HYPERSPACE AND THE TORUS REVISITED: AN AFRICAN PERSPECTIVE ON THE THEORY OF EVERYTHING
HYPERSPACE AND THE TORUS REVISITED:
AN AFRICAN PERSPECTIVE ON THE THEORY OF EVERYTHING†
A. O.E. Animalu1 and Professor Catherine O. Acholonu2
1Dept. of Physics & Astronomy, University of Nigeria, Nsukka &
Chairman/CEO, International Centre for Basic Research, Abuja
2 Catherine Acholonu Research Center, Abuja
AN AFRICAN PERSPECTIVE ON THE THEORY OF EVERYTHING†
A. O.E. Animalu1 and Professor Catherine O. Acholonu2
1Dept. of Physics & Astronomy, University of Nigeria, Nsukka &
Chairman/CEO, International Centre for Basic Research, Abuja
2 Catherine Acholonu Research Center, Abuja
Abstract We review the “ichi” linguistic geometry of Catherine Acholonu’s three books titled The Adam Trilogy and published under three book titles – Gram Code of African Adam (GCAA, 2005), They Lived Before Adam (TLBA, 2009) and Lost Testament of Ancestors of Adam (LTAA, 2010) – based on its algebraic representations as “Afa” Matrix : 8x8 = 64 = 28+36 = 26+38 = 32+32 = 24+40 and the following correspondence principle with elements of quantum field theory Points<=>Particles, Lines<=>Fields, Planes<=>Currents. As a consequence, we relate the number of the primitive elements (points,lines & planes) of 3-dimensional projective geometry of linguistic frames of reference (tetrahedron, square & hexagonal pyramids, Cartesian cube and cube-hexagon hyperspace) to the Gell-Mann-Ne’emann 8x8 representation of SU(3) symmetry and current algebra of strongly interacting particles in high energy physics. By comparing the “ichi” linguistic geometry with Kaku’s ten-dimensional hyperspace view of the (superstring) theory of everything (TOE) (unifying the four basic (electromagnetic, weak, strong and gravitational) forces in nature and Stephen Hawking’s Torus view of the universe (based on the use of quantum fluctuations to eliminate the black-hole singularity of Einstein’s general relativity theory of gravitation), we develop an African perspective on TOE based on cube- hexagon hyperspace/torus and the associated current algebra and discuss the consequences. Key Words: Linguistics, Hyperspace, Torus, Current algebra, Theory of Everything,
1. INTRODUCTION
At the 2009 International Seminar on Theoretical Physics and National Development (ISOTPAND-2009), we began under the title[1], “Ichi” linguistic geometry and evolution, to lay the mathematical/physical foundations of Catherine Acholonu’s three books[2] titled The Adam Trilogy, Vols 1, 2 & 3, published under the separate titles: The Gram Code of African Adam (hereunder abbreviated GCAA, 2005); They Lived Before Adam (TLBA, 2009); and The Lost Testament of the Ancestors of Adam (LTAA, 2010). The mathematical foundation of interest is the branch of topology known as singular homology[3] which is concerned, in geometric and algebraic terms, with the triangulation and algebraic projective geometry of linguistic frames of reference (tetrahedron, square-based and hexagonal-based pyramids, cube, pentagon, hexagon and cube-hexagon hyperspace) from which can be proved, as stated by Machio Kaku[4] on p.105 of his 1995-published book titled Hyperspace, A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension, that “the fifth dimension is topologically identical with a circle and the universe is topologically identical with a cylinder”.
