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This is P.D. Ouspensky's Tertium Organum, which he believed was the third major philosophical synthesis, the previous being those of Aristotle and Bacon. Originally issued in Russian in 1912, this is the second, revised edition. It was translated into English and published in 1922. This is the only major work by Ouspensky which is in the public domain in the US by current copyright laws.
Ouspensky (1878-1947) was a mystic who traveled widely in Europe and the East looking for esoteric knowledge. He later studied with G.I. Gurdjieff. In this book, he uses the concept of the fourth dimension as an extended metaphor for the esoteric nature of reality. Einstein and other physicists had at that time validated the study of higher dimensions, and Ouspensky was fixated on this idea. One can only wonder at what he would think of string theory, parallel universes, and the holographic universe hypothesis (the latter of which he prefigures in this book).
THE THIRD CANON OF THOUGHT
A KEY TO THE ENIGMAS OF THE WORLD
P. D. OUSPENSKY
TRANSLATED FROM THE RUSSIAN BY NICHOLAS BESSARABOFF AND CLAUDE BRAGDONâ€”WITH AN INTRODUCTION BY CLAUDE BRAGDON
SECOND AMERICAN EDITION, AUTHORIZED AND REVISED
THE MYSTERY OF SPACE AND TIME. SHADOWS AND REALITY, OCCULTISM AND LOVE. ANIMATED NATURE. VOICES OF THE STONES. MATHEMATICS OF THE INFINITE. THE LOGIC OF ECSTASY. MYSTICAL THEOSOPHY. COSMIC CONSCIOUSNESS. THE NEW MORALITY. BIRTH OF THE SUPERMAN.
NEW YORK; ALFRED A KNOPF
"And swear . . . THAT THERE SHOULD BE TIME NO LONGER."
REVELATIONS, X. 6
"That ye, being rooted and grounded in love may be able to COMPREHEND with all saints what is the BREADTH AND LENGTH AND DEPTH AND HEIGHT."
Paul the Apostle
THE EPISTLE TO THE EPHESIANS, III. 18
AUTHOR'S PREFACE TO THE SECOND EDITION
INTRODUCTION TO THE ENGLISH TRANSLATION
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?
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 perpendicularsâ€”why three? Can everything existing be measured by three perpendiculars? The indices of existence. Reality of ideas. Insufficient evidence of the existence of matter and motion. Matter and motion are only logical concepts, like "good" and "evil."
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.
In what direction may the fourth dimension lie? What is motion? Two kinds of motionâ€”motion in space and motion in timeâ€”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. p. viii 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.
Four-dimensional space. "Temporal body"â€”Linga SharÃ®ra. 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 dimensional space. Difference between three-dimensional and four-dimensional space. Not two different spaces but different methods of receptivity of one and the same world
Methods of investigation of the problem of higher dimensions. The analogy between imaginary worlds of different dimensions. The one-dimensional world on a line. "Space" and "time" of a one-dimensional being. The two-dimensional 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?
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?
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.
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 worldâ€”an illusionary perception.
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.
Science and the problem of the fourth dimension. The address of Prof. N. A. Oumoff before the Mendeleevskian Convention in 1911â€”"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.
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
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 consist? The regarding of everything upon a single plane, in one physical sequence. 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 apprehension 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 of an ascetic. The soul of a hangman and of an ascetic. The different combinations of known phenomena 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 categories 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 knowledge of the noumenal world. What we see and what we do not see. Plato's dialogue about the cavern
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 possibility 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."
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 conditions 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 existence 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.
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.
Rationality and life. Life as knowledge. Intellect and emotions. Emotion as an organ of knowledge. The evolution of emotion from the standpoint of knowledge. 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 culture. The dangers of morality. Moral esthetics. Religion and art as organized forms of emotional knowledge. The knowledge of God and the knowledge of Beauty.
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 consciousness. Sleep (the potential state of consciousness). Dreams (consciousness en-closed in itself, reflected from itself). Waking consciousness (dualistic sensation 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.
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 p. xi transition to the new logic. Our logic as founded on the observation of the laws of the phenomenal world. Its invalidity for the study of the world of noumena. The necessity for another logic. Analogy between the axioms of logic and of mathematics. TWO MATHEMATICS. The mathematics of real magnitudes (infinite and variable); and the mathematics of unreal, imaginary magnitudes (finite and constant). Transfinite numbersâ€”numbers lying beyond INFINITY. The possibility of different infinities.
Man's transition to a higher logic. The necessity for rejecting everything "real." "Poverty of the spirit." The recognition of the infinite alone as real. Laws of the infinite. Logic of the finiteâ€”the Organon of Aristotle and the Novum Organum of Bacon. Logic of the infiniteâ€”Tertium Organum. The higher logic as an instrument of thought, as a key to the mysteries of nature, to the hidden side of life, to the world of noumena. A definition of the world of noumena on the basis of all the foregoing. The impression of the noumenal world on an unprepared consciousness. "The thrice unknown darkness in the contemplation of which all knowledge is resolved into ignorance."
Theosophy of Max MÃ¼ller. Ancient India. Philosophy of the VedÃ¢nta. Tat twam asi. Knowledge by means of the expansion of consciousness as a reality. Mysticism of different ages and peoples. Unity of experiences. Tertium Organum as a key to mysticism. Signs of the noumenal world. Treatise of Plotinus On Intelligible Beauty as a misunderstood system of higher logic Illumination in Jacob Boehme. "A harp of many strings, of which each string is a separate instrument, while the whole is only one harp." Mystics of The Love of the Good. St. Avva Dorotheus and others. Clement of Alexandria. Lao-Tzu^ and Chuang-Tzu. Light on the Path. The Voice of the Silence. Mohammedan mystics. Poetry of the Sufis. Mystical states under narcotics. The Anaestetic Revelation. Experiments of Prof. James. Dostoyevsky on "time" (The Idiot). Influence of nature on the soul of man.
Cosmic Consciousness of Dr. Bucke. The three forms of consciousness according to Dr. Bucke. Simple consciousness, or the consciousness of animals. Self-consciousness, or the consciousness of men. Dr. Bucke's fundamental error. Cosmic consciousness. In what is it expressed? Sensation, perception, concept, higher MORAL conceptâ€”creative intuition. Men of cosmic consciousness. Adam's fall into sin. The knowledge of good and evil. Christ and the salvation of man. Commentary on Dr. Bucke's book. Birth of the new humanity. Two races. SUPERMAN. Table of the four forms of the manifestation of consciousness
TABLE OF THE FOUR FORMS OF CONSCIOUSNESS
AUTHOR'S PREFACE TO THE SECOND EDITION
IN revising Tertium Organum for the second edition in English my chief concern has been to coÃ¶rdinate its terminology with the more developed terminology of those of my books written after the publication of the second Russian edition of Tertium Organum, from which the English translation was made.
Such a unity of terminology is the more necessary because I am obliged to lead the reader into regions of thought and knowledge where boundaries have not been clearly established, and where different authorsâ€”and often one and the same author, in different works and during different periods of his activityâ€”have called the same thing by different names, or different things by the same name.
It must be admitted that language is a weak and inadequate vehicle even for the expression of our usual understanding of things, to say nothing of those moments when the understanding unexpectedly expands and becomes deeper, and we see revealed an entire series of facts and relations for the description of which we have neither words nor expressions. But quite aside from this, in ordinary conditions of thinking and feeling, we are frequently at a loss for words, and we use one word at different times to describe different things.
On the other hand, it is no merit in an author to invent new words, or to use old words in new meanings which have nothing in common with the accepted onesâ€”to create, in other words, a special terminology. I have always considered that it is necessary to write in the language which men commonly speak, and I have endeavored to do this, although in some cases it has been necessary to make some additions to and corrections of that language for the sake of exactness and lucidity.
In due time I shall separately consider the subject of language and the methods of its adaptation for the transmission of exact thought. For the present I have reference only to the language of Tertium Organum.
The first word demanding a more careful use is "consciousness."
In conversational language and in every-day psychology, even in psychology purporting to be scientific, the word consciousness is often used as a term for the designation of a complex of all psychic functions in general, or for their separate manifestations. At present I have not access to the necessary booksâ€”I abandoned them all in Petrograd, four years agoâ€”but to the best of my recollection Prof. William James defined thought as "a moment of consciousness."
From my standpoint, which I shall elucidate in works now being prepared for the press, it is necessary to regard consciousness as distinct from the commonly understood psychic functions: thought, feeling and sensation. Over and above all this, consciousness has several exactly definable forms or phases, in each one of which thoughts, feelings and sensations can function, giving in each different results. Thus consciousness (be it this or something other) is a background upon which thoughts, feelings and sensations reveal themselves. This background can be more or less bright. But as thoughts, feelings and sensations have their own separate life, and can be regarded independently of this background, so can it be regarded and studied independently of them. For the present I shall not insist too strongly upon the idea of this ground as something separate in its substance from psychic functions. The practical result is the same if we say that thoughts, feelings and sensations may have a different character, and that thoughts, feelings and sensations of this or that character create this or that state of consciousness. It is important only to establish the fact that thoughts, feelings and sensations, i.e., psychic functions, are not consciousness, and that this or that state of consciousness is something pertaining to them, but separate from them, and in some cases capable of being separately observed.
In the early editions of Tertium Organum I have used the word consciousness in its generally accepted meaning, i.e., as a complex of psychic functions, or in the sense of their indication and contents. But as in my future works it will be necessary for me to use the word consciousness in its real and true meaning, I have tried in this revised text of Tertium Organum to substitute for the word consciousness (wherever it is used in the sense of a complex of psychic functions)
such other words as psyche, or psychic life, which perfectly express my meaning in such cases.
Furthermore, in my work of revision, I have found numerous instances of illustrations, examples, etc., having no direct connection with the main theme. I have found also that some of these introduced themes vitiate the correctness of the main line of thought, creating associations which lead too far away. Other themes also, accidentally touched upon, demand a considerably more extended treatment than can be given them within the limits of this book, but being inadequately developed they leave a wrong impression.
In such cases I consider it necessary to eliminate this extraneous matter in order to elucidate the principal thought more clearly and directly, particularly as some of the questions touched upon demanding more or different exposition are discussed at length in my forth-coming books.
In conclusion, let me express to Mr. Nicholas Bessaraboff and to Mr. Claude Bragdon my deep appreciation of their labors on the translation of my book into English. This translation, made without my knowledge and participation, at a time when I was cut off by war and revolution from the civilized world, transmits my thought so exactly that after a very attentive review of the book I could find only one word to correct. Such a result could be achieved only because Mr. Bessaraboff and Mr. Bragdon were not translating words merely, but were grasping directly the thoughts back of them. Also, it is especially pleasant for me to remember that a number of years ago Mr. Bragdon's Man the Square reached me in Petrograd, and that I, not knowing Mr. Bragdon's other works at all, selected this little book from a whole series received from abroad, as one which carried the message of a common thought, a common understanding.
INTRODUCTION TO THE ENGLISH TRANSLATION
IN naming his book Tertium Organum Ouspensky reveals at a stroke that astounding audacity which characterizes his thought throughoutâ€”an audacity which we are accustomed to associate with the Russian mind in all its phases. Such a title says, in effect: "Here is a book which will reorganize all knowledge. The Organon of Aristotle formulated the laws under which the subject thinks; the Novum Organum of Bacon, the laws under which the object may be known; but The Third Canon of Thought existed before these two, and ignorance of its laws does not justify their violation. Tertium Organum shall guide and govern human thought henceforth."
How passing strange, in this era of negative thinking, of timid philosophizing, does such a challenge sound! And yet it has the echo in it of something heard beforeâ€”what but the title of another volume, Hinton's A New Era of Thought?
Ouspensky's Tertium Organum and Hinton's A New Era of Thought present substantially the same philosophy (though Hinton's book only sketchily), arrived at by the same routeâ€”mathematics.
Here is food for thought. In the words of Philip Henry Wynne, "Mathematics possesses the most potent and perfect symbolism the intellect knows; and this symbolism has offered for generations certain concepts (of which hyper-dimensionality is only one) whose naming and envisagement by the human intellect is perhaps its loftiest achievement. Mathematics presents the highest certitudes known to the intellect, and is becoming more and more the final arbiter and interpreter in physics, chemistry and astronomy. Like Aaron's rod it threatens to swallow all other knowledges as fast as they assume organized form. Mathematics has already taken possession of great provinces of logic and psychologyâ€”will it embrace ethics, religion and philosophy?"
In Tertium Organum mathematics enters and pervades the field of philosophy; but so adroitly, so silently as it were, that one hardly
knows that it is there. It dwells more in Ouspensky's method than in his matter, because for the most part the mathematical ideas necessary for an understanding of his thesis are such as any intelligent high school student can comprehend. The author puts to himself and to the reader certain questions, propounds certain problems, which have baffled the human mind for thousands of yearsâ€”the problems of space, time, motion, causality, of free will and determinationâ€”and he deals with them according to the mathematical method: that is all. He has sensed the truth that the problem of mathematics is the problem of the world order, and as such must deal with every aspect of human life.
Mathematics is a terrible word to those whose taste and training have led them into other fields, so lest the non-mathematical reader should be turned back at the very threshold, deciding too hastily that the book is not for him, let me dwell rather on its richly humanistic aspect.
To such as ask no "key to the enigmas of the world," but only some light to live by, some mitigation of the daily grind, some glimpse of some more enlightened polity than that which rules the world today, this book should have an appeal. The author has thrown overboard all the jargon of all the schools; he uses the language of common sense, and of every day; his illustrations and figures of speech are homely, taken from the life of every day. He simply says to the reader, "Come let us reason together," and leads him away from the haunted jungle of philosophical systems and metaphysical theories, out into the light of day, there to contemplate and to endeavor to understand those primal mysteries which puzzle the mind of a child or of a savage no less than that of the sophisticated and super-subtle ponderer on the enigmas of the world. Not that Ouspensky is a trafficker in the obviousâ€”far from it: those who know most, think most, feel most, will get most out of his bookâ€”but a great sanity pervades his pages, and he never leads away into labyrinths where guide and follower alike lose their way and fail to come to any end.
Leaving the average reader out of account for the moment, there are certain others whom the book should particularly interestâ€”if only in the way of repulsion.
First of all come the mathematicians and the theoretical physicists, for they already, without knowing it, have invaded that "dark backward and abysm of time" which the Ouspenskian philosophy lights upâ€”and are by way of losing themselves there.
That is to say, in certain of their calculations, they are employing four mutually interchangeable coÃ¶rdinates, three of space and one of time. In other words, they use time as though it were a dimension of space. Ouspensky tells them the reason they are able to do this. Time is the fourth dimension of space imperfectly sensedâ€”apprehended by consciousness successively, and thereby creating the temporal illusion.
Moreover, mathematicians are perforce concerning themselves with magnitudes to which the ordinary logic no longer applies. Ouspensky presents a new logic, or rather, he presents anew an ancient logicâ€”the logic of intuitionâ€”removing at a stroke all of the nightmare aspects, the preposterous paradoxes of the new mathematics, which by reason of its extraordinary development has shattered the old logic, as a growing oak shatters the containing jar.
It is from the philosophic camp, no doubt, that the book will receive its sharpest criticism, on account of the author's lÃ¨se-majestÃ© toward so many of the crowned kings of philosophic thought, and his devastating assault on positivismâ€”that inevitable by-product of our materialistic way of looking at the world. His attempt to prove the Kantian problemâ€”the subjectivity of space and timeâ€”doubtless will be acutely challenged, and with some chance of success, because the two chapters devoted to this are perhaps the least convincing of the book. But no one heretofore has even attempted to demonstrate absolutely or successfully to controvert the staggering proposition advanced by Kant regarding space and time as forms of consciousness.
Whatever the verdict of the philosophical pundits of the day and hour, whether favorable or otherwise, Ouspensky is sure of a place in the hierarchy of philosophers, for he has essayed to solve the most profound problems of human existence by the aid of the binocular vision of the mathematician and the mystic. Starting from the irreducible minimum of knowledge, he has carried philosophy into regions not hitherto explored.
To persons of an artistic or devotional bent the book will be as water in the desert. These, always at a disadvantage among the purely practical-minded, by whom they are overwhelmingly out-numbered, will find in Ouspensky a champion whose weapon is mathematical certitude, the very thing by which the practical-minded swear. These he puts to rout, holds up to ridicule, and applauds every effort to escape into the "world of the wondrous."
But most of all Ouspensky will be loved by all true lovers, for his chapter on the subject of love. We have had Schopenhauer on love, and Freud on love, but what dusty answers do they give to the soul of a lover! Edward Carpenter comes much nearer the mark, but Ouspensky penetrates to its very center. It is because our loves are so dampened by our egotisms, our cynicisms and our cowardices that we rot and smoulder instead of bursting into purifying flame. Just as Goethe's Werther, with its sex-sentimentality, is said to have provoked an epidemic of suicides, so may Tertium Organumâ€”which restores love to that high heaven from whence descend every beauty and benisonâ€”inaugurate a renascence of love and joy.
From one point of view this is a terrible book: there is a revolution in itâ€”a revolution of the very poles of thought. Some it will rob of their dearest illusions, it will cut the very ground from beneath their feet, it will consign them to the Abyss. It is a great destroyer of complacency. Yes, this is a dangerous bookâ€”but then, life is like that.
It is beyond the province of this Introduction either to outline the Ouspenskian philosophy at any length, or to discuss it critically; but some slight indication of its drift may be of assistance to the reader.
The book might have appropriately been called A Study of Consciousness, for Ouspensky comes early to the conclusion that all other methods of approach to an understanding of the "enigmas of the world" are vain. Chapters I to VII, inclusive, deal with the problem of the world-order by the objective method. The author erects an elaborate scaffolding for his future edifice, and after it has served its purpose, throws it down. Aware of the deficiencies
of the objective method and having made the reader conscious of them too, he suddenly alters his system of attack. From chapter VIII onward, he undertakes the study of the world-order from the standpoint of subjectivityâ€”of consciousness.
By a method both ingenious and new he correlates the different grades of consciousness observable in natureâ€”those of vegetable-animal, animal and manâ€”with the space sense, showing that as consciousness changes and develops, the sense of space changes and develops too. That is to say, the dimensionality of the world depends on the development of consciousness. Man, having reached the third stage in that development, has a sense of three-dimensional spaceâ€”and for no other reason.
Ouspensky concludes that nothing except consciousness unfolds, develops, and as there appears to be no limit to this development, he conceives of space as the multi-dimensional mirror of consciousness and of time and motion as illusionâ€”what appears to be time and motion being in reality only the movement of consciousness upon a higher space.
The problem of superior states of consciousness in which "there shall be time no longer" is thus directly opened up, and in discussing their nature and method of attainment, he quotes freely from the rich literature of mysticism. Instead of attempting to rationalize these higher states of consciousness, as some authors do, he applies to them the logic of intuitionâ€”"Tertium Organum"â€”paradoxical from the standpoint of ordinary reason, but true in relation to the noumenal world.
