Re: Simulating the Schrödinger Equation
Therefore from the first person's perspective the laws of quantum mechanics are violated. [Saibal] This paper (below)might be relevant. -s. "Whose Knowledge?" - N. David Mermin Sir Rudolph Peierls, in a reply to John Bell's last critique of the state of our understanding of quantum mechanics, maintained that it is easy to give an acceptable account of the physical significance of the quantum theory. The key is to recognize that all the density matrix characterizing a physical system ever represents is knowledge about that system. In answer to Bell's implicit rejoinder "Whose knowledge?" Peierls offered two simple consistency conditions that must be satisfied by density matrices that convey the knowledge different people might have about one and the same physical system: their density matrices must commute and must have a non-zero product. I describe a simple counterexample to his first condition, but show that his second condition, which holds trivially if the first does, continues to be valid in its absence. It is an open question whether any other conditions must be imposed. http://arxiv.org/abs/quant-ph/0107151
Re: Predictions duplications
From: [EMAIL PROTECTED]: [EMAIL PROTECTED] wrote: From [EMAIL PROTECTED]: [EMAIL PROTECTED] wrote: M measure: M(empty string)=1 M(x) = M(x0)+M(x1) nonnegative for all finite x. This sounds more like a probability distribution than a measure. In the set of all descriptions, we only consider infinite length bitstrings. Finite length bitstrings are not members. However, we can identify finite length bitstrings with subsets of descriptions. The empty string corresponds to the full set of all descriptions, so the first line M(empty string)=1 implies that the measure is normalisable (ie a probability distribution). Please check out definitions of measure and distribution! Normalisability is not the critical issue. Clearly: Sum_x M(x) is infinite. So M is not a probability distribution. M(x) is just measure of all strings starting with x: M(x) = M(x0)+M(x1) = M(x00)+M(x01)+M(x10)+M(x11) = For a measure to be normalisable, the sum over a *disjoint* set of subsets must be finite. If the set of subsets is not disjoint (ie the intersection are not empty) then the sum may well be infinite. Bringing this to the case of finite strings. Each finite string is actually a subset of the set of infinite strings, each containing the same finite prefix. So the string 101010 is actually a subset of 10101 and so on. The Sum_x M(x), where I assume x ranges over all strings will of course be infinite. However, since the set of finite strings is not disjoint, this doesn't imply M(x) is unnormalisable. Now when you realise that every finite string x is a subset of the empty string, it becomes clear that M(x) is normalised to precisely 1. The point is: prob dists and measures are different things. There is a good reason for giving them different names. Prob dists assign numbers to individual objects, not to sets. Traditional definitions as well as those for semimeasures in http://www.idsia.ch/~juergen/toesv2/ Neglecting finite universes means loss of generality though. Hence measures mu(x) in the ATOE paper do not neglect finite x: mu(empty string)=1 mu(x) = P(x)+mu(x0)+mu(x1) (all nonnegative). And here P is a probability distribution indeed! P(x)0 possible only for x with finite description. The P(x)0 case above actually breaks the countably subadditive property, so mu(x) cannot be called a measure... I'm not entirely sure what you're getting at here. The set of computable universes includes the finite ones which we may not ignore. How do they contribute to the measure of all universes? For convenience introduce a third symbol $ besides 0 and 1. Now what is the measure of the set of all universes starting with 00110? It's the sum of the measure of the set of universes starting with 001101 and the measure of the set of universes starting with 001100 and the measure of the single universe 00110$ that stops right after 00110. Once there is a $ symbol there won't be another 0 or 1. So mu(x) = P(x)+mu(x0)+mu(x1). Our favorite example is the universal Turing machine with random inputs. For finite x: P(x) is the probability that the TM output is x and nothing but x. mu(x) is something different, namely, the so-called universal measure of all strings _starting_ with x. Again mu(x) = P(x)+mu(x0)+mu(x1). Juergen Schmidhuberhttp://www.idsia.ch/~juergen/
Re: ODP: Free will/consciousness/ineffability
