### 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

### 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

### Re: on formally describable universes and measures

Stephen Paul King wrote: ...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:

### 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

### 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

### 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

### Re: on formally describable universes and measures

George Levy wrote: Saibal wrote: George Levy wrote: Even with the null set I have my doubt. Why not use the Not(null set) . which is the plenitude eh??? :-) How do you avoid Russel's paradox? The Plenitude is not a set so strictly speaking the operation Not(null set)

### 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

### 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

### 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]

### 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

### 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

### 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

### Re: on formally describable universes and measures

: 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

### 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

### 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

### 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

### 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

### 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

### 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

### Re: on formally describable universes and measures

Brent Meeker wrote: On 03-Mar-01, George Levy wrote: ... 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

### 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

### Re: on formally describable universes and measures

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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### Re: on formally describable universes and measures

[EMAIL PROTECTED] to hpm [re. the existence of non-computable real-valued observers] 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 [Re. Dubito ergo cogito] Many things are doubtful. 2+2=4 isn't. There you go again.

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### Re: on formally describable universes and measures

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

### 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'

### 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

### 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:

### 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

### 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

### 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%

### Re: on formally describable universes and measures

Marchal wrote: 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

### 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

### 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,

### 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

### 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

### 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.

### 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

### 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

### 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

### 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

### 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

### 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

### 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:

### 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

### Re: on formally describable universes and measures

From: George Levy, Wed, 3 Jan 2001 13:16:37 Talking about optimizing the universal Turing machine is completely ridiculous and pointless. It could be blindingly fast or slow as molasses. The point of optimizing it is precisely to build the theoretically fastest computer C. The results in

### 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,

### 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

### Re: on formally describable universes and measures

On Wed, Dec 20, 2000 at 04:32:47PM +0100, [EMAIL PROTECTED] wrote: It's all in Section 6. Please read 6.1 to get the basic idea, read 6.2 to understand why Levin Search and FAST are optimal. FAST computes the n-th bit of each universe x as quickly as the fastest algorithm for x (save for a

### Re: on formally describable universes and measures

I just got around to reading Schmidhuber's new paper, and noticed there is something strange about the Speed Prior S. With all of the candidate priors we have seen so far, the probability of a random (incompressible) string of length n is about 2^-n. But with the Speed Prior S, the probability is