Joseph Conrad and Ford Madox Hueffer once wrote a novel called The Inheritors and by this they meant the people of the fourth dimension. Though there is small resemblance between Ouspensky's "superman" and theirs, it is his idea also that those of this world who succeed in developing higher-dimensional, or "cosmic" consciousness will indeed inheritâ€”will control and regulate human affairs by reason of their superior wisdom and power. In this, and in this alone, dwells the "salvation" of the world. His superman is the "just man made perfect" of the Evangelist. The struggle for mastery between the blind and unconscious forces of materialism on the one hand, and the spiritually illumined on the other, is already upon us, and all conflicts between nations, peoples
and classes must now be interpreted in terms of this greater warfare between "two races" of men, in which the superior minority will either conquer or disappear.
These people of the fourth dimension are in the world but not of it: their range is far wider than this slum of space. In them dormant faculties are alert. Like birds of the air, their fitting symbol, they are at home in realms which others cannot enter, even though already "there." Nor are these heavenly eagles confined to the narrow prison of the breast. Their bodies are as tools which they may take up or lay aside at will. This phenomenal world, which seems so real, is to them as insubstantial as the image of a landscape in a lake. Such is the Ouspenskian superman.
The entire book is founded upon a new generalizationâ€”new, that is, in philosophy, but already familiar to mathematicians and theoretical physicists. This generalization involves startling and revolutionary ideas in regard to space, time and motion far removed from those of Euclidian geometry and classical physics.
Ouspensky handles these new ideas in an absolutely original way, making them the basis of an entire philosophy of life. To the timid and purblind this philosophy will be nothing short of terrifying, but to the clear-eyed and steadfast watcher, shipwrecked on this shoal of time, these vistas, overflowing with beauty, strangeness, doubt, terror and divinity, will be more welcome than anything in life.
Fear not the new generalization.
Ouspensky's clearness of thought is mirrored in a corresponding clarity of expression. He sometimes repeats the difficult and important passages in an altered form of words, he uses short sentences and short paragraphs, and italicizes significant phrases and significant words. He defines where definition is needed, and suggests collateral trains of thought with a skill which makes the reader who is intuitive a creator on his own account. Schopenhauer has said that it is always a sign of genius to treat difficult matters simply, as it is a sign of dullness to make simple matters appear recondite. Ouspensky exhibits this order of genius, and that other,
mentioned by Schopenhauer, which consists in choosing always the apt illustration, the illuminating simile.
The translators have tried to be rigidly true to the Russian original, and they have been at great pains to verify every English quotation so far as has been possible. It is therefore a source of great gratification to them that their efforts should have received the unqualified endorsement of the author himself.
Rochester, N. Y.
January 31, 1922
"I have called this system of higher logic Tertium Organum because for us it is the third canonâ€”third instrumentâ€”of thought after those of Aristotle and Bacon. The first was Organon, the second, Novum Organum. But the third existed earlier than the first."
TERTIUM ORGANUM (page 262)
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 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?
"Learn to discern the real from the false"
THE VOICE OF THE SILENCE
H. P. B.
THE most difficult thing is to know what we do know, and what we do not know.
Therefore, desiring to know anything, we shall before all else determine WHAT we accept as given, and WHAT as demanding definition and proof; that is, determine WHAT we know already, and WHAT we wish to know.
In relation to the knowledge of the world and of ourselves, the conditions would be ideal could we venture to accept nothing as given, and count all as demanding definition and proof. In other words, it would be best to assume that we know nothing, and make this our point of departure.
But unfortunately such conditions are impossible to create. Knowledge must start from some foundation, something must be recognized as known; otherwise we shall be obliged always to de-fine one unknown by means of another.
Looking at the matter from another point of view, we shall hesitate to accept as the known thingsâ€”as the given onesâ€”those in the main completely unknown, only presupposed, and therefore the things sought for. Should we do this, we are likely to fall into such a dilemma as that in which positive philosophy now finds itselfâ€”and by positive philosophy I mean a general trend of thought
based on the data of those sciences which are now accepted as experimental and positive. This philosophy is founded on the existence of matter (materialism) or energy: that is, of a force, or motion, (energeticism); though in reality matter and motion were always the unknown x and y, and were defined by means of one another.
It must be perfectly clear to everyone that it is impossible to accept the thing sought as the given; and impossible to define one unknown by means of another. The result is nothing but the identity of the unknown: x=y, y=x.
This identity of the unknown is the ultimate conclusion to which positive philosophy comes.
Matter is that in which proceed the changes called motion: and motions are those changes which proceed in matter.
But what do we know?
We know that with the very first awakening of knowledge, man is confronted with two obvious facts:
The existence of the world in which he lives; and the existence of psychic life in himself.
Neither of these can he prove or disprove, but they are facts: they constitute reality for him.
It is possible to meditate upon the mutual correlation of these two facts. It is possible to try to reduce them to one; that is, to regard the psychic or inner world as a part, reflection, or function of the world, or the world as a part, reflection, or function of that inner world. But such a procedure constitutes a departure from facts, and all such considerations of the world and of the self, to the ordinary non-philosophical mind, will not have the character of obviousness. On the contrary the sole obvious fact remains the antithesis of I and Not-Iâ€”our inner psychic life and the outer world.,
Further on we shall return to this fundamental thesis. But thus far we have no basis on which to found a contradiction of the obvious fact of the existence of ourselvesâ€”i.e., of our inner lifeâ€”and of the world in which we live. This we shall therefore accept as the given.
This however is the only thing that we have the right to accept as
given: all the rest demands proof and definition in terms of these two given data.
Space, with its extension; time, with the idea of before, now, after; quantity, mass, substantiality; number, equality and inequality; identity and difference; cause and effect; the ether, atoms, electrons, energy, life, deathâ€”all things that form the foundation of our so-called knowledge: these are the unknown things.
The existence in us of psychic life, i.e., of sensations, perceptions, conceptions, reasoning, feeling, desires etc., and the existence of the world outside of usâ€”from these two fundamental data immediately proceed our common and clearly understood division of everything that we know into subjective and objective.
Everything that we accept as a property of the world, we call objective; and everything that we accept as a property of our psyche, we call subjective.
The subjective world we recognize directly: it is in ourselvesâ€”we are one with it.
The objective world we picture to ourselves as existing somewhere outside of usâ€”we and it are different things.
It seems to us that if we should close our eyes, then the objective world would continue to exist, such as we just saw it; and if our inner life were to disappear, so would the subjective world disappearâ€”yet the objective world would exist as before, as it existed at the time when we were not; when our subjective world was not.
Our relation to the objective world is most exactly defined by the fact that we perceive it as existing in time and space; otherwise, out of these conditions, we can neither conceive nor imagine it. In general, we say that the objective world consists of things and phenomena, i.e., things and changes in states of things. The PHENOMENA exist for us in time; the THINGS, in space.
But such a division of the subjective and the objective world does not satisfy us.
By means of reasoning we can establish the fact that in reality we know only our own sensations, perceptions and conceptions, and we cognize the objective world by projecting outside of ourselves the causes of our sensations, presupposing them to contain these causes.
Then we find that our knowledge of the subjective world, and of
the objective world also, can be true and false, correct and incorrect.
The criterion for the definition of correctness or incorrectness of our knowledge of the subjective world is the form of the relations of one sensation to others, and the force and character of the sensation itself. In other words, the correctness of one sensation is verified by the comparison of it with another of which we are more sure, or by the intensity and "taste" of a given sensation.
The criterion for the definition of correctness or incorrectness of our knowledge of the objective world is the very same. It seems to us that we define the things and phenomena of the objective world by means of comparing them among themselves; and we think we find the laws of their existence outside of us, and independent of our perception of them. But it is an illusion. We know nothing about things separately from us; and we have no other means of verifying the correctness of our knowledge of the objective world than BY SENSATIONS.
Since the remotest antiquity the question of our relation to the true causes of our sensations has constituted the main subject of philosophical research. Men have always felt that they should have some solution for this question, some answer for it. And these answers have vacillated between two poles, from the full negation of the causes themselves, and the assertion that the causes of sensations are contained within ourselves and not in anything outside of usâ€”up to the recognition that we know these causes, that they are embodied in the phenomena of the outer world, that these phenomena constitute the cause of sensations; and that the cause of all observed phenomena lies in the movement of "atoms," and the oscillations of the "ether." It is believed that if we cannot observe these motions and oscillations it is only because we have not sufficiently powerful instruments, and that when such instruments are at our disposal we shall be able to see the movements of atoms as well as we see, through powerful telescopes, stars the very existence of which were never guessed.
In modern philosophy Kant's system occupies a middle position in relation to this problem of the causes of sensations, not sharing either of these extreme views. Kant proved that the causes of our sensations are in the outside world, but that we cannot know these causes through any sensuous approachâ€”that is, by such means as we know phenomenaâ€”and that we cannot know these causes, and shall never know them.
Kant established the fact that everything that is known through the senses is known in terms of time and space, and that out of time and space we cannot know anything by way of the senses; that time and space are necessary conditions of sensuous receptivity (i.e., receptivity by means of the five organs of sense). Moreover, what is most important, he established the fact that extension in space and existence in time are not properties appertaining to things, but just the properties of our sensuous receptivity; that in reality, apart from our sensuous knowledge of them, things exist independently of time and space; but we can never perceive them out of time and space, and perceiving things and phenomena thus sensuously, by virtue of it we impose upon them the conditions of time and space, as belonging to our form of perception.
Thus space and time, defining everything that we cognize by sensuous means, are in themselves just forms of our receptivity, categories of our intellect, the prism through which we regard the worldâ€”or in other words, space and time do not represent properties of the world, but just properties of our knowledge of the world gained through our sensuous organism. From this it follows that the world, apart from our knowledge of it, has neither extension in space nor existence in time; these are properties which we add to it.
Cognitions of space and time arise in our intellect during its touch with the external world by means of the organs of sense, and do not exist in the external world apart from our contact with it.
Space and time are categories of intellect, i.e., properties which are ascribed by us to the external world. They are signal posts, signs put up by ourselves because we cannot picture the external world without their help. They are graphics by which we represent
the world to ourselves. Projecting outside of ourselves the causes of our sensations, we are designing those causes in space, and we picture continuous reality to ourselves as a series of moments of time following one another. This is necessary for us because a thing having no definite extension in space, not occupying a certain part of space and not lasting a certain length of time, does not exist for us at all. That is, a thing not in space, divorced from the idea of space, and not included in the category of space, will not differ from some other thing in any particular; it will occupy the very same place, will coincide with it. Also, all phenomena not in time, divorced from the idea of time, not taken in this or that fashion from the standpoint of before, now, after, would co-exist for us simultaneously, and all mixed up with one another, and our weak mind would not be able to distinguish one moment in the infinite variety.
Therefore our consciousness segregates, out of a chaos of impressions, separate groups, and we construct in space and time the perceptions of things according to these groups of impressions.
It is necessary for us to divide things somehow, and we divide them into the categories of space and time.
But we should remember that these divisions exist only in us, in our knowledge of things and not in the things themselves; that we do not know the true relations of things among themselves, and the real things we do not know, but only phantoms, visions of thingsâ€”we do not know the relation existing among the things in reality. At the same time we quite definitely know that our division of things into the categories of space and time does not at all correspond to the division of things in themselves, independently of our receptivity of them; and we quite definitely know that if there exist any division at all among things in themselves, it will in no case be a division in terms of space and time according to our usual understanding of these words, because such a division is not a property of things, but of our knowledge of things gained through the senses. Moreover, we do not know if it is even possible to distinguish those divisions which we see, i.e., in space and time, if things are looked at not through human eyes, not from the human standpoint. In point of fact we do not know but that
our world would present an entirely different aspect for a differently built organism.
We cannot perceive things as images outside of the categories of space and time, but we constantly think of them outside of space and time.
When we say that table, we picture the table to ourselves in space and time; but when we say an object made of wood, not meaning any definite thing, but speaking generally, it will relate to all things made of wood throughout the world, and in all ages. An imaginative person could conceive that we are referring to some great thing made of wood, composed of all objects whenever and wherever wooden things existed, these forming its constituent atoms, as it were.
We do not comprehend all these matters quite clearly, but in general it is plain that we think in space and time by perceptions only; but by concepts we think independently of space and time.
Kant named his views critical idealism, in contradiction to dogmatic idealism, of which Berkeley was a representative.
According to dogmatic idealism, all the world, all thingsâ€”i.e., the true causes of our sensationsâ€”do not exist except in our consciousness: they exist only so far as we know them. The entire world perceived by us is just a reflection of ourselves.
Kantian idealism recognizes a world of causes outside of us, but asserts that we cannot know the world by means of sensuous perception, and everything that we perceive, generally speaking, is of our own creationâ€”the product of a cognizing being.
So, according to Kant, everything that we find in things is put in them by ourselves. Independently of ourselves we do not know what the world is like. And our cognition of things has nothing in common with the things as they are outside of usâ€”that is, in themselves. Furthermore, and most important, our ignorance of things in themselves does not depend upon our insufficient knowledge, but is due to the fact that by means of sensuous perception we cannot know the world correctly at all. That is
to say, we cannot truly declare that although now we perhaps know little, presently we shall know more, and at length shall come to a correct understanding of the world. It is not true because our experimental knowledge is not a confused perception of a real world. It is a very acute perception of an entirely unreal world appearing round about us at the moment of our contact with the world of true causes, to which we cannot find the way because we are lost in an unreal "material" world. For this reason the extension of the objective sciences does not bring us any nearer to the knowledge of things in themselves, or of true causes.
In A Critique of Pure Reason Kant affirms that:
Nothing which is intuited in space is a thing in itself, and space is not a form which belongs as a property to things; but objects are quite unknown to us in themselves, and what we call outward objects are nothing else but mere representations of our sensibility, whose form is space, but whose real correlated thing in itself is not known by means of these representations, nor ever can be, but respecting which, in experience, no inquiry is ever made.
The things which we intuit are not in themselves the same as our representation of them in intuition, nor are their relations in themselves so constituted as they appear to us; and if we take away the subject, or even only the subjective constitution of our senses in general, then not only the nature and relations of objects in space and time disappear, but even space and time themselves.
What may be the nature of objects considered as things in themselves and without reference to the receptivity of our sensibility is quite unknown to us. We know nothing more than our own mode of perceiving them, which is peculiar to us and which though not of necessity pertaining to every animated being, is so to the whole human race.
Supposing that we should carry our empirical intuition even to the very highest degree of clearness we should not thereby advance one step nearer to the constitution of objects as things in themselves.
To say then that our sensibility is nothing but the confused representation of things containing exclusively that which belongs to them as things in themselves, and this under an accumulation of characteristic marks and partial representations which we cannot distinguish in consciousness, is a falsification of the conception of sensibility and phenomenization, which renders our whole doctrine thereof empty and
useless. The difference between a confused and a clear representation is merely logical, and has nothing to do with content.
Up to the present time Kant's propositions have remained in the very form that he left them. Despite the multiplicity of new philosophical systems which appeared during the nineteenth century, and despite the number of philosophers who have particularly studied, commented upon, and interpreted Kant's writings, Kant's principal propositions have remained quite undeveloped, primarily because most people do not know how to read Kant at all, and they therefore dwell upon the unimportant and non-essential, ignoring the substance.
Yet really Kant simply put the question, threw to the world the problem, demanding the solution but not pointing the way toward it.
This fact is usually omitted when speaking of Kant. He propounded the riddle, but did not give the solution of it.
And to the present day we repeat Kant's propositions, we consider them incontrovertible, but in the main we represent them to our understanding very badly, and they are not correlated with other departments of our knowledge. All our positive scienceâ€”physics (with chemistry) and biologyâ€”is built upon hypotheses CONTRADICTORY to Kant's propositions.
Moreover, we do not realize how we ourselves impose upon the world the properties of space, i.e., extension; nor do we realize how the worldâ€”earth, sea, trees, menâ€”cannot possess such extension.
We do not understand how we can see and measure that extension if it does not existâ€”nor what the world represents in itself, if it does not possess extension.
But does the world really exist? Or, as a logical conclusion from Kant's ideas, shall we recognize the validity of Berkeley's idea, and deny the existence of the world itself except in imagination?
Positive philosophy stands in a very ambiguous relation to Kant's views. It accepts them and it does not accept them: it accepts,
and considers them correct in their relation to the direct experience of the organs of senseâ€”what we see, hear, touch. That is, positive philosophy recognizes the subjectivity of our receptivity, and recognizes everything that we perceive in objects as imposed upon them by ourselvesâ€”but this in relation to the direct experience of the senses only.
When it concerns itself with "scientific experience" however, in which precise instruments and calculations are used, positive philosophy evidently considers Kant's view in relation to that invalid, assuming that "scientific experience" makes known to us the very substance of things, the true causes of our sensationsâ€”or if it does not do so now, it brings us closer to the truth of things, and can inform us later.
Contrary to Kant, the positivists are sure that "more clear knowledge of phenomena makes them acquainted with things in themselves." They think that in looking upon physical phenomena as the motions of the ether, or as electrical or magnetic phenomena, and calculating their motions, they begin to know the very substance of things, i.e., the causes of phenomena; in other words, they believe exactly in the possibility of what Kant deniedâ€”the comprehension of the true substance of things by means of the investigation of phenomena. Moreover many physicists do not consider it necessary even to know Kant; and they could not themselves exactly define in what relation they stand toward him. Of course it is possible not to know Kant, but it is impossible to controvert him. Every description of physical phenomena, by its every word, is related to the problems set forth by Kantâ€”remains in this or that relation to them.
In general, the position of "science" in regard to this question of "subjectively imposed" or "objectively cognized" is more than tottering, and in order to form its conclusions "science" is forced to accept many purely hypothetical suppositions as things knownâ€”as indubitable data, not demanding proof.
Moreover, physicists forget one very significant fact: in his book, Analysis of Sensations, Mach says:
In the investigation of purely physical processes we generally employ concepts of so abstract a character that as a rule we think only cursorily, or not at all, of the sensations (elements) that lie at their base. . .
[paragraph continues] The foundation of all purely physical operations is based upon an almost unending series of sensations, particularly if we take into consideration the adjustment of the apparatus which must precede the actual experiment. Now it can easily happen to the physicist who does not study the psychology of his operations, that he does not (to reverse a well-known saying) see the trees for the wood, that he overlooks the sensory element at the foundation of his work. . . Psychological analysis has taught us that this is not surprising, since the physicist is always operating with sensations. 1
Mach here calls attention to a very important thing. Physicists de not consider it necessary to know psychology and to deal with it in their conclusions.
But when they are more or less acquainted with psychology, with that part of it which treats of the forms of receptivity, and take it into consideration, then they hold the most fantastic duality of opinion, as in the case of the man of orthodox belief who tries to reconcile the dogmas of faith with the arguments of reason, and who is obliged to believe simultaneously in the creation of the world in seven days, seven thousand years ago, and in geological periods hundreds of thousands of years long, and in the evolutionary theory. He is thus forced to resort to sophisms, and demonstrate that by seven days is meant seven periods. But why seven, exactly, he is unable to explain. For physicists the rÃ´le of the "creation of the world" is played by the atomic theory and the ether, with its wave-like vibrations, and further by the electrons, and the energetic, or electromagnetic theory of the world.