In order to anchor this paper on available physical data (artefacts) from traditional African culture, let us recall[5] the prevalence of conical-shaped huts on polygonal base throughout Africa which was adopted in the architecture of the National Institute for Policy and Strategic Studies (NISS) at Jos, replicating the famous groundnut pyramids on polygonal base (in Northern Nigeria) and, the more intriguing architecture of the step pyramid at Nsude in Enugu State of Nigeria photographed by missionaries in the 1930s and reproduced in Fig. 1 below. By enclosing the step pyramid in a cylinder whose circular section is defined by the six tips of a hexagon and the height by the five tips of a square pyramid (to represent growth along the cylindrical axis), one can generate the inter-joined 5&6-quadrangle pattern indicated in Fig. 1 which is a recurrent motif of Igbo artistic expression (LTAA, p.81) and replicate the distinctive hexagon grid on the “enigmatic” Igbo-Ukwu bronze tyre/hyperdoughnut (TLBA, p.447), i.e. a torus, immersed in a cube-hexagon hyperspace!. This semiology, that is, physics and logic, of African culture goes beyond the post-colonial theme of struggle between invading European culture (represented by a rectangular box totem of Christian missionaries) and African culture (represented by the “creation snake”) that got trapped in the box in Chinua Achebe’s novel, Arrow of God.[6].
At the 2009 International Seminar on Theoretical Physics and National Development (ISOTPAND-2009), we began under the title[1], “Ichi” linguistic geometry and evolution, to lay the mathematical/physical foundations of Catherine Acholonu’s three books[2] titled The Adam Trilogy, Vols 1, 2 & 3, published under the separate titles: The Gram Code of African Adam (hereunder abbreviated GCAA, 2005); They Lived Before Adam (TLBA, 2009); and The Lost Testament of the Ancestors of Adam (LTAA, 2010). The mathematical foundation of interest is the branch of topology known as singular homology[3] which is concerned, in geometric and algebraic terms, with the triangulation and algebraic projective geometry of linguistic frames of reference (tetrahedron, square-based and hexagonal-based pyramids, cube, pentagon, hexagon and cube-hexagon hyperspace) from which can be proved, as stated by Machio Kaku[4] on p.105 of his 1995-published book titled Hyperspace, A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension, that “the fifth dimension is topologically identical with a circle and the universe is topologically identical with a cylinder”.
In order to anchor this paper on available physical data (artefacts) from traditional African culture, let us recall[5] the prevalence of conical-shaped huts on polygonal base throughout Africa which was adopted in the architecture of the National Institute for Policy and Strategic Studies (NISS) at Jos, replicating the famous groundnut pyramids on polygonal base (in Northern Nigeria) and, the more intriguing architecture of the step pyramid at Nsude in Enugu State of Nigeria photographed by missionaries in the 1930s and reproduced in Fig. 1 below. By enclosing the step pyramid in a cylinder whose circular section is defined by the six tips of a hexagon and the height by the five tips of a square pyramid (to represent growth along the cylindrical axis), one can generate the inter-joined 5&6-quadrangle pattern indicated in Fig. 1 which is a recurrent motif of Igbo artistic expression (LTAA, p.81) and replicate the distinctive hexagon grid on the “enigmatic” Igbo-Ukwu bronze tyre/hyperdoughnut (TLBA, p.447), i.e. a torus, immersed in a cube-hexagon hyperspace!. This semiology, that is, physics and logic, of African culture goes beyond the post-colonial theme of struggle between invading European culture (represented by a rectangular box totem of Christian missionaries) and African culture (represented by the “creation snake”) that got trapped in the box in Chinua Achebe’s novel, Arrow of God.[6].
The correspondence between the “ichi” (linear writing) codes and the alphabet systems identified in ref.[1], i.e. Arabic(28), English(26), Igbo(36&38), etc and man (Adam) as the symbol of creation (32) is based on complementary representations of the “Afa” Matrix : 8x8 = 64 = 28+36 = 26+38 = 32+32 = 24+40, with consequential doubling of the reference objects.
Physically, linguistic geometry is based on sound as the vehicle of communication of the first human, called “Ele Chi Ife” or “Bearer of Light” (p.30 LTAA). Ele was the father of the forest people (Bushmen) which was the original meaning of the word Igbo who called themselves Sons of the Soil, i.e. the Adama and the Nshi. It is the claim of The Adam Trilogy that Ele evolved from the Big Bang before the Niphilim came and changed the course of things from evolution to creation; that Ele lived in Ugwuele Okigwe (Imo State) and environs and his language was the Igbo Afa word Atu (the origin of the Egyptian word Atum) which, according to Prof. J.A. Umeh [9] on p.81 of his 1977-published book titled After God Dibia, means “The Word of the Creator”. Afa is the Igbo word for Oracle - the Primeval Oracle Matrix given to the first people by God; its equivalent among the Yoruba is called Ifa. It was a language used by all growing things (man, beast and crystalline minerals) alike, a language of symbols and of geometry. which is why it is possible to lay the foundation for the creation of man (“Adam”) and the theory of everything (TOE) in geometry.
