Re: The Riemann Zeta Pythagorean TOE
Le 16-avr.-06, à 06:08, danny mayes a écrit : Could you expound on this a little more? Both the MWI through a wavy approach to numbers, and the point about primes are possibly new concepts to me. Or maybe you're talking about things I am familiar with in an unfamiliar way. I'm not sure... I guess you know Euler has found a sort of of direct relationship between the primes and the natural numbers. See my 29 mars post in this thread: http://groups.google.com/group/everything-list/browse_frm/thread/ 2a285967d769a5c0/747d84038129a26f#747d84038129a26f This gives Euler Zeta function, which is defined for s bigger than one. Riemann extended it in the complex plane, and you can already interpret the real and imaginary parts of (some transformation of zeta having the same zero) as linear combination of sinusoidal wavy functions (up to some logarithmic rescaling). More generally you can approximate typical arithmetical functions by sort of fourier transform (in a base build from the complex roots of unity). Voronin theorem says that zeta can approximate any analytical functions (verifying some conditions), and it is an open problem to know if zeta can approximate itself in this way. But apparently it has been shown that this problem is equivalent to Riemann hypothesis. Now if Voronin theorem can be applied on zeta itself, it gives to zeta, and then to the primes distribution through Euler, some self-referential abilities showing that the behavior of zeta on some vertical line in the Riemann strip could simulate some information preserving transformation of arbitrary solution of Schroedinger equation (I am not yet sure of that). The zero of zeta would correspond to a spectra related to some observation of a very complex quantum object, and with enough universality, it could describe a quantum computer, if not directly a sort of universal topological quantum field theory (a modular functor, I can give references later). This makes it possible to shift the MWI of the SWE to zeta's behavior on some vertical line. Empirically the zero seems to describe a quantum chaos with some classical regime which could mean that the primes could describe a selection function as well! No many-worlders ask for that, I know, but then numbers behave so strangely, that I am forced to recognize the plausibility of some bohmian interpretation of number theory, at this stage. Nothing rigorous here, to be sure. Logically, at first sight, zeta should not be universal but sub-universal, but that could be enough locally, from the first person points of views. This would also entails that zeta (and other function of the Dirichlet family) would have some amazing computational speeding up ability. I hope to be able to say more the day I will find and read the papers by Bohr (Harald, not Niels) and Bagchi referred in Wolfram's MathWorld: http://mathworld.wolfram.com/VoroninUniversalityTheorem.html For the non-mathematicians who are interested, Marc Geddes is right, the book 'Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics' (John Derbyshire) http://www.amazon.com/gp/product/0309085497/ is very readable and provides a good trade-off rigor/depth. Hope this helps a little bit, Bruno 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 everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Numbers
Le 13-avr.-06, à 15:37, 1Z a écrit : Your version of comp seems to be that an abstract algorithm In Plato's heaven can implement a mind, even though it isn't a process occurring over a span of time. Admitedly you seem to get there via the idea that minds can be transferred into processes running on material computers (which is what I regard as the standard version of computationalism), but you then decide that the matter and the process is redundant -- becaus the pereceived world of a computational mind would appear to be physical and temporal. But an computational mind can only have those -- or any -- perceptions if it can have consciousness in the first place. If matter and process are needed to make an algorithm conscious, as the standard version of computationalims tacitly assumes, they are NOT redundant ! Yes but I have shown that, once the comp hyp is taken seriously enough, then matter and process are not needed for consciousness; indeed everything communicable (quanta) and uncommunicable (qualia) about matter and process emerges from the relations between numbers. From a strict logical point of view you can still believe in comp and in (primitive, stuffy) matter and processes, but then you can prove that, if ever you are lucky enough to get there, the probability you stay there is null. You just cannot attach your consciousness or even just the results of your experiments, to any material world, so why introduce one? Of course you can decide that this is a so startling result that you don't need to read the proof, but then, what could I add? Are you willing to doubt the existence of stuffy stuff, or are you *sure* about it? Could you conceive you being wrong about that question? I know people believe in what they see since about 1500 years (since the end of (neo) platonism). Bruno 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 everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: The Riemann Zeta Pythagorean TOE
A couple of quick thoughts out loud. My previous thought on the possible connection between the OR/AND dual (along with addition/multiplication) and the Riemann Hypothesis might be extended by looking at the Riemann zeta function. Notice that the infinite series form of the zeta function's uses addition and the infinite product uses multiplication. Could it be that the zeta function somehow gives information on observer moments? (Or instead of the zeta function, maybe it would end up being something more general function like the Dirichlet-L series which appears in the generalized Riemann Hypothesis.) Suppose an observer moment is specified by s, or maybe the imaginary part of s. One possibility is something like this, heuristically: The zeta series could describe the 1st person pov, and the zeta product the 3rd person pov. For the 1st person pov, each term in the series, 1/n^s, could somehow correspond to the probability of having a particular next observer moment. Then the whole series describes the probability of (observer moment #1) OR (observer moment #2) OR... (ad infinitum?, with exclusive ORs). For the 3rd person pov, each term in the product, 1/(1-p(^-s)), could somehow correspond to the probabilities of NOT having a particular next observer moment. Then the whole product describes the probability of (NOT observer moment #1) AND (NOT observer moment #2) AND... (ad infinitum?, with somehow finally having a selection of ONE observer moment out of the infinite(?) possible next observer moments). The equating of the series and product forms is analogous to a deMorgan's law (however with an exclusive OR and the ANDing of one affirmative selected observer moment). A possible variation on this starts with the observation that the zeros of the Riemann zeta function lie in 0 Re(s) 1 and are symmetrical about the critical line, Re(s) = 1/2. Could it be that the real part of s corresponds to the probability of a next observer moment given a current observer moment specified by the imaginary part of s? The zeros of the Riemann zeta function could somehow describe the 1st person indeterminacy, with the Riemann Hypothesis corresponding to a 50/50 chance. Along those line, I notice that Chaitin (referencing du Sautoy) says that if it could be proved that the Riemann Hypothesis is undecidable then it is true, since if it were false then it would be decidable by finding a zero off of the critical line. (http://maa.org/features/chaitin.html). But could it be that the Riemann Hypothesis follows quantum indeterminacy in something like the following way? Just role-playing: The Riemann zeta function does indeed have zeros which are off of the critical line (or even, it has zeros having real parts taking on every real value between 0 and 1.) This is the non-computable truth. However, whenever a zero of the Riemann zeta function is actually computed (observed), it falls on the critical line. Just having fun, Tom --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
