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What do we know and what do we not know? Our data, and the things for which
we seek. The unknown mistaken for the known. Matter and motion. What
does the positive philosophy come to? Identity of the unknown: x=y, y=x.
What we really know. The existence of consciousness in us, and of the world
outside of us. Dualism or monism? Subjective and objective knowledge.
Where do the causes of the sensations lie? Kant's system. Time and Space.
Kant and the "ether." Mach's observation. With what does the physicist
really deal?
CHAPTER II
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A new view of the Kantian problem. The books of Hinton. The "space-sense"
and its evolution. A system for the development of a sense of the fourth
dimension by exercises with colored cubes. The geometrical conception of
space. Three perpendiculars-why three? Can everything existing be measured
by three perpendiculars? The indices of existence. Reality of ideas. Insuf-
ficient evidence of the existence of matter and motion. Matter and motion
are only logical concepts, like "good" and "evil." .
CHAPTER III
What may we learn about the fourth dimension by a study of the geometrical
relations within our space? What should be the relation between a three-
dimensional body and one of four dimensions? The four-dimensional body as
the tracing of the movement of a three-dimensional body in the direction which
is not confined within it. A four-dimensional body as containing an infinite
number of three-dimensional bodies. A three dimensional body as a section
of a four-dimensional one. Parts of bodies and entire bodies in three and in
four dimensions. The incommensurability of a three-dimensional and a four-
dimensional body. A material atom as a section of a four-dimensional line. .
CHAPTER IV
In what direction may the fourth dimension lie? What is motion? Two kinds
of motion-motion in space and motion in time-which are contained in every
movement. What is time? Two ideas contained in the conception of time.
The new dimension of space, and motion upon that dimension. Time as the
fourth dimension of space. Impossibility of understanding the fourth dimension
without the idea of motion. The idea of motion and the "time-sense." The time
sense as a limit (surface) of the "space-sense.' Hinton on the law of surfaces,
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99
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The "ether" as a surface. Riemann's idea concerning the translation of time
into space in the fourth dimension. Present, past, and future. Why do we not
see the past and the future. Life as a feeling of one's way. Wundt on the
subject of our sensuous knowledge.
CHAPTER V
Four-dimensional space. "Temporal body"-Linga Sharira. The form of a human
body from birth to death. Incommensurability of three-dimensional and four-
dimensional bodies. Newton's fluents. The unreality of constant quantities in
our world. The right and left hands in three-dimensional and in four dimen-
sional space. Difference between three-dimensional and four-dimensional space.
Not two different spaces but different methods of receptivity of one and the
same world..
CHAPTER VI
Methods of investigation of the problem of higher dimensions. The analogy be-
tween imaginary worlds of different dimensions. The one-dimensional world
on a line. "Space" and "time" of a one-dimensional being. The two-dimen-
sional world on a plane. "Space" and "time," "ether," "matter," and "motion"
of a two-dimensional being. Reality and illusion on a plane. The impossibility
of seeing an "angle." An angle as motion. The incomprehensibility to a two-
dimensional being of the functions of things in our world. Phenomena and
noumena of a two-dimensional being. How could a plane being comprehend
the third dimension?
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 exent 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.
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.
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CONTENTS
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.
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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 electro-
magnetic theory. The principle of relativity. The works of Einstein and Min-
kowsky. 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.
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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.
CHAPTER XIII
The apparent and hidden side of life. Positivism as the study of the phenomenal
side of life. Of what does the "two-dimensionality" of positive philosophy con-
sist? The regarding of everything upon a single plane, in one physical se-
quence. The streams which flow underneath the earth. What can the study of
life, as a phenomenon, yield? The artificial world which science erects for
itself. The unreality of finished and isolated phenomena. The new apprehen-
sion of the world.
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CHAPTER XIV
The voices of stones. The wall of a church and the wall of a prison. The mast of a
ship and a gallows. The shadow of a hangman and of an ascetic. The soul
of a hangman and of an ascetic. The different combinations of known phe-
nomena in higher space. The relationship of phenomena which appear unrelated,
and the difference between phenomena which appear similar. How shall we
approach the noumenal world? The understanding of things outside the cate-
gories of space and time. The reality of many "figures of speech." The occult
understanding of energy. The letter of a Hindu occultist. Art as the knowl-
edge of the noumenal world. What we see and what we do not see. Plato's
dialogue about the cavern.
156
CHAPTER XV
Occultism and love. Love and death. Our different relations to the problems of
death and to the problems of love. What is lacking in our understanding of
love? Love as an every-day and merely psychological phenomena. The possi
bility of a spiritual understanding of love. The creative force of love. The
negation of love. Love and mysticism. The "wondrous" in love. Nietzsche,
Edward Carpenter and Schopenhauer on love. "The Ocean of Sex."
CHAPTER XVI
The phenomenal and noumenal side of man. “Man-in-himself." How do we know
the inner side of man? Can we know of the existence of consciousness in con-
ditions of space not analogous to ours? Brain and consciousness. Unity of the
world. Logical impossibility of the simultaneous existence of spirit and matter.
Either all spirit or all matter. Rational and irrational actions in nature and in
the life of man. Can rational actions exist alongside irrational? The world
as an accidentally self-created mechanical toy. The impossibility of reason in
a mechanical universe. The irreconcilability of mechanicalness with the exist
ence of reason. Kant concerning "hosts." Spinoza on the knowledge of the
invisible world. Necessity for the intellectual definition of that which can be,
and that which cannot be, in the world of hidden. .
CHAPTER XVII
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A living and rational universe. Different forms and lines of rationality. Animated
nature. The souls of stones and the souls of trees. The soul of a forest. The
human "I" as a collective rationality. Man as a complex being. "Humanity"
as a being. The world's soul. The face of Mahadeva. Prof. James on the
consciousness of the universe. Fechner's ideas. Zendavesta. A living Earth. 198
CHAPTER XVIII
Rationality and life. Life as knowledge. Intellect and emotions. Emotion as an
organ of knowledge. The evolution of emotion from the standpoint of knowl-
edge. Pure and impure emotions. Personal and impersonal emotions. Personal
and super-personal emotions. The elimination of self-elements as a means of
approach to true knowledge. "Be as little children. . . "Blessed are the
pure in heart. . . ." The value of morals from the standpoint of knowledge.
The defects of intellectualism. Dreadnaughts as the crown of intellectual cult-
ure. The dangers of morality. Moral esthetics. Religion and art as organized
forms of emotional knowledge. The knowledge of God and the knowledge of
Beauty.
CHAPTER XIX
The intellectual method, objective knowledge. The limits of objective knowledge.
The possibility of the expansion of the application of the psychological method.
New forms of knowledge. The ideas of Plotinus. Different forms of conscious-
ness. Sleep (the potential state of consciousness). Dreams (consciousness en-
closed in itself, reflected from itself). Waking consciousness (dualistic sensa-
tion of the world, the division of the I and the Not-I). Ecstasy (the liberation
of the Self). Turiya (the absolute consciousness of all, as of the self). "The
dewdrop slips into the shining sea.” Nirvana.
CHAPTER XX
The sense of infinity. The neophyte's first ordeal. An intolerable sadness. The
loss of everything real. What would an animal feel on becoming a man? The
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