Absolute space

“ Absolute space, of its own nature without reference to anything external, always remains uniform and immovable. Relative space is any movable measure or dimension of absolute space. It is a variable distance that is determined by our senses according to its position with respect to bodies. Common people use relative space instead of immovable space, as when we measure space underground, in the air, or in the heavens with respect to its position relative to the earth. ”

“ If we refuse to agree that it is absolute space itself which directs and guides the free bodies and which is thus the cause of this wonderful pre-established harmony, where else shall we look for a regulating cause? ”

“ Space is not a General Notion collected by abstraction from particular cases; for we do not speak of Spaces in general, but of universal or absolute Space. Absolute Space is infinite. All special spaces are in absolute space, and are parts of it. ”

“ Thus, experiences of forces variously correlated, are those from which our consciousness of Space is abstracted.
That which we know as Space being thus shown, alike by its genesis and definition, to be purely relative, what are we to say of that which causes it? Is there an absolute Space which relative Space in some sort represents? Is Space in itself a form or condition of absolute existence, producing in our minds a corresponding form or condition of relative existence? These are unanswerable questions. Our conception of Space is produced by some mode of the Unknowable ”

“ We discover that we can also touch the things which we see, on the single condition that we perform the necessary movements. Hence we suppose that we sense distance and size immediately. Space as such cannot be perceived any more than color as such. Which of the two spaces which we actually know— visual or touch space— shall we regard as "absolute" space? ”

“ Space is cognized à posteriori, space is cognized à priori. Space has parts and proportions, space has no parts or proportions. Space is divisible, space is indivisible—an absolute unity. Space is finite, space is infinite. Space is susceptible of exact measurement, space is immeasurable—that is, absolute immensity.
Space and extension are not identical. Extension is simply an attribute of body—the continuity of matter. Space is place, distance, direction, relations of bodies. Space is a certain correlation of finite existences. ”

“ The notion of infinite space is the notion of extension in all its generality—that is, as conceived by the abstraction of all limits.
“5th. Indefinite space is a figment of our imagination, which strives to follow the intellectual process of generalization by destroying all limits.
“6th. Where no body exists, there is no space.
“7th. Distance is the interposition of a body, and nothing more.
“8th. If the body interposed vanishes, all distance vanishes, and contiguity, or absolute contact, will be the result. ”

“ We cannot, therefore, exclude the possibility that the stars might in some way generate a field endowing space with a structure which we had mistakenly taken to represent the absolute intrinsic structure of space. ”

“ Space, time, substance, cause, are necessary notions, existing in the mind à priori, and evolved, but not constituted by experience. It is the existence of the notion of space in the mind, prior to, and independent, in a certain sense, of experience, that gives to mathematical demonstration the character of absolute necessity. ”

“ Nature, therefore, is subject with absolute precision to all the precepts of geometry as to all the properties of space there demonstrated, this being the subjective condition, not hypothetically but intuitively given, of every phenomenon in which nature can ever be revealed to the senses. ”

“ Now, we occupy a lowly position, both in space and rank in comparison with the heavenly sphere, and the Almighty is Most High not in space, but with respect to absolute existence, greatness and power. ”

“ How the idea of infinite Space may affect a mind incomparably more powerful than my own, I cannot know;—neither can I divine the nature of certain problems which the laws of space-relation present to the geometrician. ”

“ I do not define Time, Space, Place, and Motion, as being well known to all. Only I must observe, that the common people conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into Absolute and Relative, True and Apparent, Mathematical and Common. ”

“ Let us suppose a glass to be hermetically sealed, and the interior to remain empty by the annihilation of what it contained; this cavity or capacity which in our way of understanding it may be occupied by a body is a part of space. Let us imagine the world to be an immense receptacle in which all bodies are contained; let us suddenly make it empty and we have a cavity equal in space to the universe. If we imagine beyond the limits of the world a capacity to contain other bodies, we have an unlimited or imaginary space.
Space appears to us at first sight, if not infinite, at least indefinite. ”

“ But this is not the idea of space; it is only an imagination of it, a sort of rude, sensible idea, probably common to man and the beasts. The true idea, and the only one deserving the name, is that which our mind possesses when it conceives extension in itself, without any mixture of sensation, and which is, as it were, the seed of the whole science of geometry. ”

“ To my mind the ether of space is a substantial reality with extraordinarily perfect properties, with an immense amount of energy stored up in it, with a constitution which we must discover, but a substantial reality far more impressive than that of matter. Empty space, as we call it, is full of ether, but it makes no appeal to our senses. The appearance is as if it were nothing. It is the most important thing in the material universe. ”

“ Let a vast sphere be described of such mighty dimensions that it embraces not only all the objects visible to the unaided eye, not only all the objects visible in our most powerful telescopes, but even every object that the most fertile imagination can conceive, what relation must this stupendous sphere bear to the whole of space? The mighty sphere can only be an infinitely small part of space. ”

“ And when we have once obtained our spiritual balance we shall doubtless find that our space world has taken to itself another direction, inconceivable as that now seems.
Space is more than room wherein to move about; it is, first of all, the room in which we think, and upon how we do so depends the number of its dimensions. If the attention has become 'riveted to the object of its practical interest' to the extent that this is the only good the creature knows, then is its thought-form one-dimensional even though its bodily movements are three-spaced. ”

