This book is an attempt to set a stage for reconstructing the consciousness of the world with regard to Africa along a complementary duality of two geometries Euclidean and non-Euclidean. It presupposes by extension a complementary duality of Newtonian Mechanics and wave mechanics. It is a complementary duality between European (pre-Einstein) traditional culture and African traditional culture. This study shows different geometrical levels of this complementary duality of the Western linear and the African curvilinear creation axioms. This exposition also shows alternative pathways for opening up the confinement of the African worldview and stirring up scientific culture in the African world.lines through arts and science in the 21st Century.