Or sometimes it is even worse, for the physicist in the depth of his soul feels the falsity of all old and new scientific theories but fears to hang in the air, as it were; to take refuge in mere negation. He has no system in place of that whose falsity he already feels; he is afraid to make a plunge into mere emptiness. Lacking sufficient courage to declare that he believes in nothing at all, he accoutres himself in all contradictory theories, as in an official uniform, only because with this uniform are bound up certain rights and privileges, outer as well as inner, consisting of a certain confidence in himself and in his surroundings, to forego which he has no strength and determination. The unbelieving positivistâ€”this is the tragic figure of our times, analogous to the atheist or unbelieving priest of the times of Voltaire.
Out of this abhorrence of a vacuum come all dualistic theories which recognize "spirit" and "matter" existing simultaneously and independently of one another.
In general, to a disinterested observer, the state of our contemporary science should be of great psychological interest. In all branches of scientific knowledge we are absorbing an enormous number of facts destructive of the harmony of existing systems. And these systems can maintain themselves only by reason of the heroic attempts of scientific men who are trying to close their eyes to a long series of new facts which threatens to submerge everything in an irresistible stream. If in reality we were to collect these system-destroying facts they would be so numerous in every department of knowledge as to exceed those upon which existing systems are founded. The systematization of that which we do not know may yield us more for the true understanding of the world and the self than the systematization of that which in the opinion of "exact science" we do know.
21:1 Open Court Publishing Co.'s edition of Mach's work. 1914, pages 41, 42, and 43.
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 perpendicularsâ€”why three? Can everything existing be measured by three perpendiculars? The indices of existence. Reality of ideas. Insufficient evidence of the existence of matter and motion. Matter and motion are only logical concepts, like "good" and "evil."
AS already stated, Kant propounded the problem, but gave no solution of it, nor did he point the way to a solution. And not one of the known commentators, interpreters, followers or adversaries of Kant has found a solution, or the way to it.
I find the first flashes of a right understanding of the Kantian problem, and the first suggestions in regard to a possible way toward its solution, in the attempts at a new treatment of the problem of space and time, involving the concept of the "fourth dimension" and higher dimensions in general. An interesting synopsis of many things developed in this direction is that of C. H. Hinton, author of the books, A New Era of Thought, and The Fourth Dimension.
Hinton notes, among other things, that in commenting upon Kantian ideas, only their negative side is usually insisted upon, namely, the fact that we can cognize things in a sensuous way, in terms of space and time only, is regarded as an obstacle, hindering us from seeing what things in themselves really are, preventing the possibility of cognizing them as they are, imposing upon them that which is not inherent in them, shutting them off from us.
But [says Hinton] if we take Kant's statement simply as it isâ€”not seeing in the spatial conception a hindrance to right receptivityâ€”that we apprehend things by means of spaceâ€”then it is equally allowable to consider our space sense not as a negative condition, hindering our perception of the world, but as a positive means by which the mind grasps its experiences, i.e., by which we cognize the world.
There is, in so many books in which the subject is treated, a certain air of despondencyâ€”as if this space apprehension were a kind of veil which shut us off from nature. But there is no need to adopt this feeling. The first postulate of this book is a full recognition of the fact that it is by means of space that we apprehend what is.
Space is the instrument of the mind.
Very often a statement which seems to be most deep and abstruse and hard to grasp, is simply the form into which deep thinkers have thrown a very simple and practical observation. And for the present let us look on Kant's great doctrine of space from a practical point of view, and it comes to thisâ€”it is important to develop the space sense, for it is the means by which we think about real things.
Now according to Kant [Hinton goes on to say] the space sense, or the intuition of space, is the most fundamental power of the mind. But I do not find anywhere a systematic and thorough-going education of the space sense. It is left to be organized by accident. Yet the special development of the space sense makes us acquainted with a whole series of new conceptions.
Fichte, Schelling, Hegel, have developed certain tendencies and have written remarkable books, but the true successors of Kant are Gauss and Lobachevsky.
For if our intuition of space is the means whereby we apprehend, then it follows that there may be different kinds of intuitions of space. Who can tell what the absolute space intuition is? This intuition of space must be colored, so to speak, by the conditions (of psychical activity) of the being which uses it.
By a remarkable analysis the great geometers above mentioned have shown that space is not limited as ordinary experience would seem to inform us, but that we are quite capable of conceiving different kinds of space.
(A New Era of Thought.)
Hinton invented a complicated system for the education and development of the space sense by means of exercises with groups the cubes of different colors. The books above mentioned are devoted to the exposition of this system. In my opinion Hinton's exercises are interesting from a theoretical standpoint, but they are practically valuable only for such as have the same turn of mind as Hinton's own.
Exercises of the mind according to his system must first of all lead to the development of the ability to imagine objects, not as the eye sees them, i.e., in perspective, but as they are geometricallyâ€”to learn to imagine the cube, for example, simultaneously from all sides. Moreover such a development of the imagination
as overcomes the illusions of perspective results in the expansion of the limits of consciousness, thus creating new conceptions and augmenting the faculty for perceiving analogies.
Kant established the fact that the development of knowledge under the existing conditions of receptivity will not bring us any closer to things in themselves. But there are theories asserting that it is possible, if desired, to change the very conditions of receptivity, and thus to approach the true substance of things. In the books above referred to, Hinton tries to unite the scientific foundations of such theories.
Our space as we ordinarily think of it is conceived as limitedâ€”not in extent, but in a certain way which can only be realized when we think of our ways of measuring space objects. It is found that there are only three independent directions in which a body can be measuredâ€”it must have height, length and breadth, but it has no more than these dimensions, if any other measurement be taken in it, this new measurement will be found to be compounded of the old measurements.
It is impossible to find a point in the body which could not be arrived at by travelling in combinations of the three directions already taken.
But why should space be limited to three independent directions?
Geometers have found that there is no reason why bodies which we can measure should thus be limited. As a matter of fact all the bodies which we can measure are thus limited. So we come to this conclusion, that the space which we use for conceiving ordinary objects in the world is limited to three dimensions. But it might be possible for there to be beings living in a world such that they would conceive a space of four dimensions. 1
It is possible to say a great deal about space of higher dimensions than our own, and to work out analytically many problems which suggest themselves. But can we conceive four-dimensional space in the same way in which we can conceive our own space? Can we think of a body in four dimensions as a unit having properties in the same way as we think of a body having a definite shape in the space with which we are familiar?
There is really no more difficulty in conceiving four-dimensional shapes, when we go about it in the right way, than in conceiving the idea of solid shapes, nor is there any mystery at all about it.
When the faculty to apprehend in four dimensions is acquiredâ€”or rather when it is brought into consciousnessâ€”for it exists in every
one in imperfect formâ€”a new horizon opens. The mind acquires a development of power, and in this use of ampler space as a mode of thought, a path is opened by using that very truth which, when first stated by Kant, seemed to close the mind within such fast limits. Our perception is subject to the condition of being in space. But space is not limited as we at first think.
The next step after having formed this power of conception in ampler space, is to investigate nature and see what phenomena are to be explained by four-dimensional relations.
The thought of past ages has used the conception of a three-dimensional space, and by that means has classified many phenomena and has obtained rules for dealing with matters of great practical utility. The path which opens immediately before us in the future is that of applying the conception of four-dimensional space to the phenomena of nature, and of investigating what can be found out by this new means of apprehension. . . .
For development of knowledge it is necessary to separate the self-elements, i.e., the personal elements which we put in everything cognized by us, from that which is cognized, in order that our attention may not be distracted (upon ourselves) from the properties which we, in substance, perceive.
Only by getting rid of the self-elements in our receptivity do we put ourselves in a position in which we can propound sensible questions. Only by getting rid of the notion of a circular motion of the sun around the earth (i.e., around usâ€”self-element) do we prepare our way to study the sun as it really is.
But the worst about a self-element is that its presence is never dreamed of till it is got rid of.
In order to understand what the self-element in our receptivity means, imagine ourselves to be translated suddenly to another part of the universe, and to find there intelligent beings and to hold conversation with them. If we told them that we came from this world, and were to describe the sun to them, saying that it was a bright, hot body which moved around us, they would reply: "You have told us something about the sun, but you have also told us something about yourselves.". . .
Therefore, desiring to tell something about the sun, we shall first of all get rid of the self-element which is introduced into our knowledge of the sun by the movement of the earth, upon which we are, round it. . . .
One of our serious pieces of work will be to get rid of the self-elements in the knowledge of the arrangement of objects.
The relations of our universe or our space with regard to the wider universe of four-dimensional space are altogether undetermined. The real relationship will require a great deal of study to apprehend, and when apprehended will seem as natural to us as the position of the earth among the other planets seems to us now. . . .
I would divide studies of arrangement into two classes: those which
create the faculty of arrangement, and those which use it and exercise it. Mathematics exercises it, but I do not think it creates it; and unfortunately, in mathematics as it is now often taught, the pupil is launched into a vast system of symbols: the whole use and meaning of symbols (namely, as means to acquire a clear grasp of facts) is lost to him. . . .
Of the possible units which will serve for the study of arrangement, I take the cube; and I have found that whenever I took any other unit I got wrong, puzzled, and lost my way. With the cube one does not get along very fast, but everything is perfectly obvious and simple, and builds up into a whole of which every part is evident. . . .
Our work then will be this: a study, by means of cubes, of the facts of arrangement; and the process of learning will be an active one of actually putting up the cubes. Thus we will bring our minds into contact with nature.
(A New Era of Thought.)
Taking all these things into consideration, we should try to define clearly our understanding of those sides of our receptivity dealt with by Kant.
What is space?
Taken as object, that is, perceived by our consciousness, space is for us the form of the universe or the form of the matter in the universe.
Space possesses an infinite extension in all directions. But it can be measured in only three directions independent of one anotherâ€”in length, breadth, and height; these directions we call the dimensions of space, and we say that our space has three dimensions: it is three-dimensional.
By independent direction we mean in this case a line at right angles to another line.
Our geometry (or the science of measurement of the earth, or matter in space) knows only three such lines, which are mutually at right angles to one another and not parallel among themselves.
But why three only, and not ten or fifteen?
This we do not know.
And here is another very significant fact: either because of some mysterious property of the universe, or because of some mental
limitation, we cannot even imagine to ourselves more than three independent directions.
But we speak of the universe as infinite, and because the first condition of infinity is infinity in all directions and in all possible relations, so we must presuppose in space an infinite number of dimensions: that is, we must presuppose an infinite number of lines perpendicular and not parallel to each other; and yet out of these lines we know, for some reason, only three.
It is usually in some such guise that the question of higher dimensionality appears to normal human consciousness.
Since we cannot construct more than three mutually independent perpendiculars, and if the three-dimensionality of our space is conditional upon this, we are forced to admit the indubitable fact of the limitedness of our space in relation to geometrical possibilities: though of course if the properties of space are created by some limitation of consciousness, then the limitedness lies in ourselves.
No matter what this limitedness depends on, it is a fact that it exists.
A given point can be the vertex of only eight independent tetrahedrons. Through a given point it is possible to draw only three perpendicular and not parallel straight lines.
Upon this as a basis, we define the dimensionality of space by the number of lines it is possible to draw in it which are mutually at right angles one with another.
The line upon which there cannot be a perpendicular, that is, another line, constitutes linear, or one-dimensional space.
Upon the surface two perpendiculars are possible. This is superficial, or two-dimensional space.
In "space" three perpendiculars are possible. This is solid, or three-dimensional space.
The idea of the fourth dimension arose from the assumption that in addition to the three dimensions known to our geometry there exists still a fourth, for some reason unknown and inaccessible to us, i.e., that in addition to the three known to us, a mysterious fourth perpendicular is possible.
This assumption is practically founded on the consideration
that there are things and phenomena in the world undoubtedly really existing, but quite incommensurable in terms of length, breadth and thickness, and lying as it were outside of three-dimensional space.
By really existing we understand that which produces definite action, which possesses certain functions, which appears to be the cause of something else.
That which does not exist cannot produce any action, has no function, cannot be a cause.
But there are different modes of existence. There is physical existence, recognized by certain sorts of actions and functions, and there is metaphysical existence, recognized by its actions and its functions.
A house exists, and the idea of good and evil exists. But they do not exist in like manner. One and the same method of proof of existence does not suffice for the proof of the existence of a house and for the proof of the existence of an idea. A house is a physical fact, an idea is a metaphysical fact. Physical and metaphysical facts exist, but they exist differently.
In order to prove the idea of a division into good and evil, i.e., a metaphysical fact, I have only to prove its possibility. This is already sufficiently established. But if I should prove that a house, i.e., a physical fact, may exist, it does not at all mean that it exists really. If I prove that a man may own the house it is no proof that he owns it.
Our relation to an idea and to a house are quite different, It is possible by a certain effort to destroy a houseâ€”to burn, to wreck it. The house will cease to exist. But suppose you attempt to destroy, by an effort, an idea. The more you try to contest, argue, refute, ridicule, the more the idea is likely to spread, grow, strengthen. And contrariwise, silence, oblivion, non-action, "non-resistance" will exterminate, or in any case will weaken the idea. Silence, oblivion, will not wreck a house, will not hurt a stone.
[paragraph continues] It is clear that the existence of a house and that of an idea are quite different existences.
Of such different existences we know very many. A book exists, and also the contents of a book. Notes exist, and so does the music that the notes combine to make. A coin exists, and so does the purchasing value of a coin. A word exists, and the energy which it contains.
We discern on the one hand, a whole series of physical facts, and on the other hand, a series of metaphysical facts.
As facts of the first kind exist, so also do facts of the second kind exist, but differently.
From the usual positivist point of view it will seem naive in the highest degree to speak of the purchasing value of a coin separately from the coin; of the energy of a word separately from the word; of the contents of a book separately from the book, and so on. We all know that these are only "what people say," that in reality purchasing value, energy of a word, and contents of a book do not exist, that by these conceptions we only denote a series of phenomena in some way linked with coin, word, book, but in substance quite separate from them.
But is it so?
We decided to accept nothing as given, consequently we shall not negate anything as given.
We see in things, in addition to what is external, something internal. We know that this internal element in things constitutes a continuous part of things, usually their principal substance. And quite naturally we ask ourselves, where is this internal element, and what does it represent in and by itself. We see that it is not embraced within our space. We begin to conceive of the idea of a "higher space" possessing more dimensions than ours. Our space then appears to be somehow a part of higher space, i.e., we begin to believe that we know, feel, and measure only part of space, that part which is measurable in terms of length, width and height.
As was said before, we usually regard space as a form of the universe, or as a form of the matter of the universe. To make this
clear it is possible to say that a "cube" is the form of the matter in a cube; a "sphere" is the form of the matter in a sphere; "space"â€”an infinite sphereâ€”is the form of the entire matter of the universe.
H. P. Blavatsky, in The Secret Doctrine, has this to say about space:
The superficial absurdity of assuming that Space itself is measurable in any direction is of little consequence. The familiar phrase (the fourth dimension of space) can only be an abbreviation of the fuller formâ€”the "Fourth dimension of Matter in Space.". . . The progress of evolution may be destined to introduce us to new characteristics of matter. . . ." 1
But the formula defining "space" as "the form of matter in the universe" suffers from this deficiency, that there is introduced in it the concept of "matter," i.e., the unknown.
I have already spoken of that "dead-end siding," x=y, y=x, to which all attempts at the physical definition of matter inevitably lead.
Psychological definitions lead to the same thing.
In a well-known book, The Psychology of the Soul, A. I. Herzen says:
We call matter everything which directly or indirectly offers resistance to motion, directly or indirectly produced by us, manifesting a remarkable analogy with our passive states.
And we call force (motion) that which directly or indirectly communicates movement to us or to other bodies, thus manifesting the greatest similitude to our active states.
Consequently, "matter" and "motion" are something like projections of our active and passive states. It is clear that it is possible to define the passive state only in terms of the active, and the active in terms of the passiveâ€”again two unknowns, defining one another.
E. Douglas Fawcett, in an article entitled Idealism and the Problem of Nature in The Quest (April, 1910), discusses matter from this point of view.
Matter (like force) does not give us any trouble. We know all about it, for the very good reason that we invented it. By "matter" we think of sensuous objects. It is mental change of concrete but too complicated facts, which are difficult to deal with.
Strictly speaking, matter exists only as a concept. Truth to tell, the character of matter, even when treated only as a conception, is so unobvious that the majority of persons are unable to tell us exactly what they mean by it.
An important fact is here brought to light: matter and force are just logical concepts, i.e., only words accepted for the designation of a lengthy series of complicated facts. It is difficult for us, educated almost exclusively along physical lines, to understand this clearly, but in substance it may be stated as follows: Who has seen matter and force, and when? We see things, see phenomena. Matter, independently of the substance from which a given thing is made, or of which it consists, we have never seen and never shall see; but the given substance is not quite matter, this is wood, or iron or stone. Similarly, we shall never see force separately from motion. What does this mean? It means that "matter" and "force" are just such abstract conceptions as "value" or "labor," as "the purchasing value of a coin" or the "contents" of a book; it means that matter is "such stuff as dreams are made of." And because we can never touch this "stuff" and can see it only in dreams, so we can never touch physical matter, nor see, nor hear, nor photograph it, separately from the object. We cognize things and phenomena which are bad or good, but we never cognize "matter" and "force" separately from things and phenomena.
Matter is as much an abstract conception as are truth, good and evil.
It is as impossible to put matter or any part of matter into a chemical retort or crucible as it is impossible to sell "Egyptian darkness" in vials. However as it is said that "Egyptian darkness" is sold as a black powder in Athos, or elsewhere, therefore perhaps somewhere, by some one, even matter has been seen. 1
In order to discuss questions of this order a certain preparation is necessary, or a high degree of intuition; but unfortunately it is customary to consider fundamental questions of cosmogony very lightly.
A man easily admits his incompetency in music, dancing, or higher mathematics, but he always maintains the privilege of having an opinion and being a judge of questions relating to "first principles."
It is difficult to discuss with such men.
For how will you answer a man who looks at you in perplexity, knocks on the table with his fingers and says, "This is matter. I know it; feel! How can it be an abstract conception?" To answer this is as difficult as to answer the man who says: "I see that the sun rises and sets!"
Returning to the consideration of space, we shall under no circumstances introduce unknown quantities in the definition of it. We shall define it only in terms of those two data which we decided to accept at the very beginning.
The world and consciousness are the facts which we decided to recognize as existing.
By the world we mean the combination of all the causes of our sensations in general.
By the material world we mean the combination of causes of a definite series of sensations: those of sight, hearing, touch, smell, taste, sensations of weight, and so on.
Space is either a property of the world or a property of our knowledge of the world.
Three-dimensional space is either a property of the material world or a property of our receptivity of the material world.
Our inquiry is confined to the problem: how shall we approach the study of space?
25:1 Italics by P. D. Ouspensky. Transl.
31:1 "The Secret Doctrine," The Theosophical Publishing Society. Third Edition, p. 271, vol. I.
32:1 This is irony which the English speaking may easily fail to understand. Some unscrupulous monks of the monastery of Athos, famous throughout Greece and Russia, made a practice, it is said, of selling "Egyptian darkness" in little vials, thus making capital out of the credulity and piety of the illiterate Russian pilgrims who were wont to visit this monastery in great numbers. Transl.