Russell Standish wrote: As I am bound to paraphrase, Free Will is the ability to do somehthing completely stupid! Would you accept: Freedom is the right to deny 2 + 2 = 5. (cf. George Orwell torture scene in 1984) Free Will is the right to say 2 + 2 = 5 (cf. Russell Standish) ? Interpreting freely to deny 2 + 2 = 5 by -[]f ( f = FALSE or 0 = 1) and to say 2 + 2 = 5 by []f, you get through Orwell + Standish, this interpretation of Godel: Freedom makes Free Will consistent. (-[]f - []f) (Or the inconsistency of free will entails no freedom). I am guessing you give a good definition of free-will, at least for the non stupid (sound) machines. For the stupid one (those inconsistent really believing that 2 + 2 = 5 or some equivalent proposition) it is not clear if their stupid acts will bear any witness to free-will. Perhaps free will is the ability to do something we *bet* as being completely stupid, and freedom is the ability of *not* doing that completely stupid thing? when George Levy said Now let's look at observing free will in the self. Do we perceive ourselves to be indeterminate in our behavior? Absolutely sometimes. When the decision is clear then free will is really not an issue. Free will becomes important when the decision factors are close to being evenly split. In those cases, before a decision is made, there is no way to know what this decision will be unless one makes the decision. If someone asked you why did you choose this, you wouldn't be able to say. This is free will. I tend to disagree. When the decision factors are close to being evenly split, then I cannot choose and let the first circumstance choose for me. No need of free will. Following Russell I would say that free will could perhaps be the ability of choosing what seems to be the stupider choice, ... and freedom could perhaps be the ability to reject that stupider solution. I should think a little more about that. Bruno
RE: ODP: Free will/consciousness/ineffability
It seems unlikely that it could be otherwise. Presumably the impulse to make a decision has to originate from a lower level, assuming that consciousness is supported by layers of unconscious processing? However the decisions in question were to do with when to perform a simple action - pressing a key, or something similar. What about conscious decisions that are arrived at by evaluating evidence, weighing possibilities, etc? Presumably they are also supported by unconscious layers which know how to evaluate evidence etc... Surely the feeling of free will comes from us not being aware of these underlying processes. Charles -Original Message- From: Brent Meeker [mailto:[EMAIL PROTECTED]] Sent: Wednesday, 24 October 2001 9:34 a.m. To: rwas Cc: [EMAIL PROTECTED] Subject: Re: ODP: Free will/consciousness/ineffability Whatever free will is, it is very doubtful that it depends on consciousness. See Daniel Dennett's dicussion of the Grey Walter carousel experiment. This experiment shows (although there is a little ambiguity left) that free will decisions occure *before* on is conscious of them. Brent Meeker The freedom of the will consists in the fact that future actions cannot be known now. --- Ludwig Wittgenstein
Re: ODP: Free will/consciousness/ineffability
Pete Carlton wrote: Hi all, I've been lurking for months and am continually amazed by the discussions going on - I got into this list after branching out from philosophy of mind, after something like the GP/UDA (though completely lacking in rigor) had surfaced in a discussion I was in about artificial intelligence.. My interest in this channel has more to do with ai and synthetic consciousness as well. If you like, we could start our own thread. Robert W. _ Do You Yahoo!? Get your free @yahoo.com address at http://mail.yahoo.com
Re: Entropic Dynamics
Saibal Mitra, [EMAIL PROTECTED] A new article by Caticha: http://xxx.lanl.gov/abs/gr-qc/0109068 I explore the possibility that the laws of physics might be laws of inference rather than laws of nature. What sort of dynamics can one derive from well-established rules of inference? Specifically, I ask: Given relevant information codified in the initial and the final states, what trajectory is the system expected to follow? The answer follows from a principle of inference, the principle of maximum entropy, and not from a principle of physics. The entropic dynamics derived this way exhibits some remarkable formal similarities with other generally covariant theories such as general relativity. I agree that the laws of physics are related with inference. That paper seems interesting. I keep it until I get more time to read it. Thanks. (He used Fisher Information, and I have still some problems with it, no doubt those problems relie on my lack of understanding in statistics). Bruno
RE: ODP: Free will/consciousness/ineffabili
