# A Grand Unification of the Sciences, Arts & Consciousness: Rediscovering the Pythagorean Plato’s Golden Mean Number System

### Abstract

In this condensed paper, by combining the insights from E-Infinity theory, along with Plato‘s initiatory insights into the golden section imbedded in his Principles of the One and Indefinite Dyad, David Bohm‘s ontological framework of the superimplicate, implicate and explicate orders, and the pervasive presence throughout physics, chemistry, biology and cosmology of the golden ratio (often veiled in Fibonacci and Lucas numbers), a profound golden mean number system emerges underlying the cosmos, nature and consciousness. This ubiquitous presence is evident in quantum mechanics, including quark masses, the chaos border, fine structure constant and entanglement, entropy and thermodynamic equilibrium, the periodic table of elements, nanotechnology, crystallography, computing, digital information, cryptography, genetics, nucleotide arrangement, Homo sapiens and Neanderthal genomes, DNA structure, cardiac anatomy and physiology, biometric measurements of the human and mammalian skulls, weather turbulence, plant

phyllotaxis, planetary orbits and sizes, black holes, dark energy, dark matter, and even cosmogenesis – the very origin and structure of the universe. This has been pragmatically extended through the most ingenious biomimicry, from robotics, artificial intelligence, engineering and urban design, to extensions throughout history in architecture, music and the arts. We propose herein a grand unification of the sciences, arts and consciousness, rooted in an ontological superstructure known to the ancients as the One and Indefinite

Dyad, that gives rise to a golden mean number system which is the substructure of all existence.

### References

[2] Marek-Crnjac, L., El Naschie, M.S. and He, J.H., 2013. Chaotic fractals at the root of relativistic quantum physics and cosmology. International Journal of Modern Nonlinear Theory and Application, 2(1), pp.78-88.

[3] Marek-Crnjac, L., 2015. On El Naschie‘s fractal-cantorian space-time and dark energy-a tutorial review. Natural Science, 7(13), pp.581-598.

[4] Argyris, J. and Ciubotariu, C., 1997. On El Naschie's complex time and gravitation. Chaos, Solitons & Fractals, 8(5), pp.743-751.

[5] Olsen, S.A., 2017. Golden ratio beauty as scientific function. Lebenswelt. Aesthetics and philosophy of experience. (11).

[6] El Naschie, M.S., 2019.On the Fractal Counterpart of C. Vafa‘s Twelve-Dimensional F-theory and the A. Schoenberg Twelve-tone Music Implicit in the Standard Model of High Energy Elementary Particles. International

Journal of Innovation in Science and Mathematics. Volume 7, Issue 5, pp. 222-230.

[7] Otto, Hans. 2019. Reciprocity as an Ever-Present Dual Property of Everything. researchgate.net.

[8] El Naschie, M.S., 2018. Symmetria Massima of the fractal M-theory via the golden mean number system- A new language for a deep dialogue between man and nature. International Journal of Artificial Intelligence and

Mechatronics, 7(3), pp.11-14.

[9] Perelman, C.C. 2019. Note on the Golden Mean, Nonlocality in Quantum Mechanics and Fractal Cantorian Spacetime. researchgate.net and academia.edu.

[10] James Hopkins. Pythagorean Harmonix Healing. "Pythagoras" on " delamora" - Transformational Experiences. https://www.delamora.life/pythagoras.

[11] Fauvel, J., Flood, R. and Wilson, R.J. eds., 2006. Music and mathematics: from Pythagoras to fractals. Oxford University Press on Demand.

[12] Kahn, C.H., 2001. Pythagoras and the Pythagoreans. Hackett Publishing. Indianapolis&Cambridge.

[13] El Naschie, M.S., 2006. Elementary number theory in superstrings, loop quantum mechanics, twistors and E-infinity high energy physics. Chaos, Solitons & Fractals, 27(2), pp.297-330.

[14] El Naschie, M.S., 2013. The quantum gravity Immirzi parameter—A general physical and topological interpretation. Gravitation and Cosmology, 19(3), pp.151-155.

[15] El Naschie, M.S., 2016. On a fractal version of Witten's M-theory. International Journal of Astronomy and Astrophysics, 6, pp.135-144.

[16] El Naschie, M.S., 2014. Cosmic Dark Energy from‗t Hooft‘s Dimensional Regularization and Witten‘s Topological Quantum Field Pure Gravity. Journal of Quantum Information Science, 4, pp.83-91.

