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 [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 -~----------~----~----~----~------~----~------~--~---