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.
IF we consider the very great difference between the point and the line, between the line and the surfaceâ€”surface and solid, i.e., the difference between the laws to which line and plane, plane and surface, etc., are subjected, and the difference of phenomena possible in point, in line, in surface, we shall indeed come to understand how much of the new and inconceivable the fourth dimension holds for us.
As in the point it is impossible to imagine the line and the laws of the line; as in the line it is impossible to imagine the surface and the laws of the surface; as in the surface it is impossible to imagine the solid and the laws of the solid; so in our space it is impossible to imagine the body having more than three dimensions, and impossible to understand the laws of the existence of such a body.
But studying the mutual relations between the point, the line, the surface, the solid, we begin to learn something about the fourth dimension, i.e., of four-dimensional space. We begin to learn what it can be in comparison with our three-dimensional space, and what it cannot be.
This last we learn first of all. And it is especially important, because it saves us from many deeply inculcated illusions, which are very detrimental to right knowledge.
We learn what cannot be in four-dimensional space, and this permits us to set forth what can be there.
In his book, The Fourth Dimension, Hinton makes an interesting statement concerning the method by which we may approach the problem of higher dimensions. He says:
Our space itself bears within it relations through which we can establish relations to other (higher) spaces.
For within space are given the conception of point and line, line and plane, which really involve the relation of space to a higher space.
Let us consider these relations within our space, and see what conclusions we can derive from their investigation.
We know that our geometry regards the line as a tracing of the movement of a point; the surface as a tracing of the movement of a line; and the solid as a tracing of the movement of a surface. On these premises we put to ourselves this question: Is it not possible to regard the "four-dimensional body" as a tracing of the movement of a three-dimensional body?
But what is this movement, and in what direction?
The point, moving in space, and leaving the tracing of its movement, a line, moves in a direction not contained in it, because in a point there is no direction whatsoever.
The line, moving in space, and leaving the tracing of its movement, the surface, moves in a direction not contained in it because, moving in a direction contained in it, a line will continue to be a line.
The surface, moving in space, and leaving a tracing of its movement, the solid, moves also in a direction not contained in it. If it should move otherwise, it would remain always the surface. In order to leave a tracing of itself as a "solid," or three-dimensional figure, it must set off from itself, move in a direction which in itself it has not.
In analogy with all this, the solid, in order to leave as the tracing of its movement, the four-dimensional figure (hypersolid) shall move in a direction not confined in it; or in other words it shall come out of itself, set off from itself, move in a direction which is not present in it. Later on it will be shown in what manner we shall understand this.
But for the present we can say that the direction of the movement in the fourth dimension lies out of all those directions which are possible in a three-dimensional figure.
We consider the line as an infinite number of points; the surface as an infinite number of lines; the solid as an infinite number of surfaces.
In analogy with this it is possible to consider that it is necessary to regard a four-dimensional body as an infinite number of three-dimensional bodies, and four-dimensional space as an infinite number of three-dimensional spaces.
Moreover, we know that the line is limited by points, that the surface is limited by lines, that the solid is limited by surfaces.
It is possible that a four-dimensional body is limited by three-dimensional bodies.
Or it is possible to say that the line is the distance between two points; the surface the distance between two lines; the solidâ€”between two surfaces.
Or again, that the line separates two points or several points from one another (for a straight line is the shortest distance between two points); that the surface separates two or several lines from each other; that the solid separates several surfaces one from another; as the cube separates six flat surfaces one from anotherâ€”its faces.
The line binds several separate points into a certain whole (the straight,, the curved, the broken line); the surface binds several lines into a certain whole (the quadrilateral, the triangle); the solid binds several surfaces into a certain whole (the cube, the pyramid).
It is possible that four-dimensional space is the distance between a group of solids, separating these solids, yet at the same time binding them into some to us inconceivable whole, even though they seem to be separate from one another.
Moreover, we regard the point as a section of a line; the line as a section of a surface; the surface as a section of a solid.
By analogy, it is possible to regard the solid (the cube, sphere, pyramid) as a section of a four-dimensional body, and our entire three-dimensional space as a section of a four-dimensional space. If every three-dimensional body is the section of a four-dimensional one, then every point of a three-dimensional body is the
section of a four-dimensional line. It is possible to regard an "atom" of a physical body, not as something material, but as an intersection of a four-dimensional line by the plane of our consciousness.
The view of a three-dimensional body as the section of a four-dimensional one leads to the thought that many (for us) separate bodies may be the sections of parts of one four-dimensional body.
A simple example will clarify this thought. If we imagine a horizontal plane, intersecting the top of a tree, and parallel to the surface of the earth, then upon this plane the sections of branches will seem separate, and not bound to one another. Yet in our space, from our standpoint, these are sections of branches of one tree, comprising together one top, nourished from one root, casting one shadow.
Or here is another interesting example expressing the same idea, given by Mr. Leadbeater, the theosophical writer, in one of his books. If we touch the surface of a table with our finger tips, then upon the surface will be just five circles, and from this plane presentment it is impossible to construe any idea of the hand, and of the man to whom this hand belongs. Upon the table's surface will be five separate circles. How from them is it possible to imagine a man, with all the richness of his physical and spiritual life? It is impossible. Our relation to the four-dimensional world will be analogous to the relation of that consciousness which sees five circles upon the table to a man. We see just "finger tips"â€”to us the fourth dimension is inconceivable.
We know that it is possible to represent a three-dimensional body upon a plane, that it is possible to draw a cube, a polyhedron or a sphere. This will not be a real cube or a real sphere, but the projection of a cube or of a sphere on a plane. We may conceive of the three-dimensional bodies of our space somewhat in the nature of images in our space of to us incomprehensible four-dimensional bodies.
In what direction may the fourth dimension lie? What is motion? Two kinds of motionâ€”motion in space and motion in timeâ€”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. The "ether" as a surface. Riemann's idea concerning the translation of time into space in the fourth dimension. Present, past, and future. Why we do not see the past and the future. Life as a feeling of one's way. Wundt on the subject of our sensuous knowledge.
WE have established by a comparison of the relation of lower dimensional figures to higher dimensional ones that it is possible to regard a four-dimensional body as the tracing of the motion of a three-dimensional body upon the dimension not contained in it; i.e., that the direction of the motion upon the fourth dimension lies outside of all the directions which are possible in three-dimensional space.
But in what direction is it?
In order to answer this question it will be necessary to discover whether we do not know some motion not confined in three-dimensional space.
We know that every motion in space is accompanied by that which we call motion in time. Moreover, we know that everything existing, even if not moving in space, moves eternally in time.
And equally in all cases, whether speaking of motion or absence of motion, we have in mind an idea of what was before, what now becomes, and what will follow after. In other words, we have in mind the idea of time. The idea of motion of any kind, also the idea of absence of motion, is indissolubly bound up with the idea of time. Any motion or absence of motion proceeds in time and
cannot proceed out of time. Consequently, before speaking of what motion is, we must answer the question, what is time?
Time is the most formidable and difficult problem which confronts humanity.
Kant regards time as he does space: as a subjective form of our receptivity; i.e., he says that we create time ourselves, as a function of our receptive apparatus, for convenience in perceiving the outside world. Reality is continuous and constant, but in order to make possible the perception of it, we must dissever it into separate moments; imagine it as an infinite series of separate moments out of which there exists for us only one. In other words, we perceive reality as if through a narrow slit, and what we are seeing through this slit we call the present; what we did see and now do not seeâ€”the past; and what we do not quite see but are expectingâ€”the future.
Regarding each phenomenon as an effect of another, or others, and this in its turn as a cause of a third; that is, regarding all phenomena in functional interdependence one upon another, by this very act we are contemplating them in time, because we picture to ourselves quite clearly and precisely first a cause, then an effect; first an action, then its function; and cannot contemplate them otherwise. Thus we may say that the idea of time is bound up with the idea of causation and functional interdependence. Without time, causation cannot exist, just as without time, motion or the absence of motion cannot exist.
But our perception concerning our "being in time" is entangled and misty up to improbability.
First of all let us analyze our relation toward the past, present and future. Usually we think that the past already does not exist. It has passed, disappeared, altered, transformed itself into something else. The future also does not existâ€”it does not exist as yet. It has not arrived, has not formed. By the present we mean the moment of transition of the future into the past, i.e., the moment of transition of a phenomenon from one non-existence into another non-existence. For that moment only does the phenomenon exist for us in reality; before, it existed in potentiality, afterward it will exist in remembrance. But this short moment is after all only a fiction: it has no measurement. We have a full right to say that
the present does not exist. We can never catch it. That which we did catch is always the past!
If we are to stop at that we must admit that the world does not exist, or exists only in some phantasmagoria of illusions, flashing and disappearing.
Usually we take no account of this, and do not reflect that our customary view of time leads to utter absurdity.
Let us imagine a stupid traveller going from one city to another and half way between these two cities. A stupid traveller thinks that the city from which he has departed last week does not exist now: only the memory of it is left; the walls are ruined, the towers fallen, the inhabitants have either died or gone away. Also, that city at which he is destined to arrive in several days does not exist now either, but is being hurriedly built for his arrival, and on the day of that arrival will be ready, populated, and set in order, and on the day after his departure will be destroyed just as was the first one.
We are thinking of things in time exactly in this wayâ€”everything passes away, nothing returns! The spring has passed, it does not exist still. The autumn has not come, it does not exist as yet.
But what does exist?
But the present is not a seizable moment, it is continuously transitory into the past.
So, strictly speaking, neither the past, nor the present, nor the future exists for us. Nothing exists! And yet we are living, feeling, thinkingâ€”and something surrounds us. Consequently, in our usual attitude toward time there exists some mistake. This error we shall endeavor to detect.
We accepted at the very beginning that something exists. We called that something the world. How then can the world exist if it is not existing in the past, in the present and in the future?
That conception of the world which we deduced from our usual view of time makes the world appear like a continuously gushing out igneous fountain of fireworks, each spark of which flashes for a moment and disappears, never to appear any more. Flashes are going on continuously, following one after another, there are an
infinite number of sparks, and everything together produces the impression of a flame, though it does not exist in reality.
The autumn has not yet come. It will be, but it does not exist now. And we give no thought to how that can appear which is not.
We are moving upon a plane, and recognize as really existing only the small circle lighted by our consciousness. Everything out of this circle, which we do not see, we negate; we do not like to admit that it exists. We are moving upon the plane in one direction. This direction we consider as eternal and infinite. But the direction at right angles to it, those lines which we are intersecting, we do not like to recognize as eternal and infinite. We imagine them as going into non-existence at once, as soon as we, have passed them, and that the lines before us have not as yet risen out of non-existence. If, presupposing that we are moving upon a sphere, upon its equator or one of its parallels, then it will appear that we recognize as really existing only one meridian: those which are behind us have disappeared and those ahead of us have not appeared as yet. .
We are going forward like a blind man, who feels paving stones and lanterns and walls of houses with his stick and believes in the real existence of only that which he touches now, which he feels now. That which has passed has disappeared and will never return! That which has not as yet been does not exist. The blind man remembers the route which he has traversed; he expects that ahead the way will continue, but he sees neither forward nor backward because he does not see anything; because his instrument of knowledgeâ€”the stickâ€”has a definite, and not very great length, and beyond the reach of his stick non-existence begins.
Wundt, in one of his books, called attention to the fact that our vaunted five organs of sense are in reality just feelers by which we feel the world around us. We live groping about. We never see anything. We are always just feeling everything. With the help of the microscope and the telescope, the telegraph and the telephone, we are extending our feelers a little, so to speak, but we are not beginning to see. To say that we are seeing would be possible only in case we could know the past and the future. But we do not see, and because of this we can never assure ourselves of that which we cannot feel.
This is the reason why we count as really existing only that circle which our feelers grasp at a given moment. Beyond thatâ€”darkness and non-existence.
But have we any right to think in this way?
Let us imagine a consciousness that is not bound by the conditions of sensuous receptivity. Such a consciousness can rise above the plane upon which we are moving; it can see far beyond the limits of the circle enlightened by our usual consciousness; it can see that not only does the line upon which we are moving exist, but also all lines perpendicular to it which we are intersecting, which we have ever intersected, and which we shall intersect. After rising above the plane this consciousness can see the plane, can convince itself that it is really a plane, and not a single line. Then it can see the past and the future, lying together and existing simultaneously.
That consciousness which is not bound by the conditions of sensuous receptivity can outrun the stupid traveller, ascend the mountain to see in the distance the town to which he is going, and be convinced that this town is not being built anew for his arrival, but exists quite independently of the stupid traveller. And that consciousness can look off and see on the horizon the towers of that city where that traveller had been, and be convinced that those towers have not fallen, that the city continues to stay and live just as it stayed and lived before the traveller's advent.
It can rise above the plane of time and see the spring behind and the autumn ahead, see simultaneously the budding flowers and ripening fruits. It can make the blind man recover his sight and see the road along which he passed and that which still lies before him.
The past and the future cannot not exist, because if they do not exist then neither does the present exist. Unquestionably they exist somewhere together, but we do not see them.
The present, compared with the past and the future, is the most unreal of all unrealities.
We are forced to admit that the past, the present and the future do not differ in anything, one from another; there exists just one presentâ€”the Eternal Now of Hindu philosophy. But we do not perceive this, because in every given moment we experience just a
little bit of that present, and this alone we count as existent, denying a real existence to everything else.
If we admit this, then our view of everything with which we are surrounded will change very considerably.
Usually we regard time as an abstraction, made by us during the observation of really existing motion. That is, we think that observing motion, or changes of relations between things and comparing the relations which existed before, which exist now, and which may exist in the future, that we are deducing the idea of time. We shall see later on how far this view is correct.
Thus the idea of time is composed of the conception of the past, of the present, and of the future.
Our conceptions of the past and present, though not very clear, are yet very much alike. As to the future there exists a great variety of views.
It is necessary for us to analyze the theories of the future as they exist in the mind of contemporary man.
There are in existence two theoriesâ€”that of the foreordained future, and that of the free future.
Foreordination is established in this way: we say that every future event is the result of those which happened before, and is created such as it will be and not otherwise as a consequence of a definite direction of forces which are contained in preceding events. This means, in other words, that future events are 'wholly contained in preceding ones, and if we could know the force and direction of all events which have happened up to the present moment, i.e., if we knew all the past, by this we could know all the future. And sometimes, knowing the present moment thoroughly, in all its details, we may really foretell the future. If the prophecy is not fulfilled, we say that we did not know all that had been, and we discover in the past some cause which had escaped our observation.
The idea of the free future is founded upon the possibility of voluntary action and accidental new combinations of causes. The future is regarded as quite indefinite, or defined only in part, because in every given moment new forces, new events and new phenomena are born which lie in a potential state, not causeless, but so incommensurable with causesâ€”as the firing of a city from one sparkâ€”that it is impossible to detect or measure them.
This theory affirms that one and the same action can have different results; one and the same cause, different effects; and it introduces the hypothesis of quite arbitrary volitional actions on the part of a man, bringing about profound changes in the subsequent events of his own life and the lives of others.
Supporters of the foreordination theory contend on the contrary that volitional, involuntary actions depend also upon causes, making them necessary and unavoidable at a given moment; that there is nothing accidental, and that there cannot be; that we call accidental only those things the causes of which we do not see by reason of our limitations; and that different effects of causes seemingly the same occur because the causes are different in reality and only seem similar for the reason that we do not understand them well enough nor see them sufficiently clearly.
The dispute between the theory of the foreordained future and that of the free future is an infinite dispute. Neither of these theories can say anything decisive. This is so because both theories are too literal, too inflexible, too material, and one repudiates the other: both say, "either this or the other." In the one case there results a complete cold predestination: that which will be, will be, nothing can be changedâ€”that which will befall tomorrow was predestined tens of thousands of years ago. There results in the other case a life upon some sort of needle-point called the present, which is surrounded on all sides by an abyss of non-existence, a journey in a country which does not as yet exist, a life in a world which is born and dies every moment, in which nothing ever returns. And both these opposite views are equally untrue, because the truth, in the given case, as in so many others, is contained in a union of two opposite understandings in one.
In every given moment all the future of the world is predestined and is existing, but is predestined conditionally, i.e., it will be such or another future according to the direction of events at a given moment, unless there enters a new fact, and a new fact can enter only from the side of consciousness and the will resulting from it. It is necessary to understand this, and to master it.
Besides this we are hindered from a right conception of the relation of the present toward the future by our misunderstanding of the relation of the present to the past. The difference of opinion
exists only concerning the future; concerning the past all agree that it has passed, that it does not exist now!â€”and that it was such as it has been. In this last lies the key to the understanding of the incorrectness of our views of the future. As a matter of fact, in reality our relation both to the past and to the future is far more complicated than it seems to us. In the past, behind us, lies not only that which really happened, but that which could have been. In the same way, in the future lies not only that which will be, but everything that may be.
The past and the future are equally undetermined, equally exist in all their possibilities, and equally exist simultaneously with the present.
By time we mean the distance separating events in the order of their succession and binding them in different wholes. This distance lies in a direction not contained in three-dimensional space, therefore it will be the new dimension of space.
This new dimension satisfies all possible requirements of the fourth dimension on the ground of the preceding reasoning.
It is incommensurable with the dimensions of three-dimensional space, as a year is incommensurable with St. Petersburg. It is perpendicular to all directions of three-dimensional space and is not parallel to any of them.
As a deduction from all the preceding we may say that time (as it is usually understood) includes in itself two ideas: that of a certain to us unknown space (the fourth dimension), and that of a motion upon this space. Our constant mistake consists in the fact that in time we never see two ideas, but see always only one. Usually we see in time the idea of motion, but cannot say from whence, where, whither, nor upon what space. Attempts have been made heretofore to unite the idea of the fourth dimension with the idea of time. But in those theories which have attempted to combine the idea of time with the idea of the fourth dimension appeared always the idea of some spatial element as existing in time, and along with it was admitted motion upon that space. Those who were constructing these theories evidently did not understand that leaving out the possibility of motion they were advancing the demand for a new time, because motion cannot proceed out of time. And as a result time goes ahead of us, like our shadow, receding according
as we approach it. All our perceptions of motion have become confused. If we imagine the new dimension of space and the possibility of motion upon this new dimension, time will still elude us, and declare that it is unexplained, exactly as it was unexplained before.
It is necessary to admit that by one term, time, we designate really two ideasâ€”"a certain space" and "motion upon that space." This motion does not exist in reality, and it seems to us as existing only because we do not see the spatiality of time. That is, the sensation of motion in time (and motion out of time does not exist) arises in us because we are looking at the world as if through a narrow slit, and are seeing the lines of intersection of the time-plane with our three-dimensional space only.
Therefore it is necessary to declare how profoundly incorrect is our usual theory that the idea of time is deduced by us from the observation of motion, and is really nothing more than the idea of that succession which is observed by us in motion.
It is necessary to recognize quite the reverse: that the idea of motion is deduced by us out of an incomplete sensation of time, or of the time-sense, i.e., out of a sense or sensation of the fourth dimension, but out of an incomplete sensation. This incomplete sensation of time (of the fourth dimension)â€”the sensation through the slitâ€”gives us the sensation of motion, that is, creates an illusion of motion which does not exist in reality, but instead of which there exists in reality only the extension upon a direction inconceivable to us.
