometimes I'd prefer a simplified outline to > get the basic idea and the main conclusions before going into detail. > If you have written such an outline (in English or in French as well) > I would be thankful to get the link. Otherwise I'll read one of the > formal versions in the future. Actually I like to say that the UDA is informal, yet rigorous. The *formal* counterpart of the UDA is given by the "interview" of a lobian machine (or a couple of lobian machines). Thios part is called sometimes AUDA for Arithmetical UDA because it gives a translation of the thought experiment and its consequence into arithmetic. It leads also to a theory of everything: intensional number theory (which is equivalent to informal extensional number theory + computer science/mathematical logic, in a large sense). Now the main consequence of the UDA is so startling (relatively to our current Aristotelian (naturalistic, materialist, physicalist prejudices) that I prefer that people got them by themselves. By knowing just the result, you could aswell decide I should go in some asylum! But I can give you a short (but risky, thus) outline: I use the computationalist thesis as a working hypothesis. The idea is to take seriously that hypothesis and to derive consequences from it. If the consequences are too much absurd, then this can be seen as an argument against comp. But up to now comp does not lead to contradiction; it leads just too some weirdness. BY comp I mean CT + "Yes doctor". CT is for CHURCH THESIS (sometimes called Church Turing Thesis; Post Law, etc.). CT asserts the existence of a *universal* language (or of a universal machine, which is the one "understanding" that language). The universality concerns computability abilities (not the provability one, for which there is no equivalent theses). CT has many forms, like: the language LAMBDA is universal, FORTRAN is universal, JAVA is universal, etc. Those are provably equivalent. "Yes doctor" is the assumption that there is a level of description of myself such that I survive (or see nothing changed) when a functional substitution is made at that level. It is almost an operational definition: you are a comp practitioners when you accept that your doctor substitutes *any* part of what you think to be your body. Amateurs of MATRIX and novels like SIMULACRON III can appreciate this ... (like amateurs of Plato ...). The UDA then consists in a many steps thought experiment showing that IF comp is correct THEN physicalism is false, and to solve the mind body problem you have to, not only get a theory of mind, but you have to justify the belief in natural law entirely through a relative measure on Sigma_1 sentences (corresponds to the state accessible by the UD). > > On 18 Sep., 16:23, Bruno Marchal <[EMAIL PROTECTED]> wrote: >> So without putting any >> extra-stcruture on the set of infinite strings, you could as well have >> taken as basic in your ontology the set of subset of N, written P(N). >> Now, such a set is not even nameable in any first order theory. In a >> first order theory of those strings you will get something equivalent >> to Tarski theory of Real: very nice but below the turing world: the >> theory is complete and decidable and cannot be used for a theory of >> everything (there is no natural numbers definable in such theories). >> From this I can deduce that your intuition relies on second order >> arithmetic or analysis (and this is confirmed by the way you introduce >> time). > > Bruno and Russell, I don't want to interfere with your discussion. But > I want to say something concerning the mathematics applied to study > the ensemble of infinite bitstrings (which is, as you, Bruno, > mentioned correctly, equivalent to the power set of the natural > numbers). For me, the Everything ensemble is something given. I have no problem with that. > I'm not > forced to restrict myself to the use of mathematical structures > definable by the structure of the Everything ensemble. I can use the > whole of mathematics developed until today in order to study the > Everything ensemble. Yes, you are right; at least concerning the way you prove propositions about the "Everything Ensemble". But obviously, if your "everything ensemble" is supposed to be the ontiic pa
Re: No(-)Justification Justifies The Everything Ensemble
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".
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.
> 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. This is
the main point of departure between Schmidhuber's and my approach.
> >
> > Not equivalent. Equivalent status. Assumption of the set of all
> > infinite strings plays the same role as your assumption of
> > arithmetical realism, and that is of the ontological background.
>
>
> I don't know. Let us fix a simple alphabet: {0, 1}. Then an infinite
> string like
>010001001110001010010111101001 . (infinite on the
> right) can be seen as the chracteristic function of a subset of N (the
> first 1 in the string means then that 0 is in the set,, the second one
> that 1 is in the set etc. The resulting set is
> {0, 1, 2, 3, 5, 9, 12, 13, 14, 22, 24, 27, 29, 34, 35, 37, 40, ...}
> So there is a bijection between the set of infinite strings on the
> {0,1} alphabet, and the subset of N. So without putting any
> extra-stcruture on the set of infinite strings, you could as well have
> taken as basic in your ontology the set of subset of N, written P(N).
> Now, such a set is not even nameable in any first order theory. In a
> first order theory of those strings you will get something equivalent
> to Tarski theory of Real: very nice but below the turing world: the
> theory is complete and decidable and cannot be used for a theory of
> everything (there is no natural numbers definable in such theories).
> From this I can deduce that your intuition relies on second order
> arithmetic or analysis (and this is confirmed by the way you introduce
> time). But then this again is really a strong assumption, far stronger
> than arithmetical realism.
Stronger in what sense? I have only assumed just enough to make sense
of the notion of complexity.
> To be sure, I still don't know if your ontic base is just "nothing"
> (but then in which theory?) or the infinite strings (again, in which
> theory and as I said you will to use rich mathematics for that), etc.
> As you know, I am trying to go a little beyond the UDA result so as to
> give a little smell of the real thing. The trouble is that the basic
> tools of logic and axiomatic are not very well known by anybody but the
> professional logicians.
>
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.
>
>
>
> > 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/
> 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?
>
> > I put your objection
> > into the same category as those who claim the multiverse is
> > ontologically profligate. Apologies to intuistionists out there.
>
>
> Apologies to intutionists and also to constructivist like Schmidhuber,
> but also to weak arithmetical platonist like, imo, digital mechanist
> ought to be.
>
>
>
> >>> 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
Re: No(-)Justification Justifies The Everything Ensemble
On Sep 19, 2:23 am, Bruno Marchal <[EMAIL PROTECTED]> wrote: Schmidhuber and me do agree on comp (100% > agreement: we have the same hypothesis). And relatively to the comp hyp > and the importance of the universal machine Schmidhuber and me are much > closer than with Tegmark whi is just very naïve about notion of > mathematical reality. *sigh*. I of course, don't even agree with comp. One day when I'm better educated, I'm going to have to come back and teach both you, Schmidhuber and Tegmark a lesson ;) Now the problem is that, unlike many people in > this list, Schmidhuber does not address neither the mind body problem > nor the 1-3 person distiinction, and the relativity of states which > derives from that distinction. This forces him to literally defend the > idea that randomness in nature never really exist, which is hard to > justify in front of the physical branch of history we are living. This > does not makes his work wrong, but at least incomplete (and then he > should use Bennett notion of depth for the cosmological/geographical > aspect (like I do in Conscience et mécanisme: using just Kolmogorov is > not enough, but here I am going out topic. You should think carefully about the distinctions you just mentioned (1st-3rd person distinction) and mind-body problem, because it seems to me that the reality of these distinctions is precisely what is at odds with comp. I've talked often about 'the three types of properties' (for my property dualism) : Mathematical, Teleological and Physical. These three properties are based on three different kinds of distinction: Mathematics: The distinction is *model/reality* (or mind-body, information, concept). Teleology: The distinction is *observer/observerd* (self-other or 1st person/3rd person, intention) Physics: The distinction is *here/there* (space, geometry). These are simply three incommensurable types of distinction. You (believers in comp) can try to derieve the observer/observed and here/ there distinctions from the model/reality distinction all you want, you just won't succeed. Nor will materialists ever succeed in extracting a model/reality and observer/observed distinction from a here/there distinction. That's why both materialism *and* comp must fail. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
On Sep 19, 1:18 pm, Hal Ruhl <[EMAIL PROTECTED]> wrote: > Hi Marc: > > The objects I use are divisions of the list - such divisions are > static elements of the power set. > > My objects have nothing to do with programing and do not change - > they can be the current state of a something on its path to completion. > > Hal > It sounded to me like you were confusing universals and particulars. The list of properties used to define an object (the univerasl) cannot be equated to a particular instance of an object possessing these properties (a particular). That's why in programming there's a sharp division between classes and objects when modelling the world. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
On 18 Sep., 16:23, Bruno Marchal <[EMAIL PROTECTED]> wrote: > So without putting any > extra-stcruture on the set of infinite strings, you could as well have > taken as basic in your ontology the set of subset of N, written P(N). > Now, such a set is not even nameable in any first order theory. In a > first order theory of those strings you will get something equivalent > to Tarski theory of Real: very nice but below the turing world: the > theory is complete and decidable and cannot be used for a theory of > everything (there is no natural numbers definable in such theories). > From this I can deduce that your intuition relies on second order > arithmetic or analysis (and this is confirmed by the way you introduce > time). Bruno and Russell, I don't want to interfere with your discussion. But I want to say something concerning the mathematics applied to study the ensemble of infinite bitstrings (which is, as you, Bruno, mentioned correctly, equivalent to the power set of the natural numbers). For me, the Everything ensemble is something given. I'm not forced to restrict myself to the use of mathematical structures definable by the structure of the Everything ensemble. I can use the whole of mathematics developed until today in order to study the Everything ensemble. Let's consider our universe that is studied by physics. Probably, we won't find the set of natural numbers within this universe, the number of identical particles (as far as we can talk about that) of any kind is finite. Nonetheless, it is useful to define the natural numbers and to construct rational, real and even complex numbers in order to study the universe. A vivid though quite ridiculous example might be: When we study the unaffected tropics, we go there with cameras despite of the fact that cameras don't come from the tropics. As Everything ensemble, we use the set of infinite bitstrings. But the Theory of Everything, which doesn't really exist so far, may use every mathematical structure that proves to be useful. This of course differs seriously from arithmetical realism. Youness --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
I do see one mistake I made. >A "Nothing" is incomplete since it can not resolve any question but >there is one it must resolve - that of its own duration. So it is >unstable - it eventually "decays" [Big Bang] into a something that >follows a path to completion by becoming an ever increasing sub >division of its list - that is, it evolves by becoming one object after another - a progression of objects - an evolving universe. I said the post was surely informal. To clarify a few issues: by "question" I mean "meaningful question" and by "path to completion" I mean the incorporation of one or another resolution of a meaningful question the current system has insufficient content to otherwise resolve. So the process is "mathematical" but not mathematical system specific. By "duration" re the Nothing I do not intend a time factor but something more like a resource. Hal Ruhl --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
Hi Marc: The objects I use are divisions of the list - such divisions are static elements of the power set. My objects have nothing to do with programing and do not change - they can be the current state of a something on its path to completion. Hal At 12:13 AM 9/18/2007, you wrote: >On Sep 18, 1:24 pm, Hal Ruhl <[EMAIL PROTECTED]> wrote: > > Hi Youness: > > > > Bruno has indeed recommended that I study in more detail the > > underlying mathematics that I may be appealing to. The response that > > I have made may be a bit self serving but at this point in my life I > > am having difficultly adding yet another area of skill to my resume. > >My advise: Listen to Bruno. Your ideas are riddled with very basic >errors. Example below: > > >Basic Error: > > > > There is no reason to create a multi-layered system distinguishing > > between a sub list and the object it identifies. > >Yes there is. Objects not only have identities, they also have states >and behaviours. This is object-oriented-programming 101. A set of >properties only defines an identity condition. > > > > --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
Le 17-sept.-07, à 14:22, Russell Standish a écrit :
> Sorry my fingers are slipping. Machines (computable functions) are a
> type of map, but not all maps are machines (or perhaps you prefer the
> word function to map).
