Exploring Novel Cyclic Extensions of Hamilton’s Dual-Quaternion Algebra

Abstract

We make a preliminary exploratory study of higher dimensional (HD) orthogonal forms of the quaternion algebra in order to explore putative novel Nilpotent/Idempotent/Dirac symmetry properties. Stage-1 transforms the dual quaternion algebra in a manner that extends the standard anticommutative 3-form, i, j, k into a 5D/6D triplet. Each is a copy of the others and each is self-commutative and believed to represent spin or different orientations of a 3-cube. The triplet represents a copy of the original that contains no new information other than rotational perspective and maps back to the original quaternion vertex or to a second point in a line element. In Stage-2 we attempt to break the inherent quaternionic property of algebraic closure by stereographic projection of the Argand plane onto rotating Riemann 4-spheres. Finally, we explore the properties of various topological symmetries in order to study anticommutative-commutative cycles in the periodic rotational motions of the quaternion algebra in additional HD dualities.

‘Shut The Front Door!’: Obviating the Challenge of Large-Scale Extra Dimensions and Psychophysical Bridging

“…A wrinkle in atomic spectra may not initially appear as an appropriate crack in the 'cosmic egg' -meaning a door to empirically demonstrating the 1 st indicia of the existence of Cartesian Interactive Dualism. To clarify, NFT [7][8][9][10][11][12][13] now has sufficiently firm theoretical grounds to declare that the Planck scale is 'not the basement of reality', albeit it is an oasis between the 1 st and 3 rd regimes of reality -a nilpotent boundary of the infinite potentia [5][6][7] hidden behind it or domain wall forming the virtual reality perceived by the Euclidean/ Minkowski observer. Just as the quantum regime was until recently invisible to the empirical tools of Newtonian or Classical Mechanics, so until now Unified Field Mechanics, U F has remained invisible to the tools of quantum mechanics primarily because of the barrier associated with the uncertainty principle.…”

“…Although the mathematics of Rowlands avantgarde nilpotent physics works brilliantly in extending our understanding of the nature of a fermionic singularity (as yet an open question in physics), for Noetic Field Theory (NFT): The quantization of Mind, for which Rowland's model has recently even become a basis for solidifying NFT's foundation [6,7]; elegant math is not necessarily tantamount to physics. The nature of the so-called fermionic singularity is profoundly unique in NFT; and even though the protocol introduced here would not work without that noetic nature being physically realistic, its technical description is beyond the scope of this paper [8][9][10] within which we outline the experiment and only delineate a minimum of associated parameters to help explain its radical theoretical foundations.…”