I like this group, the people are razor sharp in here.... Bruno is too, nevertheless he gives me a headache.
even if he was right, I hope hes wrong. On Jun 5, 11:19 pm, 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. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.