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
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).
RSSA reasoner does not necessarily condemn ASSA as useless or false for
the explanation of geographical and cosmological aspect of our physical
reality, but pure ASSA, without taking into account the 1-3 distinction
is bound up to fail on the mind body problem (with or without the comp
hyp.), that is ASSA could explain things, but cannot explain the
nature of mind and the nature of matter and the nature of the relation
in between (and that is why they most often use "Aritotle like identity
theories".
>
> Not equivalent. Equivalent status. Assumption of the set of all
> infinite strings plays the same role as your assumption of
> arithmetical realism, and that is of the ontological background.
I don't know. Let us fix a simple alphabet: {0, 1}. Then an infinite
string like
010001001110001010010111101001 . (infinite on the
right) can be seen as the chracteristic function of a subset of N (the
first 1 in the string means then that 0 is in the set,, the second one
that 1 is in the set etc. The resulting set is
{0, 1, 2, 3, 5, 9, 12, 13, 14, 22, 24, 27, 29, 34, 35, 37, 40, ...}
So there is a bijection between the set of infinite strings on the
{0,1} alphabet, and the subset of N. So without putting any
extra-stcruture on the set of infinite strings, you could as well have
taken as basic in your ontology the set of subset of N, written P(N).
Now, such a set is not even nameable in any first order theory. In a
first order theory of those strings you will get something equivalent
to Tarski theory of Real: very nice but below the turing world: the
theory is complete and decidable and cannot be used for a theory of
everything (there is no natural numbers definable in such theories).
From this I can deduce that your intuition relies on second order
arithmetic or analysis (and this is confirmed by the way you introduce
time). But then this again is really a strong assumption, far stronger
than arithmetical realism.
To be sure, I still don't know if your ontic base is just "nothing"
(but then in which theory?) or the infinite strings (again, in which
theory and as I said you will to use rich mathematics for that), etc.
As you know, I am trying to go a little beyond the UDA result so as to
give a little smell of the real thing. The trouble is that the basic
tools of logic and axiomatic are not very well known by anybody but the
professional logicians.
> 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. ?
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?
> I put your objection
> into the same category as those who claim the multiverse is
> ontologically profligate. Apologies to intuistionists out there.
Apologies to intutionists and also to constructivist like Schmidhuber,
but also to weak arithmetical platonist like, imo, digital mechanist
ought to be.
>>> 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.
> so it is a universal dovetailer in all but
> name perhaps. But the ontological basis of the "Great Programmer"
> differs very much from COMP.
Again this is not corect. Schmidhuber and me do agree on comp (100%
agreement: we
Re: No(-)Justification Justifies The Everything Ensemble
Many thanks! I'll give my current attitudes to your hints:
Bruno:
You mentioned the ASSA. Yesterday, motivdated by your hint, I have
read about the ASSA/RSSA debate that is said to have divided the list
into two camps. Since I have trouble with the reasoning I read, I will
probably send a new message hoping for leaving the misunderstanding
behind.
Searching for the Universal Dovetailer Argument, I found a quite
formal demonstration that you wrote in the list, and an even more
formal demonstration that you published in the original work. I do see
the advantage to have such a formal demonstration when it comes to
detailed discussions, but sometimes I'd prefer a simplified outline to
get the basic idea and the main conclusions before going into detail.
If you have written such an outline (in English or in French as well)
I would be thankful to get the link. Otherwise I'll read one of the
formal versions in the future.
Hal (and partially Russell):
I still like your approach to the Everything ensemble using a
countable set P of 'properties'. In fact, if we describe any object or
world by a sequence of properties, the objects form a set equivalent
to {0,1}^P (e.g. we assign 0 if the object does not have the property
and 1 if it has the property) which is the power set of P
(equivalently we could have formed subsets of P). Since P is
countable, we can work with the Everything ensemble {0,1}^IN of
infinite bitstrings. As you have mentioned, this set is uncountable.
So far, there isn't any mathematical problem. In contrast to Marc, I
do also agree identifying objects with the corresponding subset of P.
In this picture, "states and behaviours" as Marc calls it, must also
lie in the properties. Thus, the term 'property' is used in a more
comprehensive sense than in programming.
But now, we come to much more serious criticism. Russell noticed that
regarding the ensemble of infinite bitstrings to be based on
properties jumbles the ensemble (a simple mathematical entity) with
interpretations by the observer. His separation between "syntactic"
and "semantic" space is essential. I agree with Russell, but I do also
see the necessity to interpret (not in an exact sense) mathematical
entities in our theories within our "everyday theory"; because this is
what makes a mathematical theory a (meta)physical theory as I have
pointed out. Russell also uses such an interpretation, but on a more
implicit level: An observer reads bits of the world's description. In
order to make this a (meta)physical theory, we must be able to find
ourselves within the theory, namely as observers. So, we must know
what the process of reading bits of the word's description is meaning
for us. And I'd say that it means measuring 'properties' of the world.
To give a concise explanation: Properties should not be a fundamental
ingredient to the mathematical theory. The mathematical theory uses
"syntactic" space. Though, in order to understand the mathematical
theory by means of the everyday theory (and thus to link the
mathematical theory to "concrete reality"), we need (at some point of
our theories) a translation. This translation can possibly be done by
interpreting the ensemble via 'properties'. Conversely, we can
motivate the ensemble of infinite bitstrings (ant thus "syntactic"
space) starting from a countable set of 'properties'.
Maybe it would be the best for your theories, Hal, to interrupt after
having motivated the ensemble of infinite bitstrings. Then, the
infinite bitstrings are considered to be fundamental (and no longer
the properties themselves). Russell (and surely others, too) has
provided a good framework to work with this ensemble and the role of
observers. Perhaps, you can try to translate some of your ideas to
Russell's more strict and formal language. Then, it will be easier for
us to follow your thinking.
Marc:
Thank you very much for the definitions. I did not know how this was
commonly called.
Brent:
I do still defend extensional definitions even for infinite sets.
Mathematics shows how useful this is. I come back to the example of a
real function f that maps every real number to another real number. In
mathematics, this function is defined by the infinite set {(x,f(x)); x
being a real number}. And the space of all these functions has very
nice mathematical properties, we can work with it and prove theorems.
Of course, in practice I will not have the set but merely a formula
defining f. For example f(x)=x+1. But this does not disprove the
possibilty of working with the sets on an abstract level. Mathematics
indeed proves that it is possible.
Your second point, Russell's ("Bertie's") paradox, is much more
striking. In fact, if we allow every property the English (or the
German, following Cantor) language can express, we will end up with
contradictions. This is why the set of properties is somehow
restricted. We need, as I wrote, "a set of distinct and independent
properties". I don't really know if such a postulate makes
Re: No(-)Justification Justifies The Everything Ensemble
[EMAIL PROTECTED] wrote:
>
> On Sep 13, 11:47 pm, Youness Ayaita <[EMAIL PROTECTED]> wrote:
>
>
>> I see two perfectly equivalent ways to define a property. This is
>> somehow analogous to the mathematical definition of a function f: Of
>> course, in order to practically decide which image f(x) is assigned to
>> a preimage x, we usually must know a formula first. But the function f
>> is not changed if I do not consider the formula, but the whole set
>> {(x,f(x))} instead, where x runs over all preimages.
>>
>> Concerning properties, we normally have some procedure to define which
>> imaginable thing has that property. But I can change my perspective
>> and think of the property as being the set of imaginable things having
>> the property. This is how David Lewis defines properties (e.g. in his
>> book "On the Plurality of Worlds").
>>
>> If you insist on the difference between the two definitions, you may
>> call your property "property1" and Lewis's property "property2".- Hide
>> quoted text -
>>
>>
>
> Surely you are just talking about the well-known distinction between
> intensional and extensional definitions:
>
> http://en.wikipedia.org/wiki/Intensional_definition
>
> "An intensional definition gives the meaning of a term by giving all
> the properties required of something that falls under that definition;
> the necessary and sufficient conditions for belonging to the set being
> defined."
>
> http://en.wikipedia.org/wiki/Extensional_definition
>
> "An extensional definition of a concept or term formulates its meaning
> by specifying its extension, that is, every object that falls under
> the definition of the concept or term in question."
>
But both have difficulties for Youness. You can't use extensional
definitions for infinite sets. On the other hand, using properties
leads to Russell's paradox unless limited in some way.
Brent Meeker
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Re: No(-)Justification Justifies The Everything Ensemble
On Sep 18, 1:24 pm, Hal Ruhl <[EMAIL PROTECTED]> wrote: > Hi Youness: > > Bruno has indeed recommended that I study in more detail the > underlying mathematics that I may be appealing to. The response that > I have made may be a bit self serving but at this point in my life I > am having difficultly adding yet another area of skill to my resume. My advise: Listen to Bruno. Your ideas are riddled with very basic errors. Example below: Basic Error: > There is no reason to create a multi-layered system distinguishing > between a sub list and the object it identifies. Yes there is. Objects not only have identities, they also have states and behaviours. This is object-oriented-programming 101. A set of properties only defines an identity condition. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
On Sep 13, 11:47 pm, Youness Ayaita <[EMAIL PROTECTED]> wrote:
>
> I see two perfectly equivalent ways to define a property. This is
> somehow analogous to the mathematical definition of a function f: Of
> course, in order to practically decide which image f(x) is assigned to
> a preimage x, we usually must know a formula first. But the function f
> is not changed if I do not consider the formula, but the whole set
> {(x,f(x))} instead, where x runs over all preimages.
>
> Concerning properties, we normally have some procedure to define which
> imaginable thing has that property. But I can change my perspective
> and think of the property as being the set of imaginable things having
> the property. This is how David Lewis defines properties (e.g. in his
> book "On the Plurality of Worlds").
