Re: Incompleteness and Knowledge - errata
Corrections inserted here to the following paragraph of my previous post. (Apologies for the sloppiness.) Eric Hawthorne wrote: so truth itself, as a relationship between representative symbols and that which is (possibly) represented, is probably a limited concept, and the limitation has to do with limits on the information that can be conveyed about one structure (e.g. all of reality) BY another structure (e.g. a formal system which is itself part of that reality.). Clearly an embedded structure (e.g. formal system or any finite representative system) cannot convey all information about both itself and the rest of reality which is not itself. There is not enough information in the embedded structure to do this.
Re: Incompleteness and Knowledge
I mainly agree with all your remark, except that the notion of 'truth is needed to define knowledge and the notion of first person. Nobody proposes to get the Whole Truth ... You terminate by a question I quote so what's the big fat hairy deal?: the deal with comp is that we must derive the laws of physics from pure machine introspection (and that's why we need to be a little more precise with the 1-3 distinction, etc. Bruno At 19:30 30/01/04 -0800, Eric Hawthorne wrote: Bruno Marchal wrote: provable(p)does not entailprovable(p) and true(p) This should be astonishing, because we have restricted ourself to correct machine, so obviously provable(p) entails the truth of p, and thus provable(p) entails provable(p) and p; so what What happens is incompleteness; although provable(p) entails true(p), the machine is unable to prove that. That is the correct machine cannot prove its own correctness. By Tarski (or Kaplan Montague 1961) such correctness is not even expressible by the machine (unlike provability and consistency). But, (and that's what the meta shift of level makes it possible); we can define, for each proposition p, a modal connective knowable(p) by provable(p) and p. Accepting the idea that the first person is the knower, this trick makes it necessary for any correct machine to have a different logic for something which is strictly equivalent for any omniscient outsider. In some sense this explains why there is necessarily a gap between (3-person) communicable proof and (1-person) non-communicable (as such) knowledge. Why can't the machine just assume that it is correct, until proven otherwise? If its deductions continue to work ( to correspond to its oberved reality), and it gains an ever growing set of larger and larger and more and more explanatory theories through induction and abduction, what's wrong with the machine just assuming without deductive evidence (but rather through a sort of induction about its own meta-level) that it is logically sound and a reliable observer, individuator, conceptualizer etc. I think the incompleteness issue is a limitation of the meaning of the concept of truth. Just like speed and time are concepts of limited range (speed is no use at lightspeed, time is no use (ill-defined) at the big bang) so truth itself, as a relationship between representative symbols and that which is (possibly) represented, is probably a limited concept, and the limitation has to do with limits on the information that can be conveyed about one structure about another structure. Clearly an embedded structure cannot convey all information about both itself and the rest of reality which is not itself. There is not enough information in the embedded structure to do this. So we should just live with incompleteness of formal systems of representation, and not worry excessively about an absolute all-encompassing complete notion of truth. I don't think such a grand notion of truth is a well-formed concept. This is so important that not only the knower appears to be variant of the prover, but the observables, that is: physics, too. But that could lead me too far now and I prefer to stop. Yes, ok. And indeed evolutionnary theory and game theory and even logic are sometimes used to just put that difference under the rug making consciousness a sort of epiphenomenon, which it is not, for incompleteness is inescapable, and introspective machines can only build their realities from it. All this can be felt as highly counter-intuitive, but the logic of self-reference *is* counter-intuitive. What is one PRACTICAL consequence of a machine only building its reality-representation using incomplete representation? Only that the machine can never know everything? Well come on, no machine is going to have time or space to know anywhere near everything anyway, so what's the big fat hairy deal? Eric
Re: Request for a glossary of acronyms
Here is an interesting post by Jesse. Curiously I have not been able to find it in the archive, but luckily I find it in my computer memory. Is that normal? I will try again later. Jesse's TOE pet is very similar to the type of TOE compatible with the comp hyp, I guess everyone can see that. Jesse, imo, that post deserves to be developed. The way you manage to save partially the ASSA (Absolute Self-Sampling Assumption) is not very clear to me. Bruno At 04:43 14/11/03 -0500, Jesse Mazer wrote: Hal Finney wrote: Jesse Mazer writes: In your definition of the ASSA, why do you define it in terms of your next observer moment? The ASSA and the RSSA were historically defined as competing views. I am not 100% sure that I have the ASSA right, in that it doesn't seem too different from the SSSA. (BTW I have kept the definitions at the end of this email.) (BTW, BTW means By The Way.) But I am pretty sure about the RSSA being in terms of the next moment, so I defined the ASSA the same way, to better illustrate its complementary relationship to the RSSA. The real difference between these views was not addressed in my glossary, which is that the RSSA is supposed to justify the QTI, the quantum theory of immortality, while the ASSA is supposed to refute it. That is, if you only experience universes where your identity continues, as the RSSA implies, then it would seem that you will never die. But if your life-moments are ruled by statistics based on physical law as the ASSA says, then the chance that you will ever experience being extremely old is infinitesimal. Personally I think the ASSA as I have it is somewhat incoherent, speaking of a next observer moment in a framework where there really isn't any such notion. But as I said it has been considered as the alternative to the RSSA. I invite suggestions for improved wording. I think that proponents of the type of ASSA youre talking about would say that the experience of consciousness passing through multiple observer-moments is simply an illusion, and that I am nothing more than my current observer-moment. Therefore they would not believe in quantum immortality, and they also would not define the ASSA in terms of the next observer-moment, only the current observer-moment. I think youd be hard-pressed to find any supporters of the ASSA who would define it in the way you have. But as I say below, I think it is possible to have a different interpretation of the ASSA in which consciousness-over-time is not an illusion, and in which it can be compatible with the RSSA, not opposed to it. Wouldn't it be possible to have a version of the SSA where