HYPERSPACE AND THE TORUS REVISITED: AN AFRICAN After God Dibia, means “The Word of the Creatorâ€‌

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African Journal of Physics Vol.3, 2010.

HYPERSPACE AND THE TORUS REVISITED: AN AFRICAN PERSPECTIVE ON THE THEORY OF EVERYTHING†

A. O.E. Animalu1 and Professor Catherine O. Acholonu2 1 Dept. of Physics & Astronomy, University of Nigeria, Nsukka &

Chairman/CEO, International Centre for Basic Research, Abuja

2 Catherine Acholonu Research Center, Abuja

e-mail: 1

ibr32@aol.com 2 ikomgram@yahoo.com

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

PointsParticles, LinesFields, PlanesCurrents.

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,

† African Journal of Physics Vol.3, pp. 31-50, (2010)

ISSN: PRINT: 1948-0229 CD ROM:1948-0245 ONLINE: 1948-0237

mailto:ibr32@aol.com mailto:ikomgram@yahoo.com

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African Journal of Physics Vol.3, 2010.

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 10 th

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].

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African Journal of Physics Vol.3, 2010.

2. REVIEW OF THE ADAM TRILOGY Our primary interest in ref.[1] was to characterize the linear writing code

(preserved in Ikom Monoliths) of the African[Igbo] Mother tongue of world

languages discussed in GCAA and the various artefacts excavated by the British

archaeologist, Thurston Shaw[7], in 1950s at Igbo-Ukwu in South Eastern

Nigeria, especially the bronze hyper-doughnut(torus) (TLBA, p.447) shown in

Fig. 1 in terms of the facial scarification, (called “ichi”) discussed in TLBA &

LTAA, and the stone age axe excavated by Anozie[7]. Projective geometry comes

into play through Da Vinci codes[8] defined (like Miller indices in solid state

physics) by the ratios and total number (S) of the three primitive geometric

elements, points(vertices) :lines(edges): planes(faces), of the various geometric

objects, e.g. 4:6:4 (S=14) for the tetrahedron and 5:8:5 (S=18) for square-based

pyramid, 8:12:6 (S=26) for cube, 7:12:7 (S=26) for hexagonal-based pyramid and

12:18:8 (S=38) for hexagon, etc. Accordingly, from the statement (p. 128,

TLBA) that “Eve or Shi in plane geometry meant the side of a square or triangle”

and (pp. 155 & 177,TLBA) quoting from Nag Hammadi that “the entities Father

[Nna], mother [Nne] and Child [Nwa] exist as perceptible speech” having in them

Fig. 1

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African Journal of Physics Vol.3, 2010.

“three powers, and abiding in three NNN, three quadrangles, secretly in ineffable

silence” [of the Ikom Monoliths], we set up a correspondence in Fig. 2.

FIG.2: Summary of “ichi” Linguistic Geometry: Row (i)

Realization of 28+36=64=8x8;(ii) 26+38=64=8x8 & (iii) 32+32=64=8x8

as Hyperspace Geometries for systems of alphabets: Arabic(28),

Igbo(36,38), English(26), & Man (Adam) symbol of Creation (32).

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African Journal of Physics Vol.3, 2010.

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 Par