>
> If you insist on the difference between the two definitions, you may
> call your property "property1" and Lewis's property "property2".- Hide quoted
> text -
>
Surely you are just talking about the well-known distinction between
intensional and extensional definitions:
http://en.wikipedia.org/wiki/Intensional_definition
"An intensional definition gives the meaning of a term by giving all
the properties required of something that falls under that definition;
the necessary and sufficient conditions for belonging to the set being
defined."
http://en.wikipedia.org/wiki/Extensional_definition
"An extensional definition of a concept or term formulates its meaning
by specifying its extension, that is, every object that falls under
the definition of the concept or term in question."
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Re: No(-)Justification Justifies The Everything Ensemble
Hi Youness: Bruno has indeed recommended that I study in more detail the underlying mathematics that I may be appealing to. The response that I have made may be a bit self serving but at this point in my life I am having difficultly adding yet another area of skill to my resume. This notwithstanding I present below the current state of my model [surely an informal one] which is a combination of previous posts. - "List of all properties: The list of all possible properties objects can have. The list can not be empty since there is at least one object: A Nothing. A Nothing has at least one property - emptiness. The list is most likely at least countably infinite and is assumed herein to be so. Any list can be divided into two sub-lists - the process of defining two objects - a definitional pair. The set of all possible subsets of the list is a power set and therefore uncountably infinite. Therefore there are uncountably infinite objects." One sub list would identify the "Nothing" having the property "empty". There is no reason to create a multi-layered system distinguishing between a sub list and the object it identifies. The list itself, being a particular sub list, is therefore an object with properties - so the list is a member of itself. This nesting yields an infinite number of "Nothings". A "Nothing" is incomplete since it can not resolve any question but there is one it must resolve - that of its own duration. So it is unstable - it eventually "decays" [Big Bang] into a something that follows a path to completion by becoming an ever increasing sub division of its list - that is, it becomes an evolving object - an evolving universe. Since there is an infinite number of "Nothings" we have a multiverse. Some such paths to completion will have SAS, "Inflation" and "Dark energy" which are expressions of the information flow dynamics resulting from the particular completion dynamics. The completion path is naturally random but always grows in information. Very large completion steps should be less common than smaller ones so SAS - if present - would therefore mostly "observe" small changes. Hal Ruhl At 02:22 AM 9/17/2007, you wrote: >Thank you for this remark, Hal. Indeed, you mentioned very similar >ideas: > >"List of all properties: The list of all possible properties >objects can have. The list can not be empty since there is at least >one object: A Nothing. A Nothing has at least one property - >emptiness. The list is most likely at least countably infinite and >is assumed herein to be so. Any list can be divided into two >sub-lists - the process of defining two objects - a definitional >pair. The set of all possible subsets of the list is a power set and >therefore uncountably infinite. Therefore there are uncountably >infinite objects." > >But your theories are much more complex than that if my first >impression is correct. Sooner or later, I'll give attention to them in >more detail. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
On Mon, Sep 17, 2007 at 12:36:51PM +0200, Bruno Marchal wrote:
> >
> > It doesn't matter. The most interesting ones, however, have inverse
> > images of non-zero measure. ie \forall n \in N, the set
> >O^{-1}(n) = {x: O(x)=n}
> > is of nonzero measure.
>
>
>
> I have no clue of what you are saying here. Perhaps you could elaborate
> or give a reference where you say more.
>
Is there a problem with the notation? Perhaps you are reading too much
into it?
>
>
>
>
>
> >>> And that can be given by the
> >>> observer,
> >> But what is the observer? Is the observer an infinite string itself, a
> >> machine, ?
> > The only thing assumed about the observer is that there is a map
> > between descriptions and interpretations.
>
>
> Which kind of map? This is already problematic once CT is assumed: it
> should be at least a map between descriptions and set of
> interpretations (or you assume a form of operational interpretation,
Yes.
> but then you are implicitly assuming some universal machine behind the
> curtains ...
>
No. It is just a map. Not all maps correspond to machines.
>
>
>
>
> > The additional assumption
> > about inverse images having nonzero measure is needed to solve the
> > White Rabbit problem.
> > An observer can be a machine (which is a subset of such mapping),
>
>
> I guess you mean: a machine can be interpreted as a very special sort
> of subset of such a mapping (which one?).
>
Sorry my fingers are slipping. Machines (computable functions) are a
type of map, but not all maps are machines (or perhaps you prefer the
word function to map).
>
> > but
> > needn't be a machine in general.
> > Some strings, _under the interpretation of the observer_, are mapped
> > to observers, including erself. Without the interpretation, though,
> > they are just infinite strings, inert and meaningless.
> >>> where the integers are an enumeration of the oberver's
> >>> possible interpretations.
> >> I still don't understand what you accept at the ontic level, and what
> >> is epistemological, and how those things are related.
> > I'm not sure these terms are even meaningful. Perhaps one can say the
> > strings are ontic, and the interpretations are epistemological.
>
>
>
> Yes, ok. I was just alluding to the 1-3 distinction. With comp you can
> associate a mind to machine, but you have to associate an (uncountable)
> infinity of machine to a mind, and all the problem consists in making
> this clear enough so as to be able to measure the amount of white
> rabbits. This has been done for important subcases in my work, like the
> case of probability/measure/credibility *one*, which does indeed obey
> to (purely arithmetical) "quantum law". This makes the quantum feature
> of the observable realities a case of "digitality" as seen from inside.
>
>
>
> imagine how to *represent* an history by an infinite string. But
> then
> you are using comp and you know the consequences. Unless like some
> people (including Schmidhuber) you don't believe in the difference
> between first and third person points of view.
>
>
> (Youness Ayaita wrote:
>
> > When I first wanted to capture mathematically the Everything, I
> > tried
> > several mathematicalist approaches. But later, I prefered the
> > Everything ensemble that is also known here as the Schmidhuber
> > ensemble.
>
>
> Could you Youness, or Russell, give a definition of "Schmidhuber
> ensemble", please.
> >>>
> >>> The set of all infinite length strings in some chosen alphabet.
> >>
> >>
> >> Is not Shmidhuber a computationalist? I thought he tries to build a
> >> constructive physics, by searching (through CT) priors on a program
> >> generating or 'outputting" a physical universe. Is not the ensemble an
> >> ensemble of computations, and is not Schmidhuber interested in the
> >> finite one or the limiting one? Gosh, you will force me to take again
> >> a
> >> look at his papers :)
> >>
> >
> > Schmidhuber has his ensemble generated by a machine, and perhaps this
> > makes him computationalist.
>
>
> Completely so indeed. But then his proposal for a constructive (and
> apparently deterministic) physics appears to be in contradiction with
> the comp consequences about the 1-3 relations.
>
>
>
> > However I take the ensemble as simply
> > existing, not requiring an further justification.
>
>
> ?
>
>
>
> > It has equivalent
> > status to your "arithmetical realism".
>
> How could I know? You assume the existence of a (very big set) without
> making clear what are your assumptions in general. A priori, accepting
> the (ontic) existence of such big sets means that you presuppose a part
> of set theory (and thus with infinity). This is a far stronger
> assumption than arithmetical realism (accepted by most intuitionists
> and finitists). That cannot be equivalent.
Not equivalent. Equivalent status. Assumption of the set of
Re: No(-)Justification Justifies The Everything Ensemble
Le 17-sept.-07, à 08:51, Russell Standish a écrit :
>
> On Sat, Sep 15, 2007 at 03:13:09PM +0200, Bruno Marchal wrote:
>> Le 14-sept.-07, à 01:02, Russell Standish a écrit :
>>> On Thu, Sep 13, 2007 at 03:04:34PM +0200, Bruno Marchal wrote:
Le 13-sept.-07, à 00:48, Russell Standish a écrit :
> These sorts of discussions "No-justification", "Zero-information
> principle", "All of mathematics" and Hal Ruhl's dualling All and
> Nothing (or should that be "duelling") are really just motivators
> for
> getting at the ensemble, which turns out remarkably to be the same
> in
> each case - the set of 2^\aleph_0 infinite strings or histories.
Once you fix a programming language or a universal machine, then I
can
>>> You don't even need a universal machine. All you need is a mapping
>>> from infinite strings to integers.
>> Which one?
>
> It doesn't matter. The most interesting ones, however, have inverse
> images of non-zero measure. ie \forall n \in N, the set
>O^{-1}(n) = {x: O(x)=n}
> is of nonzero measure.
I have no clue of what you are saying here. Perhaps you could elaborate
or give a reference where you say more.
>>> And that can be given by the
>>> observer,
>> But what is the observer? Is the observer an infinite string itself, a
>> machine, ?
> The only thing assumed about the observer is that there is a map
> between descriptions and interpretations.
Which kind of map? This is already problematic once CT is assumed: it
should be at least a map between descriptions and set of
interpretations (or you assume a form of operational interpretation,
but then you are implicitly assuming some universal machine behind the
curtains ...
> The additional assumption
> about inverse images having nonzero measure is needed to solve the
> White Rabbit problem.
> An observer can be a machine (which is a subset of such mapping),
I guess you mean: a machine can be interpreted as a very special sort
of subset of such a mapping (which one?).
> but
> needn't be a machine in general.
> Some strings, _under the interpretation of the observer_, are mapped
> to observers, including erself. Without the interpretation, though,
> they are just infinite strings, inert and meaningless.
>>> where the integers are an enumeration of the oberver's
>>> possible interpretations.
>> I still don't understand what you accept at the ontic level, and what
>> is epistemological, and how those things are related.
> I'm not sure these terms are even meaningful. Perhaps one can say the
> strings are ontic, and the interpretations are epistemological.
Yes, ok. I was just alluding to the 1-3 distinction. With comp you can
associate a mind to machine, but you have to associate an (uncountable)
infinity of machine to a mind, and all the problem consists in making
this clear enough so as to be able to measure the amount of white
rabbits. This has been done for important subcases in my work, like the
case of probability/measure/credibility *one*, which does indeed obey
to (purely arithmetical) "quantum law". This makes the quantum feature
of the observable realities a case of "digitality" as seen from inside.
imagine how to *represent* an history by an infinite string. But
then
you are using comp and you know the consequences. Unless like some
people (including Schmidhuber) you don't believe in the difference
between first and third person points of view.
(Youness Ayaita wrote:
> When I first wanted to capture mathematically the Everything, I
> tried
> several mathematicalist approaches. But later, I prefered the
> Everything ensemble that is also known here as the Schmidhuber
> ensemble.
Could you Youness, or Russell, give a definition of "Schmidhuber
ensemble", please.
