“In Space” or “As Space”?: Spatial Autocorrelation Properties of the Earth’s Interior


In this analysis, natural systems are posed to subsystemize in a manner facilitating both structured information/energy sharing and an entropy maximization process projecting a three-dimensional, spatial outcome. Numerical simulations were first carried out to determine whether n × n input-output matrices could, once entropy-maximized, project a three-dimensional Euclidean metric. Only 4 × 4 matrices could; a small proportion passed the test. Larger proportions passed when grouped random patterns on and within two- and three-dimensional forms were tested. The pattern of structural zonation within the earth was then tested in analogous fashion using spatial autocorrelation measures, and for three time periods: current, 95 million years b.p. and 200 million years b.p. All expected results were obtained; not only do the geometries of zonation project a three-dimensional structure as anticipated, but also do secondary statistical measures reveal levels of equilibrium among the zones in all three cases that are nearly total, distinguishing them from simulations that do not incorporate a varying-surface zone-width element.

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Smith, C. (2014) “In Space” or “As Space”?: Spatial Autocorrelation Properties of the Earth’s Interior. International Journal of Geosciences, 5, 375-382. doi: 10.4236/ijg.2014.54036.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Wallace, A.R. (1894) The Fourth Dimension. Light (London), 14, 467.
[2] Ehrenfest, P. (1917) In What Way Does It Become Manifest in the Fundamental Laws of Physics that Space Has Three Dimensions? Proceedings of the Royal Academy, Amsterdam, 20, 200-209.
[3] Whitrow, G.J. (1955) Why Physical Space Has Three Dimensions. British Journal for the Philosophy of Science, 6, 13-31. http://dx.doi.org/10.1093/bjps/VI.21.13
[4] Tangherlini, F.R. (1963) Schwartzschild Field in n Dimensions and the Dimensionality of Space Problem. Nuovo Cimento, 27, 636-651. http://dx.doi.org/10.1007/BF02784569
[5] Tegmark, M. (1997) On the Dimensionality of Spacetime. Classical and Quantum Gravity, 14, L69-L75.
[6] Gurevich, L. and Mostepanenko, V. (1971) On the Existence of Atoms in n-Dimensional Space. Physics Letters, 35A, 201-202. http://dx.doi.org/10.1016/0375-9601(71)90148-4
[7] Barrow, J.D. (1983) Dimensionality. Philosophical Transactions of the Royal Society of London, A310, 337-346.
[8] Tangherlini, F.R. (1985) Dimensionality of Space and the Pulsating Universe. Il Nuovo Cimento B, Series 11, 91, 209-217.
[9] Smith, C.H. (1986) A General Approach to the Study of Spatial Systems. International Journal of General Systems, 12, 359-384, 385-400. http://dx.doi.org/10.1080/03081078608934943
[10] Smith, C.H. (1987) Note on “A General Approach to the Study of Spatial Systems”. International Journal of General Systems, 13, 285-287.
[11] Caruso, F. and Moreira Xavier, R. (1987) On the Physical Problem of Spatial Dimensions: An Alternative Procedure to Stability Arguments. Fundamenta Scientiae, 8, 73-91.
[12] Hosoya, A., Jensen, L.G. and Stein-Schabes, J.A. (1987) The Critical Dimension for Chaotic Cosmology. Nuclear Physics, B283, 657-668. http://dx.doi.org/10.1016/0550-3213(87)90291-4
[13] Chatterjee, S. (1992) A Class of Multidimensional Cosmological Models and Its Possible Astrophysical Consequences. Annals of Physics, 218, 121-138. http://dx.doi.org/10.1016/0003-4916(92)90270-V
[14] Callender, C. (2005) Answers in Search of a Question: “Proofs” of the Tri-Dimensionality of Space. Studies in History and Philosophy of Modern Physics, 36, 113-136. http://dx.doi.org/10.1016/j.shpsb.2004.09.002
[15] Caruso, F. (n.d.) The Three-Dimensionality of the Universe: A Reason for the Existence of Chemists and Beyond. CPBF-CS-004/08.
[16] Smith, C.H. and Derr, M. (2012) “In Space” or “As Space”?: A New Model. Life, 2, 243-254.
[17] Smith, C.H. (2014) The Once and Future Wallace: Simulations: Introduction, and Random Numbers.
[18] Slater, P.B. (1976) Hierarchical Internal Migration Regions of France. IEEE Transactions on Systems, Man and Cybernetics, SMC-6, 321-324. http://dx.doi.org/10.1109/TSMC.1976.5408783
[19] Smith, C.H. (1983) A System of World Mammal Faunal Regions. Journal of Biogeography, 10, 455-466, 467-482.
[20] Smith, C.H. (1984) Areographic Representation of Faunal Characteristics through a “Second-Order” Relational Approach. Evolutionary Theory, 6, 225-232.
[21] Schoeneich, F. and Klapp, B.F. (1998) Standardization of Interelement Distances in Repertory Technique and Its Consequence for Psychological Interpretation of Self-Identity Plots: An Empirical Study. Journal of Constructivist Psychology, 11, 49-58. http://dx.doi.org/10.1080/10720539808404638
[22] Smith, C.H. (2014) The Once and Future Wallace: Simulations: A Theory of Spatial Systems.
[23] Smith, C.H. (2014) The Once and Future Wallace: Real World Studies II: Stream Basins Morphometry. A: Primary Tests. http://people.wku.edu/charles.smith/once/streams1.html
[24] Smith, A.G., Smith, D.G. and Funnell, B.M. (1994) Atlas of Mesozoic and Cenozoic Coastlines. Cambridge University Press, Cambridge.
[25] Smith, C.H. (2014) The Once and Future Wallace: Real World Studies I: Interior Zonation of the Earth.
[26] Lane, N. (2002) Oxygen: The Molecule That Made the World. Oxford University Press, Oxford.
[27] Berner, R.A., Beerling, D.J., Dudley, R., Robinson, J.M. and Wildman Jr., R.A. (2003) Phanerozoic Atmospheric Oxygen. Annual Review of Earth and Planetary Sciences, 31, 105-134.
[28] Smith, C.H. (2014) The Once and Future Wallace: A Theory of Spatial Systems.
[29] Quine, W.V. (1951) Two Dogmas of Empiricism. Philosophical Review, 60, 20-43. http://dx.doi.org/10.2307/2181906
[30] Wallace, A.R. (1866) The Scientific Aspect of the Supernatural. F. Farrah, London, i.
[31] Wallace, A.R. (1871) On the Attitude of Men of Science towards the Investigators of Spiritualism. In: Tuttle, H. and Peebles, J.M., Eds., The Year-Book of Spiritualism for 1871, William White, Boston, 28-31.
[32] Wallace, A.R. (1877) Rise and Progress of Modern Views as to the Antiquity and Origin of Man. In: Report of the British Association for the Advancement of Science 46, John Murray, London, 110-119.

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