One other aspect of the question has very great significance. The fourth dimension is bound up with the ideas of "time" and "motion." But up to this point we shall not be able to understand the fourth dimension unless we shall understand the fifth dimension.
Attempting to look at time as at an object, Kant says that it has one dimension: i.e., he imagines time as a line extending from the infinite future into the infinite past. Of one point of this line we are consciousâ€”always only one point. And this point has no dimension because that which in the usual sense we call the present, is the recent past, and sometimes also the near future.
This would be true in relation to our illusory perception of time. But in reality eternity is not the infinite dimension of time, but the one perpendicular to time; because, if eternity exists, then every moment is eternal. The line of time extends in that order of succession of phenomena which are in causal interdependenceâ€”first the cause, then the effect: before, now, after. The line of eternity extends perpendicularly to that line.
It is impossible to understand the idea of time without conceiving in imagination the idea of eternity; it is likewise impossible to understand space if we have no idea of time.
From the standpoint of eternity, time does not differ in anything from the other lines and dimensions of spaceâ€”length, breadth, and height. This means that just as in space exist the things that we do not see, or speaking differently, not alone that which we see, so in time "events" exist before our consciousness has touched them, and they still exist after our consciousness has left them behind.
Consequently, extension in time is extension into unknown space, and therefore time is the fourth dimension of space.
It is necessary that we should regard time as a spatial conception considered with relation to our two dataâ€”the world and consciousness (psychic life).
The idea of time arises through the knowledge of the world by means of sensuous receptivity. It has been previously explained that because of the properties of our sensuous receptivity we see the world as through a narrow slit.
Out of this the following questions arise:
1. What accounts for the existence in the world of illusionary motion? That is, why do we not see, through this slit, the same thing? Why, behind the slit, do changes proceed creating the illusion of motion: that is, how and in what manner does the focus of our receptivity run over the world of phenomena? In addition to all this it is necessary to remember that through the same slit through which we see the world we observe ourselves and see in ourselves changes similar to the changes in the rest of things.
2. Why can we not extend that slit?
It is necessary to answer these questions.
First of all it is important to note that within the limits of our usual observation our receptivity is always conditioned in the same way and cannot escape these conditions. In other words, it is chained, as it were, to some plane above which it cannot rise. These conditions, or that plane we call, in the inner world, consciousness or level of consciousness; in the outer world we call them matter or the density of matter. (The word density is used in this connection not in the sense of a solid, liquid or gaseous state, but in the sense of the physical, the astral and the mental planeâ€”accepting temporarily the terminology employed in contemporary theosophical literature.) Our usual psychic life proceeds upon some definite plane (of consciousness or matter) and never rises above it. If our receptivity could rise above this plane it would undoubtedly perceive simultaneously, below itself, a far greater number of events than it usually sees while on a plane. Just as a man, ascending a mountain, or going up in a balloon, begins to see simultaneously and at once many things which it is impossible to see simultaneously and at once from belowâ€”the movement of two trains toward one another between which a collision will occur; the approach of an enemy detachment to a sleeping camp; two cities divided by a ridge, etc.â€”so consciousness rising above the plane in which it usually functions, must see simultaneously the events divided for ordinary consciousness by periods of time. These will be the events which ordinary consciousness never sees together, as: cause and effect; the work and the payment; the crime and the punishment; the movement of trains toward one another and their collision; the approach of the enemy and the battle; the sunrise and the sunset; the morning and the evening; the day and the night; spring, autumn, summer and winter; the birth and the death of a man.
The angle of vision will enlarge during such an ascent, the moment will expand.
If we imagine a receptivity which is on a level higher than our consciousness, possessing a broader angle of view, then this receptivity will be able to grasp, as something simultaneous, i.e., as a moment, all that is happening for us during a certain length of timeâ€”minutes, hours, a day, a month. Within the limits of its moment such a receptivity will not be in a position to discriminate
between before, now, after; all this will be for it now. Now will expand.
But in order for this to happen it would be necessary for us to liberate ourselves from matter, because matter is nothing more than the conditions of space and time in which we dwell. Thence arises the question: can consciousness leave the conditions of a given material existence without itself undergoing fundamental changes, or without disappearing altogether, as men of positivistic views would affirm?
This is a debatable question, and later I shall give examples and proofs, speaking on behalf of the idea that our consciousness can leave the conditions of a given materiality. For the present I wish to establish what must proceed during this leaving.
There would ensue the expansion of the moment, i.e., all that we are apprehending in time would become something like a single moment, in which the past, the present, and the future would be seen at once. This shows the relativity of motion, as depending for us upon the limitation of the moment, which includes only a very small part of the moments of life perceived by us.
We have a perfect right to say, not that "time" is deduced from "motion," but that motion is sensed because of the time-sense. We have that sense, therefore we sense motion. The time-sense is the sensation of changing moments. If we did not have this time-sense we could not feel motion. The "time-sense" is itself, in substance, the limit or the surface of our "space-sense." Where the "space-sense" ends, there the "time-sense" begins. It has been made clear that "time" is identical in its properties with "space," i.e., it has all the signs of space extension. However, we do not feel it as spatial extension, but we feel it as time, that is, as something specific, inexpressibleâ€”in other words, uninterruptedly bound up with "motion." This inability to sense time spatially has its origin in the fact that the time-sense is a misty space-sense; by means of our time-sense we feel obscurely the new characteristics of space, which extend out from the sphere of three dimensions.
But what is the time-sense and why does there arise the illusion of motion?
To answer this question at all satisfactorily is possible only by studying the forms and levels of psychic life.
"I" is a complicated quantity, and within it goes on a continuous motion. About the nature of this motion we shall speak later, but this very motion inside of us creates the illusion of motion around us, motion in the material world.
The noted mathematician Riemann understood that when higher dimensions of space are in question, time, by some means, translates itself into space, and he regarded the MATERIAL ATOM as the entrance of the fourth dimension into three-dimensional space.
In one of his books Hinton writes very interestingly about "surface tensions."
The relationship of a surface to a solid or of a solid to a higher solid is one which we often find in nature.
A surface is nothing more nor less than the relation between two things. Two bodies touch each other. The surface is the relationship of one to the other.
If our space is in the same co-relation with higher space as is the surface to our space, then it may be that our space is really the surface, that is, the place of contact, of two higher-dimensional spaces.
It is a fact worthy of notice that in the surface of a fluid different laws obtain from those which hold throughout the mass. There is a whole series of facts which are grouped together under the name of surface tensions, which are of great importance in physics, and by which the behavior of the surfaces of liquids is governed.
And it may well be that the laws of our universe are the surface tensions of a higher universe.
If the surface be regarded as a medium lying between bodies, then indeed it will have no weight, but be a powerful means of transmitting vibrations. Moreover, it would be unlike any other substance, and it would be impossible to get rid of it. However perfect a vacuum be made, there would be in this vacuum just as much of this unknown medium (i.e., of that surface) as there was before.
Matter would pass freely through this medium . . . vibrations of this medium would tear asunder portions of matter. And involuntarily the conclusion would be drawn that this medium was unlike any ordinary matter. . . . These would be very different properties to reconcile in one and the same substance.
Now is there anything in our experience which corresponds to this medium? . . .
Do we suppose the existence of any medium through which matter freely moves, which yet by its vibrations destroys the combinations of matterâ€”some medium which is present in every vacuum however perfect, which penetrates all bodies, is weightless, and yet can never be laid hold of.
The "substance" which possesses all these qualities is called the "ether."
The properties of the ether are a perpetual object of investigation in science. . . . But taking into consideration the ideas expressed before it would be interesting to look at the world supposing that we are not in it but on the ether; where the "ether" is the surface of contact of two bodies of higher dimensions. 1
Hinton here expresses an unusually interesting thought, and brings the idea of the "ether" nearer to the idea of time. The materialistic, or even the energetic understanding of contemporary physics of the ether is perfectly fruitlessâ€”a dead-end siding. For Hinton the ether is not a substance but only a "surface," the "boundary" of something. But of what? Again not that of a substance, but the boundary, the surface, the limit of one form of receptivity and the beginning of another. . . .
In one sentence the walls and fences of the materialistic dead-end siding are broken down and before our thought open wide horizons of regions unexplored.
51:1 Hinton, "A New Era of Thought," pp. 52, 56, 57.
Four-dimensional space. "Temporal body"â€”Linga SharÃ®ra. 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 the left hands in three-dimensional and in four-dimensional space. Difference between three-dimensional and four-dimensional space. Not two different spaces but different methods of receptitivity of one and the same world.
FOUR-DIMENSIONAL space, if we try to imagine it to ourselves, will be the infinite repetition of our space, of our infinite three-dimensional sphere, as a line is the infinite repetition of a point.
Many things that have been said before will become much clearer to us when we dwell on the fact that the fourth dimension must be sought for in time.
It will become clear what is meant by the fact that it is possible to regard a four-dimensional body as the tracing of the movement in space of a three-dimensional body in a direction not confined within that space. Now the direction not confined in three-dimensional space in which any three-dimensional body movesâ€”this is the direction of time. Any three-dimensional body, existing, is at the same time moving in time and leaves as a tracing of its movement the temporal, or four-dimensional body. We never see or feel this body, because of the limitations of our receptive apparatus, but we see the section of it only, which section we call the three-dimensional body. Therefore we are in error in thinking that the three-dimensional body is in itself something real. It is the projection of the four-dimensional bodyâ€”its pictureâ€”the image of it on our plane.
The four-dimensional body is the infinite number of three-dimensional bodies. That is, the four-dimensional body is the infinite number of moments of existence of the three-dimensional oneâ€”its states and positions. The three-dimensional body which we see
appears as a single figureâ€”one of a series of pictures on a cinematographic film as it were.
Four-dimensional space (time) is really the distance between the forms, states, and positions of one and the same body (and different bodies, i.e., those seeming different to us). It separates those states, forms, and positions each from the other, and it binds them also into some to us incomprehensible whole. This incomprehensible whole can be formed in time out of one physical bodyâ€”and out of different bodies.
It is easier for us to imagine the temporal whole as related to one physical body.
If we consider the physical body of a man, we shall find in it besides its "matter" something, it is true, changing, but undoubtedly one and the same from birth until death.
This something is the Linga-SharÃ®ri of Hindu philosophy, i.e., the form on which our physical body is moulded. (H. P. Blavatsky: The Secret Doctrine.) Eastern philosophy regards the physical body as something impermanent which is in a condition of perpetual interchange with its surroundings. The particles come and go. After one second the body is already not absolutely the same as it was one second before. Today it is in a considerable degree not that which it was yesterday. After seven years it is a quite different body. But despite all this, something always persists from birth to death, changing its aspect a little, but remaining the same. This is the Linga-SharÃ®ra.
The Linga-SharÃ®ra is the form, the image: it changes, but remains the same. That image of a man which we are able to represent to ourselves is not the Linga-SharÃ®ra. But if we try to represent to ourselves mentally the image of a man from birth to death, with all the particularities and traits of childhood, manhood and senility, as if extended in time, when it will be the Linga-SharÃ®ra.
Form pertains to all things. We say that everything consists of matter and form. Under the category of "matter," as already stated, the cause of a lengthy series of mixed sensations is predicated, but matter without form is not comprehensible to us; we cannot even think of matter without form. But we can think and imagine form without matter.
The thing, i.e., the union of form and matter, is never constant;
it always changes in the course of time. This idea afforded Newton the possibility of building his theory of fluents and fluxions.
Newton came to the conclusion that constant quantities do not exist in nature. Variables do existâ€”flowing, fluents only. The velocities with which different fluents change were called by Newton fluxions.
From the standpoint of this theory all things known to usâ€”men, plants, animals, planetsâ€”are fluents, and they differ by the magnitude of their fluxions. But the thing, changing continuously in time, sometimes very much, and quickly, as in the case of a living body for example, still remains one and the same. The body of a man in youth, and the body of a man in senilityâ€”these are one and the same, though we know that in the old body there is not one atom left that was in the young one. The matter changes, but something remains one under all changes, this something is the Linga-SharÃ®ra. Newton's theory is valid for the three-dimensional world existing in time. In this world there is nothing constant. All is variable because every consecutive moment the thing is already not that which it was before. We never see the Linga-SharÃ®ra, we see always its parts, and they appear to us variable. But if we observe more attentively we shall see that it is an illusion. Things of three dimensions are unreal and variable. They cannot be real because they do not exist in reality, just as the imaginary sections of a solid do not exist. Four-dimensional bodies alone are real.
In one of the lectures contained in the book, A Pluralistic Universe, Prof. James calls attention to Prof. Bergson's remark that science studies always only the t of the universe, i.e., not the universe in its entirety, but the moment, the "temporal section" of the universe.
The properties of four-dimensional space will become clearer to us if we compare in detail three-dimensional space with the surface, and discover the differences existing between them.
Hinton, in his book, A New Era of Thought, examines these differences very attentively. He represents to himself, on a plane, two equal rectangular triangles, cut out of paper, the right angles of which are placed in opposite directions. These triangles will be
equal, but for some reason quite different. The right angle of one is directed to the right, that of the other to the left. If anyone wants to make them quite similar, it is possible to do so only with the help of three-dimensional space. That is, it is necessary to take one triangle, turn it over, and put it back on the plane. Then they will be two equal, and exactly similar triangles. But in order to effect this, it was necessary to take one triangle from the plane into three-dimensional space, and turn it over in that space. If the triangle is left on the plane, then it will never be possible to make it identical with the other, keeping the same relation of angles of the one to those of the other. If the triangle is merely rotated in the plane this similarity will never be established. In our world there are figures quite analogous to these two triangles.
We know certain shapes which are equal the one to the other, which are exactly similar, and yet which we cannot make fit into the same portion of space, either practically or by imagination.
If we look at our two hands we see this clearly, though the two hands represent a complex case of a symmetrical similarity. Now there is one way in which the right hand and the left hand may practically be brought into likeness. If we take the right hand glove and the left hand glove, they will not fit any more than the right hand will coincide with the left hand; but if we turn one glove inside out, then it will fit. Now suppose the same thing done with the solid hand as is done with the glove when it is turned inside out, we must suppose it, so to speak, pulled through itself. . . . If such an operation were possible, the right hand would be turned into an exact model of the left hand. 1
But such an operation would be possible in the higher dimensional space only, just as the overturning of the triangle is possible only in a space relatively higher than the plane. Even granting the existence of four-dimensional space, it is possible that the turning of the hand inside out and the pulling of it through itself is a practical impossibility on account of causes independent of geometrical conditions. But this does not diminish its value as an example. Things like the turning of the hand inside out are possible theoretically in four-dimensional space because in this space different, and even distant points of our space and time touch, or have the possibility of contact. All points of a sheet of paper lying on a table are separated
one from another, but by taking the sheet from the table it is possible to fold it in such a way as to bring together any given points. If on one corner is written St. Petersburg, and on another Madras, nothing prevents the putting together of these corners. And if on the third corner is written the year 1812, and on the fourth 1912, these corners can touch each other too. If on one corner the year is written in red ink, and the ink has not yet dried, then the figures may imprint themselves on the other corner. And if afterwards the sheet is straightened out and laid on the table, it will be perfectly incomprehensible, to a man who has not followed the operation, how the figure from one corner could transfer itself to another corner. For such a man the. possibility of the contact of remote points of the sheet will be incomprehensible, and it will remain incomprehensible so long as he thinks of the sheet in two-dimensional space only. The moment he imagines the sheet in three-dimensional space this possibility will become real and obvious to him.
In considering the relation of the fourth dimension to the three known to us, we must conclude that our geometry is obviously insufficient for the investigation of higher space.
As before stated, a four-dimensional body is as incommensurable with a three-dimensional one as a year is incommensurable with St. Petersburg.
It is quite clear why this is so. The four-dimensional body consists of on infinitely great number of three-dimensional bodies; accordingly, there cannot be a common measure for them. The three-dimensional body, in comparison with the four-dimensional one is equivalent to the point in comparison with the line.
And just as the point is incommensurable with the line, so is the line incommensurable with the surface; as the surface is incommensurable with the solid body, so is the three-dimensional body incommensurable with the four-dimensional one.
It is clear also why the geometry of three dimensions is insufficient for the definition of the position of the region of the fourth dimension in relation to three-dimensional space.
Just as in the geometry of one dimension, that is, upon the line, it is impossible to define the position of the surface, the side of which constitutes the given line; just as in the geometry of two dimensions,
i.e., upon the surface, it is impossible to define the position of the solid, the side of which constitutes the given surface, so in the geometry of three dimensions, in three-dimensional space, it is impossible to define a four-dimensional space. Briefly speaking, as planimetry is insufficient for the investigation of the problems of stereometry, so is stereometry insufficient for four-dimensional space.
As a conclusion from all of the above we may repeat that every point of our space is the section of a line in higher space, or as B. Riemann expressed it: the material atom is the entrance of the fourth dimension into three-dimensional space.
For a nearer approach to the problem of higher dimensions and of higher space it is necessary first of all to understand the constitution and properties of the higher dimensional region in comparison with the region of three dimensions. Then only will appear the possibility of a more exact investigation of this region, and a classification of the laws governing it.
What is it that it is necessary to understand?
It seems to me that first of all it is necessary to understand that we are considering not two regions spatially different, and not two regions of which one (again spatially, "geometrically") constitutes a part of the other, but two methods of receptivity of one and the same unique world of a space which is unique.
Furthermore it is necessary to understand that all objects known to us exist not only in those categories in which they are perceived by us, but in an infinite number of others in which we do not and cannot sense them. And we must learn first to think things in other categories, and then so far as we are able, to imagine them therein. Only after doing this can we possibly develop the faculty to apprehend them in higher spaceâ€”and to sense "higher" space itself.
Or perhaps the first necessity is the direct perception of everything in the outside world which does not fit into the frame of three dimensions, which exists independently of the categories of time and spaceâ€”everything that for this reason we are accustomed to consider as non-existent. If variability is an indication of the three-dimensional world, then let us search for the constant and
thereby approach to an understanding of the four-dimensional world.
We have become accustomed to count as really existing only that which is measurable in terms of length, breadth and height; but as has been shown it is necessary to expand the limits of the really existing. Mensurability is too rough an indication of existence, because mensurability itself is too conditioned a conception. We may say that for any approach to the exact investigation of the higher dimensional region the certainty obtained by the immediate sensation is probably indispensable; that much that is immeasurable exists just as really as, and even more really than, much that is measurable.
55:1 C. H. Hinton, "A New Era of Thought," p. 44.
Methods of investigation of the problem of higher dimensions. The analogy between imaginary worlds of different dimensions. The one-dimensional world on a line. "Space" and "time" of a one-dimensional being. The two-dimensional 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?
A SERIES of analogies and comparisons are used for the definition of that which can be, and that which cannot be, in the region of the higher dimension.
We imagine "worlds" of one, and of two dimensions, and out of the relations of lower-dimensional worlds to higher ones we deduce possible relations of our world to one of four dimensions; just as out of the relations of points to lines, of lines to surfaces, and of surfaces to solids we deduce the relations of our solids to four-dimensional ones.
