Tertium Organum

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And sware . . . that there should be time no longer.
Revelation 10: 6
That ye, being rooted and grounded in love, may be able to comprehend with all 
saints what is the breadth, the length, the depth and the height.
St Paul's Epistle to the Ephesians 3: 17, 18

What do we know and what do we not know? Our known data 
and our unknown data. Unknown quantities taken as known 
quantities. Matter and motion. What does positivist philosophy
arrive at? Identity of the unknown quantities: 
x = y, y

What do we actually know? The existence of consciousness in 
us and of the world outside us. Dualism or monism? 
Subjective and objective cognition. Where do the causes of 
sensations lie? Kant's system. Time and space. Mach's 
observation. What the physicist actually works with. 
A new view of Kant's problem. Hinton's books. 'Space-sense' 
and its evolution. A system for developing the sense of the 
fourth dimension by means of exercises with different 
coloured cubes. The geometrical concept of space. Three 
perpendiculars. Why are there only three? Can everything 
existing be measured by three perpendiculars? Physical and 
metaphysical facts. Signs of existence. The reality of ideas. 
The insufficient evidence of the existence of matter and 
motion. Matter and motion are only logical concepts, like 
'good' and 'evil'. 
What can we learn about the fourth dimension by studying 
geometrical relationships within our space? What should be 
the relationship of a three-dimensional body to a four­
dimensional one? A four-dimensional body as the trace of the 
movement of a three-dimensional body in a direction not 
contained in it. A four-dimensional body as composed of an 

number of three-dimensional bodies. A three-dimensional 
body as a section of a four-dimensional one. Parts of bodies 
and whole bodies in three and in four dimensions. 
Incommensurability of a three-dimensional and a four­
dimensional body. A material atom as a section of a four­
dimensional line. 
In what direction may the fourth dimension lie? What is 
motion? Two kinds of movement - movement in space and 
movement in time - contained in every motion. What is time? 
Present past and future. Wundt on sense-cognition. Groping 
through life. Why we do not see the past and the future. A new 
extension in space and motion in that space. Two ideas 
contained in the concept of time. Time as the fourth dimension 
of space. Impossibility of understanding the idea of the fourth 
dimension without the idea of motion. The idea of motion and 
'time-sense'. 'Time-sense' as the limit (surface) of space sense. 
Riemann's idea of the translation of time into space in the 
fourth dimension. Hinton on the law of surfaces. 'Ether' as a 
Four-dimensional space. 'Time-body' - Linga Sharira. Form of 
the human body from birth to death. Incommensurability of a 
three-dimensional and a four-dimensional body. Newton's 
fluents. Unreality of constant magnitudes in our world. Right 
and left hand in three-dimensional and a four-dimensional 
space. Differences between three-dimensional and four­
dimensional space. Not two different spaces, but two different 
modes of perception of one and the same world. 
Methods of investigating the problem of higher dimensions. 
Analogy between imaginary worlds of different dimensions. 
One-dimensional world on a line. 'Space' and 'time' of a one­
dimensional being. Two-dimensional world on a plane. 'Space' 
and 'time', 'ether', 'matter' and 'motion' of a two-dimensional 

being. Reality and illusion on a plane. Impossibility of seeing an
'angle'. An 'angle' as motion. Incomprehensibility, for a two­
dimensional being of the functions of the objects of our world. 
Phenomena and noumena of a two-dimensional being. How 
could a plane being understand the third dimension? 
Impossibility of a mathematical definition of dimensions. Why
does mathematics not feel dimensions? The entirely 
conventional character of the designation of dimensions by 
powers. The possibility of representing all the powers on a line. 
Kant and Lobachevsky. The difference between non-Euclidean 
geometry and metageometry. Where should we seek the 
explanation of the three-dimensionality of the world, if Kant's 
ideas are correct? Are not the three-dimensional conditions of 
the world to be found in our perceiving apparatus, in our mind? 
Our perceiving apparatus. Sensation. Representation Concept.
Art as the language of the future. To what extent does the three­
dimensionality of the world depend on the properties of our 
perceiving apparatus? What could prove this dependence? 
Where could we find a real confirmation of this dependence? 
Psychology of animals. In what does it differ from the human? 
Reflex. Irritability of the cell. Instinct. Pleasure - pain. 
Emotional thinking. Absence of concepts. Language of animals. 
Logic of animals. Different levels of intelligence in animals. 
The goose, the cat, the dog and the monkey. 
Perception of the world by man and by animals. Illusions of 
animals and their lack of control over perceptions. A world of 
moving planes. Angles and curves as motion. Third dimension 
as motion. The two-dimensional appearance, for animals, of our 
three-dimensional world. Animals as real two-dimensional 
beings. Lower animals as one-dimensional beings. 

