Re: on formally describable ...
Bruno Marchal explained to Jesse Mazer: Schmidhuber's solution is based on a belongness relation between observer and universes which is impossible to keep once we take comp seriously. But even if we make sense to such a relation, it would only eliminates third person white rabbits and not the first person white rabbits: remember that the great programmer emulates all (semi)computable universe but also all possible dreams. In fact Schmidhuber assume a solution of the mind body problem which is just incompatible with comp. Technically that makes his work incomplete (at least). Such statements keep failing to make sense to me and others I know. Anybody out there who does understand what is meant?
Re: on formally describable universes and measures
Here is an old reply to Russell Standish and Stephen Paul King. Russell Standish wrote: I have often said myself the plenitude is not a set, however when trying to write up some of this work for another audience, I tried following up the web documents on set theory, I came up with nothing, so in the end simply didn't raise the issue. I agree it is foolish to see the plenitude as a *set* and I have explain why before. Now, you can perhaps *modelize* the plenitude by a set, but *big* set are notoriously difficult to handle. So you need a set theory. Now, and this is a subtil point hardly understood, a model of a set theory is called *universe¨* and is intuitively a collection of *all* possible sets. If we want to say Group Theory instead of Transformation Theory we should say Universe Theory instead of Set Theory!!! In most set theories, (like ZF, NBG, ...), the universe is not itself a set. There exists set theories with universal sets in which the universe is a set. The best known is NF (Quine's New Foundation), build from some works by Church. Well NF is not even known by some specialist of set theory, and to study NF you need great familiarity with mathematical logic. But sets are not enough. Even in mathematics there are mathematical object which are to big to put in a universe (model) of ZF. For exemples some categories. Do you know category theory? It is mathematical structure intermediate between group and lattices. They are bridge between logic, topology, Algebra, etc. Stephen Paul King wrote: Oppps, I forgot to mention the notion of expressiveness... I am trying to keep my posts concise... Please read this paper by Peter Wegner which explains the notions of expressiveness and introduces Non-Well Founded sets, my thinking draws strongly from it: http://www.cs.brown.edu/~pw/papers/math1.ps Formidable idea, let's do math. Non-Well Founded sets are certainly interesting ... but it can lead us in the forest of mathematical mermaids and keep us with some beautiful songs away from our search toward a theory of everything. It seems to me that many-worlder should so some modal logic, if only to taste the second part of my thesis :-) But even without my thesis I think that modal logic is a formidable tool for rigorous philosophy. See my last post to George Levy. Bruno PS I have also problem to load http://www.cs.brown.edu/~pw/papers/math1.ps I will try with the recent suggestion by Russell.
Re: on formally describable universes and measures
Russell Standish wrote: ...The plenitude would include all sets that don't contain themselves, as well as sets that do. We know the plenitude contains itself. However, since the set of all sets that don't contain themselves is a logical contradiction, it is presumably excluded from the plenitude in just the same way as square circles are. So this still doesn't imply that the plenitude is not a set, only that the set of all sets that don't contain themselves is not a subset of the plenitude. (Perhaps this make it not a set ??) The plenitude is the absolute whole and is complete. It is however inconsistent, irrational... choke full of white rabbits. It includes the barbers who shave all those who don't shave themselves, and those horrible sets that Russell dreamed about, those that include sets that do not include themselves. In biblical terms it is the primeval chaos ( tohu bohu, French, Hebrew). Our world, that is our perception of the plenitude, anthropically constrained by our consciousness, is incomplete but rational and completely devoid of white rabbits. George
Re: on formally describable universes and measures
From [EMAIL PROTECTED] Sat Mar 3 18:05:53 2001
From: Saibal Mitra [EMAIL PROTECTED]
Jürgen wrote:
- Original Message -
From: [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Sent: Thursday, February 22, 2001 5:32 PM
Subject: Re: on formally describable universes and measures
Saibal Mitra wrote:
I think the source of the problem is equation 1 of Juergen's paper. This
equation supposedly gives the probability that I am in a particular
universe, but it ignores that multiple copies of me might exist in
one universe. Let's consider a simple example. The prior probability
of universe i (i0) is denoted as P(i), and i copies of me exist in
universe i. In this case, Juergen computes the propability that if you
pick a universe at random, sampled with the prior P, you pick universe
i. This probability is, of course, P(i). Therefore Juergen never has
to identify how many times I exist in a particular universe, and can
ignore what consciousness actually is. Surely an open universe where an
infinite number of copies of me exist is infinitely more likely than a
closed universe where I don't have any copies, assuming that the priors
are of the same order?
To respond, let me repeat the context of eq. 1 [In which universe am I?]
Let h(y) represent a property of any possibly infinite bitstring y, say,
h(y)=1 if y represents the history of a universe inhabited by yourself
and h(y)=0 otherwise. According to the weak anthropic principle, the
conditional probability of finding yourself in a universe compatible with
your existence equals 1. But there may be many y's satisfying h(y)=1.
What is the probability that y=x, where x is a particular universe
satisfying h(x)=1? According to Bayes,
P(x=y | h(y)=1) =
(P(h(y)=1 | x=y) P(x = y)) / (sum_{z:h(z)=1} P(z))
propto P(x),
where P(A | B) denotes the probability of A, given knowledge of B, and
the denominator is just a normalizing constant. So the probability of
finding yourself in universe x is essentially determined by P(x), the
prior probability of x.
Universes without a single copy of yourself are ruled out by the weak
anthropic principle. But the others indeed suggest the question: what can
we say about the distribution on the copies within a given universe U
(maybe
including those living in virtual realities running on various computers
in U)?
I believe this is the issue you raise - please correct me if I am wrong!
(Did you really mean to write i copies in universe i?)
I did mean to write i copies in universe i, maybe it would have been better
to write
n(i) copies in universe i. Anyway, according to equation 1 the probability
of universe x
given that n(x) 0 is proportional to P(x), which is also intuitively
logical. My point is
that from the perspective of the observer, of which there are n(x) copies in
universe x, things
look different. Intuitively, it seems that the measure of the observer
should be n(x)* P(x).
E.g. suppose there exist x1 and x2 such that P(x1) = P(x2) and n(x1)
n(x2) 0.
It seems to me that the observer is more likely to find himself in universe
x1 compared to
universe x2.
From an algorithmic TOE perspective the only important thing is
that the measure is computable in the limit - a bit more below.
Intuitively, some copies might be more likely than others. But what
exactly does that mean? If the copies were identical in the sense no
outsider could distinguish them, then the concept of multiple copies
wouldn't make sense - there simply would not be any multiple copies. So
there must be detectable differences between copies, such as those
embodied by their different environments.
So my answer would be: as soon as you have a method for identifying and
separating various observer copies within a universe U, each
distinguishable
copy_i is different in the sense that it lives in a different universe
U_i, just like you and me can be viewed as living in different universes
because your inputs from the environment are not identical to mine.
In general, the pair (U_i, copy_i) conveys more information than U by
itself (information is needed to separate them). The appropriate domain
of universes x (to use the paper's notation) would be the set of all
possible
pairs of the form (separate universe, separate observer).
Equation 1 above is perfectly applicable to this domain.
Okay, but since I don't know which of the copies I am, the probability
that I am one of the copies inside universe i is given as:
Sum_{i = 1}^{n(U)} P(U_i)
Is this proportional to P(U) or is it
proportional to n(U) P(U) ?
Saibal
To say something about some observer's future, given the past, we need a
probability distribution on the possible futures. Does it really make
sense to speak of several different copies of some observer within a
given universe? Not really, because the observers in general will have
Re: on formally describable universes and measures
I'm not sure that it would actually. The plenitude would include all sets that don't contain themselves, as well as sets that do. We know the plenitude contains itself. However, since the set of all sets that don't contain themselves is a logical contradiction, it is presumably excluded from the plenitude in just the same way as square circles are. So this still doesn't imply that the plenitude is not a set, only that the set of all sets that don't contain themselves is not a subset of the plenitude. (Perhaps this make it not a set ??) Cheers Brent Meeker wrote: Hello Russell On 07-Mar-01, Russell Standish wrote: From the dim recesses of my memory, the set of all sets is a logical contradiction, although I can't remember why. Is the plenitude like the set of all sets in some way? It would include the set of all sets which are not members of themselves - but the existence of this set is self-contradictory. Brent Meeker Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967 UNSW SYDNEY 2052 Fax 9385 6965 Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks
Re: on formally describable universes and measures
Dear George, Interleaving... George Levy wrote: Hi Stephen Stephen Paul King wrote: Dear George, George Levy wrote: Stephen Paul King wrote: I am suggesting that *all* objects are either an observer or a part of an observer. I am attacking the anthrocentrist definition of observer. I am suggesting that any object that can have a QM wave function associated with it *is an observer*, this would apply to an electron, a human, a galaxy, etc. I am taking the work of Prof. Hitoshi Kitada to its logical conclusion (See: http://www.kitada.com/time_III.html ) [GL] hmmm... .. make electrons and human equivalent as far as their observer status are concerned..and in so doing demote the word observer to nothing that would be fine if we restrict our discussion to third person perspective... but we don't. first person perspective admit some differences which are function of the nature of consciousness of the observer... [SPK] Oppps, I forgot to mention the notion of expressiveness... I am trying to keep my posts concise... Please read this paper by Peter Wegner which explains the notions of expressiveness and introduces Non-Well Founded sets, my thinking draws strongly from it: http://www.cs.brown.edu/~pw/papers/math1.ps snip [SPK] I am exploring the idea that communication between observers plays an important role in restricting and/or distinguishing the two. I hope that you understand this difference between a priori and a posteriori that I am writing about. ;-) [GL] I don't understand. In the constext of Markov chain, all the information is contained in the current states. [SPK] Right, but consider how it is that current states are concatenated (strung together), especially when you have to consider concurrency issues. [GL] hm. I don't know concatenation implies sequence and therefore seems to smuggle the answer in. Is concatenation necessary? [SPK] Yes, if we are going to consider logical implication chaining and seek to explain the appearance of temporal flow we must include concatenation. If we throw out the possibility of partial orderings what do we have left? [GL] I do not believe that logical concatenation from apriori and a posteriori implies or require temporal flow. Imagine a computer program listing. All the relationships are there, yet the whole thing is on paper. A logical graph, similarly requires no temporal flow. It is just there. [SPK] Just read the Wegner paper and get back to me. The idea is bloody obvious to me and I don't have the time to spoon feed it to you. [GL] Kind of. They are connected by a web-like set of allowed logical transitions. [SPK] I agree. But could you get into detail on the nature of allowed? What is the constraint? (I think that all that is needed is the weak anthropic principle but I could be missing something.) [GL] The constraint is the I (Anthropic principle) [SPK] Ok, but I think that the self-reference implicit in I is not necessary. That is the strong anthropic principle. Let's just stick to a very weak version, were the observers are not necessarily carbon based. [GL] I have never been able to get a rigorous explanation of the diverse Anthropic Principles. Just to say that the world is such because carbon life is here, or life is here, or humanity is here, is fuzzy. How about the world is such because the Canadians are here, or the Yanomamo of central America? In my mind the only way to resolve this issue is to go all the way to the I. However, since I am not a solipsist, I must admit to several I's. The result, therefore, is a relativistic perception of the world in which each I has his own perception. I don't know if other people use the Anthropic Principle in this way. [SPK] There is a lot of work on the anthropic principle. Research it. [SPK] I think that we should consider the rule All is allowed that is not Forbidden (by logical contradiction) instead of the usual notion All is forbidden that is not allowed (by prespecification, e.g. a priori algorithms) Peter Wegner has done a lot of research on this issue: [GL] I agree fully with the above. The plenitude provides the principle of All is allowed and the anthropic principle the restriction imposed by ***your own*** existence that is not forbidden. Thus each I is an initial boundary condition for an anthropic causal chain. When the anthropic principle is taken back all the way to its source, the I, the result is a relativistic perception of the plenitude by each I. Thus there is only one universe... the plenitude. The only difference is our perception of it. [SPK] The problem that I have with that is that we can run into severe problems with the notion of a source. It looks
Re: on formally describable universes and measures
Russell Standish [EMAIL PROTECTED]: From the dim recesses of my memory, the set of all sets is a logical contradiction, although I can't remember why. Is the plenitude like the set of all sets in some way? I think you remember the set of all set that are not members of themselves Call it S. Is S a member of itself?