Let us try to investigate everything that this method of analogy can yield.
Let us imagine a world of one dimension.
It will be a line. Upon this line let us imagine living beings. Upon this line, which represents the universe for them, they will be able to move forward and backward only, and these beings will be as the points, or segments of a line. Nothing will exist for them outside their lineâ€”and they will not be aware of the line upon which they are living and moving. For there will exist only two points, ahead and behind, or may be just one point ahead. Noticing the change in states of these points, the one-dimensional being will call these changes phenomena. If we suppose the line upon which the one-dimensional being lives to be passing through the different objects of our world, then of all these objects the one-dimensional
being will perceive one point only; if different bodies intersect his line, the one-dimensional being will sense them only as the appearance, the more or less prolonged existence, and the disappearance of a point. This appearance, existence, and disappearance of a point will constitute a phenomenon. Phenomena, according to the character and properties of passing objects and the velocity and properties of their motions, for the one-dimensional being will be constant or variable, long or short timed, periodical or unperiodical. But the one-dimensional being will be absolutely unable to understand or explain the constancy or variability, the duration or brevity, the periodicity or unperiodicity of the phenomena of his world, and will regard these simply as properties of such phenomena. The solids intersecting his line may be different, but for the one-dimensional being all phenomena will be absolutely identicalâ€”just the appearance or the disappearance of a pointâ€”and phenomena will differ only in duration and in greater or less periodicity.
Such strange monotony and similarity of the diverse and heterogeneous phenomena of our world will be the characteristic peculiarity of the one-dimensional world.
Moreover, if we assume that the one-dimensional being possesses memory, it is clear that recalling all the points seen by him as phenomena, he will refer them to time. The point which was: this is the phenomenon already non-existent, and the point which may appear tomorrow: this is the phenomenon which does not exist as yet. All of our space except one line will be in the category of time, i.e., something wherefrom phenomena come and into which they disappear. And the one-dimensional being will declare that the idea of time arises for him out of the observation of motion, that is to say, out of the appearance and disappearance of points. These will be considered as temporal phenomena, beginning at that moment when they become visible, and endingâ€”ceasing to existâ€”at that moment when they become invisible. The one-dimensional being will not be in a position to imagine that the phenomenon goes on existing somewhere, though invisibly to him; or he will imagine it as existing somewhere on his line, far ahead of him.
We can imagine this one-dimensional being more vividly. Let us take an atom hovering in space, or simply a particle of dust, carried along by the air, and let us imagine that this atom or particle
of dust possesses a consciousness, i.e., separates himself from the outside world, and is conscious only of that which lies in the line of his motion, and with which he himself comes in contact. He will then be a one-dimensional being in the full sense of the word. He can fly and move in all directions, but it will always seem to him that he is moving upon a single line; outside of this line will be for him only a great Nothingnessâ€”the whole universe will appear to him as one line. He will feel none of the turns and angles of his line, for to feel an angle it is necessary to be conscious of that which lies to right or left, above or below. In all other respects such a being will be absolutely identical with the before-described imaginary being living upon the imaginary line. Everything that he comes in contact with, that is, everything that he is conscious of, will seem to him to be emerging from time, i.e., from nothing, vanishing into time, i.e., into nothing. This nothing will be all our world. All our world except one line will be called time and will be counted as actually non-existent.
Let us next consider the two-dimensional world, and the being living on a plane. The universe of this being will be one great plane. Let us imagine beings on this plane having the shape of points, lines, and flat geometrical figures. The objects and "solids" of that world will have the shape of flat geometrical figures too.
In what manner will a being living on such a plane universe cognize his world?
First of all we can affirm that he will not feel the plane upon which he lives. He will not do so because he will feel the objects, i.e., figures which are on this plane. He will feel the lines which limit them, and for this reason he will not feel his plane, for in that case he would not be in a position to discern the lines. The lines will differ from the plane in that they produce sensations; therefore they exist. The plane does not produce sensations; therefore it does not exist. Moving on the plane, the two-dimensional being, feeling no sensations, will declare that nothing now exists. After having encountered some figure, having sensed its lines, he will say that something appeared. But gradually, by a process of reasoning, the two-dimensional being will come to the conclusion that the figures
he encounters exist on something, or in something. Thereupon he may name such a plane (he will not know, indeed, that it is a plane) the "ether." Accordingly he will declare that the "ether" fills all space, but differs in its qualities from "matter." By "matter" he will mean lines. Having come to this conclusion the two-dimensional being will regard all processes as happening in his "ether," i.e., in his space. He will not be in a position to imagine anything outside of this ether, that is, out of his plane. If anything, proceeding out of his plane, comes in contact with his consciousness, then he will either deny it, or regard it as something subjective, the creation of his own imagination; or else he will believe that it is proceeding right on the plane, in the ether, as are all other phenomena.
Sensing lines only, the plane being will not sense them as we do. First of all, he will see no angle. It is extremely easy for us to verify this by experiment. If we will hold before our eyes two matches, inclined one to the other in a horizontal plane, then we shall see one line. To see the angle we shall have to look from above. The two-dimensional being cannot look from above and therefore cannot see the angle. But measuring the distance between the lines of different "solids" of his world, the two-dimensional being will come continually in contact with the angle, and he will regard it as a strange property of the line, which is sometimes manifest and sometimes is not. That is, he will refer the angle to time; he will regard it as a temporary, evanescent phenomenon, a change in the state of a "solid," or as motion. It is difficult for us to understand this. It is difficult to imagine how the angle can be regarded as motion. But it must be absolutely so, and cannot be otherwise. If we try to represent to ourselves how the plane being studies the square, then certainly we shall find that for the plane being the square will be a moving body. Let us imagine that the plane being is opposite one of the angles of the square. He does not see the angleâ€”before him is a line, but a line possessing very curious properties. Approaching this line, the two-dimensional being observes that a strange thing is happening to the line. One point remains in the same position, and other points are withdrawing back from both sides. We repeat, that the two-dimensional being has no idea of an angle. Apparently the line remains the same as it was, yet something is happening to it, without a doubt. The plane being will say
that the line is moving, but so rapidly as to be imperceptible to sight. If the plane being goes away from the angle and follows along a side of the square, then the side will become immobile. When he comes to the angle, he will notice the motion again. After going around the square several times, he will establish the fact of regular, periodical motions of the line. Quite probably in the mind of the plane being the square will assume the form of a body possessing the property of periodical motions, invisible to the eye, but producing definite physical effects (molecular motion)â€”or it will remain there as a perception of periodical moments of rest and motion in one complex line, and still more probably it will seem to be a rotating body.
Quite possibly the plane being will regard the angle as his own subjective perception, and will doubt whether any objective reality corresponds to this subjective perception. Nevertheless he will reflect that if there is action, yielding to measurement, so must there be the cause of it, consisting in the change of the state of the line, i.e., in motion.
The lines visible to the plane being he may call matter, and the anglesâ€”motion. That is, he may call the broken line with an angle, moving matter. And truly to him such a line by reason of its properties will be quite analogous to matter in motion.
If a cube were to rest upon the plane upon which the plane being lives, then this cube will not exist for the two-dimensional being, but only the square face of the cube in contact with the plane will exist for himâ€”as a line, with periodical motions. Correspondingly, all other solids lying outside of his plane., in contact with it, or passing through it, will not exist for the plane being. The planes of contact or cross-sections of these bodies will alone be sensed. But if these planes or sections move or change, then the two-dimensional being will think, indeed, that the cause of the change or motion is in the bodies themselves, i.e., right there on his plane.
As has been said, the two-dimensional being will regard the straight lines only as immobile matter; irregular lines and curves will seem to him as moving. So far as really moving lines are concerned, that is, lines limiting the cross-sections or planes of contact passing through or moving along the plane, these will be for
the two-dimensional being something inconceivable and incommensurable. It will be as though there were in them the presence of something independent, depending upon itself only, animated. This effect will proceed from two causes: He can measure the immobile angles and curves, the properties of which the two-dimensional being calls motion, for the reason that they are immobile; moving figures, on the contrary, he cannot measure, because the changes in them will be out of his control. These changes will depend upon the properties of the whole body and its motion, and of that whole body the two-dimensional being will know only one side or section. Not perceiving the existence of this body, and contemplating the motion pertaining to the sides and sections he probably will regard them as living beings. He will affirm that there is something in them which differentiates them from other bodies: vital energy, or even soul. That something will be regarded as inconceivable, and really will be inconceivable to the two-dimensional being, because to him it is the result of an incomprehensible motion of inconceivable solids.
If we imagine an immobile circle upon the plane, then for the two-dimensional being it will appear as a moving line with some very strange and to him inconceivable motions.
The two-dimensional being will never see that motion. Perhaps he will call such motion molecular motion, i.e., the movement of minutest invisible particles of "matter."
Moreover, a circle rotating around an axis passing through its center, for the two-dimensional being will differ in some inconceivable way from the immobile circle. Both will appear to be moving, but moving differently.
For the two-dimensional being a circle or a square, rotating around its centre, on, account of its double motion will be an inexplicable and incommensurable phenomenon, like a phenomenon of life for a modern physicist.
Therefore, for a two-dimensional being, a straight line will be immobile matter; a broken or a curved lineâ€”matter in motion; and a moving lineâ€”living matter.
The centre of a circle or a square will be inaccessible to the plane being, just as the centre of a sphere or of a cube made of solid matter is inaccessible to usâ€”and for the two-dimensional being even
the idea of a centre will be incomprehensible, since he possesses no idea of a centre.
Having no idea of phenomena proceeding outside of the planeâ€”that is, out of his "space"â€”the plane being will think of all phenomena as proceeding on his plane as has been stated. And all phenomena which he regards as proceeding on his plane, he will consider as being in causal interdependence one with another: that is, he will think that one phenomenon is the effect of another which has happened right there, and the cause of a third which will happen right on the same plane.
If a multi-colored cube passes through the plane, the plane being will perceive the entire cube and its motion as a change in color of lines lying in the plane. Thus, if a blue line replaces a red one, then the plane being will regard the red line as a past event. He will not be in a position to realize the idea that the red line is still existing somewhere. He will say that the line is single, but that it becomes blue as a consequence of certain causes of a physical character. If the cube moves backward so that the red line appears again after the blue one, then for the two-dimensional being this will constitute a new phenomenon. He will say that the line became red again.
For the being living on a plane, everything above and below (if the plane be horizontal), and on the right or left (if the plane be vertical) will be existing in time, in the past and in the future: that which in reality is located outside of the plane will be regarded as non-existent, either as that which is already past, i.e., as something which has disappeared, ceased to be, will never return; or as in the future, i.e., as not existent, not manifested, as a thing in potentiality.
Let us imagine that a wheel with the spokes painted different colors is rotating through the plane upon which the plane being lives. To such a being all the motion of the wheel will appear as a variation of the color of the line of intersection of the wheel and the plane. The plane being will call this variation of the color of the line a phenomenon, and observing these phenomena he will notice in them a certain succession. He will know that the black line is followed by the white one, the white by the blue, the blue by the red, and so on. If simultaneously with the appearance of the white line some other phenomenon occursâ€”say the ringing of a
bellâ€”the two-dimensional being will say that the white line is the cause of that ringing. The change of the color of the lines, in the opinion of the two-dimensional being, will depend on causes lying right in his plane. Any pre-supposition of the possibility of the existence of causes lying outside of the plane he will characterize as fantastic and entirely unscientific. It will seem so to him because he will never be in a position to represent the wheel to himself, i.e., the parts of the wheel on both sides of the plane. After a rough study of the color of the lines, and knowing the order of their sequence, the plane being, perceiving one of them, say the blue one, will think that the black and the white ones have already passed, i.e., disappeared, ceased to exist, gone into the past; and that those lines which have not as yet appearedâ€”the yellow, the green, and so on, and the new white and black ones still to comeâ€”do not yet exist, but lie in the future.
Therefore, though not conceiving the form of his universe, and regarding it as infinite in all directions, the plane being will nevertheless involuntarily think of the past as situated somewhere at one side of all, and of the future as somewhere at the other side of this totality. In such manner will the plane being conceive of the idea of time. We see that this idea arises because the two-dimensional being senses only two out of three dimensions of space; the third dimension he senses only after its effects become manifest upon the plane, and therefore he regards it as something different from the first two dimensions of space, calling it time.
Now let us imagine that through the plane upon which the two-dimensional being lives, two wheels with multi-colored spokes are rotating and are rotating in opposite directions. The spokes of one wheel come from above and go below; the spokes of the other come from below and go above.
The plane being will never notice it.
He will never notice that where for one line (which he sees) there lies the past, for another line there lies the future. This thought will never even come into his head, because he will conceive of the past and the future very confusedly, regarding them as concepts, not as actual facts. But at the same time he will be firmly convinced that the past goes in one direction, and the future in another. Therefore
it will seem to him a wild absurdity that on one side something past and something future can lie together, and on another sideâ€”and also beside these twoâ€”something future and something past. To the plane being the idea that some phenomena come whence others go, and vice versa, will seem equally absurd. He will tenaciously think that the future is that wherefrom everything comes, and the past is that whereto everything goes and wherefrom nothing returns. He will be totally unable to understand that events may arise from the past just as they do from the future.
Thus we see that the plane being will regard the changes of color of the lines lying on the plane very naively. The appearance of different spokes he will regard as the change of color of one and the same line, and the repeated appearance of the same colored spoke he will regard every time as a new appearance of a given color.
But nevertheless, having noticed periodicity in the change of the color of the lines upon the surface, having remembered the order of their appearance, and having learned to define the "time" of the appearance of certain spokes in relation to some other more constant phenomenon, the plane being will be in a position to foretell the change of the line from one color to another. Thereupon he will say that he has studied this phenomenon, that he can apply to it "the mathematical method"â€”can "calculate" it.
If we ourselves enter the world of plane beings, then its inhabit-ants will sense the lines limiting the sections of our bodies. These sections will be for them living beings; they will not know from whence they appear, why they alter, or whither they disappear in such a miraculous manner. So also, the sections of all our inanimate but moving objects will seem independent living beings.
If the consciousness of a plane being should suspect our existence, and should come into some sort of communion with our consciousness, then to him we would appear as higher, omniscient, possibly omnipotent, but above all incomprehensible beings of a quite inconceivable category.
We could see his world just as it is, and not as it seems to him. We could see the past and the future; could foretell, direct, and even create events.
We could know the very substance of thingsâ€”could know what "matter" (the straight line) is, what "motion" (the broken line, the curve, the angle) is. We could see an angle, and we could see a centre. All this would give us an enormous advantage over the two-dimensional being.
In all the phenomena of the world of the two-dimensional being we could see considerably more than he seesâ€”or could see quite other things than he.
And we could tell him very much that was new, amazing, and unexpected about the phenomena of his world, provided indeed that be could hear us and understand us.
First of all we could tell him that what he regards as phenomenaâ€”angles and curves, for instanceâ€”are properties of higher figures; that other "phenomena" of his world are not phenomena, but only "parts" or "sections" of phenomena; that what he calls "solids" are only sections of solidsâ€”and many things besides.
We would be able to tell him that on both sides of his plane (i.e., of his space or ether) lies infinite space (which the plane being calls time); and that in this space lie the causes of all his phenomena, and the phenomena themselves, the past as well as the future ones; moreover, we might add that "phenomena" themselves are not something happening and then ceasing to be, but combinations of properties of higher solids.
But we should experience considerable difficulty in explaining anything to the plane being; and it would be very difficult for him to understand us. First of all it would be difficult because he would not have the concepts corresponding to our concepts. He would lack "necessary words."
For instance, "section"â€”this would be for him a quite new and inconceivable word; then "angle"â€”again an inconceivable word; "centre"â€”still more inconceivable; the third perpendicularâ€”something incomprehensible, lying outside of his geometry.
The fallacy of his conception of time would be the most difficult thing for the plane being to understand. He could never understand that that which has passed and that which is to be are existing simultaneously on the lines perpendicular to his plane. And he could never conceive the idea that the past is identical with the future, because phenomena come from both sides and go in both directions.
But the most difficult thing for the plane being would be to conceive the idea that "time" includes in itself two ideas: the idea of space, and the idea of motion upon this space.
We have shown that what the two-dimensional being living on the plane calls motion has for us a quite different aspect.
In his book The Fourth Dimension, under the heading "The First Chapter in the History of Four-space," Hinton writes:
Parmenides, and the Asiatic thinkers with whom he is in close affinity, propound a theory of existence which is in close accord with a conception of a possible relation between a higher and lower dimensional space. . . . It is one which in all ages has had a strong attraction for pure intellect, and is the natural mode of thought for those who refrain from projecting their own volition into nature under the guise of causality.
According to Parmenides of the school of Elea the all is one, unmoving and unchanging. The permanent amid the transientâ€”that foothold for thought, that solid ground for feeling, on the discovery of which depends all our lifeâ€”is no phantom; it is the image amidst deception of true being, the eternal, the unmoved, the one. Thus says Parmenides.
But how is it possible to explain the shifting scene, these mutations of things?
"Illusion," answers Parmenides. Distinguishing between truth and error, he tells of the true doctrine of the oneâ€”the false opinion of a changing world. He is no less memorable for the manner of his advocacy than for the cause he advocates.
Can the mind conceive a more delightful intellectual picture than that of Parmenides pointing to the one, the true, the unchanging, and yet on the other hand ready to discuss all manner of false opinion! . . .
In support of the true opinion he proceeded by the negative way of showing the self-contradictions in the ideas of change and motion. . . . To express his doctrine in the ponderous modern way we must make the statement that motion is phenomenal, not real.
Let us represent his doctrine.
Imagine a sheet of still water into which a slanting stick is being lowered with a motion vertically downward. Let 1, 2, 3 (Fig. 1) be three consecutive positions of the stick. A, B, C will be three connective positions of the meeting of the stick with the surface of the water. As the stick passes down, the meeting will move from A on to B and C.
Suppose now all the water to be removed except a film. At the meeting of the film and the stick there will be an interruption of the film. If we suppose the film to have a property, like that of a soap bubble, of closing up round any penetrating object, then as the stick goes vertically down-ward the interruption in the film will move on. If we pass a spiral through the film the intersection will give a point moving in a circle (shown by the dotted lines in Fig. 2).
For the plane being such a point, moving in a circle in its plane, would probably constitute a cosmical phenomenon, something like the motion of a planet in its orbit.
Suppose now the spiral to be still and the film to move vertically upward, the whole spiral will be represented in the film in the consecutive positions of the point of intersection.
If instead of one spiral we take a complicated construction consisting of spirals, inclined and straight lines, broken and curved lines, and if the film move vertically upward we shall have an entire universe of moving points the movements of which will appear to the plane being as original.
The plane being will explain these movements as depending one upon another, and indeed he will never happen to think that these movements are fictitious and are dependent upon the spirals and other lines lying outside his space. 1
Returning to the plane being and his perception of the world, and analyzing his relations to the three-dimensional world, we see that for the two-dimensional or plane being it will be very difficult to understand all the complexity of the phenomena of our world, as it appears to us. He (the plane being) is accustomed to perceive the world as being too simple.