>>>
>>> The set of all infinite length strings in some chosen alphabet.
>>
>>
>> Is not Shmidhuber a computationalist? I thought he tries to build a
>> constructive physics, by searching (through CT) priors on a program
>> generating or 'outputting" a physical universe. Is not the ensemble an
>> ensemble of computations, and is not Schmidhuber interested in the
>> finite one or the limiting one? Gosh, you will force me to take again
>> a
>> look at his papers :)
>>
>
> Schmidhuber has his ensemble generated by a machine, and perhaps this
> makes him computationalist.
Completely so indeed. But then his proposal for a constructive (and
apparently deterministic) physics appears to be in contradiction with
the comp consequences about the 1-3 relations.
> However I take the ensemble as simply
> existing, not requiring an further justification.
?
> It has equivalent
> status to your "arithmetical realism".
How could I know? You assume the existence of a (very big set) without
making clear what are your assumptions in general. A priori, accepting
the (ontic) existence of such big sets means that you pre
Re: No(-)Justification Justifies The Everything Ensemble
Le 17-sept.-07, à 08:22, Youness Ayaita a écrit : > > Thank you for this remark, Hal. Indeed, you mentioned very similar > ideas: > > "List of all properties: The list of all possible properties > objects can have. The list can not be empty since there is at least > one object: A Nothing. A Nothing has at least one property - > emptiness. The list is most likely at least countably infinite and > is assumed herein to be so. Any list can be divided into two > sub-lists - the process of defining two objects - a definitional > pair. The set of all possible subsets of the list is a power set and > therefore uncountably infinite. Therefore there are uncountably > infinite objects." This quotation illustrates the trouble I have with some participants in the list: a big lack of clarity/rigor. There are confusions between list of objects and set of objects. Confusion between set of objects and set of subsets of the set of objects, making this quote too much formal relatively to the informal idea behind. I have often explain to Hal Ruhl that albeit I can appreciate some of his intuitions, his attempts to make things formal are form of 1004 fallacies. It can only discourage those who use all the standard terms in their usual meaning. I continue to suggest Hal to study mainly set theory (given that he uses set vocabulary). > > But your theories are much more complex than that if my first > impression is correct. Sooner or later, I'll give attention to them in > more detail. > > This list really is a rich source of unconventional ideas! Since I'm > new in the list, I am always thankful if someone refers me to > interesting earlier discussions where I can read up on several topics. Many late remark are based on the ASSA approach, and even more or less on quasi physicalist assumptions like the presupposition that there is a sense to allow observer to belong to physical (?) universes. The Universal Dovetailer Argument (original paper is Marchal 1991, but see also the sequel cf my URL) shows how such assumptions are incompatible with the computationalist assumption. The first and third person distinction is of fundamental importance to get that point. Ihave explain the UDA more than one time in this list, but I can explain again. I don't think most RSSA people have a problem with it, although I know the 8th step in the 8 steps version of the UDA has noit really been already discussed. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
Just a further comment - Youness asked me about his properties idea. For me a property is something that belongs to the semantic level, not the syntactic one. It is something that distinguishes one subset of the ensemble from another. This later ends up being the results of projections in a Hilbert space. Conversely, what distinguishes one string from the next is bits, ie they're pure data without information. Cheers -- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://www.hpcoders.com.au --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
On Sat, Sep 15, 2007 at 03:13:09PM +0200, Bruno Marchal wrote:
>
>
> Le 14-sept.-07, à 01:02, Russell Standish a écrit :
>
> >
> > On Thu, Sep 13, 2007 at 03:04:34PM +0200, Bruno Marchal wrote:
> >>
> >>
> >> Le 13-sept.-07, à 00:48, Russell Standish a écrit :
> >>
> >>> These sorts of discussions "No-justification", "Zero-information
> >>> principle", "All of mathematics" and Hal Ruhl's dualling All and
> >>> Nothing (or should that be "duelling") are really just motivators for
> >>> getting at the ensemble, which turns out remarkably to be the same in
> >>> each case - the set of 2^\aleph_0 infinite strings or histories.
> >>
> >>
> >> Once you fix a programming language or a universal machine, then I can
> >
> > You don't even need a universal machine. All you need is a mapping
> > from infinite strings to integers.
>
> Which one?
>
>
It doesn't matter. The most interesting ones, however, have inverse
images of non-zero measure. ie \forall n \in N, the set
O^{-1}(n) = {x: O(x)=n}
is of nonzero measure.
>
> > And that can be given by the
> > observer,
>
>
> But what is the observer? Is the observer an infinite string itself, a
> machine, ?
>
The only thing assumed about the observer is that there is a map
between descriptions and interpretations. The additional assumption
about inverse images having nonzero measure is needed to solve the
White Rabbit problem.
An observer can be a machine (which is a subset of such mapping), but
needn't be a machine in general.
Some strings, _under the interpretation of the observer_, are mapped
to observers, including erself. Without the interpretation, though,
they are just infinite strings, inert and meaningless.
>
>
> > where the integers are an enumeration of the oberver's
> > possible interpretations.
>
>
> I still don't understand what you accept at the ontic level, and what
> is epistemological, and how those things are related.
>
I'm not sure these terms are even meaningful. Perhaps one can say the
strings are ontic, and the interpretations are epistemological.
>
>
>
> >
> >> imagine how to *represent* an history by an infinite string. But then
> >> you are using comp and you know the consequences. Unless like some
> >> people (including Schmidhuber) you don't believe in the difference
> >> between first and third person points of view.
> >>
> >>
> >> (Youness Ayaita wrote:
> >>
> >>> When I first wanted to capture mathematically the Everything, I tried
> >>> several mathematicalist approaches. But later, I prefered the
> >>> Everything ensemble that is also known here as the Schmidhuber
> >>> ensemble.
> >>
> >>
> >> Could you Youness, or Russell, give a definition of "Schmidhuber
> >> ensemble", please.
> >
> > The set of all infinite length strings in some chosen alphabet.
>
>
> Is not Shmidhuber a computationalist? I thought he tries to build a
> constructive physics, by searching (through CT) priors on a program
> generating or 'outputting" a physical universe. Is not the ensemble an
> ensemble of computations, and is not Schmidhuber interested in the
> finite one or the limiting one? Gosh, you will force me to take again a
> look at his papers :)
>
Schmidhuber has his ensemble generated by a machine, and perhaps this
makes him computationalist. However I take the ensemble as simply
existing, not requiring an further justification. It has equivalent
status to your "arithmetical realism". 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 and my "All infinite
strings exist prima facie" idea. This is mostly because Schmidhuber's
second paper (on the speed prior) makes it quite clear he is talking
about something quite different.
>
>
>
> >
> >> Also I still don't know if the "physical universe" is considered as an
> >> ouptut of a program, or if it is associated to the running of a
> >> program.)
> >
> > No, it is considered to be the stable, sharable dream, as you
> > sometimes put it.
>
>
>
> It is the case, by and through the idea that the observer is a lobian
> machine for which the notion of dream is well defined (roughly
> speaking: computations as seen through the spectacles of the
> hypostases/point-of-vies).
>
> The set of all infinite strings, according to the structure you allow
> on it, could give the real line, the set of subset of natural numbers,
> the functions from N to N, etc. It is not enough precise I think.
All of these concepts are more precise and have additional properties
to the set of all infinite strings. For instance, the reals have
group properties of addition and multiplication that the strings
don't.
>
> I don't understand either how you put an uniform measure on those
> infinite strings, I also guess you mean a (non-uniform) measure on the
> subsets of the set of infinite strings. Interesting things can come
Re: No(-)Justification Justifies The Everything Ensemble
Thank you for this remark, Hal. Indeed, you mentioned very similar
ideas:
"List of all properties: The list of all possible properties
objects can have. The list can not be empty since there is at least
one object: A Nothing. A Nothing has at least one property -
emptiness. The list is most likely at least countably infinite and
is assumed herein to be so. Any list can be divided into two
sub-lists - the process of defining two objects - a definitional
pair. The set of all possible subsets of the list is a power set and
therefore uncountably infinite. Therefore there are uncountably
infinite objects."
But your theories are much more complex than that if my first
impression is correct. Sooner or later, I'll give attention to them in
more detail.
This list really is a rich source of unconventional ideas! Since I'm
new in the list, I am always thankful if someone refers me to
interesting earlier discussions where I can read up on several topics.
Youness
On 16 Sep., 21:50, Hal Ruhl <[EMAIL PROTECTED]> wrote:
> Hi Youness:
>
> I have been posting models based on a list of properties as the
> fundamental for a few years.
>
> Hal Ruhl
>
> At 06:36 PM 9/13/2007, you wrote:
>
> >On 13 Sep., 19:44, Brent Meeker <[EMAIL PROTECTED]> wrote:
> > > Youness Ayaita wrote:
>
> >This leads to the
> >2nd idea:
> >We don't say that imaginable things are fundamental, but that the
> >properties themselves are. This idea was also expressed by 1Z in his
> >last reply ("We define imaginable things through hypothetical
> >combinations of properties", Z1) and I think it's a very good
> >candidate for a solution. Then, we start from S being the set of all
> >properties (perhaps with the cardinality of the natural numbers). As
> >above, we define {0,1}^S as the ensemble of descriptions. This would
> >have the cardinality of the real numbers and could mathematically be
> >captured by the infinite strings {0,1}^IN (the formal definition of
> >the Schmidhuber ensemble to give an answer for Bruno).
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Re: No(-)Justification Justifies The Everything Ensemble
Hi Youness:
I have been posting models based on a list of properties as the
fundamental for a few years.
Hal Ruhl
At 06:36 PM 9/13/2007, you wrote:
>On 13 Sep., 19:44, Brent Meeker <[EMAIL PROTECTED]> wrote:
> > Youness Ayaita wrote:
>
>This leads to the
>2nd idea:
>We don't say that imaginable things are fundamental, but that the
>properties themselves are. This idea was also expressed by 1Z in his
>last reply ("We define imaginable things through hypothetical
>combinations of properties", Z1) and I think it's a very good
>candidate for a solution. Then, we start from S being the set of all
>properties (perhaps with the cardinality of the natural numbers). As
>above, we define {0,1}^S as the ensemble of descriptions. This would
>have the cardinality of the real numbers and could mathematically be
>captured by the infinite strings {0,1}^IN (the formal definition of
>the Schmidhuber ensemble to give an answer for Bruno).