Re: on formally describable universes and measures
Hello Russell On 07-Mar-01, Russell Standish wrote: From the dim recesses of my memory, the set of all sets is a logical contradiction, although I can't remember why. Is the plenitude like the set of all sets in some way? It would include the set of all sets which are not members of themselves - but the existence of this set is self-contradictory. Brent Meeker
Re: on formally describable universes and measures
Dear George, George Levy wrote: Stephen Paul King wrote: I am considering the idea that each observer (consciousness point) has its own set of a priori probable observations, it is when we introduce the possibility of communication between observers that these sets alter... [GL] I hope you are not suggesting that observers have a special status and that communication with an observer is qualitatively different with communication with an inanimate object. [SPK] Umm, no! I am suggesting that *all* objects are either an observer or a part of an observer. I am attacking the anthrocentrist definition of observer. I am suggesting that any object that can have a QM wave function associated with it *is an observer*, this would apply to an electron, a human, a galaxy, etc. I am taking the work of Prof. Hitoshi Kitada to its logical conclusion (See: http://www.kitada.com/time_III.html ) [GL] (i.e., Loosely speaking, if each transition has infinite measure, the only way to compare two transitions is to take the limit of their ratios.) Hence, relatively to the observer, his own measure can always be assumed to be one. This remains true as long as the number of, or magnitude of the adversities in his environment remains of a lower cardinality than his own measure. When the adversities are too severe then his consciousness stops from propagating (being linked) to those very adverse states. It's kind of a Cosmological Principle. [SPK] That is interesting! Do you have more information on that? [GL] It's in the book I wrote. As I have already mentioned in the other post. I did not go very far along the formal route. Unfortunaltely it's more English than Math. :-( [SPK] Were can I find it? Could you give me an exact URL? [SPK] I am exploring the idea that communication between observers plays an important role in restricting and/or distinguishing the two. I hope that you understand this difference between a priori and a posteriori that I am writing about. ;-) [GL] I don't understand. In the constext of Markov chain, all the information is contained in the current states. [SPK] Right, but consider how it is that current states are concatenated (strung together), especially when you have to consider concurrency issues. hm. I don't know concatenation implies sequence and therefore seems to smuggle the answer in. Is concatenation necessary? [SPK] Yes, if we are going to consider logical implication chaining and seek to explain the appearance of temporal flow we must include concatenation. If we throw out the possibility of partial orderings what do we have left? [GL] Kind of. They are connected by a web-like set of allowed logical transitions. [SPK] I agree. But could you get into detail on the nature of allowed? What is the constraint? (I think that all that is needed is the weak anthropic principle but I could be missing something.) [GL] The constraint is the I (Anthropic principle) [SPK] Ok, but I think that the self-reference implicit in I is not necessary. That is the strong anthropic principle. Let's just stick to a very weak version, were the observers are not necessarily carbon based. http://dhushara.tripod.com/book/quantcos/anth/anth.htm [SPK] I think that we should consider the rule All is allowed that is not Forbidden (by logical contradiction) instead of the usual notion All is forbidden that is not allowed (by prespecification, e.g. a priori algorithms) Peter Wegner has done a lot of research on this issue: [GL] I agree fully with the above. The plenitude provides the principle of All is allowed and the anthropic principle the restriction imposed by ***your own*** existence that is not forbidden. Thus each I is an initial boundary condition for an anthropic causal chain. When the anthropic principle is taken back all the way to its source, the I, the result is a relativistic perception of the plenitude by each I. Thus there is only one universe... the plenitude. The only difference is our perception of it. [SPK] The problem that I have with that is that we can run into severe problems with the notion of a source. It looks to me that your statement here contradict your earlier statement that There is no previous in the sense of previous time, only in terms of logical antecedent. In addition, the conscious points are multiply connected and the connections are a function of the points themselves. In other words each point could have several priors and several successors. I t would make more sense if the initial boundary condition were given within each and every instantiation of an observation, e.g. every time an observation is made a new universe is created. What you call the one Universe is what I call the Totality. Each observer has a universe as its percept. [SPK]
Re: on formally describable universes and measures
Hi Stephen Stephen Paul King wrote: Dear George, George Levy wrote: Stephen Paul King wrote: I am suggesting that *all* objects are either an observer or a part of an observer. I am attacking the anthrocentrist definition of observer. I am suggesting that any object that can have a QM wave function associated with it *is an observer*, this would apply to an electron, a human, a galaxy, etc. I am taking the work of Prof. Hitoshi Kitada to its logical conclusion (See: http://www.kitada.com/time_III.html ) hmmm... .. make electrons and human equivalent as far as their observer status are concerned..and in so doing demote the word observer to nothing that would be fine if we restrict our discussion to third person perspective... but we don't. first person perspective admit some differences which are function of the nature of consciousness of the observer... [SPK] That is interesting! Do you have more information on that? [GL] It's in the book I wrote. As I have already mentioned in the other post. I did not go very far along the formal route. Unfortunaltely it's more English than Math. :-( [SPK] Were can I find it? Could you give me an exact URL? Not yet... working on it. By any chance do you have a good relationsip with publishers given your very interesting name? [SPK] I am exploring the idea that communication between observers plays an important role in restricting and/or distinguishing the two. I hope that you understand this difference between a priori and a posteriori that I am writing about. ;-) [GL] I don't understand. In the constext of Markov chain, all the information is contained in the current states. [SPK] Right, but consider how it is that current states are concatenated (strung together), especially when you have to consider concurrency issues. hm. I don't know concatenation implies sequence and therefore seems to smuggle the answer in. Is concatenation necessary? [SPK] Yes, if we are going to consider logical implication chaining and seek to explain the appearance of temporal flow we must include concatenation. If we throw out the possibility of partial orderings what do we have left? I do not believe that logical concatenation from apriori and a posteriori implies or require temporal flow. Imagine a computer program listing. All the relationships are there, yet the whole thing is on paper. A logical graph, similarly requires no temporal flow. It is just there. [GL] Kind of. They are connected by a web-like set of allowed logical transitions. [SPK] I agree. But could you get into detail on the nature of allowed? What is the constraint? (I think that all that is needed is the weak anthropic principle but I could be missing something.) [GL] The constraint is the I (Anthropic principle) [SPK] Ok, but I think that the self-reference implicit in I is not necessary. That is the strong anthropic principle. Let's just stick to a very weak version, were the observers are not necessarily carbon based. I have never been able to get a rigorous explanation of the diverse Anthropic Principles. Just to say that the world is such because carbon life is here, or life is here, or humanity is here, is fuzzy. How about the world is such because the Canadians are here, or the Yanomamo of central America? In my mind the only way to resolve this issue is to go all the way to the I. However, since I am not a solipsist, I must admit to several I's. The result, therefore, is a relativistic perception of the world in which each I has his own perception. I don't know if other people use the Anthropic Principle in this way. [SPK] I think that we should consider the rule All is allowed that is not Forbidden (by logical contradiction) instead of the usual notion All is forbidden that is not allowed (by prespecification, e.g. a priori algorithms) Peter Wegner has done a lot of research on this issue: [GL] I agree fully with the above. The plenitude provides the principle of All is allowed and the anthropic principle the restriction imposed by ***your own*** existence that is not forbidden. Thus each I is an initial boundary condition for an anthropic causal chain. When the anthropic principle is taken back all the way to its source, the I, the result is a relativistic perception of the plenitude by each I. Thus there is only one universe... the plenitude. The only difference is our perception of it. [SPK] The problem that I have with that is that we can run into severe problems with the notion of a source. It looks to me that your statement here contradict your earlier statement that There is no previous in the sense of previous time, only in terms of logical antecedent. Are you saying that taking I as a logical source for the anthropic causal chain
Re: on formally describable universes and measures
Stephen Paul King wrote: I am considering the idea that each observer (consciousness point) has its own set of a priori probable observations, it is when we introduce the possibility of communication between observers that these sets alter... I hope you are not suggesting that observers have a special status and that communication with an observer is qualitatively different with communication with an inanimate object. [GL] (i.e., Loosely speaking, if each transition has infinite measure, the only way to compare two transitions is to take the limit of their ratios.) Hence, relatively to the observer, his own measure can always be assumed to be one. This remains true as long as the number of, or magnitude of the adversities in his environment remains of a lower cardinality than his own measure. When the adversities are too severe then his consciousness stops from propagating (being linked) to those very adverse states. It's kind of a Cosmological Principle. [SPK] That is interesting! Do you have more information on that? It's in the book I wrote. As I have already mentioned in the other post. I did not go very far along the formal route. Unfortunaltely it's more English than Math. :-( [SPK] I am exploring the idea that communication between observers plays an important role in restricting and/or distinguishing the two. I hope that you understand this difference between a priori and a posteriori that I am writing about. ;-) [GL] I don't understand. In the constext of Markov chain, all the information is contained in the current states. [SPK] Right, but consider how it is that current states are concatenated (strung together), especially when you have to consider concurrency issues. hm. I don't know concatenation implies sequence and therefore seems to smuggle the answer in. Is concatenation necessary? Kind of. They are connected by a web-like set of allowed logical transitions. [SPK] I agree. But could you get into detail on the nature of allowed? What is the constraint? (I think that all that is needed is the weak anthropic principle but I could be missing something.) The constraint is the I (Anthropic principle) I think that we should consider the rule All is allowed that is not Forbidden (by logical contradiction) instead of the usual notion All is forbidden that is not allowed (by prespecification, e.g. a priori algorithms) Peter Wegner has done a lot of research on this issue: I agree fully with the above. The plenitude provides the principle of All is allowed and the anthropic principle the restriction imposed by ***your own*** existence that is no forbidden. Thus each I is an initial boundary condition for an anthropic causal chain. When the anthropic principle is taken back all the way to its source, the I, the result is a relativistic perception of the plenitude by each I. Thus there is only one universe... the plenitude. The only difference is our perception of it. [SPK] Ok, would we agree that the anthropic principle (weak?) is true in the sense that any observer will have first person perspectives (experiences) that have a probability of 1 if and only if such are consistent with its existence. Also, if you are going to say that consciousness is a static phenomenon then could you explain how the appearance of change comes about? [GL] In the same way a derivative describes movement while being itself static.The logical links would have to contain directionality information. [SPK] Sure, I agree in principle with that but it is easy to see that something somehow IS changing. h... phase space for example provides the information of movement while being itself staticTo say that the plenitude itself is changing leads to a paradoxThe illusion of change is embedded in each conscious point and is a result of the directional logical links which depend themselves on the type of consciousness we have. George
Re: on formally describable universes and measures
Dear George, Interleaving... George Levy wrote: Stephen Paul King wrote: [SPK] Umm, let me break this down into chucks and try to see if we are understanding each other. My notion of a previous time was couched within a notion that is similar to J. A. Wheeler's notion of a Surprise 20 Questions Game and I did not state so explicitly. I am playing with the idea that time is a first person attribute and thus is not to be considered as objective nor absolute (as in the Newtonian sense). I think that our ideas are similar but we may have semantic differences here. ;-) [GL] OK but I am not familiar with Wheeler's game. [SPK] This is a good on-line elaboration of Wheeler's idea: http://suif.stanford.edu/~jeffop/WWW/wheeler.txt My thinking generalizes to were we have to consider many concurrently existing games, e.g., each observer would be a Questioner and it's Universe would be the Answerer, or something along that line. The game semantics and logics used would fall under the computational concurrency umbrella. [GL] In addition, the conscious points are multiply connected and the connections are a function of the points themselves. In other words each point could have several priors and several successors. [SPK] I would agree, but I would argue that we could cause some confusion if we are not careful. We have to distinguish the a priori possible (or probable) experiences from the a posteriori experiences themselves. [GL] I don't think I follow you. There is no such a thing as probable. All connections are actualized albeit in different degrees according to their RELATIVE measures. We now get into the discussion of measure which has been endlessly debated before. Suffice to say that I think that while measure can be relatively different between two transitions, there is NO WAY to establish an ABSOLUTE value for measure because of the infinity of the plenitude. [SPK] The results of observations are probable prior to the actual instatiation of a particular observation. I am merely retaining as much of the structure of QM as possible since it works. ;-) I agree that there is no absolute value for the same reason that there is no unique inner product for the linear vector space of the states that represents the complete and mutually exclusive set of observations or occurrences prior to a particular instatiation. (See Lee Smolin's paper: Space and Time in the Quantum Universe for a good discussion of this.) Perhaps what you refer to as relative measure is similar to my idea. I am considering the idea that each observer (consciousness point) has its own set of a priori probable observations, it is when we introduce the possibility of communication between observers that these sets alter... [GL] (i.e., Loosely speaking, if each transition has infinite measure, the only way to compare two transitions is to take the limit of their ratios.) Hence, relatively to the observer, his own measure can always be assumed to be one. This remains true as long as the number of, or magnitude of the adversities in his environment remains of a lower cardinality than his own measure. When the adversities are too severe then his consciousness stops from propagating (being linked) to those very adverse states. It's kind of a Cosmological Principle. [SPK] That is interesting! Do you have more information on that? [SPK] I am exploring the idea that communication between observers plays an important role in restricting and/or distinguishing the two. I hope that you understand this difference between a priori and a posteriori that I am writing about. ;-) [GL] I don't understand. In the constext of Markov chain, all the information is contained in the current states. [SPK] Right, but consider how it is that current states are concatenated (strung together), especially when you have to consider concurrency issues. [GL] The structure is web-like. [SPK] Yes, I agree. I have been exploring this idea with several people for some time using the notions of Leibniz and Spinoza. Let me recap. Are you saying that conscious points (I can them them monads ala Leibniz) has a web-like structure? [GL] Kind of. They are connected by a web-like set of allowed logical transitions. [SPK] I agree. But could you get into detail on the nature of allowed? What is the constraint? (I think that all that is needed is the weak anthropic principle but I could be missing something.) I think that we should consider the rule All is allowed that is not Forbidden (by logical contradiction) instead of the usual notion All is forbidden that is not allowed (by prespecification, e.g. a priori algorithms) Peter Wegner has done a lot of research on this issue: http://www.cs.brown.edu/~pw/papers/math1.ps [GL] (The universe does not just splits with each Quantum event, it can also merge) [SPK]
Re: on formally describable universes and measures
George is saying an OM containing 'It is 10:30' is someohow connected to an OM that contains 'It is 10:31'. I disagree. The two are bound to exist; Person A might say there is a relationship between OM1 and OM2 but the relationship only exists in Person A's own mind (more strictly, 'in OM3') . Saying they are connected is meaningless. All things are connected in this way. It's like attaching significance to winning the lottery. James - Original Message - From: Stephen Paul King [EMAIL PROTECTED] To: [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Monday, March 05, 2001 2:11 PM Subject: Re: on formally describable universes and measures Dear George, If I might ask a few questions... George Levy wrote: Brent Meeker wrote: A transition from one conscious point (observer moment) to the next must be logical at the conscious level and simultaneously at the physical law level. I'm not sure what you mean by logical transition - entailed by the previous theorems plus rules of inference would be the plain meaning. Logic just like phycical laws is not abolute. It only exists in the mind of the beholder. So a transition is logical only if it makes sense for the consciousness which experiences it. And a consciousness experiences such a transition only if it makes or can make sense of it. Would it be possible to elaborate on this? Could it be that for a transition to make sense for the consciousness that experiences it such a transition must not contradict any other previous experience? But I certainly wouldn't claim that for my own train of thoughts. Also I don't see how transition and simultaneity can be defined until time is defined. Time and space are not defined yet. The only thing that is defined so far is a logic and an associated consciousness. So a transition is just an unidirectional logical arrow from this conscious point to another conscious point. Time is an experience emerging from the unidirectionality of these arrows. Some have argued that the time, in the sense that it can be considered as a transition of the physical state of a system, is the dual of the logic. See: http://boole.stanford.edu/chuguide.html#P5 Additionally, I think that we should distinguish the different aspects of time. There is the notion of time as a measure of change, time as an order of succession and time and time as a directed transition. But it seems that time (and space) should be emergent phenomena in this theory. But it the laws of physics are not uniform then how can time and space emerge - since they are themselves just symmetries of the laws. See above Consciousness exists because of the physical laws (causality), and the physical laws exist because of consciousness (anthropy). This is why the world makes sense and also why we don't see white rabbits. Propagation of the wave function is the logical linkage between conscious points. Propagates thru time and space? Propagation is THE LOGICAL LINKAGE. It does not occur in time. Time is an emergent experience resulting from these unidirectional links. If you are considering the aspect of time that is an order of succession, then I would agree, but I believe that Brett (?) was considering the directed transition aspect. By the way, space is definable as the order of co-existence (Leibniz). It appears to obey universal physical laws only because third person perspective is an illusion supported by the fact that different observers share the same logical/physical reference frame. If this is supported by different observers (differentiated how?) why call it an illusion. I call it an illusion because it gives credence that there is an absolute set of physical laws, when in fact there isn't. The same could be said about the earth. It appears to be motionless, when in fact it is moving. It is common experience that a single person is more likely to have an illusion than that a common illusion be shared by several persons. Hence 'the third person perspective' is not an illusion. Now we are in the semantic domain. Let's define third person perspective as one shared by observers occupying the same logical/physical laws frame of reference as well as having the same set of contingencies on their existence. They will experience the world in the same way and therefore have the illusion that their perception of the world is absolute when in fact it isn't. I agree with this definition of the third person perspective! Note that if each observer has their own time and space which is their first person perspective, then the third person perspective is the intersection of many first person perspectives. James Higgo wrote: I agree, except that there is no 'transition' from one OM to the next. What is it that 'transits' ? Nothing transits in time. Its