[17] El Naschie, M.S., 2018. World formula interpretation of E = mc2. International Journal of Applied Science and Mathematics,5(1), pp. 67-75.

[18] El Naschie, M.S., 2017. Cosmic Accelerated Expansion, Dark Matter and Dark Energy from a Heterotic Superstrings Scenario.International Journal of Innovation in Science and Mathematics. Volume 5, Issue 2, ISSN (Online): 2347–9051, pp. 53-56.

[19] El Naschie, M.S., 2017. Elements of a new set theory based quantum mechanics with applications in high energy quantum physics and cosmology. International Journal of High Energy Physics, 4, pp.65-74.

[20] El Naschie, M.S., 2015. Banach Spacetime-Like Dvoretzky Volume Concentration as Cosmic Holographic Dark Energy. International Journal of High Energy Physics, 2(1), pp.13-21.

[21] El Naschie, M.S., 2019. Simulating the quantum Universe via the golden mean number expert-like -system. International Journal of Artificial Intelligence and Mechatronics, Volume 7, Issue 4, ISSN 2320 – 5121, pp.15-

18.

[22] El Naschie, M.S., 2015. Application of Dvoretzky's Theorem of Measure Concentration in Physics and Cosmology. Open Journal of Microphysics, 5, pp.11-15.

[23] Waldschmidt, M., Moussa, P., Luck, J.M., Itzykson, C., Cartier, P., Bost, J.B., Cohen, H., Zagier, D., Gergondey, R., Stark, H.M. and Reyssat, E. eds., 1992. From Number Theory to Physics. Springer - Berlin.

[24] El Naschie, M.S., 2009. The theory of Cantorian spacetime and high energy particle physics (an informal review). Chaos, Solitons & Fractals, 41(5), pp.2635-2646.

[25] El Naschie,M.S.,1998. Penrose universe and Cantorian spacetime as a model for noncommutative quantum geometry. Chaos Solitons & Fractals, 9(6), pp. 931-933.

[26] Marek-Crnjac, L., 2011. The Hausdorff dimension of the Penrose universe. Physics Research International,pp.1-4.

[27] Iovane, G., 2006. El Naschie Ε-Infinity Cantorian spacetime and lengths scales in cosmology. International Journal of Nonlinear Sciences and Numerical Simulation, 7(2), pp.155-162.

[28] El Naschie, M.S., 1998. Superstrings, Knots, and Noncommutative Geometry in E-infinity Space. International Journal of Theoretical Physics, 37(12), pp.2935-2951.

[29] El Naschie, M.S., 2013. A Resolution of Cosmic Dark Energy via a Quantum Entanglement Relativity Theory. Journal of Quantum Information Science, 3(1), pp.23-26.

[30] El Naschie, M.S., 2017. The Physics, Mathematics and Common Sense of Cosmic Dark Energy and Spacetime Extra Dimensions. International Journal of Innovations in Science and Mathematics, 5(6), pp. 201-204.

[31] El Naschie, M.S., 2013. Experimentally based theoretical arguments that Unruh‘s temperature, Hawking‘s vacuum fluctuation and Rindler‘s wedge are physically real. American Journal of Modern Physics, 2(6), pp.357-361.

[32] El Naschie, M.S., 2013. What Is the Missing Dark Energy in a Nutshell and the Hawking-Hartle Quantum Wave Collapse. International Journal of Astronomy and Astrophysics, 3(03), pp. 205-211.

[33] Babchin, A.J. and El Naschie, M.S., 2016. On the real Einstein beauty E= kmc2. World Journal of Condensed Matter Physics, 6(1), pp.1-6.

[34] El Naschie, M.S., 2018. From Nikolay Umov E= kmc2 via Albert Einstein's E= mc2 to the dark energy density of the cosmos E=(21/22) mc2. World Journal of Mechanics, 8, pp.73-81.

[35] El Naschie, M.S., 2017. The Aether of Spacetime Physics Is the Empty Set of Pure Mathematics. Natural Science, 9(9), pp.289-292.

[36] El Naschie, M.S., Marek-Crnjac, L. and He, J.H., 2012. On the Mathematical Philosophy of Being and Nothingness in Quantum Physics. Fractal Space- Time &Noncommutative Geometry in Quantum and High Energy Physics, 2(2), pp.103-106.

[37] Somit, A., 1950. Sartre's Existentialism as a Political Theory. Social Science, 25(1), pp.40-47.

[38] El Naschie, M.S., 2016. High energy physics and cosmology as computation. American Journal of Computational Mathematics, 6(03), pp.185-199.