Consequently, the linguistic frames of reference (tetrahedron, square- based and hexagonal-based pyramids, cube, hexagon and pentagon) indicated in Fig. 2 are capable of uniting, on one hand, Gell-Mann-Ne’eman[10] 8x8 representation of the (SU(3)) symmetry of the strongly interaction particles in high energy physics from their occurrence in the product 8x8 = 1 + 8 + 17 + 8 + 10 + 10*, which (as shown on p. 31 of Y. Ne’eman’s [10] 1963-published book entitled Algebraic Theory of Particle Physics) contains two equivalent octets and splits into a symmetric 1 + 8 + 27 = 13+23+33 = 36 (dual pyramid) and antisymmetric 8+10+10* = 2x(12+22+32) = 28 (dual tetrahedron) parts. On the other hand the cube (S=26) [or hexagonal-based pyramid(S=26)] and the hexagon (S=38) satisfy a similar relation 26+38 = 64 = 8x8 which we shall explain in Sec. 3 of this paper after presenting the cosmological framework of the ancient African(Igbo-Ukwu) craftsmen, for the purpose of developing in Sec. 4 an African perspective on the string and superstring theory of everything espoused in the articles in Cambridge University Press 1988-published Superstrings, A Theory of Everything? edited by Davies and Brown[11] as well as Kaku’s[4] 1995- published Hyperspace and Time Magazine[12] Dec. 31, 1999 edition on Albert
Physically, linguistic geometry is based on sound as the vehicle of communication of the first human, called “Ele Chi Ife” or “Bearer of Light” (p.30 LTAA). Ele was the father of the forest people (Bushmen) which was the original meaning of the word Igbo who called themselves Sons of the Soil, i.e. the Adama and the Nshi. It is the claim of The Adam Trilogy that Ele evolved from the Big Bang before the Niphilim came and changed the course of things from evolution to creation; that Ele lived in Ugwuele Okigwe (Imo State) and environs and his language was the Igbo Afa word Atu (the origin of the Egyptian word Atum) which, according to Prof. J.A. Umeh [9] on p.81 of his 1977-published book titled After God Dibia, means “The Word of the Creator”. Afa is the Igbo word for Oracle - the Primeval Oracle Matrix given to the first people by God; its equivalent among the Yoruba is called Ifa. It was a language used by all growing things (man, beast and crystalline minerals) alike, a language of symbols and of geometry. which is why it is possible to lay the foundation for the creation of man (“Adam”) and the theory of everything (TOE) in geometry.
Consequently, the linguistic frames of reference (tetrahedron, square- based and hexagonal-based pyramids, cube, hexagon and pentagon) indicated in Fig. 2 are capable of uniting, on one hand, Gell-Mann-Ne’eman[10] 8x8 representation of the (SU(3)) symmetry of the strongly interaction particles in high energy physics from their occurrence in the product 8x8 = 1 + 8 + 17 + 8 + 10 + 10*, which (as shown on p. 31 of Y. Ne’eman’s [10] 1963-published book entitled Algebraic Theory of Particle Physics) contains two equivalent octets and splits into a symmetric 1 + 8 + 27 = 13+23+33 = 36 (dual pyramid) and antisymmetric 8+10+10* = 2x(12+22+32) = 28 (dual tetrahedron) parts. On the other hand the cube (S=26) [or hexagonal-based pyramid(S=26)] and the hexagon (S=38) satisfy a similar relation 26+38 = 64 = 8x8 which we shall explain in Sec. 3 of this paper after presenting the cosmological framework of the ancient African(Igbo-Ukwu) craftsmen, for the purpose of developing in Sec. 4 an African perspective on the string and superstring theory of everything espoused in the articles in Cambridge University Press 1988-published Superstrings, A Theory of Everything? edited by Davies and Brown[11] as well as Kaku’s[4] 1995- published Hyperspace and Time Magazine[12] Dec. 31, 1999 edition on Albert
Einstein as Person of the Century). While Witten’s supergravity (string) theory[12], also called the M-theory, is constructed in 11-dimensional hyperspace geometry inhabited by weird objects called branes, superstring TOE distinguishes an open string model with gauge group SO(32) and a closed (“heterotic”) string model with gauge group E8xE8 for grand unification of strong and electroweak forces with gravity in hyperspaces of 10- and 26-dimensions that get compactified to the observed O(3,1) Minkowki space-time. The crux of the problem in these theories is the dichotomy of point-like and extended (string-like) particles and analytically, hyperspaces of more than four dimensions[13] used in TOE correspond to the Da Vinci Codes number (S) of the geometrically closed (linguistic) objects of the theory while the uncertainty principle relating energy and time in conventional quantum mechanics and energy and extremely short distances (much smaller than the observed size of elementary particles) in quantum theory of gravity is linked to the existence of black hole singularity in the universe (see, M. Green’s article at p.123 of ref.