>
>
>
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-~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
Le 14-sept.-07, à 01:02, Russell Standish a écrit : > > On Thu, Sep 13, 2007 at 03:04:34PM +0200, Bruno Marchal wrote: >> >> >> Le 13-sept.-07, à 00:48, Russell Standish a écrit : >> >>> These sorts of discussions "No-justification", "Zero-information >>> principle", "All of mathematics" and Hal Ruhl's dualling All and >>> Nothing (or should that be "duelling") are really just motivators for >>> getting at the ensemble, which turns out remarkably to be the same in >>> each case - the set of 2^\aleph_0 infinite strings or histories. >> >> >> Once you fix a programming language or a universal machine, then I can > > You don't even need a universal machine. All you need is a mapping > from infinite strings to integers. Which one? > And that can be given by the > observer, But what is the observer? Is the observer an infinite string itself, a machine, ? > where the integers are an enumeration of the oberver's > possible interpretations. I still don't understand what you accept at the ontic level, and what is epistemological, and how those things are related. > >> imagine how to *represent* an history by an infinite string. But then >> you are using comp and you know the consequences. Unless like some >> people (including Schmidhuber) you don't believe in the difference >> between first and third person points of view. >> >> >> (Youness Ayaita wrote: >> >>> When I first wanted to capture mathematically the Everything, I tried >>> several mathematicalist approaches. But later, I prefered the >>> Everything ensemble that is also known here as the Schmidhuber >>> ensemble. >> >> >> Could you Youness, or Russell, give a definition of "Schmidhuber >> ensemble", please. > > The set of all infinite length strings in some chosen alphabet. Is not Shmidhuber a computationalist? I thought he tries to build a constructive physics, by searching (through CT) priors on a program generating or 'outputting" a physical universe. Is not the ensemble an ensemble of computations, and is not Schmidhuber interested in the finite one or the limiting one? Gosh, you will force me to take again a look at his papers :) > >> Also I still don't know if the "physical universe" is considered as an >> ouptut of a program, or if it is associated to the running of a >> program.) > > No, it is considered to be the stable, sharable dream, as you > sometimes put it. It is the case, by and through the idea that the observer is a lobian machine for which the notion of dream is well defined (roughly speaking: computations as seen through the spectacles of the hypostases/point-of-vies). The set of all infinite strings, according to the structure you allow on it, could give the real line, the set of subset of natural numbers, the functions from N to N, etc. It is not enough precise I think. I don't understand either how you put an uniform measure on those infinite strings, I also guess you mean a (non-uniform) measure on the subsets of the set of infinite strings. Interesting things can come there. > It is the interpretation of the observer, but it > isn't arbitrary. Certainly not in Schmidhuber, as I remember (cf our discussions in this list). OK, with comp, but in some RSSA way, and not in any ASSA way based on an ensemble. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
On 14 Sep., 02:27, Brent Meeker <[EMAIL PROTECTED]> wrote: > In order to observe something about the world it will be necessary to observe > relations, not just things with properties. If you allow countably many > n-place relations, how will you encode them and how will you express that > things like "George owes an explanation of counting to Bob." Do you assume > that every thing has enough distinct properties to make it unique? > > Brent Meeker The approach constructing the Everything ensemble using "properties" as fundamental building blocks has its difficulties. We need a set of distinct and independent properties (such that having property p and having property q is no contradiction if p and q are different) because otherwise we wouldn't get the whole Schmidhuber ensemble which ensures zero information content. Hence, the way I proposed is still vague---It's only a postulate that such a set of properties exists. Though, I think it gives an idea of how we imagine the Schmidhuber ensemble. I'll give an example: Let's study the ensemble of all possible images your monitor can display. It is then possible to describe the images pixel by pixel, every pixel being mapped to a color value. This would be a description using perfectly independent properties (since every combination of colors gives a possible image). "Relations" are not part of this description, they are seen by observers who assign a meaning to what they see. For example they see a person on the image holding a pencil. Similarly, we imagine the Schmidhuber ensemble. Descriptions are built up of elementary and independent properties (corresponding to the pixels on your monitor). Youness Ayaita --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
Youness Ayaita wrote:
> I want to correct an error, the "1st idea" in my last reply was
> erroneous, since in the set {0,1}^P(T) one will find descriptions that
> do not belong to any imaginable thing t in T. Thus, it would not be
> possible to use the total set and the whole idea is rather useless.
>
> So, I restrict my arguments to the second idea that I present in
> detail:
>
> The task is to justify why Russell and I use the Schmidhuber ensemble
> of infinite bitstrings in order to represent the Everything. The
> Schmidhuber ensemble can be constructed if we start from the set P of
> properties. Ad hoc we assume P to have the cardinality of the natural
> numbers. Every imaginable thing t can be described as follows:
> We take every property p in P and say whether the thing t has the
> property p or not. We express this by assigning a 0 if it has the
> property and a 1 if it doesn't. The set of descriptions is thus given
> by the infinite bitstrings:
>
> {0,1}^P
>
> If P has the cardinality of the natural numbers than this can be
> identified with the Schmidhuber ensemble
>
> {0,1}^IN (IN being the set of the natural numbers).
>
> In a final step I will say why this approach to the Schmidhuber
> ensemble is very useful. When we talk about observation, than we
> imagine (according to Russell) an observer reading some of the bits
> contained in the infinite bitstring. The observer can now restrict the
> plurality of worlds he is in: The worlds' descriptions must have the
> bit values he has read. But a priori, there is no justification to
> think that these remaining worlds are somehow "similar" to each other
> (because we did not mention how the descriptions were made. The
> English expressions "combat" and "fight" denote similar things though
> their spellings are very different. "Light" and "fight" are spelled
> similarly though they denote completely different things. Analogous
> situations could happen for unfortunate choices of how to describe a
> world using bitstrings). If we construct the Schmidhuber ensemble as I
> proposed it, then our intuitive expectation that worlds having a
> similar description are "similar in kind". If two worlds have the
> bitstring "01011" after let's say 3 bits, then they definitely have
> (5) properties in common.
>
> I'd be thankful for a comment, Russell.
>
> Youness
In order to observe something about the world it will be necessary to observe
relations, not just things with properties. If you allow countably many
n-place relations, how will you encode them and how will you express that
things like "George owes an explanation of counting to Bob." Do you assume
that every thing has enough distinct properties to make it unique?
Brent Meeker
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Re: No(-)Justification Justifies The Everything Ensemble
I want to correct an error, the "1st idea" in my last reply was
erroneous, since in the set {0,1}^P(T) one will find descriptions that
do not belong to any imaginable thing t in T. Thus, it would not be
possible to use the total set and the whole idea is rather useless.
So, I restrict my arguments to the second idea that I present in
detail:
The task is to justify why Russell and I use the Schmidhuber ensemble
of infinite bitstrings in order to represent the Everything. The
Schmidhuber ensemble can be constructed if we start from the set P of
properties. Ad hoc we assume P to have the cardinality of the natural
numbers. Every imaginable thing t can be described as follows:
We take every property p in P and say whether the thing t has the
property p or not. We express this by assigning a 0 if it has the
property and a 1 if it doesn't. The set of descriptions is thus given
by the infinite bitstrings:
{0,1}^P
If P has the cardinality of the natural numbers than this can be
identified with the Schmidhuber ensemble
{0,1}^IN (IN being the set of the natural numbers).
In a final step I will say why this approach to the Schmidhuber
ensemble is very useful. When we talk about observation, than we
imagine (according to Russell) an observer reading some of the bits
contained in the infinite bitstring. The observer can now restrict the
plurality of worlds he is in: The worlds' descriptions must have the
bit values he has read. But a priori, there is no justification to
think that these remaining worlds are somehow "similar" to each other
(because we did not mention how the descriptions were made. The
English expressions "combat" and "fight" denote similar things though
their spellings are very different. "Light" and "fight" are spelled
similarly though they denote completely different things. Analogous
situations could happen for unfortunate choices of how to describe a
world using bitstrings). If we construct the Schmidhuber ensemble as I
proposed it, then our intuitive expectation that worlds having a
similar description are "similar in kind". If two worlds have the
bitstring "01011" after let's say 3 bits, then they definitely have
(5) properties in common.
I'd be thankful for a comment, Russell.
Youness
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Re: No(-)Justification Justifies The Everything Ensemble
On Thu, Sep 13, 2007 at 03:04:34PM +0200, Bruno Marchal wrote: > > > Le 13-sept.-07, à 00:48, Russell Standish a écrit : > > > These sorts of discussions "No-justification", "Zero-information > > principle", "All of mathematics" and Hal Ruhl's dualling All and > > Nothing (or should that be "duelling") are really just motivators for > > getting at the ensemble, which turns out remarkably to be the same in > > each case - the set of 2^\aleph_0 infinite strings or histories. > > > Once you fix a programming language or a universal machine, then I can You don't even need a universal machine. All you need is a mapping from infinite strings to integers. And that can be given by the observer, where the integers are an enumeration of the oberver's possible interpretations. > imagine how to *represent* an history by an infinite string. But then > you are using comp and you know the consequences. Unless like some > people (including Schmidhuber) you don't believe in the difference > between first and third person points of view. > > > (Youness Ayaita wrote: > > > When I first wanted to capture mathematically the Everything, I tried > > several mathematicalist approaches. But later, I prefered the > > Everything ensemble that is also known here as the Schmidhuber > > ensemble. > > > Could you Youness, or Russell, give a definition of "Schmidhuber > ensemble", please. The set of all infinite length strings in some chosen alphabet. > Also I still don't know if the "physical universe" is considered as an > ouptut of a program, or if it is associated to the running of a > program.) No, it is considered to be the stable, sharable dream, as you sometimes put it. It is the interpretation of the observer, but it isn't arbitrary. > > > Russell Standish wrote : > > > > Where differences lie is in the measure attached to these strings. I > > take each string to be of equal weight to any other, so that there are > > twice the measure of strings satisfying 01* as 011*. This leads > > naturally to a universal prior. > > > I don't understand. If all infinite strings have the same measure, what > is the meaning of "universal prior"? > The universal prior is a measure on certain sets of strings. > > > Neither Bruno's nor Max's theories give a measure, > > > > but remarkably the > > Occam's razor theorem and White Rabbit result is fairly insensitive to > > the measure chosen (so long as it's not too pathological!). > > > I don't understand this either. > The measure induced by the process of observation is enough to turn a uniform measure, which is wabbity into one that is not (universal prior). If the ensemble measure chosen was less wabbity (eg Schmidhuber's speed prior for instance), then the observer measure will also be non-wabbity. It is hard to imagine a more wabbity distribution than the uniform one, but perhaps a delta function on an extremely wabbity string might do the trick. > > > On your comment on permitting infinite strings - the ensemble I > > describe in my book has only infinite strings, which belong to > > syntactic space. > > > ? > I explain syntactic and semantic spaces in my book - its better to read that than to try to reproduce it here. These concepts are known by other names microscopic/macroscopic, L_1/L_2 and so on, but syntactic/semantic seemed to capture the concept best in the most generality. > > > It would be possible to construct an ensemble of purely finite strings > > (all strings of length googol bits, say). This wouldn't satisfy the > > zero information principle, or your no-justification, as you still > > have the finite string size to justify (why googol and not googol+1, > > for instance). I suspect the observable results would be > > indistinguishable from the infinite string ensembles for large enough > > string string size, however. > > Hmmm... I think that once we do care about the difference between 3-pov > and 1-pov, such difference (between ensemble of finite and infinite > strings) does become palpable (empirically), unless you take special > infinite set of arbitrarily long (but finite) strings, but then all > will depends on the chosen representations. > As they say in "Grease" - "Tell me more, tell me more" I suspect that it would only be detected empirically if your instruments were accurate enough, which is why I chose a googol, rather than say a hundred million (which Borges chose for his Library of Babel). > Bruno > > > http://iridia.ulb.ac.be/~marchal/ > > > -- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://www.hpcoders.com.au --~--~-~--~~~---~--~~ You receive
Re: No(-)Justification Justifies The Everything Ensemble
On 13 Sep., 19:44, Brent Meeker <[EMAIL PROTECTED]> wrote:
> Youness Ayaita wrote:
> > ...