[39] El Naschie, M.S., 2014. Electromagnetic—Pure gravity connection via Hardy‘s quantum entanglement. Journal of Electromagnetic Analysis and Applications, 6(9), pp.233-237.

[40] El Naschie, M.S., 2011. Quantum entanglement as a consequence of a Cantorian micro spacetime geometry. Journal of Quantum Information Science, 1(02), pp.50-53.

[41] El Naschie, M.S. and Olsen, S., 2017. The universe as a golden supercomputer. YouTube: https

https://www.youtube.com/watch?v=3GiyWK_JQxg.

[42] El Naschie, M.S., He, J.H., Nada, S., Marek-Crnjac, L. and Helal, M.A., 2012. Golden mean computer for high energy physics. Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics, 2(2),

pp.80-93.

[43] El Naschie, M.S.,2013. A Rindler-KAM spacetime geometry and scaling the Planck scale solves quantum relativity and explains dark energy. International Journal of Astronomy and Astrophysics,Vol. 3No.4, pp. 483-

493.

[44] El Naschie, M.S.,2008. The exceptional Lie symmetry groups hierarchy and the expected number of Higgs bosons. Chaos Solitons & Fractals,pp. 268-273.

[45] He, J-H andEl Naschie, M.S.,2005. Transfinite Physics. A collection of publications of E-Infinity Cantorian spacetime theory. ISBN988-98846-5-8.China.

[46] El Naschie, M.S., 2019. Gravity looks like electro-magnetism when seen through fractal logic glasses. International Journal of Innovation in Science and Mathematics. Volume 7, Issue 4, ISSN (Online): 2347–9051, pp. 180-185.

[47] El Naschie, M.S., 2019. Electromagnetic Gravity and the Quanta. International Journal of Applied Science and Mathematics. Volume 6, Issue 4, ISSN (Online): 2394-2894, pp. 131-138.

[48] El Naschie, M.S., and Marek-Crnjac, L., 2018. Set theoretical foundation of quantum mechanics. NASA's EM drive technology and minimal surface interpretation of the state vector reduction of the quantum wave collapse.

Chaos and Complexity Letters, 12(2), pp.85-100.

[49] El Naschie, M.S., 2019. Spinoza‘s God, Leibniz‘s monadology and the universal music of Einstein‘s Cantorian nature. International Journal of Innovation in Science and Mathematics, Volume 7, Issue 1, pp.33-39.

[50] Weibel, P., Ord, G. and Rössler, O., 2005. Space time physics and fractality: festschrift in honor of Mohamed El Naschie on the occasion of his 60th birthday. In Space Time Physics and Fractality. Springer – Dordrecht, The

Netherlands.

[51] Marek-Crnjac, L., 2003. The mass spectrum of high energy elementary particles via El Naschie‘s E (∞) golden mean nested oscillators, the Dunkerly–Southwell eigenvalue theorems and KAM. Chaos, Solitons &

Fractals, 18(1), pp.125-133.

[52] El Naschie, M.S., 2006. The brain and E-Infinity. International Journal of Nonlinear Sciences and Numerical Simulation, 7(2), pp.129-132.

[53] Penrose, R., 1994. Shadows of the Mind. A Search for the Missing Science of Consciousness. Oxford University Press.

[54] Marek-Crnjac, L. and El Naschie M.S.,2019. From Fractal-Cantorian classical music to the symphony of the standard model of high energy particle physics. Journal of Progressive Research in Mathematics, vol. 15,

issue 3, pp. 2700-2710.

[55] Hardy, L., 1993. Non-locality of two particles without inequalities for almost all entangled states. Physics Rev. Lett.71(11), pp. 1665-1668.

[56] Tamargo, R.J., Pindrik, J.A., 2019. Mammalian Skull Dimensions and the Golden Ratio (Phi).J Cranofac Surg,30, 1750 - 1755.

[57] Perez, J.C., 1991. Chaos, DNA, and Neuro-computers: A golden Link: The hidden language of genes, global language and order in the human genome. Speculations in Science and Technology, 14. p. 336-346.

[58] Perez, J.C., 2009. Codex Biogenesis. Resurgence. Li‘ege, Belgium.

[59] Persaud-Sharma, D., O‘Leary, J.P., 2015. Fibonacci Series, Golden Proportions, and the Human Biology. Austin J Surg, 2(5), 1066.

[60] Yetkin, E., et al., 2014. Does systolic and diastolic blood pressure follow the Golden Ratio? Int J Cardiol,176, 1457-1459.