Re: on formally describable universes and measures
Stephen Paul King wrote: Logic just like phycical laws is not abolute. It only exists in the mind of the beholder. So a transition is logical only if it makes sense for the consciousness which experiences it. And a consciousness experiences such a transition only if it makes or can make sense of it. Would it be possible to elaborate on this? Could it be that for a transition to make sense for the consciousness that experiences it such a transition must not contradict any other previous experience? There is no previous in the sense of previous time, only in terms of logical antecedent. In addition, the conscious points are multiply connected and the connections are a function of the points themselves. In other words each point could have several priors and several successors. The structure is web-like. (The universe does not just splits with each Quantum event, it can also merge) I think it best to view each points as a set of states independent of past information (i.e., first order Markov chain). To make sense, a transition needs only satisfy the current states. The past states are irrelevant or ambiguous. But I certainly wouldn't claim that for my own train of thoughts. Also I don't see how transition and simultaneity can be defined until time is defined. Time and space are not defined yet. The only thing that is defined so far is a logic and an associated consciousness. So a transition is just an unidirectional logical arrow from this conscious point to another conscious point. Time is an experience emerging from the unidirectionality of these arrows. Some have argued that the time, in the sense that it can be considered as a transition of the physical state of a system, is the dual of the logic. See: http://boole.stanford.edu/chuguide.html#P5 Additionally, I think that we should distinguish the different aspects of time. There is the notion of time as a measure of change, time as an order of succession and time and time as a directed transition. Interesting. If you are considering the aspect of time that is an order of succession, then I would agree, but I believe that Brett (?) was considering the directed transition aspect. By the way, space is definable as the order of co-existence (Leibniz). Let's define third person perspective as one shared by observers occupying the same logical/physical laws frame of reference as well as having the same set of contingencies on their existence. They will experience the world in the same way and therefore have the illusion that their perception of the world is absolute when in fact it isn't. I agree with this definition of the third person perspective! Note that if each observer has their own time and space which is their first person perspective, then the third person perspective is the intersection of many first person perspectives. Right! ...each OM is connected to other OMs by unidirectional logical arrows formulated according to a logic of which is a characteristics of the OM themselves. Thus each OM defines its own allowed set of transitions.Time is an emergent experience resulting from these arrows. Conscious flow is a static phenomenon, EXPERIENCED BY EACH POINT THAT IS CAPABLE OF EXPERIENCING IT. I think that we need to find a way of defining the act of experiencing itself! Several philosophers have argued to that experience involves a correlation or synchronization of sorts between external and internal attributes. Your statements would imply, then, that a point has some kind of internal structure... Yes. This is the next step which is anthropically driven. The structure is necessary because of the attributes of consciousness. George
Re: on formally describable universes and measures
Dear George, If I might ask a few questions... George Levy wrote: Brent Meeker wrote: A transition from one conscious point (observer moment) to the next must be logical at the conscious level and simultaneously at the physical law level. I'm not sure what you mean by logical transition - entailed by the previous theorems plus rules of inference would be the plain meaning. Logic just like phycical laws is not abolute. It only exists in the mind of the beholder. So a transition is logical only if it makes sense for the consciousness which experiences it. And a consciousness experiences such a transition only if it makes or can make sense of it. Would it be possible to elaborate on this? Could it be that for a transition to make sense for the consciousness that experiences it such a transition must not contradict any other previous experience? But I certainly wouldn't claim that for my own train of thoughts. Also I don't see how transition and simultaneity can be defined until time is defined. Time and space are not defined yet. The only thing that is defined so far is a logic and an associated consciousness. So a transition is just an unidirectional logical arrow from this conscious point to another conscious point. Time is an experience emerging from the unidirectionality of these arrows. Some have argued that the time, in the sense that it can be considered as a transition of the physical state of a system, is the dual of the logic. See: http://boole.stanford.edu/chuguide.html#P5 Additionally, I think that we should distinguish the different aspects of time. There is the notion of time as a measure of change, time as an order of succession and time and time as a directed transition. But it seems that time (and space) should be emergent phenomena in this theory. But it the laws of physics are not uniform then how can time and space emerge - since they are themselves just symmetries of the laws. See above Consciousness exists because of the physical laws (causality), and the physical laws exist because of consciousness (anthropy). This is why the world makes sense and also why we don't see white rabbits. Propagation of the wave function is the logical linkage between conscious points. Propagates thru time and space? Propagation is THE LOGICAL LINKAGE. It does not occur in time. Time is an emergent experience resulting from these unidirectional links. If you are considering the aspect of time that is an order of succession, then I would agree, but I believe that Brett (?) was considering the directed transition aspect. By the way, space is definable as the order of co-existence (Leibniz). It appears to obey universal physical laws only because third person perspective is an illusion supported by the fact that different observers share the same logical/physical reference frame. If this is supported by different observers (differentiated how?) why call it an illusion. I call it an illusion because it gives credence that there is an absolute set of physical laws, when in fact there isn't. The same could be said about the earth. It appears to be motionless, when in fact it is moving. It is common experience that a single person is more likely to have an illusion than that a common illusion be shared by several persons. Hence 'the third person perspective' is not an illusion. Now we are in the semantic domain. Let's define third person perspective as one shared by observers occupying the same logical/physical laws frame of reference as well as having the same set of contingencies on their existence. They will experience the world in the same way and therefore have the illusion that their perception of the world is absolute when in fact it isn't. I agree with this definition of the third person perspective! Note that if each observer has their own time and space which is their first person perspective, then the third person perspective is the intersection of many first person perspectives. James Higgo wrote: I agree, except that there is no 'transition' from one OM to the next. What is it that 'transits' ? Nothing transits in time. Its' just that each OM is connected to other OMs by unidirectional logical arrows formulated according to a logic of which is a characteristics of the OM themselves. Thus each OM defines its own allowed set of transitions.Time is an emergent experience resulting from these arrows. Conscious flow is a static phenomenon, EXPERIENCED BY EACH POINT THAT IS CAPABLE OF EXPERIENCING IT. I think that we need to find a way of defining the act of experiencing itself! Several philosophers have argued to that experience involves a correlation or synchronization of sorts between external and internal attributes. Your statements would imply, then, that a point has some kind of internal structure... George Kindest regards, Stephen
Re: on formally describable universes and measures
Stephen Paul King wrote: Umm, let me break this down into chucks and try to see if we are understanding each other. My notion of a previous time was couched within a notion that is similar to J. A. Wheeler's notion of a Surprise 20 Questions Game and I did not state so explicitly. I am playing with the idea that time is a first person attribute and thus is not to be considered as objective nor absolute (as in the Newtonian sense). I think that our ideas are similar but we may have semantic differences here. ;-) OK but I am not familiar with Wheeler's game. [GL] In addition, the conscious points are multiply connected and the connections are a function of the points themselves. In other words each point could have several priors and several successors. [SPK] I would agree, but I would argue that we could cause some confusion if we are not careful. We have to distinguish the a priori possible (or probable) experiences from the a posteriori experiences themselves. I don't think I follow you. There is no such a thing as probable. All connections are actualized albeit in different degrees according to their RELATIVE measures. We now get into the discussion of measure which has been endlessly debated before. Suffice to say that I think that while measure can be relatively different between two transitions, there is NO WAY to establish an ABSOLUTE value for measure because of the infinity of the plenitude. (i.e., Loosely speaking, if each transition has infinite measure, the only way to compare two transitions is to take the limit of their ratios.) Hence, relatively to the observer, his own measure can always be assumed to be one. This remains true as long as the number of, or magnitude of the adversities in his environment remains of a lower cardinality than his own measure. When the adversities are too severe then his consciousness stops from propagating (being linked) to those very adverse states. It's kind of a Cosmological Principle. I am exploring the idea that communication between observers plays an important role in restricting and/or distinguishing the two. I hope that you understand this difference between a priori and a posteriori that I am writing about. ;-) I don't understand. In the constext of Markov chain, all the information is contained in the current states. [GL] The structure is web-like. [SPK] Yes, I agree. I have been exploring this idea with several people for some time using the notions of Leibniz and Spinoza. Let me recap. Are you saying that conscious points (I can them them monads ala Leibniz) has a web-like structure? Kind of. They are connected by a web-like set of allowed logical transitions. [GL] (The universe does not just splits with each Quantum event, it can also merge) [SPK] Umm, here I have a problem! You say that the universe splits and merges; Sorry! In an effort to communicate, I was employing terms used in the popular literature about the MWI. I should NOT have said that the universe splits. It's not the universe that splits and merge. It's our conscious flow through the interconnections between the OM or conscious points. Schoedinger equation really describes the spread of our consciousness through the web. I think it best to view each points as a set of states independent of past information (i.e., first order Markov chain). To make sense, a transition needs only satisfy the current states. The past states are irrelevant or ambiguous. We could think of the splitting and merging as local topological properties of a multiply connected manifold and I think that such a thought would be in line with the idea of first order Markov chains, but I am not sure now you are thinking about how the points are related (via transitions). It is obvious that past states refer to information that is encoded within the current state and that is what I meant by my statement. I think that we agree that the past is not something that is out there outside of the experience of the present moment. ;-) I agree with this. [SPK] I am interested in your thoughts of Pratt et al's ideas. ;-) Sorry. Pardon my ignorance. I don't know who Pratt is. Would he be by any chance one of the two guys who make airplane engines. ;-) [SPK] Ok, would we agree that the anthropic principle (weak?) is true in the sense that any observer will have first person perspectives (experiences) that have a probability of 1 if and only if such are consistent with its existence. Also, if you are going to say that consciousness is a static phenomenon then could you explain how the appearance of change comes about? In the same way a derivative describes movement while being itself static.The logical links would have to contain directionality information. Have you by chance read Julian Barbour's book The End of Time? Sorry, I didn't have a chance. George
Re: on formally describable universes and measures
I agree, except that there is no 'transition' from one OM to the next. What is it that 'transits' ? - Original Message - From: George Levy [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Sunday, March 04, 2001 8:03 PM Subject: Re: on formally describable universes and measures Brent Meeker wrote: On 03-Mar-01, George Levy wrote: I do not view these so called parallel universes as *separate*. It's really one single multiverse and the wave function exists in the multiverse How can this multiverse have a single wave function when it is supposed to have different physical laws in it's different constituent universes? This seems to be just poetry, in which the meaning of words is considered infinitely malleable. Brent Meeker Great comment which shows why you and others do not understand the full implications of first and third persons perspectives. There is no single set of physical laws that spans the whole plenitude. In fact, the plenitude includes all possible physical laws. To be more precise, physical laws are first person phenomenons that are defined by the characteristics of each conscious point (observer moment, or I) Thus, consciousness and physical laws emerge together, and are reflections of each other. They occupies the same logical domain and are bounded by the same limits. A transition from one conscious point (observer moment) to the next must be logical at the conscious level and simultaneously at the physical law level. Consciousness exists because of the physical laws (causality), and the physical laws exist because of consciousness (anthropy). This is why the world makes sense and also why we don't see white rabbits. Propagation of the wave function is the logical linkage between conscious points. It appears to obey universal physical laws only because third person perspective is an illusion supported by the fact that different observers share the same logical/physical reference frame. I am not sure what the orthodox MWI but I know there are many variants. My opinion on this matter is probably one of the most extreme in this group. But, once you start travelling along the MWI path, you've got to go all the way. I believe that it is the only logical approach and is unavoidable. George
Re: on formally describable universes and measures
Brent Meeker wrote: On 03-Mar-01, George Levy wrote: I do not view these so called parallel universes as *separate*. It's really one single multiverse and the wave function exists in the multiverse How can this multiverse have a single wave function when it is supposed to have different physical laws in it's different constituent universes? This seems to be just poetry, in which the meaning of words is considered infinitely malleable. Brent Meeker Great comment which shows why you and others do not understand the full implications of first and third persons perspectives. There is no single set of physical laws that spans the whole plenitude. In fact, the plenitude includes all possible physical laws. To be more precise, physical laws are first person phenomenons that are defined by the characteristics of each conscious point (observer moment, or I) Thus, consciousness and physical laws emerge together, and are reflections of each other. They occupies the same logical domain and are bounded by the same limits. A transition from one conscious point (observer moment) to the next must be logical at the conscious level and simultaneously at the physical law level. Consciousness exists because of the physical laws (causality), and the physical laws exist because of consciousness (anthropy). This is why the world makes sense and also why we don't see white rabbits. Propagation of the wave function is the logical linkage between conscious points. It appears to obey universal physical laws only because third person perspective is an illusion supported by the fact that different observers share the same logical/physical reference frame. I am not sure what the orthodox MWI but I know there are many variants. My opinion on this matter is probably one of the most extreme in this group. But, once you start travelling along the MWI path, you've got to go all the way. I believe that it is the only logical approach and is unavoidable. George
Re: on formally describable universes and measures
Brent Meeker wrote: A transition from one conscious point (observer moment) to the next must be logical at the conscious level and simultaneously at the physical law level. I'm not sure what you mean by logical transition - entailed by the previous theorems plus rules of inference would be the plain meaning. Logic just like phycical laws is not abolute. It only exists in the mind of the beholder. So a transition is logical only if it makes sense for the consciousness which experiences it. And a consciousness experiences such a transition only if it makes or can make sense of it. But I certainly wouldn't claim that for my own train of thoughts. Also I don't see how transition and simultaneity can be defined until time is defined. Time and space are not defined yet. The only thing that is defined so far is a logic and an associated consciousness. So a transition is just an unidirectional logical arrow from this conscious point to another conscious point. Time is an experience emerging from the unidirectionality of these arrows. But it seems that time (and space) should be emergent phenomena in this theory. But it the laws of physics are not uniform then how can time and space emerge - since they are themselves just symmetries of the laws. See above Consciousness exists because of the physical laws (causality), and the physical laws exist because of consciousness (anthropy). This is why the world makes sense and also why we don't see white rabbits. Propagation of the wave function is the logical linkage between conscious points. Propagates thru time and space? Propagation is THE LOGICAL LINKAGE. It does not occur in time. Time is an emergent experience resulting from these unidirectional links. It appears to obey universal physical laws only because third person perspective is an illusion supported by the fact that different observers share the same logical/physical reference frame. If this is supported by different observers (differentiated how?) why call it an illusion. I call it an illusion because it gives credence that there is an absolute set of physical laws, when in fact there isn't. The same could be said about the earth. It appears to be motionless, when in fact it is moving. It is common experience that a single person is more likely to have an illusion than that a common illusion be shared by several persons. Hence 'the third person perspective' is not an illusion. Now we are in the semantic domain. Let's define third person perspective as one shared by observers occupying the same logical/physical laws frame of reference as well as having the same set of contingencies on their existence. They will experience the world in the same way and therefore have the illusion that their perception of the world is absolute when in fact it isn't. James Higgo wrote: I agree, except that there is no 'transition' from one OM to the next. What is it that 'transits' ? Nothing transits in time. Its' just that each OM is connected to other OMs by unidirectional logical arrows formulated according to a logic of which is a characteristics of the OM themselves. Thus each OM defines its own allowed set of transitions.Time is an emergent experience resulting from these arrows. Conscious flow is a static phenomenon, EXPERIENCED BY EACH POINT THAT IS CAPABLE OF EXPERIENCING IT. George
Re: on formally describable universes and measures
Jürgen wrote:
- Original Message -
From: [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Sent: Thursday, February 22, 2001 5:32 PM
Subject: Re: on formally describable universes and measures
Saibal Mitra wrote:
I think the source of the problem is equation 1 of Juergen's paper. This
equation supposedly gives the probability that I am in a particular
universe, but it ignores that multiple copies of me might exist in
one universe. Let's consider a simple example. The prior probability
of universe i (i0) is denoted as P(i), and i copies of me exist in
universe i. In this case, Juergen computes the propability that if you
pick a universe at random, sampled with the prior P, you pick universe
i. This probability is, of course, P(i). Therefore Juergen never has
to identify how many times I exist in a particular universe, and can
ignore what consciousness actually is. Surely an open universe where an
infinite number of copies of me exist is infinitely more likely than a
closed universe where I don't have any copies, assuming that the priors
are of the same order?
To respond, let me repeat the context of eq. 1 [In which universe am I?]
Let h(y) represent a property of any possibly infinite bitstring y, say,
h(y)=1 if y represents the history of a universe inhabited by yourself
and h(y)=0 otherwise. According to the weak anthropic principle, the
conditional probability of finding yourself in a universe compatible with
your existence equals 1. But there may be many y's satisfying h(y)=1.
What is the probability that y=x, where x is a particular universe
satisfying h(x)=1? According to Bayes,
P(x=y | h(y)=1) =
(P(h(y)=1 | x=y) P(x = y)) / (sum_{z:h(z)=1} P(z))
propto P(x),
where P(A | B) denotes the probability of A, given knowledge of B, and
the denominator is just a normalizing constant. So the probability of
finding yourself in universe x is essentially determined by P(x), the
prior probability of x.