> > I see two perfectly equivalent ways to define a property. This is
> > somehow analogous to the mathematical definition of a function f: Of
> > course, in order to practically decide which image f(x) is assigned to
> > a preimage x, we usually must know a formula first. But the function f
> > is not changed if I do not consider the formula, but the whole set
> > {(x,f(x))} instead, where x runs over all preimages.
>
> > Concerning properties, we normally have some procedure to define which
> > imaginable thing has that property. But I can change my perspective
> > and think of the property as being the set of imaginable things having
> > the property. This is how David Lewis defines properties (e.g. in his
> > book "On the Plurality of Worlds").
>
> But I don't think you can define a property this way. For example,
> suppose you want to define "red". Conceptually it is the common
> property of all things that are red. But this set isn't given, and it
> can only be constructed (even in imagination) if you already know what
> "red" is. For a strictly finite set you could use ostensive definition
> to get the set, but I suspect you don't want to limit your set size.
>
> In any case I don't think "imaginable" and "describable in some
> alphabet" are equivalent. People construct perfectly grammatical noun
> clauses that don't correspond to anything imaginable, e.g. "quadratic
> chairs".
>
> Brent Meeker
I've already explained how my (or Lewis's) definition of a property is
to be understood correctly. Of course, practically I can only try to
construct the set of imaginable things that are red if I know a
procedure how to decide if something is red in every particular case.
But this is only related to the practical applicability of the
concept. We agree that the property "red" is completely defined by the
set of imaginable things being red. So, whenever it's useful, I may
work with this set instead of our common conception of "red" (I will
never have the concrete and full set at my disposition but that won't
be necessary). And you will se below why it is useful to do so.
Your second remark is very interesting. You're right that the English
language can construct difficult situations when it comes to
descriptions of possibly imaginable things. This is why I avoid the
English language in this context (even the French language, which is
said to be very exact, is not an option). Two ideas how to get the
Schmidhuber ensemble of descriptions out of the "set" of all
imaginable things:
1st idea:
Let T be the set of all imaginable things. Then, corresponding to my
definition of a property being a subset of the T, the power set P(T)
is the set of all properties. To describe an imaginable thing t, we
might proceed as follows:
For every property p in P(T), we say wheter t has the property (then
we assign a 1) or not (we assign a 0). The set of all descriptions
then is {0,1}^P(T) similar to the Schmidhuber ensemble. The only
problem with this is the cardinality of the ensemble. The construction
{0,1}^P(T) is equivalent to the power set P(P(T)). This means, if T
has the cardinality of the natural numbers, then P(T) has the
cardinality of the real numbers and P(P(T)) has an even higher
cardinality! Since the Schmidhuber ensemble only has the cardinality
of the real numbers, we're facing a problem at this point.
This leads to the
2nd idea:
We don't say that imaginable things are fundamental, but that the
properties themselves are. This idea was also expressed by 1Z in his
last reply ("We define imaginable things through hypothetical
combinations of properties", Z1) and I think it's a very good
candidate for a solution. Then, we start from S being the set of all
properties (perhaps with the cardinality of the natural numbers). As
above, we define {0,1}^S as the ensemble of descriptions. This would
have the cardinality of the real numbers and could mathematically be
captured by the infinite strings {0,1}^IN (the formal definition of
the Schmidhuber ensemble to give an answer for Bruno).
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Re: No(-)Justification Justifies The Everything Ensemble
On 13 Sep, 12:47, Youness Ayaita <[EMAIL PROTECTED]> wrote:
> On 13 Sep., 13:26, 1Z <[EMAIL PROTECTED]> wrote:
>
>
>
> > On 12 Sep, 01:50, Youness Ayaita <[EMAIL PROTECTED]> wrote:
>
> > > No(-)Justification Justifies The Everything Ensemble
> > > The amazing result of these simple considerations is that we get the
> > > Everything ensemble gratis! We don't need any postulate. But how is
> > > this transition made? At this point I remind you of the second section
> > > of this article: The Everything ensemble, or the statement that
> > > everything exists, is the interpretation of our new perspective in the
> > > everyday theory. In our everyday theory, we use the concept of
> > > 'existence' as a property of things. A property p is given by the
> > > ensemble of (imaginable) things that have that property. Thus we can
> > > identify the property p with the ensemble of (imaginable) things
> > > having that property.
>
> > That isn't how properties are defined, and existence isn't a (first
> > order) property.
> > We place things into ensembles (classes, as opposed to sets) on the
> > basis of their properties;
> > we don't read properties off from ensembles. Properties have to come
> > first, or we would not
> > be able to classify individuals that we had not encountered before.
>
> I see two perfectly equivalent ways to define a property. This is
> somehow analogous to the mathematical definition of a function f: Of
> course, in order to practically decide which image f(x) is assigned to
> a preimage x, we usually must know a formula first. But the function f
> is not changed if I do not consider the formula, but the whole set
> {(x,f(x))} instead, where x runs over all preimages.
But that doesn't correspond to any realistic epistemology.
We are have no acquaintance with the entirety of set-of-all-red-
things.
You ha
> Concerning properties, we normally have some procedure to define which
> imaginable thing has that property.
We define imaginable things through hypothetical combinations
of properties -- eg "flying" + "pig"
> But I can change my perspective
> and think of the property as being the set of imaginable things having
> the property.
"As having *what* property?"
"The property that everything in *this* set has"
"What set? Show it to me!"
See the problem?
>This is how David Lewis defines properties (e.g. in his
> book "On the Plurality of Worlds").
>
> If you insist on the difference between the two definitions, you may
> call your property "property1" and Lewis's property "property2".
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Re: No(-)Justification Justifies The Everything Ensemble
Youness Ayaita wrote:
> ...
> I see two perfectly equivalent ways to define a property. This is
> somehow analogous to the mathematical definition of a function f: Of
> course, in order to practically decide which image f(x) is assigned to
> a preimage x, we usually must know a formula first. But the function f
> is not changed if I do not consider the formula, but the whole set
> {(x,f(x))} instead, where x runs over all preimages.
>
> Concerning properties, we normally have some procedure to define which
> imaginable thing has that property. But I can change my perspective
> and think of the property as being the set of imaginable things having
> the property. This is how David Lewis defines properties (e.g. in his
> book "On the Plurality of Worlds").
>
But I don't think you can define a property this way. For example,
suppose you want to define "red". Conceptually it is the common
property of all things that are red. But this set isn't given, and it
can only be constructed (even in imagination) if you already know what
"red" is. For a strictly finite set you could use ostensive definition
to get the set, but I suspect you don't want to limit your set size.
In any case I don't think "imaginable" and "describable in some
alphabet" are equivalent. People construct perfectly grammatical noun
clauses that don't correspond to anything imaginable, e.g. "quadratic
chairs".
Brent Meeker
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Re: No(-)Justification Justifies The Everything Ensemble
Le 13-sept.-07, à 00:48, Russell Standish a écrit : > These sorts of discussions "No-justification", "Zero-information > principle", "All of mathematics" and Hal Ruhl's dualling All and > Nothing (or should that be "duelling") are really just motivators for > getting at the ensemble, which turns out remarkably to be the same in > each case - the set of 2^\aleph_0 infinite strings or histories. Once you fix a programming language or a universal machine, then I can imagine how to *represent* an history by an infinite string. But then you are using comp and you know the consequences. Unless like some people (including Schmidhuber) you don't believe in the difference between first and third person points of view. (Youness Ayaita wrote: > When I first wanted to capture mathematically the Everything, I tried > several mathematicalist approaches. But later, I prefered the > Everything ensemble that is also known here as the Schmidhuber > ensemble. Could you Youness, or Russell, give a definition of "Schmidhuber ensemble", please. Also I still don't know if the "physical universe" is considered as an ouptut of a program, or if it is associated to the running of a program.) Russell Standish wrote : > Where differences lie is in the measure attached to these strings. I > take each string to be of equal weight to any other, so that there are > twice the measure of strings satisfying 01* as 011*. This leads > naturally to a universal prior. I don't understand. If all infinite strings have the same measure, what is the meaning of "universal prior"? > Neither Bruno's nor Max's theories give a measure, But I extract the logic of the proposition having measure one. This is enough to be compared with the logic of quantum certainties (described by some quantum logic). > but remarkably the > Occam's razor theorem and White Rabbit result is fairly insensitive to > the measure chosen (so long as it's not too pathological!). I don't understand this either. > On your comment on permitting infinite strings - the ensemble I > describe in my book has only infinite strings, which belong to > syntactic space. ? > It would be possible to construct an ensemble of purely finite strings > (all strings of length googol bits, say). This wouldn't satisfy the > zero information principle, or your no-justification, as you still > have the finite string size to justify (why googol and not googol+1, > for instance). I suspect the observable results would be > indistinguishable from the infinite string ensembles for large enough > string string size, however. Hmmm... I think that once we do care about the difference between 3-pov and 1-pov, such difference (between ensemble of finite and infinite strings) does become palpable (empirically), unless you take special infinite set of arbitrarily long (but finite) strings, but then all will depends on the chosen representations. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
On 13 Sep., 13:26, 1Z <[EMAIL PROTECTED]> wrote:
> On 12 Sep, 01:50, Youness Ayaita <[EMAIL PROTECTED]> wrote:
>
> > No(-)Justification Justifies The Everything Ensemble
> > The amazing result of these simple considerations is that we get the
> > Everything ensemble gratis! We don't need any postulate. But how is
> > this transition made? At this point I remind you of the second section
> > of this article: The Everything ensemble, or the statement that
> > everything exists, is the interpretation of our new perspective in the
> > everyday theory. In our everyday theory, we use the concept of
> > 'existence' as a property of things. A property p is given by the
> > ensemble of (imaginable) things that have that property. Thus we can
> > identify the property p with the ensemble of (imaginable) things
> > having that property.