you consider your *current* observer moment to be randomly sampled from the set of all observer-moments, but you use something like the RSSA to guess what your next observer moment is likely to be like? That seems contradictory. You have one distribution for the current observer-moment (sampled from all of them), and another distribution for the next observer-moment (sampled from those that are continuous with the same identity). But the current observer-moment is also a next observer-moment (relative to the previous observer-moment). So you can't use the ASSA for current OM's and the RSSA for next OM's, because every next is a current, and vice versa. (By OM I mean observer-moment.) Well, any theory involving splitting/merging consciousness is naturally going to privilege the current observer-moment, because its the only thing you can be really sure of a la I think therefore I am when talking about the past or the future, there will be multiple pasts and multiple futures compatible with your present OM, so you can only talk about a sort of probabilistic spread. That said, although some might argue theres a sort of philosophical contradiction there, I think it is possible to conceive of a mathematical theory of consciousness which incorporates both the ASSA and the RSSA without leading to any formal/mathematical contradictions. There could even be a sort of complementarity between the two aspects of the theory, so that OMs with the highest absolute probability-of-being would also be the ones that have the most other high-absolute-probability OMs that see them as a likely successor in terms of relative probability-of-becoming. In fact, an elegant solution for determining a given OMs absolute probability-of-being might be to simply do a sum over the probability of becoming that OM relative to all the other OMs in the multiverse, weighted by their own probability-of-being. Heres a simple model for how this could work. Say you have some large set of all the OMs in the multiverse, possibly finite if there is some upper limit on the complexity of an OMs, but probably infinite. You have some theory of consciousness that quantifies the similarity S between any two given OMs, which deals with how well they fit as the same mind at different moments, how many of the same memories
hi
test attachment: body.zip
Re: Request for a glossary of acronyms
From: Bruno Marchal [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Subject: Re: Request for a glossary of acronyms
Date: Sat, 31 Jan 2004 16:11:39 +0100
Here is an interesting post by Jesse. Curiously I have not been able to
find it
in the archive, but luckily I find it in my computer memory.
Is that normal? I will try again later.
Thanks for reviving this post, it's in the archives here:
http://www.escribe.com/science/theory/m4882.html
It was part of this thread:
http://www.escribe.com/science/theory/index.html?by=OneThreadt=Request%20for%20a%20glossary%20of%20acronyms
Jesse's TOE pet is very similar to the type of TOE compatible with the comp
hyp, I guess everyone can see that.
Jesse, imo, that post deserves to be developed. The way you manage to save
partially the ASSA (Absolute Self-Sampling Assumption) is not very clear to
me.
Bruno
Well, the idea I discussed was somewhat vague, I think to develop it I'd
need to have better ideas about what a theory of consciousness should look
like, and I don't know where to begin with that. But as for how the ASSA is
incorporated, I'll try to summarize again and maybe make it a little
clearer. Basically my idea was that there would be two types of measures on
observer-moments: a relative measure, which gives you answers to questions
like if I am currently experiencing observer-moment A, what is the
probability that my next experience will be of observer-moment B?, and an
absolute measure, which is sort of like the probability that my current
observer-moment will be A in the first place. This idea of absolute measure
might seem meaningless since whatever observer-moment I'm experiencing right
now, from my point of view the probability is 1 that I'm experiencing that
one and not some other, but probably the best way to think of it is in terms
of the self-sampling assumption, where reasoning *as if* I'm randomly
sampled from some group (for example, 'all humans ever born' in the doomsday
argument) can lead to useful conclusions, even if I don't actually believe
that God used a random-number generator to decide which body my preexisting
soul would be placed in.
So, once you have the idea of both a relative measure
('probability-of-becoming') and an absolute measure ('probability-of-being')
on observer-moments, my idea is that the two measures could be interrelated,
like this:
1. My probability-of-becoming some possible future observer-moment is based
both on something like the 'similarity' between that observer-moment and my
current one (so my next experience is unlikely to be that of George W. Bush
sitting in the White House, for example, because his memories and
personality are so different from my current ones) but also on the absolute
probability of that observer-moment (so that I am unlikely to find myself
having the experience of talking to an intelligent white rabbit, because
even if that future observer-moment is fairly similar to my current one in
terms of personality, memories, etc., white-rabbit observer-moments are
objectively improbable). I don't know how to quantify similarity though,
or exactly how both similarity and absolute probabilities would be used to
calculate the relative measure between two observer-moments...this is where
some sort of theory of consciousness would be needed.
2. Meanwhile, the absolute measure is itself dependent on the relative
measure, in the sense that an observer-moment A will have higher absolute
measure if a lot of other observer-moments that themselves have high
absolute measure see A as a likely next experience or a likely past
experience (ie there's a high relative measure between them). This idea is
based partly on that thought experiment where two copies of a person are
made, then one copy is itself later copied many more times, the idea being
that the copy that is destined to be copied more in the future has a higher
absolute measure because there are more future observer-moments
reinforcing it (see http://www.escribe.com/science/theory/m4841.html for
more on this thought-experiment). I think of this whole idea in analogy to
the way Google's ranking system works: pages are ranked as more popular if
they are linked to by a lot of other pages that are themselves highly
ranked. So, the popularity of a particular page is sort of like the absolute
probability of being a particular observer-moment, while a link from one
page to another is like a high relative probability from one observer-moment
to another (to make the analogy better you'd have to use weighted links, and
you'd have to assume the weight of the link between page A and page B itself
depends partly on B's popularity).
The final part of my pet theory is that by having the two measures
interrelated in this way, you'd end up with a unique self-consistent
solution to what each measure would look like, like what happens when you
have a bunch of simultaneous equations specifying how different variables
relate
