Chapter I (part 2)

Phenomena and noumena of a two-dimensional being. How could a plane being comprehend the third dimension? 59 CHAPTER VII The impossibility of the mathematical definition of dimensions. Why does not mathematics sense dimensions? The entire conditionality of the representation of dimensions by powers. The possibility of representing all powers on a line. Kant and Lobachevsky. The difference between non-Euclidian geometry and metageometry. Where shall we find the explanation of the three-dimensionality of the world, if Kant's ideas are true? Are not the conditions of the three-dimensionality of the world confined to our receptive apparatus, to our psyche? 73 CHAPTER VIII Our receptive apparatus. Sensation. Perception. Conception. Intuition. Art as the language of the future. To what extent does the three-dimensionality of the world depend upon the properties of our receptive apparatus? What might prove this interdependence? Where may we find the real affirmation of this interdependence? The animal psyche. In what does it differ from the human? Reflex action. The irritability of the cell. Instinct. Pleasure-pain. Emotional thinking. The absence of concepts. Language of animals. Logic of animals. Different degrees of psychic development in animals. The goose, the cat, the dog and the monkey. 80 CHAPTER IX The receptivity of the world by a man and by an animal. Illusions of the animal and its lack of control of the receptive faculties. The world of moving planes. Angles and curves considered as motion. The third dimension as motion. The animal's two-dimensional view of our three-dimensional world. The animal as a real two-dimensional being. Lower animals as one-dimensional beings. The time and space of a snail. The time-sense as an imperfect space-sense. The time and space of a dog. The change in the world coincident with a change in the psychic apparatus. The proof of Kant's problem. The three-dimensional world—an illusionary perception. 98 p. ix CHAPTER X The spatial understanding of time. The angles and curves of the fourth dimension in our life. Does motion exist in the world or not? Mechanical motion and "life." Biological phenomena as the manifestation of motions going on in the higher dimension. Evolution of the space-sense. The growth of the space-sense and the diminution of the time-sense. The transformation of the time-sense into the space-sense. The difficulties of our language and of our concepts. The necessity for seeking a method of spatial expression for temporal concepts. Science in relation to the fourth dimension. The solid of four dimensions. The four-dimensional sphere. 112 CHAPTER XI Science and the problem of the fourth dimension. The address of Prof. N. A. Oumoff before the Mendeleevskian Convention in 1911—"The Characteristic Traits and Problems of Contemporary Scientific Thought." The new physics. The electromagnetic theory. The principle of relativity. The works of Einstein and Minkowsky. Simultaneous existence of the past and the future. The Eternal Now. Van Manen's book about occult experiences. The drawing of a four-dimensional figure. 124 CHAPTER XII Analysis of phenomena. What defines different orders of phenomena for us? Methods and forms of the transition of one order of phenomena into another. Phenomena of motion. Phenomena of life. Phenomena of consciousness. The central question of our knowledge of the world: what mode of phenomena is generic and produces the others? Can the origin of everything lie in motion? The laws of transformation of energy. Simple transformation and liberation of latent energy. Different liberating forces of different orders of phenomena. The force of mechanical energy, the force of a living cell, the force of an idea. Phenomena and noumena of our world 136 CHAPTER XIII The apparent and hidden side of life.