[11] and Stephen Hawking’s [14] 1988-published Bantam book entitled A Brief History of Time from the Big Bang to Black Holes). For the geometrically closed objects, the mathematical singularity of Einstein’s general relativity theory of gravitation arises in the representation of interaction between strings (in Feynman space-time picture of quantum field theory) by world sheets which are topologically equivalent to a sphere or torus with an arbitrary number of holes. Consequently, if we adopt Kaku’s procedure (p. 160 ref’[4]) for constructing TOE from geometry along Einstein’s unified field programme: Geometry =>Field Theory=>Classical theory=>Quantum theory, the following correspondence principle with concepts of quantum field theory, Points <=> Particles, Lines <=> Fields, Planes <=> Currents, can be used to construct an African perspective on TOE based on cube-hexagon hyperspace/torus and current algebra as will be presented in Sec.4. The results will be discussed in Sec. 5 where conclusions will also be drawn.
3. AFRICAN WORLD VIEW
3.1 Cosmological Framework
3.1 Cosmological Framework
As stated by Animalu[15] in his 1988 Lecture to the Nigerian Academy of Science titled, Science, Religion and African Culture: “throughout history, human societies have developed world views and cosmological frames of reference for organizing their activities. These world views explain the how and why of daily existence and therefore constitute the essential cultural ingredient of every society. 'Usually the views are products of experiences so pregnant with drama that they give rise to symbols or totems of some sort; the symbols or totems give rise to thought; and thoughts give rise to customs and codes of the society. The world view of a society is successful to the extent that it is so internalized, from childhood onwards, that it goes unquestioned, manifesting itself in various forms of geometric symbols as written language and other artistic expressions”. Consequently, as the foremost African scientific historiographer, Professor K.O. Dike[16] put it in a paper for UNESCO in 1960
“Africa in particular has confronted scholars with communal societies where science cannot be separated from religion, or religion from law and politics, where history is nothing but the history of the whole culture, a seamless garment of such fine-woven texture, that any attempts to separate single strands merely distort the whole.”
It is from this holistic perspective that we may look at Anya’s[17] dictum: "Most African Societies. including the Nigerian society, operate on a cosmological framework in which time is conceived as cyclical and space is organized in three compartments - the heavens above, the earth below it and the underworld beneath the earth - all conceived as contiguous and continuous, once more in a cyclical continuum, as summarized succinctly in Fig.3a[below], derived from Kalu[18].
Thus in ref.[15] the distinctive concept in Kalu’s representation of African cosmic space-time continuum in Fig. 3a was identified as cyclical “African time” related by a Mobius (non-unitary) transformation to the conventional linear time of classical (Newtonian & special relativistic) and (Heisenberg) quantum mechanics. Consequently, one may follow Kepler’s[16] use of Platonic solids as “archetypes” in his reconstruction of cosmic pentagon grid around a spherical model of Sun- centred (Copernican) planetary system, and similarly use interconnected equilateral triangles to reconstruct Kalu’s African cosmic space and cyclic time continuum so as to reproduce the distinctive hexagonal grid on the African (Igbo- Ukwu) bronze torus as indicated in Fig. 3b
It is from this holistic perspective that we may look at Anya’s[17] dictum: "Most African Societies. including the Nigerian society, operate on a cosmological framework in which time is conceived as cyclical and space is organized in three compartments - the heavens above, the earth below it and the underworld beneath the earth - all conceived as contiguous and continuous, once more in a cyclical continuum, as summarized succinctly in Fig.3a[below], derived from Kalu[18].