Universes without a single copy of yourself are ruled out by the weak
anthropic principle. But the others indeed suggest the question: what can
we say about the distribution on the copies within a given universe U
(maybe
including those living in virtual realities running on various computers
in U)?
I believe this is the issue you raise - please correct me if I am wrong!
(Did you really mean to write i copies in universe i?)
I did mean to write i copies in universe i, maybe it would have been better
to write
n(i) copies in universe i. Anyway, according to equation 1 the probability
of universe x
given that n(x) 0 is proportional to P(x), which is also intuitively
logical. My point is
that from the perspective of the observer, of which there are n(x) copies in
universe x, things
look different. Intuitively, it seems that the measure of the observer
should be n(x)* P(x).
E.g. suppose there exist x1 and x2 such that P(x1) = P(x2) and n(x1)
n(x2) 0.
It seems to me that the observer is more likely to find himself in universe
x1 compared to
universe x2.
Intuitively, some copies might be more likely than others. But what
exactly does that mean? If the copies were identical in the sense no
outsider could distinguish them, then the concept of multiple copies
wouldn't make sense - there simply would not be any multiple copies. So
there must be detectable differences between copies, such as those
embodied by their different environments.
So my answer would be: as soon as you have a method for identifying and
separating various observer copies within a universe U, each
distinguishable
copy_i is different in the sense that it lives in a different universe
U_i, just like you and me can be viewed as living in different universes
because your inputs from the environment are not identical to mine.
In general, the pair (U_i, copy_i) conveys more information than U by
itself (information is needed to separate them). The appropriate domain
of universes x (to use the paper's notation) would be the set of all
possible
pairs of the form (separate universe, separate observer).
Equation 1 above is perfectly applicable to this domain.
Okay, but since I don't know which of the copies I am, the probability
that I am one of the copies inside universe i is given as:
Sum_{i = 1}^{n(U)} P(U_i)
Is this proportional to P(U) or is it
proportional to n(U) P(U) ?
Saibal
Re: on formally describable universes and measures
Guys, this is really good stuff. This is answering my question of a couple of weeks ago. I will quote it in a paper with your permission. James - Original Message - From: Marchal [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Friday, March 02, 2001 1:32 PM Subject: Re: on formally describable universes and measures Jacques Mallah wrote: Sorry, that doesn't help. What do you mean by a real actual one? What other kind is there, a fake one? Either it exists, or not. OK. In that sense we agree that the DU exist. I am glad to see that you are a classical platonist. An intuitionist would'nt accept the idea that something exist ... or not. Of course, in your macintosh example, the UD was itself implemented by some other mathematical structure - your local decor. Does that matter? A big part of my reasoning is that it *doesn't matter* indeed. For most people this is a difficulty. Actually, I would say that any mathematical structure that has real existance (in the strong sense) should be called physical.I do not know of any better definition for physical existance. What is that strong sense of existence? And why do you want to classify as physical any mathematical structures. If you do that (a little like Tegmark) you are obliged to explain how we feel a difference between physicalness and mathematicalness (why is there math courses and physics courses) etc. Tegmark, like Everett, *do* distinguish the first and third person, which helps to make sense of that idea. The physical would be some mathematical structures sufficiently rich for having inside point of views (through SAS point of views for exemple). The physical point of view (pov) would correspond to these internal pov. Nowhere did I say that _only_ a physical system could implement a computation. But you did bring to my attention the fact that I should make the definition of implementation more clear on this point. In other places, I do point out that one computation can implement another. (In turn, the second one might implement another, etc.; the first one will therefore implement all of those.) So, your objection is irrelevant. You do believe a UD implements other computations. Sure. Yes. UD implements all computations, and even all implementations of all computations. Actuality is a first person concept. I have no clue as to what you mean. In Newtonian Physics one could imagine some third person time (objective time), but since relativity I guess most believe that time is either a parameter or do refer to some relative measurement done by an observer. Actuality, modern, here, now, there, elsewhere, are words with meaning dependent of the locutor. Indexicals, as the philosophers call them. Most are true or false only from a first person point of view. 3rd person view is everything you can communicate in a scientific manner without taking into account the subjective view of a person. If the person has some set of beliefs, they can be described as part of the true description of the situation. (Which you is what I thought you call the 3rd person view.) Concerning *believes* the case is arguable. For *knowledge* I don't think you will ever succeed in describing them in some provable (objectively, 3-person) way. This can be proved with very reasonable definition. See ref by Benacerraf, or Kaplan and Montague in my thesis. (It is linked with that reconstruction of Lucas which makes difficult for Schmidhuberians to locate an observer in *a* computational history, but I think that point is obvious once you get the computational indeterminacy from the duplication thought experience). Science is (ideally) a pure 3-person discourse and will ever be. But with definition of 1-person you can make science (i.e. 3-person discourses) *about* the possible 1-person discourses. I give two definitions of 1-person discourses. The first one appears in the self duplication thought experiment, and is just personal memory (what is written in *your* personal diary). The second one, which I use in the formal part of my work is the one given by Thaetetus to Socrate. Mathematically it gives intuitionnistic logic (topos, constructive math, etc.). The use of topos(*) by quantum cosmologist (cf Lee Smolin) is the logical move made by those who want the other universal stories away. It is cosmo-solipsism. Someone who would have only first person insight is a solipsist. Someone who would have only third person insight is a zombie. If I duplicate myself succesfully in Washington and Moscow, both Bruno1 and Bruno2 can communicates the success of the experience from a third person point of view, but none can explain you that he feels to be the Washingtonian (resp Moscovian) one. The difference between the first person and the third person is basically the same as the difference between having an headache and having a friend having an headhache. From
Re: on formally describable universes and measures
Marchal wrote: The difference between the first person and the third person is basically the same as the difference between having an headache and having a friend having an headhache. True, but I believe of much greater importance for this discussion is the difference in the obervations made by two observers, of a particular event, when their continued existence is contingent in different degree by this event. They will experience with different degree of probability, the occurence of this event. The key is the contingency relationship between the event and the observers. It defines the observers' frame of reference. Each observer, then, has his own first person perspective of the event. First person perspective is therefore the fundamental perspective. Third person perspective is an illusion shared by two observers when they occupy the exact same frame of reference (as defined by the set of contingencies on their existence). Bruno, Jacques and George have a third person perspective in common because the laws of physics and other earthly environments that sustain them are identical. Science is (ideally) a pure 3-person discourse and will ever be. Let me qualify the above statement in my own words. The development by a group of observers of an objective (i.e., third person) science is only possible if they restrict themselves to the domain of events and to the studies of laws that affect their existence equally. Here is a thought experiment to illustrate this point. Let us say that a ***very reliable*** machine is designed to instantly kill several scientists unless the natural laws are modified to a different configuration than the one we currently have, but still capable of sustaining life. The wave function of these scientist will then be restricted to a set of worlds in which laws of physics are different. These scientists will have absolutely no awareness of having their wave function restricted. They could even find other scientists so restricted, and together they could develop an objective third person science customized to their world, and share what they believe to be objective information. Their science will be different from ours, but from their common points of view, it would be objective. Jacques Mallah wrote: Does merde have a special meaning, the way crap does? Marchal responded: Some time ago merde was considered as very vulgar, but since then it has been overthrown by shit, or worse ... Merde seems almost polite in comparison. I don't know about crap. It seems to me we don't use that word (in Belgium). Really? shit has become a French word? Talk about Franglais! I rather go back to the good old days when Pierre Elliot Trudeau, the Canadian Prime Minister, said on the steps of Parliament, to a group of strikers, Mange la merde. George
Re: on formally describable universes and measures
From: Marchal [EMAIL PROTECTED] Jacques Mallah wrote: I really don't know what you mean by concrete. Math is math, but is physic math? By a concrete UD I was meaning a real actual one, like the one I have implemented on a macintosh SE/30, and which has been running during two weeks in 1990 at Brussels. Of course I postulate here some physical universe as a local decor. Sorry, that doesn't help. What do you mean by a real actual one? What other kind is there, a fake one? Either it exists, or not. Of course, in your macintosh example, the UD was itself implemented by some other mathematical structure - your local decor. Does that matter? If anything, that makes it more of a virtual UD than the one we discuss for the AUH! Look, to be sure we are using impIementation in the same sense, I quote yourself (from http://hammer.prohosting.com/~mathmind/cwia.htm#II3) In turn, a computation is associated with a physical system only if it has been implemented by that system. So either you believe there is only math (including computer science and all computations), then implementation is a emerging concept, as are anything linked to physical predicates. Or you believe there exists something physical per se. Then indeed you can defined implementation in a sense relative to that physicalness. Actually, I would say that any mathematical structure that has real existance (in the strong sense) should be called physical. I do not know of any better definition for physical existance. Of course, those who do not believe in the AUH are thus forced to believe that some subset of math has somehow been singled out to be real. Nowhere did I say that _only_ a physical system could implement a computation. But you did bring to my attention the fact that I should make the definition of implementation more clear on this point. In other places, I do point out that one computation can implement another. (In turn, the second one might implement another, etc.; the first one will therefore implement all of those.) So, your objection is irrelevant. You do believe a UD implements other computations. The third person view is fully capable of describing the entire situation. (Notice that _I_ never use the term 3rd person view; a better term would be actual situation.) Actuality is a first person concept. I have no clue as to what you mean. 3rd person view is everything you can communicate in a scientific manner without taking into account the subjective view of a person. If the person has some set of beliefs, they can be described as part of the true description of the situation. (Which you is what I thought you call the 3rd person view.) Hey, what's the french word for crap? I bet it would sound much more elegant ... unless the french just stole it. Crap means merde according to my dictionnary. Is it true crap means shit? It's true, but it is not considered as vulgar. Don't ask me why, but the meaning of a word does not seem to determine whether it is vulgar. Thus excrement is considered fine. You know merde, isn't it?, The famous word used by the general Cambrone during the Napoleonian wars ... I'm not familiar with it. Does merde have a special meaning, the way crap does? - - - - - - - Jacques Mallah ([EMAIL PROTECTED]) Physicist / Many Worlder / Devil's Advocate I know what no one else knows - 'Runaway Train', Soul Asylum My URL: http://hammer.prohosting.com/~mathmind/ _ Get your FREE download of MSN Explorer at http://explorer.msn.com
Re: on formally describable universes and measures
Russell Standish wrote: Marchal wrote: Hi Juergen, I would like to nuance my last Post I send to you. First I see in other posts, written by you, that your computable real numbers are *limit* computable. It still seems to me possible to diagonalize against that, although it is probably less trivial. But I think it isn't really relevant in our present discussion, because the continuum I am talking about appears in the first person discourse of the machines, so it is better to keep discussing the main point, which is the relevance of the first person point of view, with comp, when we are searching for a TOE. It seems to me that the cardinality of UD*, or whether UD* is a continuum or not is rather irrelevant. My understanding is that the UD argument implies a first person indeterminancy, ie every first person experience will have access to a random oracle. All right. I guess you agree that such random oracle appears also with the iterative self-duplication, which is itself appearing in UD*. I think the argument goes something like this: 1) UD algorithms will have high measure in the space of all computations, much higher than a direct implementation of a conscious AI (assuming such things exist). Hopefully so. Intuitively so. Not so easy to prove. Note also that if you implement a conscious AI it will itself be embedded in UD*, from his own point of view, and it will have access also to some random oracle. 2) Therefore, it is more likely that a conscious AI will find itself imbedded in the output of a UD, with access to a random oracle That's what I was saying ! And that conscious AI will even find itself in the output of an immaterial UD in Plato heaven. (Of course my viewpoint is that consciousness _requires_ access to a random oracle, making conclusion 2 even stronger, but it is not necessary for the argument). Consciousness _requires_ access to a random oracle for having relatively stable histories. Perhaps through the phase randomisation of the white rabbits (cf my recent paper). Bruno
Re: on formally describable universes and measures
The best you can achieve is an algorithm that outputs at least the computable infinite reals in the sense that it outputs their finite descriptions or programs. I am not sure I understand you here. Are you aware that the set of descriptions of computable reals is not closed for the diagonalisation procedure. That is: you cannot generate all (and only) descriptions of computable reals. The algorithm you are mentionning does not exist. You can only generate a superset of the set of all computable reals. That set (of description of all computable reals) is even constructively not *recursively enumerable* in the sense that, if you give me an algorithm generating the (description of) computable real, I can transform it for building a computable real not being generated by your algorithm. I guess you know that. That is why most formal constructivists consider their set of constructive reals as subset of the Turing computable reals. For exemple you can choose the set of reals which are provably computable in some formal system (like the system F by Girard, in which you can formalize ..., well Hilbert space and probably the whole of the *constructive* part of Tegmark mathematical ontology! That is very nice and big but not enough big for my purpose which has some necessarily non constructive feature. About natural numbers and machines I am a classical platonist. About real numbers I have no definite opinion. The describable reals are those computable in the limit by finite GTM programs. There is a program that eventually outputs all finite programs for a given GTM, by listing all possible program prefixes. Sure, in general one cannot decide whether a given prefix in the current list indeed is a complete program, or whether a given prefix will still grow longer by requesting additional input bits, or whether it will even grow forever, or whether it will really compute a real in the limit, or whether it won't because some of its output bits will flip back and forth forever: http://rapa.idsia.ch/~juergen/toesv2/node9.html But what do such undecidability results really mean? Are they relevant in any way? They do not imply that I cannot write down finite descriptions of the describable reals - they just mean that in general I cannot know at a given time which of the current list elements are indeed complete descriptions of some real, and which are not. Still, after finite time my list of symbol sequences will contain a complete description of any given computable real. Thus undecidable properties do not necessarily make things nonconstructive. Can you imagine yourself as a Platonist for a while, if only for the sake of the reasoning? I am not even sure what exactly a Platonist is. Do I need any additional preliminaries to realize why I genuinely fail to understand your invariance lemma? Sure. The delays question for exemple. Let us follow Jesse Mazer idea of torture. Suppose I duplicate you and reconstitute you, not in Washington and Moscow but in some Paradise and some Hell. Would you feel more comfortable if I tell you I will reconstitute you in paradise tomorow and in hell only in 3001 after C. ? Is that what you would choose? Choose? Do I have a choice? Which is my choice? Computationalism is more a human right than a doctrinal truth. I skipped this statement and related ones... Juergen
Re: on formally describable universes and measures
Hi Juergen, I would like to nuance my last Post I send to you. First I see in other posts, written by you, that your computable real numbers are *limit* computable. It still seems to me possible to diagonalize against that, although it is probably less trivial. But I think it isn't really relevant in our present discussion, because the continuum I am talking about appears in the first person discourse of the machines, so it is better to keep discussing the main point, which is the relevance of the first person point of view, with comp, when we are searching for a TOE. You makes me hesitating between pointing to modal logic and self-reference or keeping insisting on the thought experiments. Mmh... I dunno. Bruno
Re: on formally describable universes and measures
