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 sense.
Youness
A question concerning the ASSA/RSSA debate
When Bruno spoke of the ASSA I looked up some messages in this list dealing with the ASSA and RSSA. My message does not aim at initiating yet another controversial discussion of the subject. But I rather hope that you will assist me resolving a misunderstanding. Searching for the self-sampling assumption in Wikipedia leads to the definition: Each observer moment should reason as if it were randomly selected from the class of all observer moments in its reference class. What remains unclear in this definition is the term reference class which is also the source of the ASSA/RSSA debate. When we want to know which observer moment to expect next, we look at the class of all observer moments provided with a measure. The ASSA applies a uniform measure over all observer moments, whereas supporters of the RSSA may for example apply the Born rule to the class of observer moments given by quantum theory. That's an outline of how I understand it. I have serious problems with this kind of reasoning. It suggests the misleading idea of some entity (let's call it the self) jumping from one observer moment to the next. In general, this is a very questionable concept, of course. I feel satisfied with the idea that the observer moments don't come up with a measure by themselves and that nothing at all is jumping. We will introduce measures for practical reasons depending on the problem we are concerned with. The same holds for the study of chains of observer moments. In each case, I will find it useful to introduce different concepts that will show resemblance to the ASSA or RSSA. 1st problem: What will I experience next? I refused the idea of the 'self' being an entity jumping between observer moments. So the word I does not refer to something fixed. It is a vague perception of self-identification (e.g. to be Youness Ayaita) that is part of the current observer moment. If we consider the evolution of the observer from a third person perspective (within our world and its usual dynamics), then we will see how the observer changes with time. Though, as far as his capacity for remembering did not disappear, the observer will still find within himself the old self-identification. This self-identification makes the observer have the feeling that his identity is something constant which is preserved. This feeling gives a meaningful understanding of the word I in the question of interest. By the word I the question restricts the class of observer moments to those who share the mentioned self-identification, e.g. to be Youness Ayaita. This class probably consists for the most part of observers that other observers would identify as Youness Ayaita, too. The word next (despite of the fact that it makes only sense in worlds with time) leads to a further restriction to the class of observer moments: The observer moment to choose must include the memory that the last experience was to ask the question: What will I experience next? The small subclass we have now typically corresponds to what we would expect from quantum theory. The measure that comes up with it corresponds to the Born rule. Nonetheless, the Born rule is not of general applicability here. For example, if the observer falls into coma and wakes up some years later or if he is frozen for some time in some futuristic machine, the observer moments waking up at a later time must have a nonzero measure as well. On the contrary, if the observer experiences a dangerous accident losing his capacity for remembering, the observer moment after the accident has a zero measure for the question of interest. To summarize, we see that a specific question leads to a specific measure. In this case, we get a result usually assigned to the RSSA. 2nd problem: Having had an accident that led to the loss of his capacity for remembering, an observer asks himself (before noticing his environment): Who am I? In this case, the self-identification process failed. Thus, the word I cannot be refered to a self-identification but rather to the identification by other observers. The class of observer moments of interest is restricted: We are only interested in conscious observers that don't have a self-identification process. Thus, in worlds similar to ours we would assign a non-zero measure to all observer moments waking up after such an accident or having lost their capability of self-identification due to some kind of mental illness. This measure has nothing in common with the quantum mechanical Born rule. So, I don't see any need for some kind of fundamental measure for observer moments. Whenever we have a restriction defining a subclass of observer moments that are of interest, we are naturally driven to the RSSA and to a specific measure. If we have no restriction, then we assign equal measure to all observer moments leading to the ASSA. I do not see the categorical difference between the two concepts. Can you make clear where the difference lies? Thank you Youness Ayaita
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 have the same hypothesis). And relatively to the
Re: Space-time is a liquid!
John Mikes skrev: JM: Then what makes them into a continuous 'string'? OR: do those individual points arrange in unassigned directions they just wish? If they only fluctuate by themselves, what reference do they (individually) follow to be callable 'string' -'fluctuate' - or just vibrate on their own? (below you said it: there the strings consist of discrete points.) JM: so THOSE (discrete) points are SPACE and also VACUUM. Now what keeps them 'discrete' if there is NO space between them? They mold together into an 'undivided' continuum - without any divider in between. Two discrete points have got to be discretized by something interstitial separational - in the geometrical view: their spatial image (what they do not have, because they ARE space). In this same image vacuum is also a bunch of discontinuous points that move. Vibrate. Fluctuate. Undulate into waves. But without anything interstitial they melt into a continuum? If you look at a meter, then there is a finite number of space points in that meter (it is about 10^35 space points in this meter). There is no space between two space points, because the space is the space points. The best way to imagine this discrete space and discrete time, is to look at the Game of Life. There you have discrete space points, that can have two states, on/off (or black/white or spin up/spin down). In this discrete space-time, you can see the gliders move. It is the same thing with the vibrating strings in the string-net liquid. There you have string-like structures, waving back and forth. These string-like structure is the wacuum. And the elementary particles are macroscopic vawes in this string-net liquid, just like sound waves in water. --~--~-~--~~~---~--~~ 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: One solution to the Measure Problem: UTM outputs a qualia, not a universe
Hal wrote: Yes, as you note later this is very similar to the concept I called UD+ASSA or just UDASSA and described in a series of postings to this list back in 2005. It was not original with me but actually was based on an idea of Wei Dai, who founded this last way back in 1998. I was working at one point on the udassa.com site to bring the ideas together but never finished it. I'm surprised that guy found it, I don't recall mentioning that URL. Must have let it slip sometime! It appears that the post where I originally proposed this idea is missing from the Google Groups archive. Something must have gone wrong when I imported the group archive into Google Groups, or data rot got to it. The Mail-Archive.com archive is in even worse shape, missing everything from before Sept 2006. Fortunately a third archive at Nabble.com seems still complete, and the post can be found here: http://www.nabble.com/consciousness-based-on-information-or-computation--tf3053801.html#a8489008 As Hal notes on his website, I've since moved away from this position. I've explain my reasons on the mailing list as they occurred to me (for example http://www.nabble.com/relevance-of-the-real-measure-tf3055627.html#a8492185 and http://www.nabble.com/forum/ViewPost.jtp?post=8496294framed=y) but perhaps I should write down a summary for the new members. PS, if anyone wants to download the complete raw mailing list archive in zipped Unix mailbox format, please email me privately. --~--~-~--~~~---~--~~ 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
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 -~--~~~~--~~--~--~---