Thus in ref.[15] the distinctive concept in Kalu’s representation of African cosmic space-time continuum in Fig. 3a was identified as cyclical “African time” related by a Mobius (non-unitary) transformation to the conventional linear time of classical (Newtonian & special relativistic) and (Heisenberg) quantum mechanics. Consequently, one may follow Kepler’s[16] use of Platonic solids as “archetypes” in his reconstruction of cosmic pentagon grid around a spherical model of Sun- centred (Copernican) planetary system, and similarly use interconnected equilateral triangles to reconstruct Kalu’s African cosmic space and cyclic time continuum so as to reproduce the distinctive hexagonal grid on the African (Igbo- Ukwu) bronze torus as indicated in Fig. 3b
3.3 Representation of Cube-Hexagon Hyperspace by a Torus.
5. CONCLUSION
The finding in this paper is that all elementary particles can be represented in 6- dimensional cube-hexagon hyperspace with axes (B,L,Q) and (B,Y,I), in agreement with the demonstration by the Australian biologist Illert[28], winner of the Nobel Prize in physics, that an accurate representation of the growth of seashells occurs via the use of a six-dimensional space, that is, a space in which each axis is doubled. This leads to the conclusion that everything in nature including languages, nano-particles and elementary particles, exhibit the phenomenon of growth and hence life whose time-irreversible evolution is characterized by non-unitary discrete symmetry of six-dimensional cube-hexagon hyperspace that relates integral-charged leptons and rational-charged quarks: we call this the principle of complementary duality to which the next paper is devoted.
The finding in this paper is that all elementary particles can be represented in 6- dimensional cube-hexagon hyperspace with axes (B,L,Q) and (B,Y,I), in agreement with the demonstration by the Australian biologist Illert[28], winner of the Nobel Prize in physics, that an accurate representation of the growth of seashells occurs via the use of a six-dimensional space, that is, a space in which each axis is doubled. This leads to the conclusion that everything in nature including languages, nano-particles and elementary particles, exhibit the phenomenon of growth and hence life whose time-irreversible evolution is characterized by non-unitary discrete symmetry of six-dimensional cube-hexagon hyperspace that relates integral-charged leptons and rational-charged quarks: we call this the principle of complementary duality to which the next paper is devoted.
REFERENCES
[1] Animalu, A.O.E. and Acholonu, C. “Ichi” Linguistic Geometry and Evolution – A Commentary and They Lived Before Adam, African J. Physics, Vol. 2, pp. 373-392 (2010)
[2] Acholonu-Olumba, Catherine (with Ajay Prabhakar & Nneka C. Egbuna), The Gram Code of African Adam – Stone Books and Cave Libraries (referred to as GCAA), Catherine Acholonu Research Centre (CARC) Publication ISBN 978-31997-8-1(2005); They Lived Before Adam – Prehistoric Origins of the Igbo (referred to as TLBA), CARC Publication ISBN-978-2579-51-10 (2009); The Lost Testaments of the Ancestors of Adam – Unearthing the Heliopolis/IGBO-UKWU The Celestial City of the Gods of Ancient Egypt and India (referred to as LTAA), CARC Publication ISBN:978-31997-3-0 ( 2010).
[3] Rowland, Todd and Weisstein, Eric W. "Homology." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Homology.html
[4] M. Kaku Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension
[5] A.O.E. Animalu and W.A. Umezinwa, From African Symbols to Physics (Desk-published 1988 reprinted by Ucheakonam Foundation (Nig.) Ltd 1994). See also Charles Jenks in Signs, Symbols and Architecture ed. G. Broadbent, R. Bunt and C. Jenks (J. Wiley & Sons Ltd. NY, 1981) p.7.