Jacques Mallah wrote: Pourquoi hurluberlu? Expliquez-moi ce mot (en anglais), s'il vous plait. (Je ne parle pas francais!) I cannot explain what hurluberlu means, except that it means crackpot. Sort of total fantasy ... I really don't know what you mean by concrete. If you believe there's a UD, you believe there's a UD. If not, stop sounding like you do and tell us in plain anglais what you mean. I am sure the distinction is totally irrelevant. Math is math. In any case, you either believe that it implements the computations, or you believe that it doesn't. If the latter, then it certainly can't be a candidate for any kind of TOE. Math is math, but is physic math? By a concrete UD I was meaning a real actual one, like the one I have implemented on a macintosh SE/30, and which has been running during two weeks in 1990 at Brussels. Of course I postulate here some physical universe as a local decor. Look, to be sure we are using impIementation in the same sense, I quote yourself (from http://hammer.prohosting.com/~mathmind/cwia.htm#II3) In turn, a computation is associated with a physical system only if it has been implemented by that system. Implementation is usually taken to mean that there is some direct correspondence between the formal states of that computation, and the states of the physical system, which can be described mathematically. So either you believe there is only math (including computer science and all computations), then implementation is a emerging concept, as are anything linked to physical predicates. Or you believe there exists something physical per se. Then indeed you can defined implementation in a sense relative to that physicalness. In either case you need to define it. And you *know* in either case it is a problem: mine and your's. The third person view is fully capable of describing the entire situation. (Notice that _I_ never use the term 3rd person view; a better term would be actual situation.) Actuality is a first person concept. 3rd person view is everything you can communicate in a scientific manner without taking into account the subjective view of a person. It seems to me that I need to repeat myself a lot here. You are not the only one. It's part of the game. Hey, what's the french word for crap? I bet it would sound much more elegant ... unless the french just stole it. Crap means merde according to my dictionnary. Is it true crap means shit? You know merde, isn't it?, The famous word used by the general Cambrone during the Napoleonian wars ... Bruno
Re: on formally describable universes and measures
From: Marchal [EMAIL PROTECTED] Jacques Mallah wrote: We discussed it; as I said then, it's wrong. You call it the crackpot proof :-) (hurluberlu in french) Pourquoi hurluberlu? Expliquez-moi ce mot (en anglais), s'il vous plait. (Je ne parle pas francais!) Sorry to break it to you, but you do. A physical universe is not the only (hypothetically real) mathematical structure that should implement computations. Obviously, you believe that a universal dovetailer (a single computation) implements all the computations it dovetails. I don't believe that. Only the concrete (implemented) DU does that, and then enter the crackpot proof, ... , or OCCAM. (see the UDA post): there is no need for a concrete running of the DU. The word concrete appears in the mouth of machine (if I can say) relatively to stable (without wabbits!) stories. Unless you postulate the existence of a concrete world. I don't. The existence of a concrete universe is what need an explanation (for me). And with comp I got only appearances of The existence of a concrete universe. *Concrete* is just *abstract* made familiar (and seen from inside). I really don't know what you mean by concrete. If you believe there's a UD, you believe there's a UD. If not, stop sounding like you do and tell us in plain anglais what you mean. I am sure the distinction is totally irrelevant. Math is math. In any case, you either believe that it implements the computations, or you believe that it doesn't. If the latter, then it certainly can't be a candidate for any kind of TOE. At least you don't believe (unless you change your mind) in the 1-person/3-person distinction, so I don't need even to try explaining my way, do I? The third person view is fully capable of describing the entire situation. (Notice that _I_ never use the term 3rd person view; a better term would be actual situation.) Anything an observer-moment sees is just a property of his observer-moment. The measure distribution predicts everything (to the extent possible); one can look at conditional effective probabilities by holding some property of an observation fixed. (Such as the observer thinks his name is Jack and that the time is 10:00 pm.) Simple. Forget your first person probabilities crap, it doesn't mean anything. By the way, computational continuation is also meaningless undefined crap. A computation either halts or doesn't; in either case the only continuation is that it either halts or doesn't. It seems to me that I need to repeat myself a lot here. Hey, what's the french word for crap? I bet it would sound much more elegant ... unless the french just stole it. - - - - - - - Jacques Mallah ([EMAIL PROTECTED]) Physicist / Many Worlder / Devil's Advocate I know what no one else knows - 'Runaway Train', Soul Asylum My URL: http://hammer.prohosting.com/~mathmind/ _ Get your FREE download of MSN Explorer at http://explorer.msn.com
Re: on formally describable universes and measures
Juergen wrote: Bruno, I am usually skipping those of your paragraphs that contain sentences such as physics is a branch of machine's psychology because I have no idea what that is supposed to mean. It is something the reasoning itself should clarify (hopefully). The expression gives the idea of the counter-intuitiveness (and out-fashion in the current philosophy of mind, where materialistic naturalism get the main attention today). It is a way of not hiding we are going toward a form of idealism. I try to explain that comp leads necessarily to some (rational) idealism. You can also got some intuition through poetical sentences. For exemple: Life what is it but a dream (Lewis Carroll). Still, I feel you do have something nontrivial to say, I just have not been able to figure out what exactly it is. Maybe if I knew why I genuinely fail to understand the invariance lemma - please show me! Actually I guess your constructive philosophy will not help you to understand what I try to show. I hope I am wrong here. But even if that is true, you can maybe still put yourself at the place of a classical logician and accept that with comp and some amount of classical (non constructive) logic I am correct. In that case, for those who believe it is necessary to be insane for believing in the physics/psychology reversal, my work will appear as an argument for your constructivisme! But any finite future is computable by a long program as well. The problems arise with infinite futures. We will come back on this (in some futur). No, it isn't, since generating an individual real is not equivalent to generating all prefixes of all reals. Generating an individual real means generating all prefixes of that individual real, AND NOTHING ELSE. All right. I was using generate in a more general sense. To help us preventing that confusion again I will say surgenerate instead. So a program surgenerates a real if it generates all the prefix of that real AND *SOME*THING ELSE. I hope you agree that the DU surgenerates all the reals. I will not be vexed if you anwer me trivial. (later it will be necessary to understand that from the first-person point of view we cannot know if we belong to a real which would be generated or surgenerated ...). The best you can achieve is an algorithm that outputs at least the computable infinite reals in the sense that it outputs their finite descriptions or programs. I am not sure I understand you here. Are you aware that the set of descriptions of computable reals is not closed for the diagonalisation procedure. That is: you cannot generate all (and only) descriptions of computable reals. The algorithm you are mentionning does not exist. You can only generate a superset of the set of all computable reals. That set (of description of all computable reals) is even constructively not *recursively enumerable* in the sense that, if you give me an algorithm generating the (description of) computable real, I can transform it for building a computable real not being generated by your algorithm. I guess you know that. That is why most formal constructivists consider their set of constructive reals as subset of the Turing computable reals. For exemple you can choose the set of reals which are provably computable in some formal system (like the system F by Girard, in which you can formalize ..., well Hilbert space and probably the whole of the *constructive* part of Tegmark mathematical ontology! That is very nice and big but not enough big for my purpose which has some necessarily non constructive feature. About natural numbers and machines I am a classical platonist. About real numbers I have no definite opinion. Can you imagine yourself as a Platonist for a while, if only for the sake of the reasoning? If it just means you don't know in advance in which possible future you'll end up, provided there is a nontrivial distribution on the possible futures, then this is ok (and trivial). Are you saying that *without* distribution I would be less ignorant? I was just saying you don't know in advance in which possible future you'll end up. Comma. Do I need any additional preliminaries to realize why I genuinely fail to understand your invariance lemma? Sure. The delays question for exemple. Let us follow Jesse Mazer idea of torture. Suppose I duplicate you and reconstitute you, not in Washington and Moscow but in some Paradise and some Hell. Would you feel more comfortable if I tell you I will reconstitute you in paradise tomorow and in hell only in 3001 after C. ? Is that what you would choose? An honest computationalist will never suggest that such a delay should make yourself feeling more comfortable. Despite the third person local appearances. After the delays, there is the virtual/real preliminaries. The first person cannot see the difference. And then the more difficult arithmetical/virtual preliminaries. First person cannot makes the differences Are you
Re: on formally describable universes and measures
[EMAIL PROTECTED] to [EMAIL PROTECTED] : Certainly things that we can imagine even slightly, like real-valued observers, already have a kind of existence, in that they cause us to argue about them. [EMAIL PROTECTED] to [EMAIL PROTECTED] : That's a bit like saying there is some truth to 1+1=3 just because we can argue about it [EMAIL PROTECTED] to GLevy: Many things are doubtful. 2+2=4 isn't. [EMAIL PROTECTED] to [EMAIL PROTECTED] : There you go again. But being sure isn't the same as being right. Despite the intuitively compelling nature of arithmetic as we know it, it is really quite arbitrary. It is compelling only because we evolved in a world that provided some survival advantage to brains that interpreted sense experience that way, by way of major approximations and conflations. But its formalizations, like the Peano axioms and the inference mechanism that produces theorems like 1+1=2 really are just arbitrary system of rewriting rules. Its perfectly easy to construct equally pretty systems where 1+1 = 3 or 1+1 = 1, starting with different initial strings or using different rewrite rules. When I say 1+1=2 isn't doubtful, without redefining 1,+,=,2, I am assuming the particular traditional rewrite rules used by everybody, not alternative systems where symbol 2 is replaced by 6, or + by addition modulo group size. And you can build universes in such systems, where the arithmetic you find so correct never rears it misshapen head. Algorithmic TOEs are indeed about all possible rewrite systems, including your nontraditional ones. Perhaps you would like to argue that our traditional rewrite system is doubtful as it cannot prove its own consistence? But algorithmic TOEs include even rewrite systems that are inconsistent, given a particular interpretation imposed on innocent symbol strings. They are limited to all possible ways of manipulating symbols. From any description-oriented and communication-oriented viewpoint, however, this does not seem much of a limitation as we cannot even describe in principle things outside the range of algorithmic TOEs. What's more, there are situations in our own neighborhood where alternate arithmetics are more natural than everyday arithmetic. For instance, in a lasing medium, if you introduce one photon in a particular quantum state, and then add another photon in the same state, it is likely that you will find three photons in that state (then more and more - Boson statistics: the probability of a new recruit to a state occupied by n particles is proportional to n/(n+1)). Photons in the same state are in principle indistinguishable from one another, so occupancy of a quantum state is a purer model of counting than the everyday one: when you count pebbles, thay remain quite distinguishable from one another, and it takes an arbitrary high-handed act of abstraction to say that THIS pebble, with its unique shape, color and scratch pattern is somehow the same as this other, completely different pebble. The quantum world in general, with its superpositions, entanglements and ephemeral virtual particles is probably poorly served by bimodal Aristotelian logic, never mind mathematical frameworks idealized from grouping pebbles. But because you are so exclusively wedded to these parochial ways of thinking, you feel you can just reject out of hand the existence (among many other things) of beings able to store, compute and communicate reals, even though many of their properties can be puzzled out. PAH! But you cannot even unambiguously define in a formal way (using any describable set of axioms or rewriting rules) what your intuitive notion of the continuum of reals really means. All provable properties of the reals are expressible as finite symbol strings, and also have an interpretation in a noncontinuous, countable model. Maybe there _are_ important things beyond formal description, things we cannot sensibly talk about. It seems wise though not to talk about them.
Re: on formally describable universes and measures
From [EMAIL PROTECTED] Sun Feb 18 01:16:16 2001 The exchange between Bruno and Juergens is, I believe, instructive and constructive as it forces them to refine their positions. Where did I have to refine mine? JS That' right I guess. You didn't have to refine yours...I guess Dubito ergo cogito does not apply to you. George Many things are doubtful. 2+2=4 isn't. Seriously - where did the present discussion force a refinement of algorithmic TOEs? I do believe they leave lots of space for refinements, but the current debate has not explored this space; it has focused on other things instead. Juergen
Re: on formally describable universes and measures
JS: Then there is your invariance lemma: the way you quantify 1-indeterminacy is independent of (3-)time, (3-)place, and (3-)real/virtual nature of the reconstitution. This does not make sense, because if the (3-) probability distribution on the possible futures and reconstitutions does depend on time or place or other things (why not?) then 1-indeterminacy does so, too. Under most distributions, some futures are less likely than others. Hence there are nontrivial, distribution-dependent, probabilistic 1-predictions as well as quantifications of 1-indeterminacy that depend on time/space/other things. BM: I see you genuily fail to understand the invariance lemma. No problem. We will come back to this until you get the TILT, (if you agree). Bruno, I am usually skipping those of your paragraphs that contain sentences such as physics is a branch of machine's psychology because I have no idea what that is supposed to mean. Still, I feel you do have something nontrivial to say, I just have not been able to figure out what exactly it is. Maybe if I knew why I genuinely fail to understand the invariance lemma - please show me! JS: Not uncomputable. Any past is finite. BM: I was talking about the immediate next futur. But any finite future is computable by a long program as well. The problems arise with infinite futures. JS: I am prejudiced against claims of rigorous proof when even the assumptions are unclear; and against statements that are plain wrong, such as the UD generates all real numbers. BM: I am not claiming I am rigorous, except when you say I am vague and when you ask me precisions which are not relevant. The sentence the UD generates all real numbers is ambiguous. Either you interpret it as The UD generates (enumerates) the set of all real numbers This does indeed contradict Cantor's theorem. Or you interpret it as All real number are (individually) generated by the UD. In which case, with the usual definition of generating a real (generating all its prefixes) it is just correct. Isn't it? No, it isn't, since generating an individual real is not equivalent to generating all prefixes of all reals. Generating an individual real means generating all prefixes of that individual real, AND NOTHING ELSE. Generating a real means you somehow have to be able to identify and completely describe that particular real. If you cannot do this without describing lots of other things then the individual real does not exist from any constructive perspective. The trivial algorithm ALPHABET ( http://rapa.idsia.ch/~juergen/toesv2/node27.html ) whose outputs are 0,1,00,01,10,11,000is not generating a description of any individual infinite real because it never creates a complete representation thereof. Ambiguity arises because each of the outputs is just a prefix of many infinite reals. The best you can achieve is an algorithm that outputs at least the computable infinite reals in the sense that it outputs their finite descriptions or programs. BM: So I ask you again: do you agree that comp entails the existence of first person indeterminacy, as it is shown by the self-duplication thought experience? If it just means you don't know in advance in which possible future you'll end up, provided there is a nontrivial distribution on the possible futures, then this is ok (and trivial). Do I need any additional preliminaries to realize why I genuinely fail to understand your invariance lemma? Juergen
Re: on formally describable universes and measures