[61] Yetkin, E., et al., 2013. Golden Ratio is beating in our heart.Int J Cardiol,168, 4926-4927.

[62] Iosa, M., et al., 2016. The connection between anthropometry and gait harmony unveiled through the lens of the golden ratio. Neurosci Lett, 612:138-144.

[63] Luminet, J-P., 2008. The Wraparound Universe. A K Peters/CRC Press.

[64] Di Valentino, E., Melchiorri, A. and Silk, J., 2019. Planck evidence for a closed Universe and a possible crisis for cosmology. Nat Astron doi,10,1038/s41550-019-0906-9.

[65] Davies, P., 2019. The Demon in the Machine: How Hidden Webs of Information Are Solving the Mystery of Life. University of Chicago Press.

[66] Coats, C., 1995. Living Energies: An Exposition of Concepts Related to the Theories of Viktor Schauberger. Gateway Books.

[67] Coldea, R., et al., 2010. Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry. Science. pp. 177-210.

[68] Affleck, I., 2010. Golden ratio seen in a magnet. Nature, 464, 362–363 doi:10.1038/464362a.

[69] Pletser, V., 2018. Orbital Period Ratios and Fibonacci Numbers in Solar Planetary and Satellite Systems and in Exoplanetary Systems. Astrophysics and Space Science.364. 10.1007/s10509-019-3649-2.

[70] Jean, R., Barabe, D., 1998. Symmetry in Plants. World Scientific Publishing Company.

[71] Stakhov, A., 2003. Hyperbolic Fibonacci and Lucas Functions: A New Mathematics for the Alive Nature. Vinnitsa.

[72] Olsen, S., 2006. The Golden Section: Nature’s Greatest Secret. Wooden Books.

[73] Martineau, J., 2002. A Little Book of Coincidence. Wooden Books.

[74] Roan, S., March 18, 2009. Becoming One in Music, Minds. Sun Sentinel.

[75] Koruga, D., et al., 2020. Molecular Nanotechnology: Golden Mean as a Driving Force of Self-Assembly.

https://pdfs.semanticscholar.org/96b1/9c9655feba51d82f7bfe191ccdcce3d3e

6c5.pdf

[76] Bohm, D., 1990. A new theory of the relationship of mind and matter. Philosophical Psychology; Vol. 3, No. 2, p. 284-285.

[77] McClain, E.G., 1984. The Pythagorean Plato: Prelude to the Song Itself. New York: Weiser.

[78] Kappraff, J., Mcclain, E.G., 2018. The Proportional System of The Parthenon and Its Connections with Vedic India. Music and Deep Memory: Speculation in Ancient Mathematic, Tuning, and Tradition In MemoriamErnest G. McClain.Eds., Bryan Carr and Richard Dumbrill. Lulu Press.

[79] Penrose, R. and Hameroff, S.R., 1995. Quantum computing in microtubules: Self-collapse as a possible mechanism for consciousness. Toward a science of consciousness. MIT Press, Cambridge, Massachusetts.

[80] Penrose, R. and Hameroff, S.R., 2011. Consciousness in the Universe: Neuroscience, Quantum Space-Time Geometry and Orch OR Theory. Journal of Cosmology; Vol. 14.

[81] James, W., 1902. Varieties of Religious Experience. snamgnoL, neerG& oC.

[82] Leonard, G., 1978. The Silent Pulse: A Search for the Perfect Rhythm That Exists in Each of Us. Dutton Books; p.13.

[83] Heath, T., 1956, Euclid’s Elements, Vol. 1, p. 137.

[84] Thomas, I., ed. 1957. Greek Mathematical Works, Vol. 1, p. 153. Cambridge: Harvard University Press.

[85] Olsen, S., 2002. Plato, Proclus and Peirce: Abduction and the Foundations of the Logic of Discovery. Neoplatonism in Contemporary Thought; Part One. Harris R.B., ed. New York: SUNY Press.

[86] El Naschie, M. and Olsen, S., 2019. Mohamed El Naschie & Scott Olsen In Conversation - Series One Part One through Series Three Part Ten. Vimeo. February 1,2019. vimeo.com/314757294.

[87] Kuhn, T., 1962. TheStructure of Scientific Revolutions. University of Chicago Press.

[88] Bohm, D. and Hiley, B., 1968. The Undivided Universe: An Ontological Interpretation of Quantum Theory. Routledge.

[89] Mitchell, E., 1996. The Way of the Explorer, An Apollo Astronaut’s Journey Through the Material and Mystical Worlds. G.P. Putnam and Sons. 1st edition.