[6] Chinua Achebe, Arrow of God (Doubleday/Anchor, NY, 1969 revised edition)
[7] See References to Thurston Shaw & Anozie in ref.[2] LTAA.
[8] Dan Brown, The Da Vinci Code , see also by the same author, Angels and Demons(Washington Square Press, available on paperback, 2009).
[9] J.A. Umeh, After God Dibia (1977)
[10] See, Y. Ne’eman, Algebraic theory of Particle Physics (Benjamin Inc, 1963).
[11] Davies and Brown edit. Superstrings, A Theory of Everything? (Cambridge Univ. Press, 1988)
[12] Time Magazine Dec 31, 1999 Edition on A. Einstein as Person of the Century.
[13] A.O.E. Animalu and A.O. Azali, Language and Dimensionality in Physics, The Prospect of African Renascence African J. Physics, Vol. 1, p. 255-283 (2008).
[14] Stephen Hawking, A Brief History of Time from the Big Bang to Black Holes (Bantam, 1988).
[15] A.O.E.Animalu, Science, Religion an African Culture, Discourses of Nigeria Academy of Science vol. 9, p.45 (1988).
[16] K.O. Dike Selected Works of Kenneth Onwuka dike, ed. C. Ifemesia (KODIC, Awka, 1988) p. 38.
[17] A. O. Anya, in Basic Science Development in Nigeria, problem and prospects ed. Sam Okoye and K. Motso Onuoha (Evans Brothers, Nig. 1987) p. 91 [17] O. Kalu, Precarious Vision in Readings in African Humanities, African Cultural Development (Fourth Dimension Publishing 1987).
[18] J. Kepler in Arthur Koestler’s[3] Sleepwalkers-A history of Man’s Changing Vision of the Universe Pelican Books (1984) p.399.
[19] M.I. Katsnelson, K.S. Novoselov, Graphene: New bridge between condensed matter physics and quantum electrodynamics, Solid State Communications 143 (2007) 3–13
[20] Animalu, A.O.E, Intermediate Quantum Theory of Crystalline Solids (Prentice-Hall, 1977); see also J.M. Ziman, Electrons and Phonons (Oxford Univ. Press, 1960).
[21] National Goegraphic Google Maps.
[22] www.puzzles.com – Puzzle Playground, geometrical Puzzles - Hexagon Inside the Cube (© 2004 ThinkFun.Inc).
[23] A. Maduemezia De-Sitter Group Approach to the Theory of Gravitation, J. Nig. Ass. Math. Phys. 3, 1 (1999).
[24] A.O.E. Animalu, Review of GAGUT available at http://www.math.buffalo.edu/mad/physics/Animalu_Alex_GAGUTreview1.pdf
[25] A.O.Barut, Phys. Rev. Letters 20, 893 (1968).
[26] A.O.E. Animalu, Phys. Rev. D4, 1922 (1971)
[27] R.M. Santilli, Hadronic J. 1, 574 (1978).
[28] Dr. Chris Illert, “sub-physical underpinnings of matter”, Alchemy Today volume 1, matter on the E5 level: Platonic Geometries in Nuclear Physics, a Centennial Commemoration of Occult Chemistry 1895-1995; First Edition 1992/5, 172 A4 pages, ISBN: 0 949357 13 8 (v1); see also C. R. Illert and R. M. Santilli, Foundation of Theoretical Conchology, Hadronic Press (1995), http://www.santilli-foundation.org/docs/Santilli-109.pdf
[2] Acholonu-Olumba, Catherine (with Ajay Prabhakar & Nneka C. Egbuna), The Gram Code of African Adam – Stone Books and Cave Libraries (referred to as GCAA), Catherine Acholonu Research Centre (CARC) Publication ISBN 978-31997-8-1(2005); They Lived Before Adam – Prehistoric Origins of the Igbo (referred to as TLBA), CARC Publication ISBN-978-2579-51-10 (2009); The Lost Testaments of the Ancestors of Adam – Unearthing the Heliopolis/IGBO-UKWU The Celestial City of the Gods of Ancient Egypt and India (referred to as LTAA), CARC Publication ISBN:978-31997-3-0 ( 2010).