I hope this is our last *too long* post, Juergen. At the end of it, I propose we come back to the initial discussion, if you agree. Juergen wrote: Normally a constructive philosopher should abandon comp right here, because it follows from that theorem that we cannot be machine in any constructive sense. Which theorem? Send pointer to its proof. Not to its informal description, but to its proof. Sorry but for reason of place I will remain a little bit informal. The theorem concerns sound (or just consistent) machines proving enough elementary theorems of arithmetic. There exists multiple versions of the theorem. Theorem : no sound (or just consistent) machine can build a copy of itself in a provable way. Theorem : No sound machine can know its own description. (where knowing is formalised by S4 modal logic (or S4Grz) and description by arithmetisation). Theorem: the mechanist knower cannot know itself. Theorem: No sound machine can build a machine which proves the same theorems as itself and at the same time proves that fact. The theorem is sometimes called the correct reconstruction of Lucas argument. Unlike the traditional Lucas/Penrose argument this theorem is not controversial, although the first reconstructions of it were not very rigorous. The first one to realise that truth, and to propose a rigorous argument is Emil Post in his 1922 anticipation (see the book of Davis 1965). Note there is still a slight error in Post's formulation. It (re) originates in the delightful paper by Benacerraf God, the Devil and Godel. Unfortunately, although all the interesting ideas are in Benacerraf's paper, the paper is wrong from the beginning to the end (as Benacerraf aknowledges himself in an appendice). Chihara, Wang, Reinhaerdt have propose, with growing level of rigor, reconstructions of Benacerraf's reconstruction of Lucas. Penrose (re)proposes Lucas's use of Godel theorem against mechanism in his first book, but correct it in his second book. So you can find a proof in the second book of Penrose too (rather involved proof). In the second book Penrose argue that mechanist philosophy is meaningfull only in the sense of being a machine and knowing which one. Then indeed *that* mechanist philosophy is refuted. Just look at my thesis page 40 - 44. With G and G* it is almost an easy exercice to formalise it completely and to prove it. You will find all formal details, + the references in my thesis. (It would just be indecent to give here a formal description of that theorem, because that would be long (as you can guess), and, until now, it would be without most distracting. (One reason why I doubt this: isn't the lowest possible level - embodied by what's computable in the limit - sufficient? Why not run all universes GTM-computable in the limit? If one of them is ours, then the set-up is constructive.) How do you know there is a lowest possible level? What do you mean by one of them is ours? Once you distinguish first and third person, you will understand (well it is a consequence of the invariance lemma) that it is at least consistent with comp that there is no lowest possible level, and you can understand that the expression our universe has necessarily no obvious meaning. We will come back to the invariance lemma later, (if you agree). Your problem is that you are attached to a very naive (and vague!) theory of mind where the first person is attached to a particular physical instantiation of a computation. In 1988 I have build the movie-graph thought experiment (platonic destructive in the James Brown's nomenclature) which shows that this view is incompatible with comp. Maudlin has proved in 1989 an equivalent result. Unlike UDA the graph movie argument *is* difficult (we discuss it at lenght in the list). For pedagogical reason I don't use it here. I use some form of Occam instead. If you want really be rigorous here you should solve first the very serious Putnam-Chalmers-Mallah's physical implementation problem. (see the thread on that implementation problem in the archive). I have not the Mallah's problem, because I have no universes at all. Just many computational histories, which together makes first person discourse possible. I have *other* problems, like the white rabbits, which force us to derive the physical law from the psychological laws of machine's dreams. But then, that's the result of the first part. Not uncomputable. Any past is finite. I was talking about the immediate next futur. So it is at worst random or Martin-Loef-random or incompressible. None of those you cite is careless when it comes to the difference between countable and uncountable sets. None claims one can compute a continuum by dovetailing. Dovetailing will be forever limited to the countable realm. I have never said that we can compute a continuum by dovetailing. Sometimes, in some context, I talk about dovetailing *on* the continuum because I have explain precisely what I
Re: on formally describable universes and measures
[EMAIL PROTECTED] wrote: From [EMAIL PROTECTED] Sun Feb 18 01:16:16 2001 The exchange between Bruno and Juergens is, I believe, instructive and constructive as it forces them to refine their positions. Where did I have to refine mine? JS That' right I guess. You didn't have to refine yours...I guess Dubito ergo cogito does not apply to you. George
Re: on formally describable universes and measures
jamikes wrote: George, ... I have only some remarks: I I think (not a Cartesian wordageG) the first step would be: 0.1: Causality IS, then you may introduce your points. The whole point of starting with I is to avoid starting with a *bare* assumption such as the one you suggest (Causality). However, I admit, I don't really know what the the perception of I is. Is it an observation, an assumption, both? Thanks Bruno for your informative discussion of Descartes. Marchal wrote: Descartes complete reasoning was (simplifying it a little bit): Dubito ergo cogito, and only then cogito ergo sum Excuse my latin. :-) I don't know what dubito means. It sounds like debit to me. Do I owe anyone money? :-) A relation between dubito ergo cogito and Godel's theorem has been provided by the philosopher Slezak. (I have not the reference here). Interesting Your reasoning is interesting but rather quick. Yes, I am a bad typist, I hate long proofs. :-) I have left out a lot... for example, my term rational is quite vague. Referring to earlier posts, consciousness can vary in kinds and degrees. I could mean for example within the set of all mathematical constructs, or implementable on a finite Turing machine or implementable on a quantum computer. The existence of rationality can only appears in the eyes of the beholder. Thus, I think that I am rational, but my perception of this rationality is contingent on this rationality. ( A reflection, or recursion) Different minds with different logics and capabilities will have different consciousnesses. I agree with John Mikes remark that Descartes' cogito doesn't refer to time. Yes, I also agree with him. Do you know his unachieved A la recherche de la verite a short beautiful text. I will look it up George
Re: on formally describable universes and measures
Jürgen wrote: ``Please read again. If "consciousness" is indeed a well-defined concept,and if there are any "conscious" computable observers, then they will becomputed. Otherwise they won't. In either case there is no need to defineconsciousness - I have not seen a convincing definition anyway. Similarly,there is no need to define "love", although it might be an importantconcept to certain computable observers in certain computable universes." I think the source of the problem is equation 1 of Jürgens paper. This equation supposedly gives the probability that Iam in a particular universe, but it ignores that multiple copies of me might exist in one universe. Let's consider a simple example. The prior probability of universe i (i0) is denoted as P(i), and i copies of me exist in universe i. In this case, Jürgencomputes the propability that if you pick a universe at random, sampled with the prior P, you pick universe i. This probability is, of course, P(i). Therefore Jürgen never has to identify how many times I exist in a particular universe, and can ignore what consciousness actually is. Surerly an open univere where an infinite number of copies of me exist is infinitely more likely than a closed universe whereI don't have any copies, assuming that the priors are of the same order? Saibal
Re: on formally describable universes and measures
This time I'll repeat only a fraction of the 500 lines in your reply: From [EMAIL PROTECTED]: Suppose you survive only through a simulation of the big bang at the level of the quantum superstring, membrane, etc. then the correct level of substitution is the level of the quantum superstring, membrane, etc. Remember the definition of COMP, it says that *there exists* such a level. It does not say that this or that *is* the correct level. Ok. It is a sort of admission of ignorance. This ignorance is fundamental. Indeed it has been shown (independently by a lot of people---ref in my papers) that comp entails we cannot know the correct levels. We can bet on it, though, and we can make reasoning relatively to correct bets. Normally a constructive philosopher should abandon comp right here, because it follows from that theorem that we cannot be machine in any constructive sense. Which theorem? Send pointer to its proof. Not to its informal description, but to its proof. (One reason why I doubt this: isn't the lowest possible level - embodied by what's computable in the limit - sufficient? Why not run all universes GTM-computable in the limit? If one of them is ours, then the set-up is constructive.) You miss the point. Even the one who as PI on his T-shirt is wrong if he believes PI helps him to predict the issue of the next self-duplication. Note that if the program remains as lenghty as the sequence, as it happens for most Schmidhubers---in the iterated self-duplication, these sequence are called uncomputable by Solovay, Chaitin, etc. Not uncomputable. Any past is finite. So it is at worst random or Martin-Loef-random or incompressible. None of those you cite is careless when it comes to the difference between countable and uncountable sets. None claims one can compute a continuum by dovetailing. Dovetailing will be forever limited to the countable realm. Is there a probability distribution on this set (if not, you cannot predict anything)? Which one? You talk really as if probability was the only manner you know for quantifying uncertainty. Beside probability there exist other ways to handle the uncertain. The one I know the best is Dempster-Shafer theory. (I have work some years with expert in that field). Not only I do not restrict myself to the uniform distribution, but I don't share your assumption that the only way for quantifying uncertainty is probability. Why not Dempster-Shafer theory of evidence ? The various Dempster-Shafer (DS) approaches are no alternatives to probability theory. They are extensions designed to facilitate handling of uncertainty in contexts where lack of belief does not imply disbelief. But DS is essentially about hulls confining sets of traditional distributions, and thus compatible with the traditional framework of Bayesian statistics. (Variants of DS that are not yield paradoxical results.) In the first part of my thesis: I am not pretending that I have solved the mind-body problem, nor the problem of the origin of the physical laws, nor the QCU. But I have rigorously proved that with comp these problems are equivalent. It is this recurring type of claim I find so irritating: rigorous proof without formal framework. A weakness is that I am lead toward hard mathematics. What a strange remark. The weakness of your texts is that they are so informal. Which unique formalisation? Please write it down! How can you possibly isolate it by informal reasoning? I was talking *there* about the modal logic G, G*, S4Grz, Z1, Z1*, etc. These formal logics are intensional (modal) variation of the provability logics of the sound self-referentially correct machine. I have provide semantics, and theorem provers. See explanation and technical details in my thesis and in my papers. Your thesis is in French. Your papers are informal. They always include sentences such as: Actually such proof and clarification is one of the main result in my thesis ... without going into details I will briefly try to convey the main line of the argument (p 4 of paper dated sept 24, 2000). Then follow informal examples, references to philosophers, and unsubstantiated claims such as the UD generates all real numbers, when it only generates all their finite prefixes, which is a fundamental difference. Then there is your invariance lemma: the way you quantify 1-indeterminacy is independent of (3-)time, (3-)place, and (3-)real/virtual nature of the reconstitution. This does not make sense, because if the (3-) probability distribution on the possible futures and reconstitutions does depend on time or place or other things (why not?) then 1-indeterminacy does so, too. Under most distributions, some futures are less likely than others. Hence there are nontrivial, distribution-dependent, probabilistic 1-predictions as well as quantifications of 1-indeterminacy that depend on time/space/other things. You are also telling us
Re: on formally describable universes and measures
Juergen Schmidhuber wrote: This time I'll annotate your entire message to demonstrate how many things I tend to find unclear in your texts. Thank you. (Hereafter TE means Thought Experiment) To derive consequences we need to know the assumptions. Of course, this holds for thought experiments as well. Without defining delays you cannot derive something from delays. You have no problem (according to your post) with the TE where you are annihilated in Brussels and reconstitute simultaneously at W and at M. (TE1) In the TE with delay, it is the same TE except that now you are reconstitute in W, and only one year later (let us say) you are reconstitute at M. (TE2) It is a thought experiment. You must imagine I am really proposing you that experiment, and I am using the expression one year in the traditionnal english sense. It is precise (although admittedly not formal) because with comp I can in principle do the experience. My question is knowing that you are at Brussels before the experience, are your expectation the same in TE1 and TE2? I am using the word delay in the english traditional sense, which is all what is need in the thought experiment. Of course if you have still not understand more than 2/15 of the UDA TE, I can believe the rest of my work *must* appear unclear. What is a correct level of substitution? People of the list will be bored if I repeat this again. I explain what is a correct level of substitution each time I recall the definition of COMP. (This prove BTW you don't have read neither ma thesis, nor my paper CCQ, nor the UDA posts.) Those who knows can skip what follows. Of course some revisal can be helpful. Suppose that the neurophilosophers (like the Churchland, Francis Crick, ...) are correct. Then you can survive with an artificial brain which emulates your neurons. In that case the correct level of substitution is roughly speaking the level of neurons. Suppose you survive only through a simulation of the big bang at the level of the quantum superstring, membrane, etc. then the correct level of substitution is the level of the quantum superstring, membrane, etc. Remember the definition of COMP, it says that *there exists* such a level. It does not say that this or that *is* the correct level. It is a sort of admission of ignorance. This ignorance is fundamental. Indeed it has been shown (independently by a lot of people---ref in my papers) that comp entails we cannot know the correct levels. We can bet on it, though, and we can make reasoning relatively to correct bets. Normally a constructive philosopher should abandon comp right here, because it follows from that theorem that we cannot be machine in any constructive sense. Where does the betting come in? On which alternatives can we bet? Which is the distribution on the alternatives? The betting comes from the theorem mentionned just above. (Although it follows partially from most of the UDA too). In the W-M TE the alternatives are given by the reconstitutions. With the assumption that we are living in something described by schroedinger equation, the alternatives are given by some quantum rules. The alternatives are unknown and part of the problem with comp. It has been shown they are linked to the structure of UD*. Defining the set of alternatives is part of our problem. What is the right level? I don't know. No machines will ever known the right level. Only the drunken Schmidhubers will say it is incomputable. Most will just say the history so far is computable by a lengthy program. You miss the point. Even the one who as PI on his T-shirt is wrong if he believes PI helps him to predict the issue of the next self-duplication. Note that if the program remains as lenghty as the sequence, as it happens for most Schmidhubers---in the iterated self-duplication, these sequence are called uncomputable by Solovay, Chaitin, etc. From the first person point of view the delay introduced by the doctor has not been and cannot been directly perceived. That seems obvious, but what exactly do you mean by perceive, I am glad you see it is obvious, because it *was* my point. What is your point asking what I mean exactly by perceive at this stage. The goal of the UDA TE is indeed to help people abandonning prejudice about the easyness of the issue. To help them ro realise the hardness of the mind/body problem with comp. (A lot of people tend to belief that comp is the solution of the problem, I show it helps on the road toward a formulation of the problem). Try perhaps to read the whole UDA for getting the general idea, first. (that's why I insist sometimes that reconstition booth has no windows!). why sometimes, why sometimes not? Are you just playing with me? I use reconstitution booth without window to illustrate the fact that no person can, from a first person point of view, guess if he/she/it is the one reconstitute at W, or the one reconstitute at
Re: on formally describable universes and measures
Dear George, If I might advance a minor change: Descartes' dictum should be: Cognito (I think), ergo eram (therefore I was). The observation of one's state of existence is always *after* the fact of the thought. This points to the possibility that the chaining implicit in conscious flow (time) is in the opposite direction to the logical linking. Kindest regards, Stephen George Levy wrote: The exchange between Bruno and Juergens is, I believe, instructive and constructive as it forces them to refine their positions. However, while there is a need for some formalism, too much formalism gets in the way. As Einstein said, Imagination is more important than knowledge. Juergens' insistence on being absolutely formal in defining delays, is truly impossible unless a TOE is in place. And if we had a TOE, then we wouldn't waste our time arguing. His constructivist approach can never achieve the required conceptual leap. Here is a suggestion: rather than getting bogged down with attempting to define time and delays, wouldn't be simpler to start as Descartes did with the fundamental assumption of the I or I think which is the primary uncontrovertible observation and also the necessary assumption for deriving everything else. From this observation (or assumption), use anthropic reasonning to deduce that the whole observed world is a set of logically linked relationship. In other words: I think (observation of the I and the now; I am rational, logical, I understand causality) therefore I am ( rationality is the definition of existence) therefore the world is (anthropic reasoning-- the initial boundary condition for the causal chain starts with I) therefore the plenitude is (absence of irrational and acausal arbitrariness in the description of the world leads to all possible rational worlds) therefore I exists in plural (absence of arbitrariness leads to the existence of several differing I's, in fact of all possible I's.) Conscious flow (time) becomes a logical linkage between I's. In other words, the time thread from one I to the next, or more generally, from one I to several other I's is constrained by the self rationality of I. Consciousness can be described as a web in the plenitude, linking all conscious points together. George
Re: on formally describable universes and measures
Dear Stephen, I believe Descartes used the verb 'cogitare', meaning the fact of thinking (prius cogitare quam conari consuesce... consider first think, then (than??) talk) Consequently he did not assume to think back into some memory and refreshing it. He spoke about the observation that one IS THINKING, IMO without any connotation of time passing. John Mikes [EMAIL PROTECTED] http://pages.prodigy.net/jamikes; - Original Message - From: Stephen Paul King [EMAIL PROTECTED] To: [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Sunday, February 18, 2001 12:07 PM Subject: Re: on formally describable universes and measures Dear George, If I might advance a minor change: Descartes' dictum should be: Cognito (I think), ergo eram (therefore I was). The observation of one's state of existence is always *after* the fact of the thought. This points to the possibility that the chaining implicit in conscious flow (time) is in the opposite direction to the logical linking. Kindest regards, Stephen George Levy wrote: The exchange between Bruno and Juergens is, I believe, instructive and constructive as it forces them to refine their positions. However, while there is a need for some formalism, too much formalism gets in the way. As Einstein said, Imagination is more important than knowledge. Juergens' insistence on being absolutely formal in defining delays, is truly impossible unless a TOE is in place. And if we had a TOE, then we wouldn't waste our time arguing. His constructivist approach can never achieve the required conceptual leap. Here is a suggestion: rather than getting bogged down with attempting to define time and delays, wouldn't be simpler to start as Descartes did with the fundamental assumption of the I or I think which is the primary uncontrovertible observation and also the necessary assumption for deriving everything else. From this observation (or assumption), use anthropic reasonning to deduce that the whole observed world is a set of logically linked relationship. In other words: I think (observation of the I and the now; I am rational, logical, I understand causality) therefore I am ( rationality is the definition of existence) therefore the world is (anthropic reasoning-- the initial boundary condition for the causal chain starts with I) therefore the plenitude is (absence of irrational and acausal arbitrariness in the description of the world leads to all possible rational worlds) therefore I exists in plural (absence of arbitrariness leads to the existence of several differing I's, in fact of all possible I's.) Conscious flow (time) becomes a logical linkage between I's. In other words, the time thread from one I to the next, or more generally, from one I to several other I's is constrained by the self rationality of I. Consciousness can be described as a web in the plenitude, linking all conscious points together. George
