Hi Stephen! -----Original Message----- From: Stephen Lin Sent: Monday, June 06, 2011 2:26 AM To: Everything List Subject: Re: Mathematical closure of consciousness and computation
Hi all, If you generalize this further, doesn't it imply that the universal dove tailer is all of existence, taking turns computing each other? So "you" and the "universe around you" take turns computing each other one step at time. In fact, that means, any two people in the world may actually be the "same" person, except taking steps computing each other one step at a time. So you and "I" might be exactly the same person, under some appropriate coordinate transformation! Food for thought. Stephen Lin ** [SPK] Indeed! But notice that this idea implies that each instance of a UD computation would have its own "time" (order of succession), which is a good idea since that would overcome the problem with a single global synchronization - which is disallowed with the non-existence of a single global computation of the whole of existence as Bruno explained in an earlier posting: From: Bruno Marchal Sent: Sunday, June 05, 2011 10:00 AM To: email@example.com Subject: Re: CUH => Quantum Gravity => MUH => God “We have a proof that (with computable = Turing emulable, and "I" = third person description of "I" at the correct substitution level): 1) If I am computable then the universe is not computable (UD Argument. It is *not* trivial). It is trivial that 2) If the universe is computable then I am computable. So if the universe is computable, the universe is not computable. That makes sense: it means that whatever I am, the universe is not computable. (p -> ~p) entails ~p May be you are not aware of the "1)" above. I explain very shortly. If I am computable, then my observable expectations are determined "here and now" by all computations executed by the UD, at any times, anywhere (even in "arithmetical platonia"), going through my current state. This makes my observable expectations, and thus physicalness in general, non Turing emulable, because it is a statistics on a complex infinite set of computations. This is what UDA is all about. Computationalist physics debunks computational physics, at least concerning the TOE (by which I mean a theory not eliminating consciousness and persons).” Notice that there are more than one computation that intersects any one given state of “being-in-the-world” thus multiple orders of succession, thus not just one global time. This also implies that. like Feynman's electron, we are all just different finite approximative versions of the Totality appearing to be interacting with each other via mutual simulations. The trick may be to find a local notion of a measure that would hold for each local finite approximation that would allow for the definition of an ultrafilter that, in turn, could be used to define a local Boolean algebra for each “observer” by extensionality. Local deformation of such algebras might manifest as gauge symmetry breaking generating the appearance of mass, charge, spin, etc. when we look at the effects on the topological dual of that algebra... Onward! Stephen Paul PS, its nice to have another Stephen on the List. :–) ** On Jun 6, 2:19 am, Felix Hoenikker <fhoenikk...@gmail.com> wrote: > Has anyone watched the movie "Contact", in which the structure of the > universe was encoded in the transcendental number Pi? What if > something like that is what is going on, and that's the answer to all > paradoxes? > > So the physical universe beings with "Pi" encoded in the Big Bang, > chaotically inflates, and eventually cools and contracts back to > itself until it is again, exactly the mathematical description of > "Pi". > > All consciousness is thus contain with Pi. > > But then, Pi is just like any other transcendental number! > > So all transcendental numbers contain all existence > > F.H. > > > > > > > > On Mon, Jun 6, 2011 at 12:57 AM, Jason Resch <jasonre...@gmail.com> wrote: > > > On Sat, Jun 4, 2011 at 3:12 PM, Stephen Paul King <stephe...@charter.net> > > wrote: > > >> Hi Jason, > > >> Very interesting reasoning! > > > Thank you. > > >> From: Jason Resch > >> Sent: Saturday, June 04, 2011 1:51 PM > >> To: firstname.lastname@example.org > >> Subject: Re: Mathematical closure of consciousness and computation > > >> On Sat, Jun 4, 2011 at 12:06 PM, Rex Allen <rexallen31...@gmail.com> > >> wrote: > > >>> On Sat, Jun 4, 2011 at 12:21 PM, Jason Resch <jasonre...@gmail.com> > >>> wrote: > >>> > One thing I thought of recently which is a good way of showing how > >>> > computation occurs due to the objective truth or falsehood of > >>> > mathematical > >>> > propositions is as follows: > > >>> > Most would agree that a statement such as "8 is composite" has an > >>> > eternal > >>> > objective truth. > > >>> Assuming certain of axioms and rules of inference, sure. > > >> Godel showed no single axiomatic system captures all mathematical truth, > >> any fixed set of axioms can at best approximate mathematical truth. If > >> mathematical truth cannot be fully captured by a set of axioms, it must > >> exist outside sets of axioms altogether. > > >> [SPK] > > >> I see two possibilities. 