Infinite space

“ Now if I inquire after the magnitude of the world, as to space and time, it is equally impossible, as regards all my notions, to declare it infinite or to declare it finite. For neither assertion can be contained in experience, because experience either of an infinite space, or of an infinite time elapsed, or again, of the boundary of the world by a void space, or by an antecedent void time, is impossible; these are mere ideas. This quantity of the world, which is determined in either way, should therefore exist in the world itself apart from all experience. ”

“ The thought of this blank form of existence which, explored in all directions as far as imagination can reach, has, beyond that, an unexplored region compared with which the part which imagination has traversed is but infinitesimal,—the thought of a Space compared with which our immeasurable sidereal system dwindles to a point is a thought too overwhelming to be dwelt upon. Of late years the consciousness that without origin or cause infinite Space has ever existed and must ever exist, produces in me a feeling from which I shrink. ”

“ Infinite Space is inconceivable by us, but it is also quite as inconceivable, or perhaps even more so, to think of Space being limited, and yet we are forced to declare that one of these two must be true. ”

“ And why should we think our idea of infinite space requires the real existence of matter to support it, when we find that we have as clear an idea of an infinite duration to come, as we have of infinite duration past ? ”

“ The matter of the universe, for instance, is according to all appearances in finite amount; and if we knew that we had counted the last bit of it, infinite knowledge in that respect, so far from being given, would be impossible. With regard to space, it is true that in drawing a bound we are aware of more. But to treat this little fringe as the equal of infinite space is ridiculous. ”

“ Is the universe bounded—is its extent immense—are the suns and planets without number? What advantage has the space which contains suns and planets, over the space which is void of them? Whether space be an existence or not, what is the space which we occupy, preferable to other space?
If our material heaven be not infinite, it is but a point in general extent. If it is infinite, it is an infinity to which something can always be added by the imagination. ”

“ We have a precise and definite idea of infinitude; we can define the idea; we can set it apart without danger of being confounded with another, and we can reason concerning it. There is nothing we more certainly and intuitively know than that space is infinite, and yet we can not comprehend or grasp within the compass of our thought the infinite space. We can not form an image of infinite space, can not traverse it in perception, or represent it by any combination of numbers ”

“ 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. ”

“ The very thought that infinite space cannot be understood, is itself a proof that the mind unconsciously realises the precise nature of such infinity, in attributing to it at once the all-comprehensiveness from which there is no escape, in which all dimensions exist, and by virtue of which all other conceptions become possible ”

“ 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. ”

“ So that in fact we go through an infinite, [space] in an infinite [time] and not in a finite [time] , and we touch infinite things with infinite things, not with finite things.” Philoponus, a sixth-century commentator (R.P. 136A, Exc. Paris Philop. in Arist. Phys., 803, 2. Vit.) , gives the following illustration: “For if a thing were moved the space of a cubit in one hour, since in every space there are an infinite number of points, the thing moved must needs touch all the points of the space: it will then go through an infinite collection in a finite time, which is impossible.” ”

“ So, too, boundless, illimitable, limitless, measureless, and unlimited are loosely used in reference to what has no apparent or readily determinable limits in space or time; as, we speak of the boundless ocean. Infinite space is without bounds, not only in fact, but in thought; infinite time is truly eternal. ”

“ On the other hand, we do not have merely the empty intuition of infinite space; but we perceive in space different phenomena at places which we cannot perceive in another order at our pleasure, but must see as they are. ”

“ The hypothesis of matter evenly disposed through infinite space, seems to labour with such difficulties, as makes it almost a contradictory supposition, or a supposition destructive of itself.
"Matter evenly disposed through infinite space," is either created or eternal; if it was created, it infers a creator ”

“ For if space is finite, every line in space must be finite also; and if space is infinite, every point in space must have infinite space beyond it in every direction, and therefore cannot be at the greatest possible distance from another point. Or thus: Any two points in space are the extremities of the line connecting them; but an infinite line has no extremities; therefore no two points in space can be connected together by an infinite line.
In fact, it is the “concrete reality,” the “something infinite,” and not the mere abstraction of infinity, which is only conceivable as a negation. ”

“ So far as physics is concerned time’s arrow is a property of entropy alone.
Are Space and Time Infinite? I suppose that everyone has at some time plagued his imagination with the question, Is there an end to space? If space comes to an end, what is beyond the end? On the other hand the idea that there is no end, but space beyond space for ever, is inconceivable. And so the imagination is tossed to and fro in a dilemma. Prior to the relativity theory the orthodox view was that space is infinite. No one can conceive infinite space ”

“ 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. ”