-Original Message- From: Brent Meeker [mailto:[EMAIL PROTECTED]] Sent: Wednesday, 24 October 2001 12:06 p.m. To: Charles Goodwin Cc: [EMAIL PROTECTED] Subject: RE: ODP: Free will/consciousness/ineffabili My intuition doesn't tell me whether or not I would have a 'feeling' of free will if I were aware of my subconscious decision processes; but it's pretty clear that I could be completely un-conscious and still behave with 'free will'; whatever it is. My suggestion is that it's lack of knowledge of these subconscious processes which gives you a feeling of free will. If you don't know what a feeling of free will means (hence the quotes?) I'd suggest it's the feeling that you reached a decision uninfluenced by anything external to yourself. However if you could follow all the subconscious processes (you couldn't of course, by definition your consciousness isn't aware of them) then you'd see that what felt like an 'uninfluenced' decision was actually the result of past numerous influences, which had caused your brain to have a particular configuration. Yes, presumably you *could* be unconscious and have free will, in the sense that your actions couldn't be predicted accurately by some other agent. (Try to swat a fly and you will see what I mean!) What if your subconscious decision processes became known to you *after* you had made your decision and 'felt' that free will. Would you feel something different then? I don't see what you mean. You'd probably feel different from how you felt when you made your decision whether you became aware of the subconscious processes or not. If you DID become aware of the s.p.s it could only be as the result of years of laboriously tracing through neural connections inside some map that someone made of your brain while you were making the decision. (And presumably more years of tracing through previous maps of your brain which showed how various events in the past caused it to be configured the way it was at the time, if you want a FULL understanding.) I'm not sure that you could ever become aware of all this in any realistic sense of the word. Perhaps a super-intelligent alien could apprehend the processes in your brain at a glance and see what was going on, and THEY would feel that your decision was an inevitable consequence of how your brain was configured, but YOU couldn't. Charles
Re: ODP: Free will/consciousness/ineffability
Interesting, although I suspect the interpretation of the ability to do somehthing completely stupid is more like asserting the truth of an unprovable statement than asserting the truth of a false statement. In modal logic, this would be (x -[]x ) n'est-ce pas? Note an automaton cannot assert the truth of anything not provable from its axioms... Cheers Marchal wrote: Russell Standish wrote: As I am bound to paraphrase, Free Will is the ability to do somehthing completely stupid! Would you accept: Freedom is the right to deny 2 + 2 = 5. (cf. George Orwell torture scene in 1984) Free Will is the right to say 2 + 2 = 5 (cf. Russell Standish) ? Interpreting freely to deny 2 + 2 = 5 by -[]f ( f = FALSE or 0 = 1) and to say 2 + 2 = 5 by []f, you get through Orwell + Standish, this interpretation of Godel: Freedom makes Free Will consistent. (-[]f - []f) (Or the inconsistency of free will entails no freedom). I am guessing you give a good definition of free-will, at least for the non stupid (sound) machines. For the stupid one (those inconsistent really believing that 2 + 2 = 5 or some equivalent proposition) it is not clear if their stupid acts will bear any witness to free-will. Perhaps free will is the ability to do something we *bet* as being completely stupid, and freedom is the ability of *not* doing that completely stupid thing? when George Levy said Now let's look at observing free will in the self. Do we perceive ourselves to be indeterminate in our behavior? Absolutely sometimes. When the decision is clear then free will is really not an issue. Free will becomes important when the decision factors are close to being evenly split. In those cases, before a decision is made, there is no way to know what this decision will be unless one makes the decision. If someone asked you why did you choose this, you wouldn't be able to say. This is free will. I tend to disagree. When the decision factors are close to being evenly split, then I cannot choose and let the first circumstance choose for me. No need of free will. Following Russell I would say that free will could perhaps be the ability of choosing what seems to be the stupider choice, ... and freedom could perhaps be the ability to reject that stupider solution. I should think a little more about that. Bruno Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile) UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 () Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02