1) Mathematical truth might only exist in our > >> minds. But an infinity of such minds is possible...2) Might it be possible > >> that our mathematical ideas are still too primitive and simplistic to > >> define > >> the kind of set that is necessary? > >> ** > > > 1) More is answered by: > > A: "Math -> Matter -> Minds" (or as Bruno suggests "Math -> Minds -> > > Matter") than by > > B: "Matter -> Minds -> Math", or > > C: "Minds -> (Matter, Math)". > > Compared to "B", "A" explains the unreasonable effectiveness of math in the > > natural sciences, the apparent fine tuning of the universe (with the > > Anthropic Principle), and with computationalism explains QM. > > "C" has the least explanatory power, and we must wonder why the experience > > contained within our minds seems to follow a compressible set of physical > > laws, and why mathematical objects seem to posses objective properties but > > by definition lack reality. > > Those who say other universes do not exist are only adding baseless entities > > to their theory, to define away that which is not observed. It was what led > > to theories such as the Copenhagen Interpretation, which postulated collapse > > as a random selection of one possible outcome to be made real and cause the > > rest to disappear. Similarly, there are string theorists which hope to find > > some mathematical reason why other possible solutions to string theory are > > inconsistent, and the one corresponding to the the standard model is the > > only one that exists. Why? They think this is necessary to make their > > theory agree with observation, but when the very thing is unobservable > > according to the theory it is completely unnecessary. > > The situation is reminiscent of DeWitt and Everett: > > >> In his letter, DeWitt had claimed that he could not feel himself split, > >> so, as mathematically attractive as Everett's theory was, he said, it could > >> not be true. Everett replied in his letter to DeWitt that, hundreds of > >> years > >> ago, after Copernicus had made his radical assertion that the Earth > >> revolved > >> around the sun instead of the reverse, his critics had complained that they > >> could not feel the Earth move, so how could it be true? Recalling Everett's > >> response to him decades later, in which he pointed out how Newtonian > >> physics > >> revealed why we don't feel the Earth move, DeWitt wrote, "All I could say > >> was touché!" > > > 2) I don't know. Godel proved that any sufficiently complex axiomatic > > system can prove that there are things that are true which it cannot prove. > > Only more powerful systems can prove the things which are not provable in > > those other axiomatic systems, but this creates an infinite hierarchy. > > Whether or not there is some ultimate top to it I don't know. > > >>> But isn't that true of nearly anything? How many axiomatic systems are > >>> there? > > >>> > Likewise the statement: the Nth fibbinacci number is X. > >>> > Has an objective truth for any integer N no matter how large. Let's > >>> > say > >>> > N=10 and X = 55. The truth of this depends on the recursive definition > >>> > of > >>> > the fibbinacci sequence, where future states depend on prior states, > >>> > and is > >>> > therefore a kind if computation. Since N may be infinitely large, then > >>> > in a > >>> > sense this mathematical computation proceeds forever. Likewise one > >>> > might > >>> > say that chaitin's constant = Y has some objective mathematical truth. > >>> > For > >>> > chaintons constant to have an objective value, the execution of all > >>> > programs > >>> > must occur. > > >>> > Simple recursive relations can lead to exraordinary complexity, > >>> > consider the > >>> > universe of the Mandelbrot set implied by the simple relation Z(n+1)= > >>> > Z(n)^2 > >>> > + C. Other recursive formulae may result in the evolution of > >>> > structures > >>> > such as our universe or the computation of your mind. > > >> The fractal is just an example of a simple formula leading to very complex > >> output. The same is true for the UDA: > >> for i = 0 to inf: > >> for each j in set of programs: > >> execute single instruction of program j > >> add i to set of programs > >> That simple formula executes all programs. > > >>> Is extraordinary complexity required for the manifestation of "mind"? > >>> If so, why? > > >> I don't know what lower bound of information or complexity is required for > >> minds. > > >> [SPK] > >> Why are we sure that a “lower bound of information” or “complexity” is > >> required? Seriously, there seems to be a bit of speculation from too few > >> facts when it comes to consciousness! > >> ** > > > I should clarify, I don't know what the lower bound is or if there is one. > > That said I do believe information and computation are importantly related > > to consciousness. > > >>> Is it that these recursive relations cause our experience, or are just > >>> a way of thinking about our experience? > > >>> Is it: > > >>> Recursive relations cause thought. > > >>> OR: > > >>> Recursion is just a label that we apply to some of our implicational > >>> beliefs. > > >>> The latter seems more plausible to me. > > >> Through recursion one can implement any form of computation. Recursion is > >> common and easy to show in different mathematical formulas, while showing a > >> Turing machine is more difficult. Many programs which can be easily > >> defined > >> through recursion can also be implemented without recursion, so I was not > >> implying recursion is necessary for minds. For example, implementing the > >> Fibonacci formula iteratively would look like: > > >> Fib(N) > >> X = 1 > >> Y = 1 > >> for int i = 2 to N: > >> i = X + Y > >> X = Y > >> Y = i > >> print Y > > >> This program iteratively computes successive Fibonacci numbers, and will > >> output the Nth Fibbonaci number. > > >> Jason > > > There was a bug in that program, replace the last two "i"s with "j", > > otherwise it breaks out of the loop too early. :-) > > >> -- > > >> [SPK] > >> The existence of such Numbers could be a telltale sign that numbers > >> require an eternal computation to define them. > > > I'm not sure, I can define Pi without an infinite description or > > computation. Pi = circumference of a unit circle / 2 > > I would agree that determining Pi from that definition probably does require > > an eternal/infinite amount of computation though. > > Jason > > > -- > > You received this message because you are subscribed to the Google Groups > > "Everything List" group. > > To post to this group, send email to email@example.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. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to firstname.lastname@example.org. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. 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