[90] Kennedy, J. B., 2014. The Musical Structure of Plato’s Dialogues. Routledge.

[91] Blavatsky, H.P., 1888. The Secret Doctrine. Vol. 1, p. 208. Adyar: Theosophical Publishing House.

[92] Blavatsky, H.P., 1877. Isis Unveiled, Vol. 2,p. 91. J. W. Bouton.

[93] Barath, H., 2020. Flocking Phase Change.Scientific American, Vol. 322, No. 2, p. 21.

[94] El Naschie, M., 2015. The Self Referential Pointless Universe Geometry as the Key to the Resolution of the Black Hole Information Paradox.

International Journal of Innovation in Science and Mathematics Volume 3, Issue 5, ISSN (Online): 2347–9051.

[95] El Naschie, M.S. and Olsen, S.,2011. When zero is equal to one: A set theoretical resolution of quantum paradoxes. Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics, 1(1):11-

24.

[96] Olsen, S.A., 2018. Reassessing the Roots of Theosophy. Insight.

https://www.claregategroup.org/files/1515/6404/3918/Insight_12_2018_Scott_Olsen__Reassessing_the_Roots_of__Theosophy_rfs.pdf

[97] Peirce, C.S., 1931-1958. Collected Papers of Charles Sanders Peirce, 8 vols., eds. A.W. Burks, C, Hartshorne, and P. Weiss, Cambridge: Harvard University Press - Cambridge.

[98] Kirk, G.S. & Raven, J.E., 1957. The Presocratic Philosophers: A Critical History with a Selection of Texts. Cambridge University Press.

[99] Sahu, S., Ghosh, S., Fujita, D. and Bandyopadhyay, A. 2015. Live visualizations of single isolated tubulin protein self-assembly via tunneling current: effect of electromagnetic pumping during spontaneous growth of

microtubule. Sci Rep 4, 7303. https://doi.org/10.1038/srep07303.

[100] Radin, D., 2013. Supernormal: Science, Yoga, and the Evidence for Extraordinary Psychic Abilities. Random House, Inc.

[101] Badawy, A. 1965. Ancient Egyptian Architectural Design: a Study of the Harmonic System. University of California Press.

[102] Vitruvius, 1960. The Ten Books on Architecture. Dover Publications.

[103] Pacioli, L., 1509. De Divina Proportione. Paganino Paganini – Venice.

[104] Kramer, H. J., 1990. Plato and the Foundations of Metaphysics: A Work on the Theory of the Principles and Unwritten Doctrines of Plato with a Collection of the Fundamental Documents. SUNY Press.

[105] Nikulin, D., 2013. The Other Plato: The Tübingen Interpretation of Plato's Inner-Academic Teachings. SUNY Press.

[106] Kennedy, J. B., 2010. Plato‘s Forms, Pythagorean Mathematics, and Stichometry. Apeiron 43 (1):1-32.

[107] Kepler, J., 2013 (1619). Harmonice Mundi. Isha Books.

[108] Warm, H., 2010. Signature of the Celestial Spheres: Discovering Order in the Solar System. Rudolf Steiner Press.

[109] Oliveira Neto, M. de, 2006. Pythagoras‘ celestial spheres in the context of a simple model for quantization of planetary orbits. Chaos, Solitons & Fractals, Volume 30, Issue 2. pp 399-406

[110] Goldfain, E., 2008. Critical behavior in continuous dimension, E-Infinity theory and particle physics. Chaos, Solitons & Fractals. Vol. 38. pp. 928-935.

[111] Weiss, H. and Weiss, V., 2003. The golden mean as clock cycle of brain waves. Chaos, Solitons & Fractals. Vol.18, Issue 4. pp. 643-652.

[112] Sheldrake, R., 1988. The Presence of the Past: Morphic Resonance and the Memory of Nature. Crown.

[113] Sheldrake, R., 1984. Morphic Resonance. Ancient Wisdom and Modern Science. Ed., Grof, S.

[114] Goodwin, B., 1994. How the Leopard Changed Its Spots: The Evolution of Complexity. Scribner.

[115] Goodwin, B., 1989. Dynamic Structures in Biology. Edinburgh University Press.

[116] Stogratz, S. 2003. Sync: How Order Emerges from Chaos in the Universe. Hachette Books. p. 3

[117] Chang, K., 2017. The Harmony that Keeps Trappist-1‘s 7 Earth-size Worlds from Colliding. The New York Times.