[3] Rowland, Todd and Weisstein, Eric W. "Homology." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Homology.html
[4] M. Kaku Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension
[5] A.O.E. Animalu and W.A. Umezinwa, From African Symbols to Physics (Desk-published 1988 reprinted by Ucheakonam Foundation (Nig.) Ltd 1994). See also Charles Jenks in Signs, Symbols and Architecture ed. G. Broadbent, R. Bunt and C. Jenks (J. Wiley & Sons Ltd. NY, 1981) p.7.
[6] Chinua Achebe, Arrow of God (Doubleday/Anchor, NY, 1969 revised edition)
[7] See References to Thurston Shaw & Anozie in ref.[2] LTAA.
[8] Dan Brown, The Da Vinci Code , see also by the same author, Angels and Demons(Washington Square Press, available on paperback, 2009).
[9] J.A. Umeh, After God Dibia (1977)
[10] See, Y. Ne’eman, Algebraic theory of Particle Physics (Benjamin Inc, 1963).
[11] Davies and Brown edit. Superstrings, A Theory of Everything? (Cambridge Univ. Press, 1988)
[12] Time Magazine Dec 31, 1999 Edition on A. Einstein as Person of the Century.
[13] A.O.E. Animalu and A.O. Azali, Language and Dimensionality in Physics, The Prospect of African Renascence African J. Physics, Vol. 1, p. 255-283 (2008).
[14] Stephen Hawking, A Brief History of Time from the Big Bang to Black Holes (Bantam, 1988).
[15] A.O.E.Animalu, Science, Religion an African Culture, Discourses of Nigeria Academy of Science vol. 9, p.45 (1988).
[16] K.O. Dike Selected Works of Kenneth Onwuka dike, ed. C. Ifemesia (KODIC, Awka, 1988) p. 38.
[17] A. O. Anya, in Basic Science Development in Nigeria, problem and prospects ed. Sam Okoye and K. Motso Onuoha (Evans Brothers, Nig. 1987) p. 91 [17] O. Kalu, Precarious Vision in Readings in African Humanities, African Cultural Development (Fourth Dimension Publishing 1987).
[18] J. Kepler in Arthur Koestler’s[3] Sleepwalkers-A history of Man’s Changing Vision of the Universe Pelican Books (1984) p.399.
[19] M.I. Katsnelson, K.S. Novoselov, Graphene: New bridge between condensed matter physics and quantum electrodynamics, Solid State Communications 143 (2007) 3–13
[20] Animalu, A.O.E, Intermediate Quantum Theory of Crystalline Solids (Prentice-Hall, 1977); see also J.M. Ziman, Electrons and Phonons (Oxford Univ. Press, 1960).
[21] National Goegraphic Google Maps.
[22] www.puzzles.com – Puzzle Playground, geometrical Puzzles - Hexagon Inside the Cube (© 2004 ThinkFun.Inc).
[23] A. Maduemezia De-Sitter Group Approach to the Theory of Gravitation, J. Nig. Ass. Math. Phys. 3, 1 (1999).
[24] A.O.E. Animalu, Review of GAGUT available at http://www.math.buffalo.edu/mad/physics/Animalu_Alex_GAGUTreview1.pdf
[25] A.O.Barut, Phys. Rev. Letters 20, 893 (1968).
[26] A.O.E. Animalu, Phys. Rev. D4, 1922 (1971)
[27] R.M. Santilli, Hadronic J. 1, 574 (1978).
[28] Dr. Chris Illert, “sub-physical underpinnings of matter”, Alchemy Today volume 1, matter on the E5 level: Platonic Geometries in Nuclear Physics, a Centennial Commemoration of Occult Chemistry 1895-1995; First Edition 1992/5, 172 A4 pages, ISBN: 0 949357 13 8 (v1); see also C. R. Illert and R. M. Santilli, Foundation of Theoretical Conchology, Hadronic Press (1995), http://www.santilli-foundation.org/docs/Santilli-109.pdf