Re: on formally describable universes and measures
The exchange between Bruno and Juergens is, I believe, instructive and constructive as it forces them to refine their positions. However, while there is a need for some formalism, too much formalism gets in the way. As Einstein said, Imagination is more important than knowledge. Juergens' insistence on being absolutely formal in defining delays, is truly impossible unless a TOE is in place. And if we had a TOE, then we wouldn't waste our time arguing. His constructivist approach can never achieve the required conceptual leap. Here is a suggestion: rather than getting bogged down with attempting to define time and delays, wouldn't be simpler to start as Descartes did with the fundamental assumption of the I or I think which is the primary uncontrovertible observation and also the necessary assumption for deriving everything else. From this observation (or assumption), use anthropic reasonning to deduce that the whole observed world is a set of logically linked relationship. In other words: I think (observation of the I and the now; I am rational, logical, I understand causality) therefore I am ( rationality is the definition of existence) therefore the world is (anthropic reasoning-- the initial boundary condition for the causal chain starts with I) therefore the plenitude is (absence of irrational and acausal arbitrariness in the description of the world leads to all possible rational worlds) therefore I exists in plural (absence of arbitrariness leads to the existence of several differing I's, in fact of all possible I's.) Conscious flow (time) becomes a logical linkage between I's. In other words, the time thread from one I to the next, or more generally, from one I to several other I's is constrained by the self rationality of I. Consciousness can be described as a web in the plenitude, linking all conscious points together. George
Re: on formally describable universes and measures
This time I'll annotate your entire message to demonstrate how many things I tend to find unclear in your texts. From: Marchal [EMAIL PROTECTED] Juergen wrote (among things): But how to answer an ill-posed question? You promise that time and space will disappear at the end of the reasoning, but your question is about delays, and how can we speak about delays without defining time? Simulation time? Real time? Both? How? There is no way to continue without formal framework. We were doing a thought experiment. I haven't say that the delays were virtual. This is done much later in the reasoning. Of course, as George Levy says the permutation real/virtual makes no changes in the first person point of view, and does not change the distribution either. To derive consequences we need to know the assumptions. Of course, this holds for thought experiments as well. Without defining delays you cannot derive something from delays. IF we accept COMP we survive with an artificial brain (Well: in case we were betting on a correct level of substitution). What is a correct level of substitution? Where does the betting come in? On which alternatives can we bet? Which is the distribution on the alternatives? That means the doctor scan (at the right level) your brain, destroy What is the right level? it, and then from the recollected information he builds a new one. The state of the artificial brain mirrors the state of your brain. You survive (with comp!). Now let us suppose the doctor keeps the information hidden in a drawer during one year. Real time delay, in the every day-type of life. After that delay he makes the reconstitution. I am just saying that, with comp, from the point of view of the one who survive, that delay cannot be perceived. It has not influence the kept information of your brain. From the first person point of view the delay introduced by the doctor has not been and cannot been directly perceived. That seems obvious, but what exactly do you mean by perceive, as opposed to directly perceive? You open your eyes - things have changed - another time, another place. Which are the limits of perception here? (that's why I insist sometimes that reconstition booth has no windows!). why sometimes, why sometimes not? Anyway, in general things will have changed - you may need some technical equipment to detect the changes, still, in principle you could find out things are different, at least in the real world. If you cannot, then why not - which are the assumptions here? Maybe you are talking about a virtual reality that you can fully control? Then which is the precise set of virtual realities you are considering? Is there a probability distribution on this set (if not, you cannot predict anything)? Which one? Are you seeing my point ? It does also not change first person perception in case of self-multiplication. Your point is the revival of an old science fiction theme. But as soon as you want to derive something you need to state formal assumptions, otherwise you'll end up with empty philosophic blabla. There is no way to continue without formal framework. I isolate a unique formalisation by an informal reasoning. Which unique formalisation? Please write it down! How can you possibly isolate it by informal reasoning? To formalise at this stage would automatically put the mind-body problem under the rug. Didn't you just say there is a unique formalisation? Why does formalisation suddenly put the mind-body problem under the rug? What's the problem with the mind-body problem? Why is it incompatible with formalisation? A TOE which doesn't address (at least) the mind-body problem is a TOS (a theory of *some* thing). Without formal assumptions you have no theory of everything, no theory of something, no theory at all. But as I show below, those self-multiplication are easily formalised (at least the third person description of those experiment are easily formalised). You can easily write a program which multiplied yourself (still betting on a correct level of course) relatively to virtual environments. Correct level? Betting? On what - which are the alternatives? Which is the distribution on the alternatives? The program that multiplies observers _seems_ to go into the direction of a formal ansatz, although it remains vague. How does the program identify an observer, or myself? It is much easier to write a program that copies entire computable universes together with the embedded observers, because such a simple program does not need to identify observers and separate them from their environment. Please state precisely what you really mean. Don't give another informal example, be precise. Are you among those who argues that talk on consciousness is a hoax ? Not necessarily. How do you manage consciousness in your TOE-approach? Algorithmic TOEs are about computable probability distributions on universe histories
Re: on formally describable universes and measures
Hereby, I comment posts by
Brent Meeker, James Higgo, and George Levy.
Brent Meeker wrote:
In response to Bruno and Jesse, perhaps I should have used a different
label in the first block of my diagram to make it correspond with past
posting, as follows:
--
(1)| observer moments|| other postulates | (6)
-- /\
|
||
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v|
|
--- |
|
(2) | the physical world me | |
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--- |
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||
|
v|
|
-|
|
| descriptions of the physical ||
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(3)| and psychological world in ||
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| terms of mathematical laws ||
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-|
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||
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v|
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-|
===|
| the information content of the |
---
(4)| mathematical description of|| other postulates | (5)
---
| the world |
-
I preferred direct perceptions and thoughts because they didn't
require an object observer which I put in quotes because, as I
indicated, I supposed that I (the observer) is an inference for the
patterns in the observer moments. However, part of the reason for my
posting was that I wanted to say that all the above blocks exist in
different senses and it is only poetic argument to say only observer
moments exist. It is all right to make such provacative, poetic
assertions, but they should be followed by an explanation of how all
the other blocks seem to exist, or exist in some other way.
Absolutely.
As for the continuity of consciousness, I think it is clear that there
is continuity in the sense that perceptions and thoughts are not
disconnected. At the level of physical descriptions, nuerological
states have some finite duration. Even if you like to assert the
physical world doesn't exist your complete theory must take into
account this appearance.
Absolutely.
These states are not disjoint, but overlap
in time. So I would say the there is continuity of consciousness but
it is not fundamental - it is contingent (having been knocked
unconscious I can attest to that directly).
Re: on formally describable universes and measures
Resent-Date: Fri, 9 Feb 2001 06:15:47 -0800 Subject: Re: on formally describable universes and measures From: Marchal [EMAIL PROTECTED] No, I do not. I suggest you first define a formal framework for measuring delays etc. Then we can continue. You should have told me this at the preceeding step which was also informal (although precise). I am proposing a thought experiment which is a kind of reductio ad absurdo here (remember that time and space will disappear at the end of the reasoning). My feeling is that, for some unknow reason you have decided to elude the reasoning. That seems clear with your answer to Russell Standish: you are saying 2+2=4 and I am saying 2+2=5! You are saying that I am fully wrong, but you don't tell me where. How am I suppose to take your disagrement here. You don't really answer the question. But how to answer an ill-posed question? You promise that time and space will disappear at the end of the reasoning, but your question is about delays, and how can we speak about delays without defining time? Simulation time? Real time? Both? How? There is no way to continue without formal framework. What does your theory predict with respect to the following experience: You are scanned read and annihilate at Amsterdam. I reconstitute you in Washington tomorrow, and at Moscow in one billion years. Are your expectations different from the situation where the two reconstitutions are simultaneous. Expectations with respect to what? Moscow one billion years from now might be different from Washington tomorrow, so there seem to be two different possible futures. The essential question is: what is the distribution on the possible futures? Is the distribution computable? How does the distribution depend on your delays and other computable (?) things? Are there just 2 possible futures? Or 10? Or infinitely many? If you want to be formal, let us accept classical Newtonian mechanics for the sake of the argument. You know that with comp such experience are possible *in principle*, and that is all what we need for the reasoning. Should we or should we not take these delays into account when evaluating the first-person indeterminacy? What does your theory say? What do you say? Again I fail to understand the question. Please define delays! How many possible delays are there? Are they computable? What exactly is this indeterminacy? Is it something different from an ordinary distribution? If so, what is it? If not, why don't you call it a distribution? The theory first asks: what is the distribution on all possible futures? Maybe you say you do not know. Since it is an algorithmic theory, it answers: ok, distribution unknown, but if it is describable (GTM-computable in the limit), then I still can say something, namely, I can exclude almost all infinite futures (those without finite descriptions) with probability one. And among those I cannot exclude, the weird ones with very long minimal descriptions are very unlikely. Maybe you now say you don't buy the describability assumption. Then the theory can't say nothing nontrivial no more. Neither can you though. Juergen
Re: on formally describable universes and measures (fwd)
On 09-Feb-01, Jesse Mazer wrote: So, if continuity of consciousness is real it is reasonable to expect that our theory of consciousness should allow for the possibility of splitting, and that from a first-person point of view, I-before-the-split would have an X% chance of becoming one copy and a Y% chance of becoming another. That is not to deny, though, that the split would happen both ways at once--in other words, each copy would be correct in saying it was continuous with the single consciousness before the split. This seems to me to be a meaningless question. What possible experiment could decide whether I had become the I-in-Washington and not the I-in-Moscow. The very hypothesis of the thought experiment makes this question unaswerable. Of course if we actually did the experiment and I-in-Washington says No I'm not the one who was in Brussels. and the I-in-Moscow says, Yes, I'm the one who was in Brussels. or they thought thusly to themselves then we might have an interesting question. But Bruno postulates in the beginning that they must both say (unless lying), I was the one in Brussels. If you scatter a photon off an excited atom you can get two identical photons - but there is no answer to the question which was the original and which was emitted by the atom. Brent Meeker
Re: on formally describable universes and measures (fwd)
Brent Meeker wrote: So, if continuity of consciousness is real it is reasonable to expect that our theory of consciousness should allow for the possibility of splitting, and that from a first-person point of view, I-before-the-split would have an X% chance of becoming one copy and a Y% chance of becoming another. That is not to deny, though, that the split would happen both ways at once--in other words, each copy would be correct in saying it was continuous with the single consciousness before the split. This seems to me to be a meaningless question. What possible experiment could decide whether I had become the I-in-Washington and not the I-in-Moscow. The very hypothesis of the thought experiment makes this question unaswerable. Yes, I agree--my point was just that a reasonable theory of consciousness should not tell you that one is the real continuation while the other's memories are false. The reason this is worth pointing out is that before the splitting, the original can talk about the probability that he will become one copy or the other, and usually the notion of probability involves mutually exclusive alternatives...so the point about splitting both ways was just to avoid giving the wrong impression. Jesse Mazer _ Get your FREE download of MSN Explorer at http://explorer.msn.com
Re: on formally describable universes and measures
Asking Juergen if the first person should take delays of reconstitution into account when evaluating first person self-undeterminacy, he wrote: No, I do not. I suggest you first define a formal framework for measuring delays etc. Then we can continue. You should have told me this at the preceeding step which was also informal (although precise). I am proposing a thought experiment which is a kind of reductio ad absurdo here (remember that time and space will disappear at the end of the reasoning). My feeling is that, for some unknow reason you have decided to elude the reasoning. That seems clear with your answer to Russell Standish: you are saying 2+2=4 and I am saying 2+2=5! You are saying that I am fully wrong, but you don't tell me where. How am I suppose to take your disagrement here. You don't really answer the question. What does your theory predict with respect to the following experience: You are scanned read and annihilate at Amsterdam. I reconstitute you in Washington tomorrow, and at Moscow in one billion years. Are your expectations different from the situation where the two reconstitutions are simultaneous. If you want to be formal, let us accept classical Newtonian mechanics for the sake of the argument. You know that with comp such experience are possible *in principle*, and that is all what we need for the reasoning. Should we or should we not take these delays into account when evaluating the first-person indeterminacy? What does your theory say? What do you say? (Remark: it is a practical question for anyone ready to say yes to a surgeon proposing them an artificial brain. Those who accepts the answer given by Robert Nozick (which says that after the duplication we survive in the closer continuer(*)) could as well not care if a copy of their brain exists. The others will say yes to the doctor, but will insists no copies of the brain will be available. There is nothing vague here.) Bruno (*) Rober Nozick, Philosophical Explanations, Oxford Clarendon Press 1981.
Re: on formally describable universes and measures
From Russell Standish Thu Feb 8 23:52:51 2001 Guys, I'm getting great enjoyment out of the titanic battle between Juergen and Bruno over the meaning of the UD. I'm learning a lot from Battle? The case is clear. You cannot battle over whether 2+2 equals 4 or 5. the exchange, however, I must admit I do see Bruno's point of view. His UD does seem to generate the reals (or equivalently the set of all infinite binary strings) in countable time. However, I know Even Bruno admits this is not true. Thus his NONalgorithmic arithmetic realism. that infinity (like probability) is a nasty concept, that can easily trip you up. It's easy: just don't confuse the countable set of all finite beginnings of the reals with the uncountable set of all reals, which does not exist from an algorithmic or constructive point of view. There other ways of approaching this - for instance a finite set of axioms, when enumerated into theorems will tell us all that can be known about the real numbers. I cut and paste from the thread Algorithmic TOEs vs Nonalgorithmic TOEs: Loewenheim-Skolem implies that any first order theory with an uncountable model such as the real numbers also has a countable model. None of the countably many theorems concerning the real numbers depends on the continuum, whatever that may be. Our vague ideas of the continuum are just that: vague ideas without formal anchor. I have sympathy for one point of Juergen's though - in the space of descriptions (which we should agree by extension of logical positivism is all that can be discussed), computable descriptions must have higher measure than noncomputable ones. However, it seems to me that a random oracle is an essential component of consciousness and free will - why this is so I can only guess - and so the anthropic principle constrains the interesting universe to having these. It could be that this random oracle is simply a consequence of 1st person indeterminism that arises through the duplicability assumption, as Bruno points out, but then why should duplicability be necessary? There is no evidence whatsoever that we need a random oracle.