Taking into consideration the sections of figures instead of the figures themselves, the plane being will compare them in relation to their length and their greater or lesser curvature, i.e., their for him more or less rapid motion.
The differences between the objects of our world, as they exist for us he would not understand. The functions of the objects of our world would be completely mysterious to his mindâ€”incomprehensible, "supernatural."
Let us imagine that a coin, and a candle the diameter of which is equal to that of the coin, are on the plane upon which the two-dimensional being lives. To the plane being they will seem two equal circles, i.e., two moving, and absolutely identical lines; he will never discover any difference between them. The functions of the coin and of the candle in our worldâ€”these are for him absolutely a terra incognita. If we try to imagine what an enormous evolution the plane being must pass through in order to understand the function of the coin and of the candle and the difference between these functions, we shall understand the nature of the division between the plane world and the world of three dimensions, and the complete impossibility of even imagining, on the plane, anything at all like the three-dimensional world, with its manifoldness of function.
The properties of the phenomena of the plane world will be extremely monotonous; they will differ by the order of their appearance, their duration, and their periodicity. Solids, and the things of this world will be flat and uniform, like shadows, i.e., like the shadows of quite different solids, which seem to us uniform. Even if the plane being could come in contact with our consciousness, he would never be in a position to understand all the manifoldness and richness the phenomena of our world and the variety of function of the things of that world.
Plane beings would not be in a position to master our most ordinary concepts.
It would be extremely difficult for them to understand that phenomena, identical for them, are in reality different; and on the other hand, that phenomena quite separate for them are in reality parts of one great phenomenon, and even of one object or one being.
This last will be one of the most difficult things for the plane being to understand. If we imagine our plane being to be inhabiting a horizontal plane, intersecting the top of a tree, and parallel to the surface of the earth, then for such a being each of the various sections of the branches will appear as a quite separate phenomenon or object. The idea of the tree and its branches will never occur to him.
Generally speaking, the understanding of the most fundamental and simple things of our world will be infinitely long and difficult
to the plane being. He would have to entirely reconstruct his concepts of space and time. This would be the first step. Unless it is taken, nothing is accomplished. Until the plane being shall imagine all our universe as existing in time, i.e., until he refers to time everything lying on both sides of his plane, he will never understand anything. In order to begin to understand "the third dimension" the inhabitant of the plane must conceive of his time concepts spatially, that is, translate his time into space.
To achieve even the spark of a true understanding of our world he will have to reconstruct completely all his ideasâ€”to revaluate all values, to revise all concepts, to dissever the uniting concepts, to unite those which are dissevered; and, what is most important, to create an infinite number of new ones.
If we put down the five fingers of one hand on the plane of the two-dimensional being they will be for him five separate phenomena.
Let us try to imagine what an enormous mental evolution he would have to undergo in order to understand that these five separate phenomena on his plane are the finger-tips of the hand of a large, active and intelligent beingâ€”man.
To make out, step by step, how the plane being would attain to an understanding of our world, lying in the region of the to him mysterious third dimensionâ€”i.e., partly in the past, partly in the futureâ€”would be interesting in the highest degree. First of all, in order to understand the world of three dimensions, he must cease to be two-dimensionalâ€”he must become three-dimensional himself, or in other words he must feel an interest in the life of three-dimensional space. After having felt the interest of this life, he will by so doing transcend his plane, and will never be in a position thereafter to return to it. Entering more and more within the circle of ideas and concepts which were entirely incomprehensible to him before, he will have already become, not two-dimensional, but three-dimensional. But all along the plane being will have been essentially three-dimensional, that is, he will have had the third dimension, without his being conscious of it himself. To become three-dimensional he must be three-dimensional. Then as the end of ends he can address himself to the self-liberation from the illusion of the two-dimensionality of himself and the world, and to the apprehension of the three-dimensional world.
70:1 C. H. Hinton, "The Fourth Dimension," pp. 23, 24 and 25.
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?
NOW that we have studied those "relations which our space itself bears within it" we shall return to the questions: But what in reality do the dimensions of space representsâ€”and why are there three of them?
The fact that it is impossible to define three-dimensionality mathematically must appear most strange.
We are little conscious of this, and it seems to us a paradox, because we speak of the dimensions of space, but it remains a fact that mathematics does not sense the dimensions of space.
The question arises, how can such a fine instrument of analysis as mathematics not feel dimensions, if they represent some real properties of space?
Speaking of mathematics, it is necessary to recognize first of all, as a fundamental premise, that correspondent to each mathematical expression is always the relation of some realities.
If there is no such a thing, if it be not trueâ€”then there is no mathematics. This is its principal substance, its principal contents. To express the correlations of magnitudes is the problem of mathematics. But these correlations must be between something. Instead of algebraical a, b and c it must be possible to substitute some reality. This is the ABC of all mathematics; a, b and c are credit bills; they can be good ones only if behind them there is a real something, and they can be counterfeited if behind them there is no reality whatever.
"Dimensions" play here a very strange rÃ´le. If we designate them by the algebraic symbols a, b and c, they have the character of counterfeit credit bills. For this a, b and c it is impossible to substitute any real magnitudes which are capable of expressing the correlations of dimensions.
Usually dimensions are represented by powers: the first, the second, the third; that is, if a line is called a, then a square, the sides of which are equal to this line, is called a2, and a cube, the face of which is equal to this square, is called a3.
This among other things gave Hinton the foundation on which he constructed his theory of tesseracts, four-dimensional solidsâ€”a4. But this is pure fantasy. First of all, because the representation of "dimensions" by powers is entirely conditional. It is possible to represent all powers on a line. For example, take the segment of a line equal to five millimetres; then a segment equal to twenty-five millimetres will be the square of it, i.e., a2 and a segment of one hundred and twenty-five millimetres will be the cubeâ€”a3.
How shall we understand that mathematics does not feel dimensionsâ€”that it is impossible to express mathematically the difference between dimensions?
It is possible to understand and explain it by one thing onlyâ€”namely, that this difference does not exist.
We really know that all three dimensions are in substance identical, that it is possible to regard each of the three dimensions either as following the sequence, the first, the second, the third, or the other way about. This alone proves that dimensions are not mathematical magnitudes. All the real properties of a thing can be expressed mathematically as quantities, i.e., numbers, showing the relation of these properties to other properties.
But in the matter of dimensions it is as if mathematics sees more than we do, or farther than we do, through some boundaries which arrest us but not itâ€”and sees that no realities whatever correspond to our concepts of dimensions.
If the three dimensions really corresponded to three powers, then we should have the right to say that only these three powers refer to geometry, and that all the other higher powers, beginning with the fourth, lie beyond geometry.
But even this is denied us. The representation of dimensions by powers is perfectly arbitrary.
More accurately, geometry, from the standpoint of mathematics, is an artificial system for the solving of problems based on conditional data, deduced, probably, from the properties of our psyche.
The system of investigation of "higher space" Hinton calls metageometry, and with metageometry he connects the names of Lobachevsky, Gauss, and other investigators of non-Euclidian geometry.
We shall now consider in what relation the questions touched upon by us stand to the theories of these scientists. Hinton deduces his ideas from Kant and Lobachevsky.
Others, on the contrary, place Kant's ideas in opposition to those of Lobachevsky. Thus Roberto Bonola, in Non-Euclidian Geometry, declares that Lobachevsky's conception of space is contrary to that of Kant. He says:
The Kantian doctrine considered space as a subjective intuition, a necessary presupposition of every experience. Lobachevsky's doctrine was rather allied to sensualism and the current empiricism, and compelled geometry to take its place again among the experienced sciences. 1
Which of these views is true, and in what relation do Lobachevsky's ideas stand to our problem? The correct answer to this question is: in no relation. Non-Euclidian geometry is not metageometry, and non-Euclidian geometry stands in the same relation to metageometry as Euclidian geometry itself.
The results of non-Euclidian geometry, which have submitted the fundamental axioms of Euclid to a revaluation, and which have found the most complete expression in the works of Bolyai, Gauss, and Lobachevsky, are embraced in the formula:
The axioms of a given geometry express the properties of a given space.
Thus geometry on the plane accepts all three Euclidian axioms, i.e.:
1. A straight line is the shortest distance between two points.
2. Any figure may be transferred into another position without changing its properties.
3. Parallel lines do not meet.
(This last axiom is formulated differently by Euclid.)
In geometry on a sphere, or on a concave surface the first two axioms alone are true, because the meridians which are separated at the equator meet at the poles.
In geometry on the surface of irregular curvatures only the first axiom is trueâ€”the second, regarding the transference of figures, is impossible because the figure taken in one part of an irregular surface can change when transferred into another place. Also, the sum of the angles of a triangle can be either more or less than two right angles.
Therefore, axioms express the difference of properties of various kinds of surfaces.
A geometrical axiom is a law of given surface.
But what is a surface?
Lobachevsky's merit consists in that he found it necessary to revise the fundamental concepts of geometry. But he never went so far as to revalue these concepts from Kant's standpoint. At the same time he is in no sense contradictory to Kant. A surface in the mind of Lobachevsky, as a geometrician, was only a means for the generalization of certain properties on which this or that geometrical system was constructed, or the generalization of the properties of certain given lines. About the reality or the unreality of a surface, he probably never thought.
Thus on the one hand, Bonola, who ascribed to Lobachevsky views opposite to Kant, and their nearness to "sensualism" and "current empiricism," is quite wrong, while on the other hand, it is not impossible to conceive that Hinton entirely subjectively ascribes to Gauss and Lobachevsky their inauguration of a new era in philosophy.
Non-Euclidian geometry, including that of Lobachevsky, has no relation to metageometry whatever.
Lobachevsky does not go outside of the three-dimensional sphere.
Metageometry regards the three-dimensional sphere as a section of higher space. Among mathematicians, Riemann, who understood the relation of time to space, was nearest of all to this idea.
The point, of three-dimensional space, is a section of a meta-geometrical line. It is impossible to generalize on any surface whatever the lines considered in metageometry. Perhaps this last is the most important for the definition of the difference between geometries (Euclidian and non-Euclidian and metageometry). It is impossible to regard metageometrical lines as distances between points in our space, and it is impossible to represent them as forming any figures in our space.
The consideration of the possible properties of lines lying out of our space, the relation of these lines and their angles to the lines, angles, surfaces and solids of our geometry, forms the subject of metageometry.
The investigators of non-Euclidian geometry could not bring themselves to reject the consideration of surfaces. There is something almost tragic in this. See what surfaces Beltrami invented in his investigations of non-Euclidian geometryâ€”one of his surfaces resembles the surface of a ventilator, another, the inner surface of a funnel. But he could not decide to reject the surface, to cast it aside once and for all, to imagine that the line can be independent of the surface, i.e., a series of lines which are parallel or nearly parallel cannot be generalized on any surface, or even in three-dimensional space.
And because of this, both he and many other geometers, developing non-Euclidian geometry, could not transcend the three-dimensional world.
Mechanics recognizes the line in time, i.e., such a line as it is impossible by any means to imagine upon the surface, or as the distance between two points of space. This line is taken into consideration in the calculations pertaining to machines. But geometry never touched this line, and dealt always with its sections only.
Now it is possible to return to the question: what is space? and to discover if the answer to this question has been found.
The answer would be the exact definition and explanation of the three-dimensionality of space as a property of the world.
But this is not the answer. The three-dimensionality of space as an objective phenomenon remains just as enigmatical and inconceivable as before. In relation to three-dimensionality it is necessary:
Either to accept it as a thing given, and to add this to the two data which we established in the beginning.
Or to recognize the fallacy of all objective methods of reasoning, and return to another method, outlined in the beginning of the book.
Then, on the basis of the two fundamental data, the world and consciousness, it is necessary to establish whether three-dimensional space is a property of the world, or a property of our knowledge of the world.
Beginning with Kant, who affirms that space is a property of the receptivity of the world by our consciousness, I intentionally deviated far from this idea and regarded space as a property of the world.
Along with Hinton, I postulated that our space itself bears within it the relations which permit us to establish its relations to higher space, and on the foundation of this postulate I built a whole series of analogies which somewhat clarified for us the problems of space and time and their mutual co-relations, but which, as was said, did not explain anything concerning the principal question of the causes of the three-dimensionality of space.
The method of analogies is, generally speaking, a rather tormenting thing. With it, you walk in a vicious circle. It helps you to elucidate certain things, and the relations of certain things, but in substance it never gives a direct answer to anything. After many and long attempts to analyze complex problems by the aid of the method of analogies, you feel the uselessness of all your efforts; you feel that you are walking alongside of a wall. Thereupon you begin to experience simply a hatred and aversion for analogies, and you find it necessary to search in the direct way which leads where you need to go.
The problem of higher dimensions has usually been analyzed by the method of analogies, and only very lately has science begun to elaborate that direct method which will be shown later on.
If we desire to go straight, without deviating, we shall keep
strictly up to the fundamental propositions of Kant. But if we formulate Hinton's above-mentioned thought from the point of view of these propositions, it will be as follows: We bear within ourselves the conditions of our space, and therefore within ourselves we shall find the conditions which will permit us to establish correlations between our space and higher space.
In other words, we shall find the conditions of the three-dimensionality of the world in our psyche, in our receptive apparatusâ€”and shall find exactly there the conditions of the possibility of the higher dimensional world.
Propounding the problem in this way, we put ourselves upon the direct path, and we shall receive an answer to our question, what is space and its three-dimensionality?
How may we approach the solution of this problem?
Plainly, by studying our consciousness and its properties.
We shall free ourselves from all analogies, and shall enter upon the correct and direct path toward the solution of the fundamental question about the objectivity or subjectivity of space, if we shall decide to study the psychical forms by which we perceive the world, and to discover if there does not exist a correspondence between them and the three-dimensionality of the worldâ€”that is, if the three-dimensional extension of space, with its properties, does not result from properties of the psyche which are known to us.
75:1 Roberto Bonola, "Non-Euclidian Geometry." The Open Court Publishing Co., Chicago, 1912, pp. 92, 93.
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.
IN order exactly to define the relation of our psyche to the external world, and to determine what, in our receptivity of the world, belongs to it, and what belongs to ourselves, let us turn to elementary psychology and examine the mechanism of our receptive apparatus.
The fundamental unit of our receptivity is a sensation. This sensation is an elementary change in the state of our psyche, produced, as it seems to us, either by some change in the state of the external world in relation to our consciousness, or by a change in the state of our psyche in relation to the external world. Such is the teaching of physics and psycho-physics. Into the consideration of the correctness or incorrectness of the construction of these sciences I shall not enter. Suffice it to define a sensation as an elementary change in the state of the psycheâ€”as the element, that is, as the fundamental unit of this change. Feeling the sensation we assume that it appears, so to speak, as the reflection of some change in the external world.
The sensations felt by us leave a certain trace in our memory. The accumulating memories of sensations begin to blend in consciousness into groups, and according to their similitude tend to associate, to sum up, to be opposed; the sensations which are usually felt in close connection with one another will arise in memory in the
same connection. Gradually, out of the memories of sensations,
perceptions are compounded. Perceptionsâ€”these are so to speak the group memories of sensations. During the compounding of perceptions, sensations are polarizing in two clearly defined directions. The first direction of this grouping will be according to the character of sensations. (The sensations of a yellow color will combine with the sensations of a yellow color; sensations of a sour taste with those of a sour taste.) The second direction will be according to the time of the reception of sensations. When various sensations, constituting a single group, and compounding one perception, enter simultaneously, then the memory of this definite group of sensations is ascribed to a common cause. This "common cause" is projected into the outside world as the object, and it is assumed that the given perception itself reflects the real properties of this object. Such group remembrance constitutes perception, the perception, for example, of a treeâ€”that tree. Into this group enter the green color of the leaves, their smell, their shadows, their rustle in the wind, etc. All these things taken together form as it were a focus of rays coming out of the psyche, gradually concentrated upon the outside object and coinciding with it either well or ill.
In the further complication of the psychic life, the memories of perception proceed as with the memories of sensations. Mingling together, the memories of perceptions, or the "images of perceptions," combine in various ways: they sum up, they stand opposed, they form groups, and in the end give rise to concepts.
Thus out of various sensations, experienced (in groups) at different times, a child gets the perception of a tree (that tree), and afterwards, out of the images of perceptions of different trees there emerges the concept of a tree, i.e., not "that tree," but trees in general.
The formation of perceptions leads to the formation of words, and the appearance of speech.
The beginning of speech may appear on the lowest level of psychic life, during the period of living by sensations, and it will become more complex during the period of living by perceptions;
but unless there be concepts it will not be speech in the true meaning of the word.
On the lower levels of psychic life certain sensations can be expressed by certain sounds. Therefore it is possible to express common impressions of horror, anger, pleasure. These sounds may serve as signals of danger, as commands, demands, threats, etc., but it is impossible to say much by means of them.
In the further development of speech, if words or sounds express perceptions, as in the case of children, this means that the given sound or the given word designates only that object to which it refers. For each new similar object must exist another new sound, or a new word. If the speaker designates different objects by one and the same sound or word, it means that in his opinion the objects are the same, or that knowingly he is calling different objects by the same name. In either case it will be difficult to understand him, and such speech cannot serve as an example of clear speech. For instance, if a child call a tree by a certain sound or word, having in view that tree only, and not knowing other trees at all, then any new tree which he may see he will call by a new word, or else he will take it for the same tree. The speech in which "words" correspond to perceptions is as it were made up of proper nouns. There are no appellative nouns; and not only substantives, but verbs, adjectives and adverbs have the character of "proper nouns"â€”that is, they apply to a given action, to a given quality, or to a given property.
The appearance of words of a common meaning in human speech signifies the appearance of concepts in consciousness.
Speech consists of words, each word expressing a concept. Concept and word are in substance one and the same thing; only the first (the concept) represents, so to speak, the inner side, and the second (the word) the outer side. Or, as says Dr. R. M. Bucke (the author of the book Cosmic Consciousness, about which I shall have much to say later on), "A word (i.e., concept) is the algebraical sign of a thing."
It has been noticed thousands of times that the brain of a thinking man does not exceed in size the brain of a non-thinking wild man in anything like the proportion in which the mind of the thinker exceeds the mind of the savage. The reason is that the brain of a Herbert Spencer has very little more work to do than has the brain of a native Australian, for
this reason, that Spencer does all his characteristic mental work by signs or counters which stand for concepts, while the savage does all or nearly all his by means of cumbersome recepts. The savage is in a position comparable to that of the astronomer who makes his calculations by arithmetic, while Spencer is in the position of one who makes them by algebra. The first will fill many great sheets of paper with figures and go through immense labor; the other will make the same calculations on an envelope and with comparatively little mental work. 1
In our speech words express concepts or ideas. By ideas are meant broader concepts, not representing the group sign of similar perceptions, but embracing various groups of perceptions, or even groups of concepts. Therefore an idea is a complex or an abstract concept.