“ In infinite space there may be infinite universes, but I hardly think they would be all universes of matter. That would indeed be a low conception of infinite power! Here, on earth, we see millions of distinct species of animals, millions of different species of plants, and each and [ 323] every species consisting often of many millions of individuals, no two individuals exactly alike; and when we turn to the heavens, no two planets, no two satellites alike; and outside our system we see the same law prevailing—no two stars, no two clusters, no two nebulæ alike. ”

“ Just as the outward journey seemed to take us towards the appreciation of what our finite senses call the infinitely great, so does this other path appear to intend to infinity, in the opposite direction, leading us to appreciate what is called the infinitely small. We have already considered this direction in View One, under the heading of "Relativity," and by combining these two experiences, we may see still more clearly that our very conception of Space is one of the modes only under which motion or physical phenomena are presented to our consciousness. ”

“ And who can affirm that, in an Infinite Being, the focus may not be everywhere? Or, since our geometry is built upon finite space-forms, who can say that it may not be without having any space-relation? If, indeed, this be a universe in which we dwell, and not a heap of isolated disjecta membra, is it not a necessity of thought that, the system of energy being totally inter-related, so also the psychic concomitants which the hypothesis requires must also have their unity? ”

“ We necessarily conceive Space as being infinite in its extent: however much space the heavenly bodies occupy, there is space beyond them: if they are not there, space is there nevertheless. That the stars and planets are so far from each other, is an arrangement which prevents their disturbing each other with their mutual attractions, to any destructive extent; and is an arrangement which the spacious, the infinite universe, admits of, without any difficulty. ”

“ But if the matter was evenly disposed throughout an infinite space, it could never convene into one mass, but some of it would convene into one mass, and some into another, so as to make an infinite number of great masses, scattered, at great distances, from one to another, throughout all that infinite space. ”

“ Is real space actually infinite in magnitude, or finite? In other words, besides the whole solar system—which is in reality merely one star plus its planets and their satellites,—is there in existence an actually infinite multitude of such stellar worlds? It is not likely that this can ever be determined empirically. Many philosophers maintain that the question must be answered in the negative, inasmuch as an actually infinite multitude is impossible. ”

“ 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. ”

“ Therefore, space is eternal. There is no motion without space; and in the first instant of the creation bodies could move and be moved. Though we suppose only one body in the world, it could be moved; and this motion could be infinitely continued. Therefore space is infinite. Annihilate now this body also, and the extension in which it moved will remain; in it new bodies, new worlds may be created. Therefore space is indestructible. But an eternal, infinite, and indestructible being cannot be created. Therefore, space is uncreated. ”

“ it became clear that to say, 'in infinite space and time everything develops, becomes more perfect and more complex, is differentiated', is to say nothing at all. These are all words with no meaning, for in the infinite there is neither complex nor simple, neither forward nor backward, nor better or worse. ”

“ 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 ”

“ With every act of perception by our senses, we have therefore not only intuition of the Visible or Finite, but we become at the same moment aware of an Invisible Infinite beyond. Time appears to us as an inconceivable, intangible something, which gives us the impression of movement without anything that moves it. Space is an omnipresent, intangible, inconceivable nothing, outside of which nothing which has existence can be even thought to exist. Let us now try and get an insight into what we mean by perception of distance in space. ”

“ Now, it seems plain that a mind so restricted by the senses can never form a just conception of the infinite. How utterly impossible it is for us to grasp the idea of endless space or endless time! To suppose there is an end to space is to suppose something beyond, and this must be space. ”

“ We can conceive of eternity, because we cannot conceive of a cessation of time. We can conceive of infinite space because we cannot conceive of so much matter that our imagination will not stand upon the farthest star, and see infinite space beyond. ”

“ What then can be clearer than that finitude comes to Man from both sides? He can comprehend a few feet of space, yet outside of this volume there lies the infinitude of space. He possesses a span of infinite time, which in the same way shrinks up into a moment as compared with this infinite time, just as his volume of space shrinks up into a point. ”

“ Let us try and appreciate the fact that, under our present conditions, our conceptions of the immense and minute—namely, extension in Space, and that of quick and slow or duration in Time—are purely relative, and that from this arise those pseudo-conceptions which we call the infinitely extended and the infinitely lasting. Under our present limitations it is impossible for us to grasp the whole of any Truth, if we could do that, there would be no such mystery of Infinity to puzzle us ”

“ The Archdeacon, however, after quoting Sir William Hamilton as to the inconceivability of space as absolute or infinite, takes occasion to say that "space is an entity." May I be permitted to ask how he knows that space is an entity? As a matter of fact, the conception of infinite space is a necessity of the mind, the same as eternity is a necessity of the mind. ”