“ Let us next see whether we can learn anything as to the extent of space itself. It is apparent that we seem to be in the presence of about equal difficulties whether we attempt to think of space as finite or as infinite; for, imagine that you go up in a straight line into the sky, and on, and on, and on, in thought for millions of miles, it would seem that the journey ought to be endless ”

“ We arbitrarily divide each of these two mysteries into two parts, which parts are separated from each other, in either case, by a point which has, apparently, as its centre, our very consciousness of living. In the case of Space we call this point the Here, and on one side of it, as we saw in our last View, we have extension towards the infinitely great, and, on the other, intension towards the infinitely small. ”

“ But what, in the case supposed, is the fact or predicament that is asserted, when we speak or think of endless space, or of space that transcends all our powers of measurement? Is it correct to say that the law of thought fails, because we can not express endless space in feet or miles? Is it true that we have only "symbolized" the product of endless space out of the data or elements of measurable space? ”

“ It would do utter violence to our notions of the law of continuity to assume that all the existent matter in the universe happened to lie inside this sphere; we need only mention such a supposition to dismiss it as wholly indefensible. I do not now make any attempt to express the number of miles in the diameter of the sphere which limits the extent of space known directly to man. ”

“ How does it deal with infinite space as something singular which comprehends both picture and spectator as mere centres of gravity of a spatial dynamic? The full Faustian life-feeling, the passion of the third dimension, takes hold of the form of the picture, the painted plane, and transforms it in an unheard-of way. ”

“ So also we imagine space, the place of all motion, with its parts immovable, the field of all separation, with its parts inseparable; but we are treating of division, not of separation. If there is true extension, it is divisible; we conceive space with its parts inseparable, but still divisible; for we measure them, count them, and it is by relation to them that we form an idea of the size, distance, and motion of bodies. ”

“ For is not the sphere, or ovoid, the unit form of nature; and is not the spiral vortex its characteristic motion, from that of the nebula in the sky to the electron in the atom? Thus, on the hypothesis that our space is traversing four-dimensional space, and that the forms of our space are cross-sections of four-dimensional forms, the unity and harmony of nature would be accounted for in a remarkably simple manner. ”

“ It seems that all particles have an urge to try to be in each other's space. And this desire is modified by the distance that separates them.
"This adds up to three rules:
"1. No two particles may occupy the same space at the same time.
"2. Even though they can't, they try.
"3. They all know where they're going, and where they've been without relation to anything but the spatial co-ordinates around them. ”

“ With the introduction, in Chapter X, of the peripheral type of force-field which appertains to levity as the usual central one does to gravity, we are compelled to revise our conception of space. For in a space of a kind we are accustomed to conceive, that is, the three-dimensional, Euclidean space, the existence of such a field with its characteristic of increasing in strength in the outward direction is a paradox, contrary to mathematical logic. ”

“ The important point of this distinction is that if we can conceive of anything as entirely devoid of the element of extension in space, it must be present in its entire totality anywhere and everywhere--that is to say, at every point of space simultaneously. ”

“ But no argument can be drawn from such premises in favor of the infinity of the space that has been filled with worlds; and if the material universe has any limits, it then follows, that it must occupy a minute and infinitesimal point in infinite space. ”

“ They would see shifting surfaces as we walked about, but being sensitive to length and breadth only, and not to height, they could gain no notion whatsoever of what we really look like. It is thus with us when we attempt to picture four-dimensional space. ”

“ THE SUBJECTIVITY OF SPACE Without going deep into the doctrine of the ideality—that is, the purely subjective reality—of space, it is easy to show that we have arrived at our conception of a space of three dimensions by an intellectual process. The sphere of the senses is two-dimensional: except for the slight aid afforded by binocular vision, sight gives us moving pictures on a plane, and touch contacts surfaces only. What circumstances, we may ask, have compelled our intellect to conceive of solid space? ”

“ Perhaps we should say that space is really the continuous ether or light which penetrates throughout the universe, and seems to fill space more continuously than wood, stone, or iron, in which there is an admixture of vacuum. Must all bodies be figured, then the figure of the infinite is the sphere. The dimensions of space coincide with those of body, and the definition given of body as tri-dimensional quantity applies [Pg 190] also to space:—there cannot be any body which is not in place, nor can its dimensions exist without equal dimensions of the containing space. ”

“ Once in possession of the form of space, mind uses it like a net with meshes that can be made and unmade at will, which, thrown over matter, divides it as the needs of our action demand. Thus, the space of our geometry and the spatiality of things are mutually engendered by the reciprocal action and reaction of two terms which are essentially the same, but which move each in the direction inverse of the other. Neither is space so foreign to our nature as we imagine, nor is matter as completely extended in space as our senses and intellect represent it. ”

“ This indicates to me that the particle has an existence in space because it is created out of space, and that space must, therefore, have some very real properties of its own regardless of what is or is not in it. ”

“ Then it is contained in another place more extended, and so on; so that it is impossible for you to conceive a body which is not in a place; and you arrive at the conception of a boundless and infinite place, that contains all limited places and all possible bodies: that boundless and infinite place is space. ”

“ But we have not got to wait for this exploration in order to commence our work of higher-space thought, for we know definitely that whatever our real physical relationship to this wider universe may be, we are practically in exactly the same relationship to it as the creature we have supposed living on the surface of a smooth sheet is to the world of threefold space.
And this relationship of a surface to a solid or of a solid, as we conjecture, 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. ”