Re: on formally describable universes and measures
[EMAIL PROTECTED] wrote: I have sympathy for one point of Juergen's though - in the space of descriptions (which we should agree by extension of logical positivism is all that can be discussed), computable descriptions must have higher measure than noncomputable ones. However, it seems to me that a random oracle is an essential component of consciousness and free will - why this is so I can only guess - and so the anthropic principle constrains the interesting universe to having these. It could be that this random oracle is simply a consequence of 1st person indeterminism that arises through the duplicability assumption, as Bruno points out, but then why should duplicability be necessary? There is no evidence whatsoever that we need a random oracle. I have posted a number of times on this subject, and from experience, I doubt I could convince you, even with a large reply. However, I consider both the phenomna of free will, and quantum mechanics to be evidence of a random oracle at play. Note - I use the word _evidence_ advisedly - its not proof. It is possible to explain away these phenomena by more straightforward mechanistic means, however, all these explanations I've seen to date have been thin and unconvincing. Incidently, whether UD* (output of the UD) is countable or uncountable is irrelevant for whether observers see random values in their histories or not, since at any point in time, their histories are finite. However, the measure issue is important, as computable histories have higher measure than ones that are only partially computable. Therefore, if there are random oracles in nature, there must be a good anthropic reason why they're there. Cheers Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967 UNSW SYDNEY 2052 Fax 9385 6965 Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks
Re: on formally describable universes and measures
Hi Juergen, With (classical) comp it exists a level such that we survive a Washington-Moscou self-duplication where the reconstitution are made at that level (WM). (Later I will prove that no machine can ever know its correct levels of substitution, but still a machine could guess one correctly, and that is all we need in the reasoning). Here is the precise question I promise. We agree that in the WM self-duplication experiment there is an uncertainty about where I will find myself after it has been done. This does not mean we have chosen the uniform distribution (P(W) = P(M) = 1/2)) to modelise this uncertainty. Now suppose that at Moscow we delaye the reconstitution. Do you agree it cannot change the distribution of uncertainty? That is: whatever ways you choose to modelize the first-person uncertainty in self-multiplication experience/experiment, comp entails it must remain invariant with respect to arbitrary delays introduced in the reconstitutions. We don't know the distribution. But we know it is invariant for the addition of delays. Do you agree ? Bruno PS 1) Of course I know that you do not accept COMP, which includes a minimal amount of arithmetical realism. That is not a problem because I don't ask people to believe in COMP, just to believe that my thesis shows that COMP entails the REVERSAL. Too bad: you will miss both the solution of the mind-body problem *and* the origin of the physical laws. Note that I am used to people abandoning COMP when they begin to understand the reversal. 2) It does not mean I believe your are consistent. This is because if you believe there is a great programmer I can prove to you the existence of uncomputable functions, which you should'nt accept with your constructive move. I guess you know that there is no Universal Machines computing all and only the total (or those with recursive domain) computable functions. Another exemple: you cannot use Lowenheim-Skolem theorem, like in your last post, for your constructive purpose, 'cause the Lowenheim -Skolem theorem does not admit constructive proof (and necessarily so according to a result by McNeil and Tennant). But the biggest problem for a constructive philosopher is the other mind problem. A constructivist cannot really believe in another person, still less understand the 1/3-person differences. A constructivist approach of the mind-body problem leads necessarily toward solipsism.
Re: on formally describable universes and measures
George Levy wrote: --97E70CB715203FAEFF2A2345 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit I said: First person observation of consciousness is the self observing the self, or possibly part of the self observing other parts of the self. Let me add to this previous post the following, which is relevant in the context of the MWI. Any object can be viewed from the first person or from the third person perspective. Let me explain. If the object does not exert any contingency on the existence of the observer, then the first and third person perspectives coincide. Yes - except in this case 3rd person means can be agreed upon by all other human observers. There is quite possibly no absolute 3rd person position that all observers can agree upon. Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967 UNSW SYDNEY 2052 Fax 9385 6965 Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks
Re: on formally describable universes and measures
Guys, I'm getting great enjoyment out of the titanic battle between Juergen and Bruno over the meaning of the UD. I'm learning a lot from the exchange, however, I must admit I do see Bruno's point of view. His UD does seem to generate the reals (or equivalently the set of all infinite binary strings) in countable time. However, I know that infinity (like probability) is a nasty concept, that can easily trip you up. There other ways of approaching this - for instance a finite set of axioms, when enumerated into theorems will tell us all that can be known about the real numbers. I have sympathy for one point of Juergen's though - in the space of descriptions (which we should agree by extension of logical positivism is all that can be discussed), computable descriptions must have higher measure than noncomputable ones. However, it seems to me that a random oracle is an essential component of consciousness and free will - why this is so I can only guess - and so the anthropic principle constrains the interesting universe to having these. It could be that this random oracle is simply a consequence of 1st person indeterminism that arises through the duplicability assumption, as Bruno points out, but then why should duplicability be necessary? Cheers Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967 UNSW SYDNEY 2052 Fax 9385 6965 Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks
Re: on formally describable universes and measures
Thanks to Bruno, I am experiencing a kind of nomenclatorial fusion with Gilles Henri. I have become Gille Levy. I wonder who George Henri is. :-) George Levy Marchal wrote: Jesse Mazer wrote: Are you saying that you support the 2/3 view, meaning that the probability of my next moment depends on a kind of integral over all possible future histories? Yes. I am less sure than Gille Levy for the precise computation of the probability, but I am sure (with the comp hyp.) that my next moment depends on a kind of integral over all possible histories. Bruno As Gilles Levy pointed out the efficiency of the UD is not relevant, for the sharing space-time emerges from the statistics of the whole set of finite and infinite computationnal histories, from the first person point of view or first person plural point of view in the case of bifurcation of deep computational histories shared by many. Bruno
Re: on formally describable universes and measures
Jesse Mazer wrote: Are you saying that you support the 2/3 view, meaning that the probability of my next moment depends on a kind of integral over all possible future histories? Yes. I am less sure than Gille Levy for the precise computation of the probability, but I am sure (with the comp hyp.) that my next moment depends on a kind of integral over all possible histories. Bruno http://iridia.ulb.ac.be/~marchal
Re: on formally describable universes and measures
George Levy wrote (in the everything list): Excellent, Bruno. Thank you for the explanation of computational indeterminacy for the first person point of view. Thanks. Most of the disagreement here originates from the failure of some participants to appreciate the distinction bewteen first vs third person perspectives. Yes. I hope Juergen will understand the distinction or at least, like Jacques Mallah, explicitely tell us he does not make that distinction. James Higgo even manages to see it both ways without being explicit about the facts that perspectives can be relative. He says All that exists of 'you' is this very present thought, he is right from the first person perspective.. His earlier comment Consciousness - a flow of related thoughts in time - does not exist, any more than time itself exists, I believe, attempts to address the issue of consciousness from the third person perspective. He comes to the obvious conclusion that first person consciousness as seen from the third person does not exist. His lacks of awareness of the relativity of these issue leads to confusion. Yes. I guess James is aware of that, and that is why he makes poems most of the time. This is the correct move from a computationalist point of view. This confirm a post by Anna M* in the FOR Deutsch List. (And that is why I send the post also to the FOR-LIST). Anna M* wrote That's what art is for and always has been even if not viewed as such. Art is just another information tool which allows for objectivization of a subjective reality. I would insist it is only partial objectivization. But, with the notable exception of the pure finitist part of mathematics (where you can completely communicate statements like 17 is prime or 42 is not the double of 24) the objectivization, even in math, is partial. Logical theorem like Lowenheim Skolem, or godel's incompleteness objectivizes that partialness. [...] In addition to the distinction between first and third person points of views, I do agree with Russell Standish and his quotes from Stanislas Dehaenne that there can be several kinds of consciousness. It can vary qualitatively depending on what mental processes are involved. Sure. And most interesting altered states of consciousness can be observed in dreams, which I take, like many others---from Descartes to Tibetan buddhist---as *the* royal road for metaphysical studies. But dreams are not necessary today. Video-games, imagination and math seems to be enough ... Cautious use of drugs can help too. Contemplation of the sky also. Bruno PS I apologize for merging the two discussion lists again, but these parallel realities do interfere, you know :-)
Re: on formally describable universes and measures
Juergen wrote:
Your vague answers to questions I did not ask keep evading the issue of
continuum vs computability in the limit. I give up. JS
Let us try to be very precise, then. I propose you the iterated
self-duplication experience.
Assuming computationalism, we survive. (I guess you agree).
Here is the question. Do you expect the (infinite) sequence in {W,M}*
appearing on your t-shirt to be
computable or uncomputable ?
In case you want to restrict to the finite sequences appearing at each
step,
I propose then we stop the experience after 1000 steps. In that experience
do you expect the sequence of W and M (lenght = 1000) to be
compressible or not compressible ?
Bruno
Re: on formally describable universes and measures
Your vague answers to questions I did not ask keep evading the issue of continuum vs computability in the limit. I give up. JS
Re: on formally describable universes and measures
Saibal wrote: Bruno wrote: ''The probabilities are defined on infinite (continuous) set of infinite histories.'' Isn't this in conflict with measure theory, because one would expect that some sets would be non-measurable? No problem a priori, because the whole set can have some measure although some subsets are not measurable. So the situation is a priori similar to what happens with the reals. Nevertheless I have just show that we must *isolate* a measure from computability and provability theory (to solve the problem of the origin of the physical law in the comp setting). And the only technical steps I've done in that direction are rather modest (the isolation of the Z logics). Those logics gives us just a hope for a gleason theorem in the computationalist realm. Anyway, the fact that some subset of the set of all histories are non measurable is not relevant. Existence or non existence of measurable sets can also depends on choice or determinacy axioms. But this ultimately depends on the Z (and Z*) logics. This would be premature. Bruno
Re: on formally describable universes and measures
On Thu Jan 18 Bruno Marchal replied: Pi is enumerable. Most reals are not. Most of the dummy data is much less likely than extraordinary data (such as Pi), if the dummy data probability is approximable by a computer. Compare Algorithmic Theories of Everything: http://www.idsia.ch/~juergen/toesv2/node23.html A program which generates all the reals is shorter than a program which generates Pi, which is itself shorter than a program which generates a particular real (for most particular reals). Perhaps you confuse program generating reals and programs generating *set* of reals. I certainly do not. There is no program generating the uncountable set of all reals. There only is a program generating countably many prefixes of reals. How to distinguish those from the countably many prefixes of the countable rational numbers? Instead of giving examples, could you just provide a short proof of your claim that there is no computable universe to which we belong? Tell me what you don't understand in my UDA post (which is the beginning of the shortest proof I know). UDA is at http://www.escribe.com/science/theory/m1726.html I did look at it and found lots of words but no formal proof, although it does say QED at some point. You are repeatedly talking about universes generated by a dovetailer. All these universes obviously must be computable, otherwise the dovetailer could not compute them. So how can you claim that there is no computable universe to which we belong, when the very tool you are using generates lots of universes to which we belong? It does not make sense to me - my best guess is that you mean something quite different from what you say. Maybe you just want to say we do not know in which of the many possible computable futures we will end, but this is obvious and precisely the reason why we need to look at the possible probability distributions on possible future histories, to make nontrivial predictions, e.g.: http://www.idsia.ch/~juergen/everything/node4.html (1997) http://www.idsia.ch/~juergen/toesv2/node15.html (2000) Let 3-you be your current computational state and 1-you your actual awareness. What happens is that 3-you belongs to an infinity of computational histories (generated by the UD) and the UDA shows that your expected futur 1-you is undetermined and that the domain of indeterminacy is given by that set of computational histories. So we belongs to an infinity (a continuum) of infinite computational histories. No continuum! The infinite computational histories are countable. The continuum is not. The concepts of dovetailing and continuum are incompatible. The dovetailer will compute many histories featuring a Bruno or two, but only countably many. No continuum! PS I am rather buzy, so I am sorry if I am to short or if I take time for answering. Don't hesitate to make any remarks, though. You are not too short as long as your legs reach the ground :-) Juergen
Re: on formally describable universes and measures
Juergen wrote: [...] Pi is enumerable. Most reals are not. Most of the dummy data is much less likely than extraordinary data (such as Pi), if the dummy data probability is approximable by a computer. Compare Algorithmic Theories of Everything: http://www.idsia.ch/~juergen/toesv2/node23.html A program which generates all the reals is shorter than a program which generates Pi, which is itself shorter than a program which generates a particular real (for most particular reals). Perhaps you confuse program generating reals and programs generating *set* of reals. Instead of giving examples, could you just provide a short proof of your claim that there is no computable universe to which we belong? Tell me what you don't understand in my UDA post (which is the beginning of the shortest proof I know). UDA is at http://www.escribe.com/science/theory/m1726.html Let 3-you be your current computational state and 1-you your actual awareness. What happens is that 3-you belongs to an infinity of computational histories (generated by the UD) and the UDA shows that your expected futur 1-you is undetermined and that the domain of indeterminacy is given by that set of computational histories. So we belongs to an infinity (a continuum) of infinite computational histories. (Remember that from our personal 1-point of view we are not aware of the number of steps the UD makes for generating our 3-states). There is no reason to associate a universe neither to a computational history nor to the set of all computational histories. The physical predicate (time space temperature ...) emerges from some sum or averaging on all histories. For me it is not even clear how to make sense of the word universe in the computationalist frame. Bruno PS I am rather buzy, so I am sorry if I am to short or if I take time for answering. Don't hesitate to make any remarks, though.
Re: on formally describable universes and measures
On Thu Dec 28 05:19:13 2000 Wei Dai wrote: Even within classic models of computation, there seem to be significant variations in speed. As far as I can tell from my theory of computation book, moving from a multi-tape TM to a single-tape TM can cause a squaring of running time for some problems, which would translate to a squaring of the speed prior for some strings. So a similar question is, how do you pick which classic TM to base S on? Juergen answered: Good point. Simulating a k-tape TM on a 1-tape TM may cause a quadratic slowdown indeed. Simulating a k-tape TM on a 2-tape TM, however, causes at most logarithmic slowdown. One should use a TM with several work tapes. Talking about optimizing the universal Turing machine is completely ridiculous and pointless. It could be blindingly fast or slow as molasses. Since perceived time is relative to the observer it would not make a bit of difference. And BTW I do believe that engineering will drive philosophy by making quantum computers work. George
Re: on formally describable universes and measures
On Wed, Dec 27, 2000 at 04:50:42PM +0100, [EMAIL PROTECTED] wrote: None of the quantum effects we observe forces us to give up the simple idea that our universe can be simulated on a classic TM, just like there is no evidence that forces us to assume the existence of complex and incomputable things such as uncountable sets. I think we understand each other sufficiently on the other issues, so I'll only follow up on this one. I agree that our universe can be simulated on a classic TM. What I don't agree with is that our universe can be simulated quickly on a classic TM, which is what a speed prior based on a classic TM would predict. In other words, the speed prior predicts that we will never observe any quantum effects that can't be simulated quickly on a classic TM. I suggest that you talk about this prediction more explicitly in your paper since it would have major consequences. Many people are busy trying to build quantum computers, which would be a waste of effort if this prediction is correct. Even within classic models of computation, there seem to be significant variations in speed. As far as I can tell from my theory of computation book, moving from a multi-tape TM to a single-tape TM can cause a squaring of running time for some problems, which would translate to a squaring of the speed prior for some strings. So a similar question is, how do you pick which classic TM to base S on?
