On Jun 6, 2011, at 7:09 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:

On 06 Jun 2011, at 08:19, Felix Hoenikker 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 existenceYou are confusing existence, and description of existence. This islike confusing "babel library" with universal dovetailing. PIcontains all encoding of computations, but does not computeanything, and does not possess the gigantic redundancy ofcomputations of the UD's activity, making the relative measure areal mathematical problem, making the comp theory testable.Note that instead of PI, you could have taken the natural numbers 0,1, 2, 3, ..., or the real number 0,12345678910111213141516... Thisone has the advantage that it is easy to prove that, like thenatural numbers, it goes through all descriptions of allcomputations (for PI it is an open problem, really). But this istrivial. You can't extract from this the "real" physical laws.Many people confuse a computation and a description of acomputation. I guess it is a subtle point.Now, if you take 0, 1, 2, 3, .... together with logic and the lawsof addition and multiplication, then, assuming we are digitalmachine, you can extract physics. Indeed, thanks to the Gödel splitting between true and provable, and through the distinction between 1-pov and 3-pov, you can even get both the laws of quanta and the laws of qualia, and their relations.Bruno

Bruno,

`How are provable and true related to first and third person`

`perspectives?`

With godel does the distinction not depend on the axiomatic system?

`Also what would a law of qualia look like? Something like "the being`

`whose brain computes X will experience Y"?`

Thanks, Jason

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: everything-list@googlegroups.com Subject: Re: Mathematical closure of consciousness and computationOn 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 showinghowcomputation 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 mathematicaltruth,any fixed set of axioms can at best approximate mathematicaltruth. Ifmathematical truth cannot be fully captured by a set of axioms,it mustexist outside sets of axioms altogether. [SPK]I see two possibilities. 1) Mathematical truth might onlyexist in ourminds. But an infinity of such minds is possible...2) Might it bepossiblethat our mathematical ideas are still too primitive andsimplistic to definethe 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 ofmath in thenatural 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 theexperiencecontained within our minds seems to follow a compressible set ofphysicallaws, and why mathematical objects seem to posses objectiveproperties butby definition lack reality.Those who say other universes do not exist are only addingbaseless entitiesto their theory, to define away that which is not observed. Itwas what ledto theories such as the Copenhagen Interpretation, whichpostulated collapseas a random selection of one possible outcome to be made real andcause therest to disappear. Similarly, there are string theorists whichhope to findsome mathematical reason why other possible solutions to stringtheory areinconsistent, and the one corresponding to the the standard modelis theonly one that exists. Why? They think this is necessary to maketheirtheory agree with observation, but when the very thing isunobservableaccording 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 himselfsplit,so, as mathematically attractive as Everett's theory was, hesaid, it couldnot be true. Everett replied in his letter to DeWitt that,hundreds of yearsago, after Copernicus had made his radical assertion that theEarth revolvedaround the sun instead of the reverse, his critics had complainedthat theycould not feel the Earth move, so how could it be true? RecallingEverett'sresponse to him decades later, in which he pointed out howNewtonian physicsrevealed why we don't feel the Earth move, DeWitt wrote, "All Icould saywas touché!"2) I don't know. Godel proved that any sufficiently complexaxiomaticsystem can prove that there are things that are true which itcannot prove.Only more powerful systems can prove the things which are notprovable inthose other axiomatic systems, but this creates an infinitehierarchy.Whether or not there is some ultimate top to it I don't know.But isn't that true of nearly anything? How many axiomaticsystems arethere?Likewise the statement: the Nth fibbinacci number is X.Has an objective truth for any integer N no matter how large.Let'ssayN=10 and X = 55. The truth of this depends on the recursivedefinitionofthe fibbinacci sequence, where future states depend on priorstates,and istherefore a kind if computation. Since N may be infinitelylarge, thenin asense this mathematical computation proceeds forever. Likewiseonemightsay that chaitin's constant = Y has some objective mathematicaltruth.Forchaintons constant to have an objective value, the execution ofallprograms must occur. Simple recursive relations can lead to exraordinary complexity, consider theuniverse of the Mandelbrot set implied by the simple relationZ(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 tovery complexoutput. 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 isrequired forminds. [SPK]Why are we sure that a “lower bound of information” or“complexity” isrequired? Seriously, there seems to be a bit of speculation fromtoo fewfacts when it comes to consciousness! **I should clarify, I don't know what the lower bound is or if thereis one.That said I do believe information and computation are importantlyrelatedto consciousness.Is it that these recursive relations cause our experience, orare justa way of thinking about our experience? Is it: Recursive relations cause thought. OR:Recursion is just a label that we apply to some of ourimplicationalbeliefs. The latter seems more plausible to me.Through recursion one can implement any form of computation.Recursion iscommon and easy to show in different mathematical formulas, whileshowing aTuring machine is more difficult. Many programs which can beeasily definedthrough recursion can also be implemented without recursion, so Iwas notimplying recursion is necessary for minds. For example,implementing theFibonacci 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 YThis program iteratively computes successive Fibonacci numbers,and willoutput the Nth Fibbonaci number. JasonThere 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 thatnumbersrequire 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 / 2I would agree that determining Pi from that definition probablydoes requirean eternal/infinite amount of computation though. Jason --You received this message because you are subscribed to the GoogleGroups"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. 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