Time and space of a snail. Time-sense as a nebulous space­
sense. Time and space of a dog. Change of the world with a 
change of the mental apparatus. Proof of Kant's problem. 
Three-dimensional world as an illusory representation. 
Spatial understanding of time. Four-dimensional angles and 
curves in our life. Does motion exist in the world or not? 
Mechanical motion and 'life'. Biological phenomena as 
manifestations of motion proceeding in higher space. Evolution 
of space-sense. Growth of space-sense and diminution of time­
sense. Translation of time-sense into space-sense. Handicaps 
presented by our concepts, our language. The need to find a 
method of expressing time-concepts spatially. Science on the 
fourth dimension. A four-dimensional body. Four-dimensional 
Science and the problem of the fourth dimension. Paper read 
by Professor N. A. Oumoff at the Mendeleev Convention in 
1911, 'The Characteristic Features and Problems of 
Contemporary Natural-scientific Thought*. New physics. 
Electro-magnetic theory. Principles of relativity. The works of 
Einstein and Minkowsky. Simultaneous existence of the past 
and the future. The eternal Now. Van Manen's book on occult 
experiences. Diagram of a four-dimensional figure. 
Analysis of phenomena. What determines for us different 
orders of phenomena? Methods and forms of the transition of 
phenomena of one order into another. Phenomena of motion. 
Phenomena of life. Phenomena of consciousness. The central 
question of our perception of the world: which kind of 
phenomena is primary and produces the others? Can motion lie 
at the beginning of everything? Laws of the transformation of 
energy. Simple transformation and the liberation of latent 
energy. Different liberating forces 

of different kinds of phenomena. The force of mechanical 
energy, the force of a living cell and the force of an idea. 
Phenomena and noumena of our world. 
The apparent and the hidden side of life. Positivism as the 
study of the phenomenal aspect of life. What constitutes the 
'two-dimensionality' of positivist philosophy? Envisaging 
everything on one plane, in one physical sequence. Streams 
flowing under the earth. What can the study of life, as a 
phenomenon, give? The artificial world which science builds 
for itself. The non-existence, in actual fact, of completed and 
isolated phenomena. A new sense of the world. 
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 the shadow of a saint. The soul of a hangman 
and the soul of a saint. The different combinations of 
phenomena known to us in higher space. The connectedness of 
phenomena which seem to us separate, and the difference 
between phenomena which appear to be similar. How should 
we approach the noumenal world? The understanding of things 
outside the categories of time and space. The reality of a great 
many 'figures of speech'. The occult understanding of energy. 
The letter of a Hindu occultist. Art as the cognition of the 
noumenal world. What we see and what we do not see. Plato's 
dialogue about the cave. 
Occultism and love. Love and death. Different attitudes to 
problems of death and problems of love. What is lacking in our 
understanding of love? Love as an everyday and a 
psychological phenomenon. Possibility of a religious 
understanding of love. The creative force of love. The negation 
of love. Running away from love. Love and mysticism. The 
'miraculous' in love. Nietzsche and Edward Carpenter on love. 

The phenomenal and the 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 conditions of space 
not analogous to ours? Brain and consciousness. Unity of the 
world. Logical impossibility of a simultaneous existence of 
spirit and matter. Either all is spirit or all is matter. Rational 
and irrational actions in nature and in man's life. Can rational 
actions exist side by side with irrational? The world as an 
accidentally produced mechanical toy. The impossibility of 
consciousness in a mechanical universe. The impossibility of 
mechanicalness if consciousness exists. The fact of human 
consciousness interfering with the mechanical system. The con­
sciousness of other cross-sections of the world. How can we 
know about them? Kant on 'spirits'. Spinoza on the cognition of 
the invisible world. Necessity for the intellectual definition of 
what is possible and what is impossible in the noumenal world. 
A living and intelligent universe. Different forms and lines of 
intelligence. Animated nature. Souls of stones and souls of 
trees. The soul of a forest. The human 'I' as a collective 
intelligence. Man as a complex being. 'Mankind' as a being. 
The soul of the world. The face of 

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