>
> That isn't how properties are defined, and existence isn't a (first
> order) property.
> We place things into ensembles (classes, as opposed to sets) on the
> basis of their properties;
> we don't read properties off from ensembles. Properties have to come
> first, or we would not
> be able to classify individuals that we had not encountered before.
I see two perfectly equivalent ways to define a property. This is
somehow analogous to the mathematical definition of a function f: Of
course, in order to practically decide which image f(x) is assigned to
a preimage x, we usually must know a formula first. But the function f
is not changed if I do not consider the formula, but the whole set
{(x,f(x))} instead, where x runs over all preimages.
Concerning properties, we normally have some procedure to define which
imaginable thing has that property. But I can change my perspective
and think of the property as being the set of imaginable things having
the property. This is how David Lewis defines properties (e.g. in his
book "On the Plurality of Worlds").
If you insist on the difference between the two definitions, you may
call your property "property1" and Lewis's property "property2".
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Re: No(-)Justification Justifies The Everything Ensemble
On 12 Sep, 15:32, Youness Ayaita <[EMAIL PROTECTED]> wrote: > For further > research, it is then natural to identify imaginable things with their > descriptions and to choose a simple alphabet for expressing the > descriptions (e.g. strings of 0 and 1). How would you express "A thing such that it cannot be expressed as a string of 1's and 0''s" in that notation.? --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
On 12 Sep, 01:50, Youness Ayaita <[EMAIL PROTECTED]> wrote: > No(-)Justification Justifies The Everything Ensemble > The amazing result of these simple considerations is that we get the > Everything ensemble gratis! We don't need any postulate. But how is > this transition made? At this point I remind you of the second section > of this article: The Everything ensemble, or the statement that > everything exists, is the interpretation of our new perspective in the > everyday theory. In our everyday theory, we use the concept of > 'existence' as a property of things. A property p is given by the > ensemble of (imaginable) things that have that property. Thus we can > identify the property p with the ensemble of (imaginable) things > having that property. That isn't how properties are defined, and existence isn't a (first order) property. We place things into ensembles (classes, as opposed to sets) on the basis of their properties; we don't read properties off from ensembles. Properties have to come first, or we would not be able to classify individuals that we had not encountered before. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
On 13 Sep., 00:48, Russell Standish wrote: > It would be possible to construct an ensemble of purely finite strings > (all strings of length googol bits, say). This wouldn't satisfy the > zero information principle, or your no-justification, as you still > have the finite string size to justify (why googol and not googol+1, > for instance). I suspect the observable results would be > indistinguishable from the infinite string ensembles for large enough > string string size, however. We've a little misunderstanding in this point. I did never suggest strings of an overall fixed length, but only of a finite length that may vary from string to string without being limited. The idea behind this was that imaginable things should be describable completely (e.g. by a person telling me about them) and not only asymptotically (which---I thought---could be the case if the descriptions were infinite). On the other hand, I do see two arguments in favor of the infinite strings: 1. It may be that something can be described by a finite description in one "language", but must be described by an infinite description in another "language". A simple example is the number pi which can be defined by finite expressions (e.g. by writing down formally the Gregory-Leibniz series). But if we restrict ourselves to describe numbers by writing down their digits in the decimal numeral system, then the description of pi is infinite. This can be seen as a motivation to allow infinite strings. 2. The difference between finite and infinite strings is somehow similar to the difference between natural and real numbers (at least as far as their cardinalities are concerned) in mathematics. If, in a far future, we want to establish analytical methods to study the Everything ensemble (this of course is a very, very problematic task and cannot be our concern here) it may turn out useful to allow infinite strings as it turned out useful for ordinary mathematics to allow real numbers instead of natural or rational numbers. > Where differences lie is in the measure attached to these strings. I > take each string to be of equal weight to any other, so that there are > twice the measure of strings satisfying 01* as 011*. This leads > naturally to a universal prior. I'm still hesitant to accept the idea that the Everything ensemble by itself comes up with a measure. Although undoubtedly the measure is a fundamental ingredient of our theories, I think that it should only be introduced for practical reasons, i.e. whenever we are interested in probabilities. Then the measure is adapted to our state of ignorance. The standard case will be that one has no information whether to prefer a given description which leads to your measure of equal weight and the universal prior. This is very analogous to statistical physics where we usually assign equal measure to every microstate. I am not yet familiar with Schmidhuber's ideas but I am going to read up on this topic soon, in particular in the context of the White Rabbit paradox. Youness Ayaita --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
On Wed, Sep 12, 2007 at 07:32:32AM -0700, Youness Ayaita wrote: > > The two concerns, how to give a precise notion of the Everything, and > how to deduce predictions from a chosen notion, lie at the very heart > of our common efforts. Though, I did not go into them for the simple > reason that I wanted to avoid discussions that are not directly linked > to the topic. > > When I first wanted to capture mathematically the Everything, I tried > several mathematicalist approaches. But later, I prefered the > Everything ensemble that is also known here as the Schmidhuber > ensemble. I assume that the no-justification naturally leads to this > ensemble. This comes from the development of the (degenerate) property > of existence which is then assigned to all imaginable things. I don't > think that a metaphysical discussion of the term "imaginable thing" is > necessary now, I'm satisfied with the idea that an imaginable thing > can be completely described by means of language. For further > research, it is then natural to identify imaginable things with their > descriptions and to choose a simple alphabet for expressing the > descriptions (e.g. strings of 0 and 1). In the past I assumed these > strings to be of finite length. I read that Russell Standish also > permits infinite strings. > These sorts of discussions "No-justification", "Zero-information principle", "All of mathematics" and Hal Ruhl's dualling All and Nothing (or should that be "duelling") are really just motivators for getting at the ensemble, which turns out remarkably to be the same in each case - the set of 2^\aleph_0 infinite strings or histories. Where differences lie is in the measure attached to these strings. I take each string to be of equal weight to any other, so that there are twice the measure of strings satisfying 01* as 011*. This leads naturally to a universal prior. Schmidhuber has a different measure, assuming that the strings are generated in real time from a machine with bounded resources. This is his "speed prior", and leads to a quite different measure on the strings. Neither Bruno's nor Max's theories give a measure, but remarkably the Occam's razor theorem and White Rabbit result is fairly insensitive to the measure chosen (so long as it's not too pathological!). On your comment on permitting infinite strings - the ensemble I describe in my book has only infinite strings, which belong to syntactic space. A finite string corresponds to a set of infinite strings all having the same finite prefix, and as such belongs to semantic space. It would be possible to construct an ensemble of purely finite strings (all strings of length googol bits, say). This wouldn't satisfy the zero information principle, or your no-justification, as you still have the finite string size to justify (why googol and not googol+1, for instance). I suspect the observable results would be indistinguishable from the infinite string ensembles for large enough string string size, however. -- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://www.hpcoders.com.au --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
If anyone is interested, I think some of the ideas at my website, www.geocities.com/roger846, apply to the current discussion. Briefly, the ideas entail: o Something exists because it is completely defined. That is, you know exactly what's contained in that thing. This applies to material things outside the mind as well as to ideas and concepts within the mind. For instance, a book exists because you know what's contained within it (cover, pages, etc.). The concept "love" exists in someone's mind because that person knows what kinds of things are contained within the concept. o The complete definition of something is the same thing as an edge or boundary. This edge or boundary gives the thing substance or what we call "existence". o What we have traditionally called "non-existence" or the lack of all matter, energy, volume, ideas/concepts, etc. is completely defined. That is, there's nothing missing and nothing somewhere else, and you know exactly what's there-nothing at all. Because it's completely defined, what we've traditionally thought of as "non-existence" can also be said to exist. In other words, when seen from a different perspective than usual, "non-existence" and "existence" are really just the same thing. Another way of coming to this conclusion is as follows: When thinking about the question "why is there something rather than nothing?", two choices are: A. "Something" has always been here. B. "Something" has not always been here. Even though choice A is possible, it doesn't provide any explanation so let's go with choice B and see where it leads. If "something" hasn't always been here, then "nothing" must have been here before it. If "nothing" were here, there would be no mechanism in "nothing" to change this "nothing" into "something". Yet, we accept that "something" is here now. So, the only possible choice is that "nothing" and "something" are one and the same thing. Thanks. Roger --- Youness Ayaita <[EMAIL PROTECTED]> wrote: > > No(-)Justification Justifies The Everything Ensemble > Youness Ayaita > > > > In this message, I present my "no-justification" of > the hypothesis > that everything exists. The no-justification argues > that no > justification at all is needed to accept the > hypothesis. This provides > a new and very satisfying approach to the Everything > ensemble. > > > > 1 Hitherto proposed justifications > > In this first section I give a brief overview of > some existing > justifications for the Everything ensemble. The > reader familiar with > the topic may skip this section. > > Several thinkers have come independently to the > hypothesis that---in > some sense or another---everything exists. The > justifications they > have found in favor of this hypothesis vary as do > their intellectual > backgrounds (philosophy, computer science, > mathematics or physics). > When I myself developed the hypothesis, I found > three > justifications which I call respectively the > 'metaphysical approach', > the 'generalized Copernican principle' and the > 'no-justification'. The > main justifications supported by contributors to the > everything-list > are the 'zero information principle' and > 'arithmetical realism' (also > called 'mathematical Platonism'). Another > justification is due to the > analytic philosopher David Lewis: > > "Why believe in a plurality of worlds?---Because the > hypothesis is > serviceable, and that is a reason to think it is > true." > > For most philosophers Lewis's justification was not > convincing. Much > more attractive to many thinkers is arithmetical > realism, assuming the > objective existence of all mathematical objects. The > zero information > principle bases upon the observation that the > Everything has no > information content. Russell Standish writes: > > "There is a mathematical equivalence between the > Everything, as > represented by this collection of all possible > descriptions and > Nothing, a state of no information." > > This justification is impressive since it shows that > Everything is--- > in some sense---not more than Nothing. It thus > provides a striking > argument against the critics' objection that > supporters of the > Everything ensemble postulate too much additional > ontology. > > As a last example, I mention the gen
Re: No(-)Justification Justifies The Everything Ensemble
