Since polynomials of higher than fourth degree, which is the algebraic counterpart of generic geometric dimension, are insolvable in general, then presumably no more than just four mutually orthogonal geometric dimensions can be placed within a single geometric space if it is expected to be fully operational. Hence a hierarchical notion of dimension is needed in order to ensure that at least virtual orthogonality is respected, which in turn implies presence of certain hierarchically organized multispatial structures. It is shown that the operational constraint on physical spaces implies of necessity presence of both: 4-dimensional (4D) spacetime and a certain 4D timespace.
International Letters of Chemistry, Physics and Astronomy (Volume 36)
J. Czajko "Operational Constraints on Dimension of Space Imply both Spacetime and Timespace", International Letters of Chemistry, Physics and Astronomy, Vol. 36, pp. 220-235, 2014