>Well, it is better to assume just the axiom of, say, Robinson >arithmetic. You assume 0, the successors, s(0), s(s(0)), etc. >You assume some laws, like s(x) = s(y) -> x = y, 0 ≠ s(x), the laws >of addition, and multiplication. Then the existence of the universal >machine and the UD follows as consequences.
Ok so the UD exists (platonically?) >Better not to conceive them as living in some place. "where" and >"when" are not arithmetical predicate. The UD exists like PI or the >square root of 2. >(Assuming CT of course, to pretend the "U" in the UD is really >universal, with respect to computability). Fine so the UD has an objective existence in spite of whatever else exists. >There is a "time order". The most basic one, after the successor law, >is the computational steps of a Universal Dovetailer. >Then you have a (different) time order for each individual >computations generated by the UD, like >phi_24 (7)^1, phi_24 (7)^2, phi_24 (7)^3, phi_24 (7)^4, ... >where "phi_i (j)^s" denotes the sth steps of the computation (by >the UD) of the ith programs on input j. If the UD was a concrete one like you ran then it would start to generate all programs and execute them all by one step etc. But are you saying that because the UD exists platonically all these programs and each of their steps exist also and hence, by the existence of a successor law they have an implicit time order? >Then there will be the time generated by first person learning and >which relies eventually on a statistical view on infinities of >computations. Is this because we are essentially constructs within these steps? >Time is not difficult. It is right in the successor axioms of >arithmetic. Here again you confirm the invocation of the successor axioms. Nick On Dec 28, 5:48 pm, Bruno Marchal <marc...@ulb.ac.be> wrote: > On 27 Dec 2009, at 18:13, Nick Prince wrote: > > > > > > > Ok so I have come up with an argument to try and convince myself of > > step 8 but it still has some catches to it. If anyone sees that I am > > using incorrect thinking at any time please correct me. > > Misunderstanding means bad foundations. > > > Up to step 7 all seems well and you begin step 8 by saying “but what > > if we don’t grant a concrete robust physical universe?” > > > Some people have attempted to suggest the possibility of a Universe > > which is sufficiently robust. For example in Frank Tipler “The > > physics of Immortality “ he explains how the universe could be > > utilised to act as a computational engine in order to generate > > consistent extensions of sentient beings. His claims have been > > heavily criticised, but I do think he has made a brave and ingenious > > try at explaining how a reductionist approach along with a belief in > > strong AI can yield interesting speculations. If he had written his > > book in a more modest and understated manner his ideas would have been > > much better received. Incidentally, the fact that, because the > > universe has been shown to be expanding at an accelerating rate does > > not invalidate his theory because there is currently no clear > > understanding of the nature of dark energy – for example it may be a > > decaying scalar field ( we understand theoretically this type of > > mechanism because it is one of the best candidate mechanisms for > > understanding the (temporary) inflation in the early universe. If it > > is like this, then re-collapse might provide the physics necessary for > > high computational capability. > > > But let’s suppose things are as you say and that the universe is not > > robust enough in any circumstances. > > Careful. If the universe contains a real UD, we don't need step 8 to > conclude that physics is derivable from computer science. I don't > assume that the universe is not robust enough, I was just considering > that move as an objection to the UDA seventh first steps. The 8th step > is an independent step showing that the physical supervenience thesis > is incoherent with the mechanist assumption. > > > I want to understand the assertion that platonic realism underpins my > > ist person reality. If I dispense with Schmidhuber’s great > > programmer > > (and his hardware) then rather than infinite regress, I assume there > > exists a platonic UD. > > Well, it is better to assume just the axiom of, say, Robinson > arithmetic. You assume 0, the successors, s(0), s(s(0)), etc. > You assume some laws, like s(x) = s(y) -> x = y, 0 ≠ s(x), the laws > of addition, and multiplication. Then the existence of the universal > machine and the UD follows as consequences. > I am not assuming more, with respect to math, than any mathematicians > (on the contrary, given that the ontology is provided by a tiny part > of arithmetic). Platonism or realism means here that we explicitly > allow non constructive proof of existence, that is we allow the > excluded-middle principle: we accept the idea that a closed > arithmetical sentences is either true, or false. > > > Now, since (I also assume) platonic reality is > > somehow timeless, > > You don't have to assume arithmetic is timeless! To do that you have > to first assume there is a time, and then say that arithmetic is true > at all the times. But arithmetical proposition, by definition or > construction are not conceive as being time dependent, at the start. > Theories of time will on the contrary depend on the assumption of some > mathematical structures. > > > then the UD algorithm must surely exist in this > > timeless “place”. > > Better not to conceive them as living in some place. "where" and > "when" are not arithmetical predicate. The UD exists like PI or the > square root of 2. > (Assuming CT of course, to pretend the "U" in the UD is really > universal, with respect to computability). > > I have implemented and run a UD in 1991, for about six days. I mean, a > UD is a very concrete object. Here is the PDF of the code and example > of executions (but it is badly > commented):http://iridia.ulb.ac.be/~marchal/bxlthesis/Volume4CC/4%20GEN%20%26%20... > > > > > > > Now it gets interesting. I have assumed the > > algorithm is there too just