The two concerns, how to give a precise notion of the Everything, and how to deduce predictions from a chosen notion, lie at the very heart of our common efforts. Though, I did not go into them for the simple reason that I wanted to avoid discussions that are not directly linked to the topic. When I first wanted to capture mathematically the Everything, I tried several mathematicalist approaches. But later, I prefered the Everything ensemble that is also known here as the Schmidhuber ensemble. I assume that the no-justification naturally leads to this ensemble. This comes from the development of the (degenerate) property of existence which is then assigned to all imaginable things. I don't think that a metaphysical discussion of the term "imaginable thing" is necessary now, I'm satisfied with the idea that an imaginable thing can be completely described by means of language. For further research, it is then natural to identify imaginable things with their descriptions and to choose a simple alphabet for expressing the descriptions (e.g. strings of 0 and 1). In the past I assumed these strings to be of finite length. I read that Russell Standish also permits infinite strings. But first of all, I'm interested in your opinions concerning the no- justification. Thank you, Stathis Papaioannou, for letting me know of Kant's ideas in this context. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
Le 12-sept.-07, à 13:08, Stathis Papaioannou a écrit : > > On 12/09/2007, Brent Meeker <[EMAIL PROTECTED]> wrote: > OK. So where are the flying pigs? >>> >>> Elsewhere. Existence is not a property, but position is. >> >> Ok. Why are they there and not here? >> >> I'm sure that Stathis takes my point that saying everything-exists is >> not only "no-justification" it is also "no-information". By itself >> it is worthless for explaining anything. > > Yes, you have to show how the theory makes predictions about the real > world, otherwise it is impossible to know whether it is true or not > and the theory is worthless. I'm more or less ok with this, except that you can *never* know when a theory (about reality) is true (about reality). I have already criticize everything-like theories when they take a too big "everything" hyp. at the start, like pure mathematicalism à-la Tegmark. From that point of view Schmidhuber is a bit clearer on the type of everything notion available once you postulate the comp hyp. (Now Schmidhuber does not take the 1-3 pov distinction into account, so he missed apparently the role of the first person indeterminacy and its verifiable consequences, like the fact that the laws of physics have to emerge from the platonic existence of the many computations). It is really Church's thesis which provides the first coherent notion of "everything". That is why I'm motivated to tentattively explain what Church thesis is, and why it is a sort of completely unexpected miracle (to talk like Godel). Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
On 12/09/2007, Brent Meeker <[EMAIL PROTECTED]> wrote: > >> OK. So where are the flying pigs? > > > > Elsewhere. Existence is not a property, but position is. > > Ok. Why are they there and not here? > > I'm sure that Stathis takes my point that saying everything-exists is not > only "no-justification" it is also "no-information". By itself it is > worthless for explaining anything. Yes, you have to show how the theory makes predictions about the real world, otherwise it is impossible to know whether it is true or not and the theory is worthless. -- Stathis Papaioannou --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
Stathis Papaioannou wrote: > On 12/09/2007, Brent Meeker <[EMAIL PROTECTED]> wrote: > >> OK. So where are the flying pigs? > > Elsewhere. Existence is not a property, but position is. Ok. Why are they there and not here? I'm sure that Stathis takes my point that saying everything-exists is not only "no-justification" it is also "no-information". By itself it is worthless for explaining anything. Brent Meeker --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
On 12/09/2007, Brent Meeker <[EMAIL PROTECTED]> wrote: > OK. So where are the flying pigs? Elsewhere. Existence is not a property, but position is. -- Stathis Papaioannou --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
On 12/09/2007, Youness Ayaita <[EMAIL PROTECTED]> wrote: > The no-justification argues that it doesn't make sense to introduce > 'existence' as a property, or expressed in another way, that it is not > possible to meaningfully separate (imaginable) things that have the > (hypothetic) property that they 'exist' from (imaginable) things > without that property. This leaves us with two options if we still > want to use the concept of existence given by the everyday theory: > that the ensemble of (imaginable) things is empty or that every > (imaginable) thing has the property that it exists. The property is > degenerate, it does not separate some (imaginable) things from others. > Since, in our everyday theory, we say that things surrounding us > exist, we must consequently take the second option: that every > (imaginable) thing has the property that it exists. This is the > Everything ensemble. Are you aware that "existence is not a property" was Immanuel Kant's answer to the ontological argument for the existence of God? Kant, however, did not derive modal realism from this. http://www.philosophyofreligion.info/existenceisnotapredicate.html -- Stathis Papaioannou --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
Youness Ayaita wrote: ... > 3 No-justification > > The no-justification is the most satisfying justification for the > Everything ensemble I know. I even think that a more satisfying > justification is impossible in principle. So what is it about? The > crucial point is to try to get to the bottom of our understanding of > 'existence'. In our everyday theory we use 'existence' as a property: > Some things 'exist', whereas other (imaginable) things don't. The > origin of this practice lies in very pragmatic reasons. It makes sense > to separate things that are 'accessible in principle' from things that > are not. This relation between 'us' and 'things which are accessible > in principle for us' was falsely understood as an objective property > of those things. I feel Wittgenstein's hands slapping on my back when > I tell you that 'existence' is nothing else than a linguistic > confusion. Strictly speaking, the concept of 'existence' doesn't make > sense. I encourage you to abandon it. If we take the right point of > view, the problem of having to find a "theory of everything" doesn't > occur. > > The amazing result of these simple considerations is that we get the > Everything ensemble gratis! We don't need any postulate. But how is > this transition made? At this point I remind you of the second section > of this article: The Everything ensemble, or the statement that > everything exists, is the interpretation of our new perspective in the > everyday theory. In our everyday theory, we use the concept of > 'existence' as a property of things. A property p is given by the > ensemble of (imaginable) things that have that property. Thus we can > identify the property p with the ensemble of (imaginable) things > having that property. > > The no-justification argues that it doesn't make sense to introduce > 'existence' as a property, or expressed in another way, that it is not > possible to meaningfully separate (imaginable) things that have the > (hypothetic) property that they 'exist' from (imaginable) things > without that property. This leaves us with two options if we still > want to use the concept of existence given by the everyday theory: > that the ensemble of (imaginable) things is empty or that every > (imaginable) thing has the property that it exists. The property is > degenerate, it does not separate some (imaginable) things from others. > Since, in our everyday theory, we say that things surrounding us > exist, we must consequently take the second option: that every > (imaginable) thing has the property that it exists. This is the > Everything ensemble. I repeat that the statement "everything exists" > can be seen as a definition of the new (and degenerate!) property of > existence: for an imaginable thing, to exist doesn't mean anything > else than being an imaginable thing. From our new perspective, it's a > tautology. But it is the interpretation of the new perspective in the > everyday theory. > > In this last paragraph it can be seen that the no-justification has a > lot in common with the zero information principle. I wrote that, if we > want to introduce the property of existence, than this property must > be degenerate (given by no entity or given by the ensemble of all > entities). In other words, there cannot be any information separating > some entities that exist from other entities that don't. OK. So where are the flying pigs? Brent Meeker --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
No(-)Justification Justifies The Everything Ensemble
No(-)Justification Justifies The Everything Ensemble Youness Ayaita In this message, I present my "no-justification" of the hypothesis that everything exists. The no-justification argues that no justification at all is needed to accept the hypothesis. This provides a new and very satisfying approach to the Everything ensemble. 1 Hitherto proposed justifications In this first section I give a brief overview of some existing justifications for the Everything ensemble. The reader familiar with the topic may skip this section. Several thinkers have come independently to the hypothesis that---in some sense or another---everything exists. The justifications they have found in favor of this hypothesis vary as do their intellectual backgrounds (philosophy, computer science, mathematics or physics). When I myself developed the hypothesis, I found three justifications which I call respectively the 'metaphysical approach', the 'generalized Copernican principle' and the 'no-justification'. The main justifications supported by contributors to the everything-list are the 'zero information principle' and 'arithmetical realism' (also called 'mathematical Platonism'). Another justification is due to the analytic philosopher David Lewis: "Why believe in a plurality of worlds?---Because the hypothesis is serviceable, and that is a reason to think it is true." For most philosophers Lewis's justification was not convincing. Much more attractive to many thinkers is arithmetical realism, assuming the objective existence of all mathematical objects. The zero information principle bases upon the observation that the Everything has no information content. Russell Standish writes: "There is a mathematical equivalence between the Everything, as represented by this collection of all possible descriptions and Nothing, a state of no information." This justification is impressive since it shows that Everything is--- in some sense---not more than Nothing. It thus provides a striking argument against the critics' objection that supporters of the Everything ensemble postulate too much additional ontology. As a last example, I mention the generalized Copernican principle. The idea is to give up the categorical difference between our world and all other possible worlds: Everything is equally real. 2 Remarks on new fundamental theories Before starting to explain my no-justification of the Everything ensemble, I want to summarize some important statements in advance which concern all new fundamental theories. Taking seriously the approach given by the no-justification, it will turn out that the term "Everything exists" is logically meaningless. Nonetheless I'll still use the term without questioning its outstanding significance. The only thing that changes is the term's role within our thinking. It will no longer be an integral part of the fundamental theory, but merely a link from the fundamental theory to our 'everyday theory'. As a typical example of such a relation may serve Einstein's theory of general relativity. The concept of mass---or to be more precise, the energy-momentum tensor---is no integral part of general relativity, it is replaced by the curvature of spacetime. Einstein's famous field equations that relate the curvature of spacetime to the energy- momentum tensor, are thus meaningless insofar as they only 'define' the energy-momentum tensor. In principle, we could abandon the concept of mass and energy and use the curvature tensor instead. So, would the theory of general relativity lose anything if we removed Enstein's field equations? The answer to this question is twofold. As a mathematical theory, general relativity would remain complete and as rich as it is today. But as a physical theory it would lose its meaning, i.e. it would lose its explanatory and predictive power. This is because a mathematical theory (in the case of general relativity: Spacetime is a smooth 4-manifold with a metric tensor and such and such properties) does not give a physical interpretation by itself. The term "physical interpretation" means that we have a procedure how to interpret elements of the theory as elements of our everyday theory. A physical interpretation serves as translation from the theory's mathematical language to our concrete everyday language. Einstein's field equations link general relativity (with the curvature of spacetime) to special relativity (with the energy-momentum tensor) which is itself linked to Newtonian mechanics (with the usual concept of mass and Euclidian space). Newtonian mechanics is understood in the everyday theory. We see from this that Einstein's field equations are part of the physical interpretation in the sense described above. The everyday theory, of course, is only a vague concept that allows us to excha