In addition to the simple sensations of these sense organs (color, sound, touch, smell and taste), in addition to the simple emotions of pleasure, pain, joy, anger, surprise, wonder, curiosity and many others, there is passing through our consciousness a series of complex sensations and higher (complex) emotions (moral, esthetic, religious). The content of emotional feelings, even the simplestâ€”to say nothing of the complexâ€”can never be wholly confined to concepts or ideas, and therefore can never be correctly or exactly expressed in words. Words can only allude to it, point to it. The interpretation of emotional feelings and emotional understanding is the problem of art. In combinations of words, in their meaning, their rhythm, their musicâ€”the combination of meaning, rhythm and music; in sounds, colors, lines, formsâ€”men are creating a new world, and are attempting therein to express and transmit that which they feel, but which they are unable to express and transmit simply in words, i.e., in concepts. The emotional tones of life, i.e., of "feelings," are best transmitted by music, but it cannot express concepts, i.e., thought. Poetry endeavors to express both music and thought together. The combination of feeling and thought of high tension leads to a higher form of psychic life. Thus in art we have already the first experiments in a language of the future. Art anticipates a psychic evolution and divines its future forms.
At the present time an average man, taken as a norm, has attained to three units of psychic life: sensation, perception, and conception. Furthermore, observation reveals the fact that some people at certain
times acquire a new, fourth unit of psychic life, which different authors and different schools name differently, but in which an element of knowledge or ideas is always united with an emotional element.
If Kant's ideas are correct, if space with its characteristics is a property of our consciousness, and not of the external world, then the three-dimensionality of the world must in this or some other manner depend upon the constitution of our psychic apparatus.
It is possible to put the question concretely in the following manner: What bearing upon the three-dimensional extension of the world has the fact that in our psychical apparatus we discover the categories above describedâ€”sensations, perceptions and concepts?
We possess such a psychical apparatus and the world is three-dimensional. How is it possible to establish the fact that the three-dimensionality of the world depends upon such a constitution of our psychical apparatus?
This could be proven or disproven undeniably only with the aid of experiments.
If we could change our psychic apparatus and should then discover that the world around us was changing, this would constitute for us the proof of the dependence of the properties of space upon the properties of our consciousness.
For example if we could make the above-mentioned higher form of psychic life (which appears now accidentally as it were and depends upon insufficiently studied conditions) just as definite, exact, and subject to our will as is the concept; and if the number of characteristics of space increased, i.e., if space became four-dimensional instead of being three-dimensional, this would affirm our presupposition, and would prove Kant's contention that space with its properties is a form of our sensuous receptivity.
Or if we could diminish the number of units of our psychic life, and deprive ourselves or someone else of conceptions, leaving the psyche to act by perceptions and sensations only; and if by so doing the number of characteristics of the space surrounding us diminished; i.e., if for the person subjected to the test the world became two-dimensional instead of three-dimensional, and indeed
one-dimensional as a result of a still greater limitation of the psychic apparatus, by depriving the person of perceptionsâ€”this would affirm our presupposition, and Kant's idea could be considered proven.
That is to say, Kant's idea would be proven experimentally if we could be convinced that for the being possessing sensations only, the world is one-dimensional; for the being possessing sensations and perceptions the world is two-dimensional; and for the being possessing, in addition to concepts and ideas, the higher forms of knowledge the world is four-dimensional.
Or, more exactly, Kant's thesis in regard to the subjectivity of space-perception could be regarded as proven (a) if for the being possessing sensations only, our entire world with all its variety of forms should seem a single line; if the universe of this being should possess but one dimension, i.e., should this being be one-dimensional in the properties of its receptivity; and (b) if for the being possessing, in addition to the faculty of feeling sensations, the faculty of forming perceptions, the world should have a two-dimensional extension; if all our world with its blue sky, clouds, green trees, mountains and precipices, should seem to him one plane; if the universe of this being should have only two dimensions, i.e., if this being were two-dimensional in the properties of its receptivity.
More briefly, Kant's thesis would be proven could we be made to see that for the conscious being the number of characteristics of the world changes in accordance with the changes of its psychic apparatus.
To perform such an experiment, effecting the diminution of psychic characteristics is not possible under ordinary conditionsâ€”we cannot arbitrarily limit our own, or anyone else's psychic apparatus.
Experiments with the augmentation of psychic characteristics have been made and are recorded, but in consequence of many diverse causes they are insufficiently convincing. The chief reason for this is that the augmentation of psychic faculties yields, first of all, so much of newness in the psychic realm that this newness obscures the changes proceeding simultaneously in the
previous perception of the world; one feels the new, but is not capable of defining the difference exactly.
The entire body of teachings of religio-philosophic movements have as their avowed or hidden purpose, the expansion of consciousness. This also is the aim of mysticism of every age and of every faith, the aim of occultism, and of the Oriental yoga. But the question of the expansion of consciousness demands special study; the final chapters of this book will be dedicated to it.
For the present, in proof of the above stated propositions with regard to the change of the world in relation to psychic changes, it is sufficient to consider the assumption concerning the possibility of a smaller number of psychic characteristics.
If experiments in this direction are impossible, perhaps observation may furnish what we seek.
Let us put the question: Are there not beings in the world standing toward us in the necessary relation, whose psyche is of a lower grade than ours?
Such psychically inferior beings undoubtedly exist. These are animals.
Of the difference between the psychical nature of an animal and of a man we know very little: the usual "conversational" psychology deals with it not at all. Usually we deny altogether that animals have minds, or else we ascribe to them our own psychology, but "limited"â€”though how and in what we do not know. Again, we say that animals do not possess reason, but are governed by instinct. As to what exactly we mean by instinct we do not ourselves know. I am speaking not alone of popular, but so-called "scientific" psychology.
Let us try to discover what instinct is, and learn something about animal psychology. First of all let us analyze the actions of animals, and see wherein they differ from ours. If these actions are instinctive, what inference is to be drawn from the fact?
What are those actions in general, and how do they differ?
In the actions of living beings within the limits of our usual observation we discriminate between those which are reflex, instinctive, rational and automatic.
Reflex actions are simply responses by motion, reactions upon external irritations, taking place always in the same way, regardless
of their utility or futility, expediency or inexpediency in any given case. Their origin and laws are due to the simple irritability of a cell.
What is the irritability of a cell, and what are these laws?
The irritability of a cell is defined as its faculty to respond to external irritation by a motion. Experiments with the simplest mono-cellular organisms, have shown that this irritability acts according to definite laws. The cell responds by a motion to outside irritation. The force of the responsive motion increases as the force of the irritation is intensified, but in no definite proportionality. In order to provoke the responsive movement the irritation must be of a sufficient intensity. Each experienced irritation leaves a certain trace in the cell, making it more receptive to the new irritations. In this we see that the cell responds to the repetitive irritation of an equal force by a more forceful motion than the first one. And if the irritations be repeated further the cell will respond to them by more and more forceful motions, up to a certain limit. Having reached this limit the cell experiences fatigue, and responds to the same irritation by more and more feeble reactions. It is as if the cell becomes accustomed to the irritation. It becomes for the cell part of a constant environment, and it ceases to react, because it is reacting generally only to changes in conditions which are constant. If from the very beginning the irritation is so weak that it fails to provoke the responsive motion, it nevertheless leaves in the cell a certain invisible trace. This can be inferred from the fact that by repeating these weak irritations, the cell finally begins to react to them.
Thus in the laws of irritability we observe, as it were, the beginnings of memory, fatigue, and habit. The cell produces the illusion, if not of a conscious and reasoning being, at any rate of a remembering being, habit-forming, and susceptible to fatigue. If we can be thus deceived by a cell, how much more liable are we to be deceived by the greater complexity of animal life.
But let us return to the analysis of actions. By the reflex actions of an organism are meant actions in which either an entire organism or its separate parts acts as a cell, i.e., within the limits of the law of variability. We observe such actions both in men and in animals. A man shudders all over from unexpected cold, or
from a touch. His eyelids wink at the swift approach or touch of some object. The freely-hanging foot of a person in a sitting position moves forward if the leg be struck on the tendon below the knee. These movements proceed independently of consciousness, they may even proceed counter to consciousness. Usually consciousness registers them as accomplished facts. Moreover these movements are not at all governed by expediency. The foot moves forward in answer to the blow on the tendon even though a knife or a fire be in front of it.
By instinctive actions are meant actions governed by expediency, but made without conscious selection or without conscious aim.
They appear with the appearance of a sensuous tincture to sensations, i.e., from that moment when the sensation begins to be associated with a sense of pleasure or pain.
As a matter of fact, before the dawn of human intellect, throughout the entire animal kingdom "actions" were governed by the tendency to receive or to retain pleasure, or to escape pain.
We may declare with entire assurance that instinct is a pleasure-pain which, like the positive and negative poles of an electro-magnet, repels and attracts the animal in this or that direction, compelling it to perform whole series of complex actions, sometimes expedient to such a degree that they appear to be sensible, and not only sensible, but founded upon foresight of the future, almost upon some clairvoyance, like the migration of birds, the building of nests for the young which have not as yet appeared, the finding of the way south in the autumn, and north in the spring, etc.
But all these actions are explained in reality by a single instinct, i.e., by the subservience to pleasure-pain.
During periods in which millenniums may be regarded as days, by selection among all animals the types have been perfected, living along the lines of this subservience. This subservience is expedient, that is, the results of it lead to the desired goal. Why this is so is clear. Had the sense of pleasure arisen from that which is detrimental, the given species could not live, and would quickly die out. Instinct is the guide of its life, but only as long as instinct is expedient solely; just as soon as it ceases to be expedient it becomes the guide of death, and the species soon dies out. Normally "pleasure-pain" is pleasant or unpleasant not for the usefulness
or the harm which may result, but because of it. Those influences which proved to be beneficial for a given species during the vegetative life, with the transition to the more active and complex animal life begin to be sensed as pleasant, the detrimental influences as unpleasant. As regards two different species, one and the same influenceâ€”say a certain temperatureâ€”may be useful and pleasant for one, and for another detrimental and unpleasant. It is clear, therefore, that the subservience to "pleasure-pain" must be governed by expediency. The pleasant is pleasant because it is beneficial, the unpleasant is unpleasant because it is harmful.
Next after instinctive actions follow those actions which are rational and automatic.
By rational action is meant such an action as is known to the acting subject before its execution; such an action as the acting subject can name, define, explain, can show its cause and purpose before its execution.
Automatic actions are actions which have been rational for a given subject, but because of frequent repetitions they have become habitual and are performed unconsciously. The acquired automatic actions of trained animals were previously rational not in the animal, but in the trainer. Such actions often appear as rational but this is a complete illusion. The animal remembers the sequence of actions, and therefore its actions appear to be considered and expedient. They really were considered, but not by it. Automatic actions are often confounded with instinctive onesâ€”in reality they resemble instinctive ones, but there is an enormous difference between them. Automatic actions are developed by the subject during its own life, and for a long time before they become automatic it must be conscious of them. Instinctive actions, on the other hand, are developed during the life-periods of the species, and the aptitude for them is transmitted in a definite manner by heredity. It is possible to call automatic actions instinctive actions worked out for itself by a given subject. It is impossible, however, to call instinctive actions automatic actions worked out by a given species, because they never were rational in different individuals of a given species, but were compounded out of a series of complex reflexes.
REFLEXES, INSTINCTIVE AND "RATIONAL" ACTIONS, ALL MAY BE REGARDED AS REFLECTED, i.e., AS NOT SELF-ORIGINATED. BOTH THESE AND OTHERS, AND STILL A THIRD CLASS, COME NOT FROM MAN
[paragraph continues] HIMSELF, BUT FROM THE OUTSIDE WORLD. MAN IS THE TRANSMITTING OR TRANSFORMING STATION FOR CERTAIN FORCES: ALL OF HIS ACTIONS IN THESE THREE CATEGORIES ARE CREATED AND DETERMINED BY HIS IMPRESSIONS OF THE OUTSIDE WORLD. MAN IN THESE THREE SPECIES OF ACTIONS IS, IN SUBSTANCE, AN AUTOMATON, UNCONSCIOUS OR CONSCIOUS OF HIS ACTIONS. NOTHING COMES FROM HIM HIMSELF.
With the exception of sensations of the outer world, only the higher category of actions, i.e., conscious actions 1 appears to depend on something else. But the aptitude for such actions is seldom met withâ€”only in some few persons whom it is possible to describe as MEN OF A HIGHER TYPE.
Having established the differences between various kinds of actions, let us return to the question propounded before: In what manner does the psyche of an animal differ from that of a human being? Out of the four categories of actions the two lower ones are accessible to animals. The category of "conscious" actions is inaccessible to animals. This is proven first of all by the fact that animals have not the power of speech as we have it.
As has been shown before, the possession of speech is indissolubly bound up with the possession of concepts. Therefore we may say that animals do not possess concepts.
Is this true, and is it possible to possess the instinctive mind without possessing concepts?
All that we know about the instinctive mind teaches us that it acts possessing sensations and perceptions only, and that in the lower grades it possesses sensation only. The being which does its thinking by means of perceptions possesses the instinctive mind which gives it the possibility of exercising that choice between the perceptions presented to it which produces the impression of judging and reasoning. In reality the animal does not reason its actions, but lives by its emotions, subject to that emotion which happens to be strongest. Although indeed, in the life of the animal, acute moments sometimes occur when it is confronted with the necessity of choosing among a certain series of perceptions. At such moments its actions may seem to be quite reasoned out. For example, the animal, being put in a situation of danger acts often very cautiously and wisely,
but in reality its actions are directed not by thoughts but principally by emotional memory and motor perceptions. It has been previously shown that emotions are expedient, and that the subjection to them in a normal being must be expedient. Any perception of an animal, any recollected image, is bound up with some emotional sensation or emotional remembranceâ€”there are no non-emotional, cold thoughts in the animal soul, or even if there are, these are in-active, and incapable of becoming the springs of action.
Thus all actions of animals, sometimes highly complex, expedient, and apparently reasoned, we can explain without attributing to them concepts, judgments, and the power of reasoning. Indeed, we must recognize that animals have no concepts, and the proof of this is that they have no speech.
If we take two men of different nationalities, different races, each ignorant of the language of the other, and put them together, they will find a way to communicate at once.
One perhaps draws a circle with his finger, the other draws another circle beside it. By these means they have already established that they can understand one another. If a thick wall were put between them it would not hamper them in the leastâ€”one of them knocks three times, and the other knocks three times in response.
The communication is established. The idea of communicating with the inhabitants of other planets is founded upon the idea of light signals. It is proposed to make on the earth an enormous lighted circle or a square to attract the attention of the inhabitants of Mars and to be answered by them by means of the same signal. We live side by side with animals and yet cannot establish such communication. Evidently the distance between us and them is greater, and the difference deeper, than between men divided by the ignorance of language, stone walls, and enormous distances.
Another proof of the absence of concepts in the animal is its inability to use a lever, i.e., its incapacity to come independently to an understanding of the principle of the action of the lever. The usual objection that an animal cannot operate a lever because its organs (paws et cetera)are not adapted to such actions does not hold for the reason that almost any animal can be taught to operate a lever. This shows that the difficulty is not in the organs.
[paragraph continues] The animal simply cannot of itself come to a comprehension of the idea of a lever.
The invention of the lever immediately divided primitive man from the animal, and it was inextricably bound up with the appearance of concepts. The psychic side of the understanding of the action of a lever consists in the construction of a correct syllogism. Without constructing the syllogism correctly it is impossible to understand the action of a lever. Having no concepts it is impossible to construct the syllogism. The syllogism in the psychic sphere is literally the same thing as the lever in the physical sphere.
His mastery of the lever differentiates man as strongly from the animal as does speech. If some learned Martians were looking at the earth, and should study it objectively from afar by means of a telescope, not hearing speech, nor entering into the subjective world of the inhabitants of the earth, nor coming in contact with them, they would divide the beings living on the earth into two groups: those acquainted with the action of the lever, and those unacquainted with such action.
The psychology of animals is in general very misty to us. The infinite number of observations made concerning all animals, from elephants to spiders, and the infinite number of anecdotes about the mind, spirit, and moral qualities of animals change nothing of all that. We represent animals to ourselves either as living automatons or as stupid men.
We too much confine ourselves within the circle of our own psychology. We fail to imagine any other, and think involuntarily that the only possible sort of soul is such as we ourselves possess. But it is this illusion which prevents us from understanding life. If we could participate in the psychic life of an animal, understand how it perceives, thinks and acts, we would find much of unusual interest. For example, could we represent to ourselves, and re-create mentally, the logic of an animal, it would greatly help us to understand our own logic and the laws of our own thinking. Before all else we would come to understand the conditionality and relativity of our own logical construction and with it the conditionality of our entire conception of the world.
An animal would have a peculiar logic. It indeed would not be logic in the true meaning of the word, because logic presupposes the existence of logos, i.e., of a word or concept.
Our usual logic, by which we live, without which "the shoemaker will not sew the boot," is deduced from the simple scheme formulated by Aristotle in those writings which were edited by his pupils under the common name of Organon, i.e., the "Instrument" (of thought). This scheme consists in the following:
A is A.
A is not Not-A.
Everything is either A or Not-A.
The logic embraced in this schemeâ€”the logic of Aristotleâ€”is quite sufficient for observation. But for experiment it is insufficient, because the experiment proceeds in time, and in the formulÃ¦ of Aristotle time is not taken into consideration. This was observed at the very dawn of the establishment of our experimental scienceâ€”observed by Roger Bacon, and formulated several centuries later by his famous namesake, Francis Bacon, Lord Verulam, in the treatise Novum Organumâ€”the "New Instrument" (of thought). Briefly, the formulation of Bacon may be reduced to the following:
That which was A, will be A.
That which was Not-A, will be Not-A.
Everything was and will be, either A or Not-A.
Upon these formula, acknowledged or unacknowledged, all our scientific experience is built, and upon them, too, is shoe-making founded, because if a shoemaker could not be sure that the leather bought yesterday would be leather tomorrow, in all probability he would not venture to make a pair of shoes, but would find some other more profitable employment.
The formulÃ¦ of logic, such as those both of Aristotle and of Bacon, are themselves deduced from the observation of facts, and do not and cannot include anything except the contents of these facts. They are not the laws of reasoning, but the laws of the outer world as it is perceived by us, or the laws of our relation to the outer world.
Could we represent to ourselves the "logic" of an animal we should understand its relation to the outer world. Our cardinal error concerning the psychology of animals consists in the fact that
we ascribe to them our own logic. We assume that logic is one, that our logic is something absolute, existing outside and independent of us, while as a matter of fact, logic but formulates the laws of the relations of our psyche to the outside world, or the laws which our psyche discovers in the outside world. Another psyche will discover other laws.
The logic of animals will differ from ours, first of all, from the fact that it will not be general. It will exist separately for each case, for each perception. Common properties, class properties, and the generic and specific signs of categories will not exist for animals. Each object will exist in and by itself, and all its properties will be the specific properties of it alone.
This house and that house are entirely different objects for an animal, because one is its house and the other is a strange house. Generally speaking, we recognize objects by the signs of their similarity; the animal must recognize them by the signs of their difference. It remembers each object by that sign which had for it the greatest emotional meaning. In such a manner, i.e., by their emotional tones, perceptions are stored in the memory of an animal. It is clear that such perceptions are much more difficult to store up in the memory, and therefore the memory of an animal