History and Philosophy of Physics

   

Resolving the Fourth Spatial Dimension via Motion in Spacetime: Toward a 5D Geometry of Force and Beyond

Authors: Stuart Hood

This paper re-examines the concept of the fourth dimension, proposing the natural next step beyond static three-dimensional forms to be the motion of those forms through both space and time. This reading eliminates the need for an abstract fourth orthogonal axis and unites two previously competing traditions — Charles Hinton’s recursive four-dimensional geometry and the spacetime framework of Hermann Minkowski and Albert Einstein.The mathematics and logic of Hinton’s tesseract have long demanded a fourth spatial axis, while relativity established time as the fourth dimension. By regarding the "four-dimensional edges" of the tesseract (and other polytopes) not as representing an additional orthogonal direction through space but instead as displacement vectors tracing paths of change through both space and time, all currently-established representations of four-dimensional forms can be conceived as worldlines — precisely the four-dimensional histories of three-dimensional objects that Minkowski described.Treating the fourth dimension as both the spatial and temporal capacities of motion (the animated, ever-moving world we live in) opens a natural extension: a fifth dimension of force. This geometric interpretation aligns with historical attempts in Kaluza—Klein theory and its modern successor, Space-Time-Matter theory. The five-dimensional penteract is shown to mirror the structure of particle interactions and cosmological dynamics. The framework then continues beyond physical space toward consciousness, proposing a sixth dimension of possibility (observation, knowledge, awareness) and a seventh of intelligence (reason/logic, choice/will).

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[v1] 2026-03-05 18:27:22

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