On Sat, Oct 15, 2011 at 06:53:59PM +0200, Bruno Marchal wrote: > > On 15 Oct 2011, at 02:50, Russell Standish wrote: > > >On Fri, Oct 14, 2011 at 05:01:26PM +0200, Bruno Marchal wrote: > >> > >>On 13 Oct 2011, at 23:50, Russell Standish wrote: > >>>I don't see why Bayes' theorem assumes a physical universe. > >> > >> > >>Bayes' theorem does not assume a physical universe. But some use of > >>bayes theorem to justify the laws of physics, presuppose that a > >>physical universe is an object (may be mathematical, like in > >>Tegmark) among other objects. > > > >Then why couldn't the physical universe be a trace (aka history) > >of UD*? > > Because the UDA show it to be a sum of infinitely many computations. > Even 2^(aleph_0) due to the dovetailing of the real (and complex > ...) inputs of the program generated and executed by the UD. This > cannot be generated by any programs. It can only be lived or > inferred by the internal observers experimenting their golabl (on > UD*) first person indeterminacies. >

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Fair point. Let me rephrase: Why couldn't the physical universe be a set of computations, all giving rise to the same experienced history. > > > > >> > >> > >>>All it > >>>assumes is a prior probability distribution. Something like the > >>>universal prior of Solomonoff-Levin, or the distribution of observer > >>>moments within UD*. > >> > >>I don't think such a distribution makes sense. What makes sense is a > >>computational state, and a distribution of (competing) universal > >>machines relating that state with other states through the > >>computations that they emulate. > >> > > > >Whenever an observer interprets multiple different input strings (ie > >observations) as the same thing, the S-L distribution makes > >sense. Particularly so if the mapping process is a computation. > > I am not sure I understand this. > The S-L distribution is defined as the sum over all programs that halt and produce a given output (x say) of 2^{- length of program expressed as a bitstring}. We can replace the Turing machine with any function that takes bitstrings, and maps them to a countable set of meanings (which can be identified with N, obviously), provided the map is prefix free (ie if we read n bits, and decide the meaning is x, we cannot change our mind after reading n+m bits). > > > >The UDA indicates we must be supervenient on all programs passing > >through our current observer moment. > > It makes sense with OM = 3-OM = relative computational state. But > this is not Bostrom's OM a priori (provably with comp). > It seems we've been around the world on this one. There is only one OM concept, which is defined by the information content of the observer at a point in time. But there may be multiple programs instantiating a given observer, so there will in general be multiple machine states corresponding to a given OM. > > > >I know there are only a countable number of programs. Does this entail > >only a countable number of histories too? Or a continuum of histories? > >I did think the latter (and you seemed to agree), but I am partially > >influenced by the continuum of histories available in the "no > >information" ensemble (aka "Nothing"). > > It is a priori a continuum, due to the dovetailing on the infinite > real input on programs by the UD. > IIUC, the programs dovetailed by the UD do not take inputs. You expanded a bit on this in your response to Brent, but I don't follow, sorry. > > > > >Could it be that there are only a countable number of histories after > >all, given there are only a countable number of programs. That would > >be one big difference right there. > > We do agree on this. The difference is that the comp statistics is a > statistics on non-random things, even if those things include > computations (non random) with random inputs. > Are you agreeing there may only be a countable number of histories after all? Or something different :). I'm not sure what you mean by random inputs. Surely, if random inputs were applicable, then the histories will be random things. > >>Well, because UDA shows that the laws of physics are logico- > >>arithmetical, and that they take the form of internal > >>(epistemological) relative statistics on computation. > > > >I actually don't get that conclusion from your work, so it might be > >worth elaborating more. > > This already happens in the UDA step 7. We don't need the > immateriality or the 'arithmeticality'. Sorry - I think I minsinterpreted what you said previously... > >The Theatetus definition leading to the AUDA has the feel of something > >"put in by hand", rather than being a logical consequence of the > >UDA. Nothing wrong with that, of course, but we should be honest with > >it, if it is the case. > > I agree I am not always clear on that. That is why I try to > distinguish comp (used in UDA), and comp+theaetetus, used in AUDA. > But the theaetetus ca be shown to be the unique definition meeting > the requirement of computer science, provability logic, and the > usual definition of knowledge (Kp -> p, Kp -> KKp, > K(p->q)->(Kp->Kq)). It can be motivated, as it is by Socrates in the > Theaetetus of Plato, by the dream argument, which is basically step > 6 of UDA. > How would you define knowledge axiomatically, accepting that you > want it to apply to an entity (a machine) whose beliefs are > rational, in the sense of obeying classical logic on the finite > things? > As I said - I don't have an answer to that. I'm not an epistemologist. All I can say is that your axioms seem to treat knowledge as rather like how we might know a mathematical fact, rather than how we know a fact of chemistry, or a fact of human life. So it seems unsatisfactory to me. It could be that knowledge resists axiomatisation. It could be that a different set of axioms is more appropriate - eg incorporating ideas from evolutionary theory. WRT the latter, I would say that life, and also evolution has also resisted axiomatisation, in spite of a number of attempts. -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.