like I assume that a perfect scalene > > triangle is in a more general platonia. However this triangle is made > > of perfect line segments combined together to make it - and in turn > > the segments were made up of a sum of ideal points (lets not go into > > details about the reals and integers at this stage). Clearly though > > the triangle does not have to be fully represented in this reality if > > everything can be made of points. As long as an algorithm exists in > > the platonic realm which enables lines and combinations of them to be > > combined as triangles. But such an algorithm would be made up of > > numbers anyway and hence it’s all numbers. Indeed the numbers > > hardly > > need to be grouped in an list as we are familiar with seeing programs > > in because ordering is hardly important. > > > Now I’ve almost convinced myself that I’m on the right track but > > then > > come the niggles. The static timeless platonic reality has to > > somehow generate my seemingly dynamic existence and we are back to the > > same problem. Where is the spotlight which shines on each platonic > > number in the right order to give the experience of succession? > > Russell’s theory of nothing idea springs to mind here. The > > arithmetical reality I am supposing underpins my existence has no > > meaning without the spotlight that some observer would have to give > > to it to make it feel like our existence feels (somehow intuition > > calls out for a sequential map from N to N with some notion of time/ > > order). Indeed there is also the idea of an “instruction set”. A > > jumble of bit strings make up a program but the physical hardware has > > to react to these numbers in a well defined way in order to know how > > to shuffle other numbers around. In other words the function mapping > > the numbers has to be represented in the platonic reality somehow and > > I am not sure it can be done with just more numbers. > > There is a "time order". The most basic one, after the successor law, > is the computational steps of a Universal Dovetailer. > Then you have a (different) time order for each individual > computations generated by the UD, like > > phi_24 (7)^1, phi_24 (7)^2, phi_24 (7)^3, phi_24 (7)^4, ... > > where "phi_i (j)^s" denotes the sth steps of the computation (by > the UD) of the ith programs on input j. > > Then there will be the time generated by first person learning and > which relies eventually on a statistical view on infinities of > computations. > > Time is not difficult. It is right in the successor axioms of > arithmetic. And all universal numbers reinvent it. What is most > intriguing is the appearance of time symmetry at the bottom. It is the > lack of appearance of time, in the physical world, which intrigues me > the most. If "nature" happens to be a bit too much symmetrical, it may > be bad news for comp. Subjective time may appear when you relate > "proof" and "truth", for technical reasons, and is not directly > related to any digital time, it is a first person continuum. > > We don't need an external spotlight, because we conceive time in the > indexical way, like personal identity. This is hardly new. I mean many > physicists, like Einstein, conceived that time could be an illusion. > Assuming comp I argue that the whole of physicalness is an indexical, > but the "we" is larger than usual: "we" = "the universal machines". > > It would be like you need a spotlight to be the one chosen in > Washington, but with comp we put a spotlight, in that sense to all > "reasonable" universal machine state, be it the one in Washington than > the one in Moscow, be it today, tomorrow, or yesterday. From the first > person point of view, it is always here and now. > > Best, > > Bruno > > > > > > > On Dec 25, 2:56 pm, Bruno Marchal <marc...@ulb.ac.be> wrote: > >> Hi Nick, hi Quentin, > > >> On 25 Dec 2009, at 04:13, Quentin Anciaux wrote: > > >> Nick Prince wrote > > >>>> I can understand that numbers and arithmetic operations (as well > >>>> as a > >>>> whole lot of other stuff) exist as some kind of objective reality > >>>> (called a platonic reality). These archetypal “things” are to > >>>> me > >>>> clearly discovered by us rather than invented. But that our > >>>> dynamic > >>>> world emerges somehow from this static ethereal repository seems > >>>> very > >>>> difficult to see. > > >> And Quentin commented: > > >>> Would it be easier if I said that all of this came from bouncing > >>> particle of matter (whatever that is) ? > > >> That is a good point, which I find rather convincing. To attribute > >> consciousness to arithmetical (static, ethereal) relations is not > >> more > >> intriguing than to attribute it to continuous particle 4D line > >> universe in any block universe conception. > > >> But remember the "Peter Jones" type of move. He understands comp as a > >> material form of comp. He posits that to be conscious, you need a > >> physical primary universe in which the computations are executed. Of > >> course this moves seems completely ad hoc. he has to invoke some > >> magic > >> in both mind and matter, which is already against the comp idea. But > >> unfortunately, with only the first seven steps, you can still believe > >> in such "ad hoc" theory. It is enough to believe that the seven steps > >> just show that we are living in a small primary physical universe > >> (small = not enough big to run the UD), and that is why the 8th step > >> is needed to prevent that type of move, and to conclude the proof. > > >> Nick Prince wrote > > >>> This must be difficult. How can any theory be interpreted without > >>> the > >>> formalisms or some model. > > >> Remember that logicians use the word "model" like the painters. The > >> model (the naked person) is the reality. The theory (the painting) is > >> the finite piece of crap trying > > ... > > read more »- Hide quoted text - > > - Show quoted text -- Hide quoted text - > > - Show quoted text -- Hide quoted text - > > - Show quoted text - -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. 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