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! 3 has 3 bidirectional vectors & 1 dimensionless operator.

! 3 has 3 bidirectional vectors & 1 dimensionless operator.

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We identify specific properties of the complex plane that allow functions of a continuous n-dimensional (Hilbert) measure space to be transformed into a well ordered counting sequence. We discuss proof strategies for problems in number theory (Goldbach Conjecture) and topology (Poincare ´ Conjecture) that suggest correspondence between the physical...

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Citations

... Identity inversion in the most natural terms, then, 2 4 = 4 2 , informs us that transitivity implies identity. 5 So we take for granted that our 2-dimension measures adjoin 4 dimensions, where the "boundary of a boundary is zero." § Yet that's not what we experience. ...
... Thus, gravity is universal negative feedback, assured by recurrence of the discrete source state. This source is everywhere local and nowhere extended-a consequence of the choice function-which as shown in (Ray, 2006) is independent of observer choice. Local meta-stability is dependent on global instability in the form of random oscillations. ...
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... g 00 g 01 g 02 g 03 g 10 g 11 g 12 g 13 g 20 g 21 g 22 g 23 3 Bekenstein and Mayo 9 made the 1-dimension case for equivalent past and future entropy, for if black holes are 1-dimensional, past and future information enters and leaves randomly, on one channel only. Cf. the Chaitin Ω 10 random result. ...
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... l infinitely orientable metric on a self-avoiding random walk, a network of random-output computers ( ! " calculating machines) corresponds to quantum time intervals randomly orienting in an infinite dimensional (Hilbert) space-in which the principle of self-similarity forces an ordered direction of continuous time in the limits of the 3-manifold. [Ray. 2006] 3.3 In other words, the output of each machine is sensitively dependent on the machine's orientation in space-the idea being that the 3-space time vector at any node is uniquely rectified in the process of the n-space self avoiding random walk. One models a folding sequence on the continuously changing rectilinear path disclosed by the ...
... The sticking point is that if, as we claim, time is a physical agent driving change, the discontinuous and random reorienting of that complex metric on a scale of measure zero generates random information in an information-rich future state (n-dimensional Hilbert space [Ray, 2006]) 4.1.3 The present state, information-poor, is shaped uniquely by random n-dimensional motion. ...
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... 2.1 In an earlier paper [Ray, 2006] we explored the physical consequences of a mathematical model of dimension self-organization, driven by the summation of cardinal points of discrete dimension sets: ...
... (*) 2.2 Figure 1 implies why this is so-the 24-1 summation of cardinal points up to non-redundant points of the tensor metric field leaves one 0-dimension point-because this singularity seeds the expansion of n-dimensional sets of cardinal points, it must recur infinitely often in the history of n-dimension evolving space, and because it is a singularity, it can only be treated by complex analysis, where the continuous n-dimension function length 1 term returns to zero (returns to itself) as a result of rotation in the complex plane. [Ray, 2006] We suppose that the cardinality of dimension D n contains, in each of its points D n!1 , the cardinality of the lower dimension. The warrant for this idea is from projective geometryduality between spaces that for dimension N with subspaces R is given by N- 2.3 Given this interpretation of time, we also see that d ! 4 (hyperspace) is the least ! ...
... These characterizations of background independence suggest an organic continuation of physics with the analytical mathematical model, the entire theme of [Ray, 2006]. ...
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