[118] He, J-H, 2006. Application of E-Infinity Theory to Biology. Chaos, Solitons & Fractals, Vol. 28, pp. 285-289.

[119] El Naschie, M.S. and Olsen, S., Helal, M.A., Marek-Crnjac, L. and Nada, S., On the Missing Link between Cosmology and Biology, International Journal of Innovation in Science and Mathematics, Vol. 6, Issue 1, ISSN

(Online): 2347-9051.

[120] Edelman, G.M., 2000. Consciousness. Penguin Books. London.

[121] Wasson, R. G., Hoffman A. and Ruck C. A. P., 1978. The Road to Eleusis: Unveiling the Secret of the Mysteries. Harcourt Brace Jovanovich.

[122] Wasson, G., Ruck, C. A. P., Kamrisch, S. and Ott, J., 1986. Persephone’s Quest: Entheogens and the Origins of Religion. Yale University Press.

[123] Petoukhov, S. V., 2001. Biperiodical Table of Genetic Code and a Number of Protons. Nauka – Moscow (Russian).

[124] Petoukhov, S. V., 2006. Metaphysical aspects of the matrix analysis of genetic code and the golden section. Metaphysics: Century XXI. BINOM – Moscow. pp. 216-250 (Russian).

[125] Grzedzielsik, J., 1986. Energy-Geometric Code of Nature. Warszawskie Centrum Studenckiego Ruchu Naukowego (Polish).

[126] Schwaller de Lubicz, R. A., 1957 (French), 1998 (English). The Temple of Man. Inner Traditions, Rochester.

[127] Rossi, C., 2004. Architecture and Mathematics in Ancient Egypt. Cambridge University Press.

[128] Stakhov, A.P. assisted by Olsen, S., 2009. The Mathematics of Harmony: From Euclid to Contemporary Mathematics and Computer Science. World Scientific – Singapore.

[129] Stakhov, A.P., 2008. The Mathematics of Harmony: Clarifying the Origins and Development of Mathematics. The International Club of the Golden Section – Bolton, Canada.

[130] Stakhov, A.P. and Aranson S., assisted by Olsen, S.A., 2016. The "Golden" Non-Euclidean Geometry. World Scientific – Singapore.

[131] Olsen, S.A., 2017. The Mathematics of Harmony and Resonant States of Consciousness. Symmetry: Culture and Science, Vol. 26, No. 4.http://journalscs.symmetry.hu/abstract/?pid=641

[132] Olsen, S.A., 2002. The Indefinite Dyad and the Golden Section: Uncovering Plato‘s Second Principle. Nexus Network Journal: Architecture and Mathematics, 2002a, 4, no. 1, 97-110.

[133] Olsen, S. 1975. Platonic Aesthetics. [Summa thesis], Minneapolis: University of Minnesota.

[134] Olsen, S.A., 1983. The Pythagorean Plato and the Golden Section: a Study in Abductive Inference. [Ph.D. Dissertation], Gainesville: University of Florida, 226pp.

[135] Wasson, G. 1972. Soma: Divine Mushroom of Immortality. Harcourt Brace Jovanovich.

[136] Horky, P. S., 2013. Plato and Pythagoreanism. Oxford University Press. p. 57.

[137] Zhang, W. andYartsev, M. M., 2019. Correlated Neural Activity Across the Brains of Socially Interacting Bats. Cell.https://www.cell.com/cell/fulltext/S0092-8674(19)30551-3 DOI:

10.1016/j.cell.2019.05.023

[138] Kingsbury, L., et al., 2019. Correlated Neural Activity and Encoding of Behavior Across Brains of Socially Interacting Animals.Cell. https://www.cell.com/cell/fulltext/S0092-8674(19)30550-1 DOI:

10.1016/j.cell.2019.05.022

[139] Critchlow, K., 1982. Time Stands Still. St. Martin‘s Press.

*Journal of Progressive Research in Mathematics*,

*16*(2), 2888-2931. Retrieved from http://www.scitecresearch.com/journals/index.php/jprm/article/view/1850

Copyright (c) 2020 Journal of Progressive Research in Mathematics

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

**TRANSFER OF COPYRIGHT**

JPRM is pleased to undertake the publication of your contribution to **Journal of Progressive Research in Mathematics.**

The copyright to this article is transferred to JPRM(including without limitation, the right to publish the work in whole or in part in any and all forms of media, now or hereafter known) effective if and when the article is accepted for publication thus granting JPRM all rights for the work so that both parties may be protected from the consequences of unauthorized use.