On 13 March 2011 18:42, Bruno Marchal <[email protected]> wrote: Thanks Bruno - now I have a reference for when you use this terminology.
David > > On 13 Mar 2011, at 18:32, David Nyman wrote: > >> On 13 March 2011 17:26, Bruno Marchal <[email protected]> wrote: >> >>> But then, consciousness might be the 'mental' state of a universal number >>> when it believes in a reality. Science might begin when it questions that >>> reality, and consciousness might reappear as the unquestionable part of >>> that >>> reality. It can be related with a form of ignorance awareness. It can get >>> a >>> role of relative self-accelerator. >> >> Bruno, I'm not sure I understand what you mean by "relative >> self-accelerator" in the above. > > It is related to two other theorems of Gödel: > The completeness theorem > and the speed-up theorem. > > The completeness theorem says that a theory is consistent if and only if the > theory has a model (a mathematical structure) verifying (making true) its > propositions. Like the structure (N, + *) make true the sentence "1+8 = 9". > Let us call that a reality. > Consistent means that the theory does not prove the falsity. Modally ~Bf, or > equivalently Dt. You can read Dt, by completeness, as the existence of a > reality. (OK, I can add explanations if you ask) > > I define consciousness by believing in a reality. This is almost like BDt. > But by incompleteness BDt -> Bf, and for the correct machine, Bf -> f > (damned!). > > But the machine/theory can also just add the arithmetical form of Dt > (consistency) as a new axiom. It is a inferential process, and not only it > does not lead to inconsistency, but the speed-up theorem of Gödel (and a > similar for universal machine) is that such process can, shorten is some > quasi arbitrary way the length of the proofs. Likewise, Blum speed-up > theorem shows that universal machine (and weaker interesting sub-universal > one) can be sped up arbitrarily, except for finite number of exception (it > concerns the computation which are correct above some argument, that is > sufficiently big inputs). > > So, it is suggested that the belief in a reality speed-up your computational > power. This I think can be seen by introspection. If you drive a car, the > more you take seriously your local reality (the road, the other cars), the > more you can actually speed-up. If you don't believe in any reality, you > could as well stop your car, even in the middle of the drive-way. > > Such a theory would endow consciousness (self-consistency inference) to > self-moving entity, which will better anticipate the now moving environment > (from their perspective) by taking such environment including one self > seriously enough. > > I can speculate that consciousness might be the ultimate accelerator. The > reason why bodies move at all. That would make it a sort of fundamental > force. By Newton force are accelerator. But this *is* speculation, or > analogy. > >> . What is "accelerating" what? > > > A universal machine M accelerates (= diminishes the length of personal > computations) a universal machine M (itself) relatively to arithmetic, or to > some other universal machine U computing M. In that case the machine M > transforms itself into a new machine "M+consistent(M)", and the process can > continue in the constructive transfinite (and are known as autonomous > progressions). > They cannot reach arithmetical truth, but they can approach it, and in the > long term it is, from their points of view, self-accelerating. The logic of > the 8 hypostases remains invariant, despite their arithmetical > interpretation (the arithmetical B and thus D) evolves. > > The length of proof theorem of Gödel paper is in the book "The undecidable" > edited by Martin Davis (the comp bible!) > Torkel Franzen wrote a little chef d'oeuvre on the autonomous progressions: > "Inexhaustibility, A Non exhaustive treatment". > > Bruno > >> >>> >>> On 12 Mar 2011, at 18:18, Ismail Atalay wrote: [in the FOR list] >>> >>> So we should not be in a position to say "for the essence of >>> consciousness >>> to exist, this type of physical/mathematical features should be present >>> in >>> this universe". Physical/mathematical features are required for its >>> manifestation, implementation and realization. >>> >>> You might conceive that the manifestation, implementation and realization >>> are concept definable relatively to universal numbers which are numbers >>> coding universal partial computable function relatively to elementary >>> arithmetic. So a minimal amount of arithmetic is required indeed. >>> Universal >>> numbers exists, and their many interactions are already emulated, >>> atemporally, by the laws of addition and multiplication of non negative >>> integers. This makes things complex because Universal numbers reflect >>> each >>> other including themselves. >>> But then, consciousness might be the 'mental' state of a universal number >>> when it believes in a reality. Science might begin when it questions that >>> reality, and consciousness might reappear as the unquestionable part of >>> that >>> reality. It can be related with a form of ignorance awareness. It can get >>> a >>> role of relative self-accelerator. >>> I agree with you that free will is not an illusion, because that >>> ignorance >>> is real, and *that* awareness is correct (trivially so for the ideal >>> simple >>> machine I study). Choice is not an alternative. There is an entertaining >>> novel by Smullyan illustrating this in the book Mind's I. (*) >>> *A* non compatibilist notion of free will is correct, but it is the one >>> where non compatibilism is relative to the personal point of view of the >>> universal number, which cannot, indeed, entirely determinate itself, and >>> yet, in the usual computations, has to decide of some action, relatively >>> to >>> some other universal numbers in its neighborhood. >>> Universal numbers are driven by self-satisfaction, I think, but in each >>> universal numbers there are conflicts between lower self and higher self >>> satisfaction. >>> Higher self satisfaction is better in the long run, but opposes itself >>> with >>> short term lower self satisfaction, and free will comes from the fact >>> that >>> we can chose in between. Perhaps. I mean it is hard not to talk under >>> torture, a situation which usually maximizes the conflict between the >>> short >>> and long term satisfactions. >>> Bruno Marchal >>> (*) (edited by Dennet and Hofstadter, which is, BTW, an excellent >>> introduction to Digital Mechanism. Dennett come close to the first person >>> indeterminacy indeed) >>> http://iridia.ulb.ac.be/~marchal/ >>> >>> >>> -- >>> You received this message because you are subscribed to the Google Groups >>> "Everything List" group. >>> To post to this group, send email to [email protected]. >>> To unsubscribe from this group, send email to >>> [email protected]. >>> For more options, visit this group at >>> http://groups.google.com/group/everything-list?hl=en. >>> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To post to this group, send email to [email protected]. >> To unsubscribe from this group, send email to >> [email protected]. >> For more options, visit this group at >> http://groups.google.com/group/everything-list?hl=en. >> > > http://iridia.ulb.ac.be/~marchal/ > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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