When we see colour, we observe at least a uniform surface environed by other surfaces, from which it is differentiated by its special characteristics. If we exclude these other surfaces, we stare into nothingness and all colour is gone, or, at best, there remains only a vague feeling. [Is that so?] Closed-eye vision, again, presents a changing multitude of dots, very like pricks on the skin; but even these dots are the result of a selective or complicated process. When this process does not take place, we have no volume and no dimensions left, but merely cutaneous feelings. [Is this so?] A shapeless cloud, a gust of wind, a swarm of bees, an indifferent form like that of a rock, may be regarded as having volume ; but a strange medley of dots, as in dim closed-eye vision, in no way resembles masses, volumes or lines. The undeveloped man, then, is blind, and lacks a colour sense and space sense, the former sense, like the latter, arising from development. By organised attempts the chaos is reduced to cosmos, and this is done by systematically developing visual systems, singling out in this way portions of the chaos and creating points, lines, surfaces and volumes. Space, strictly speaking, has no dimensions. We have only a complex of lines, or changes in the field of visual development or attention. By persistent changes that field becomes gradually exhausted, and with it the content of space. Hence space, as we know it, is all the space possible.
We speak, indeed, of three dimensions, i.e., height, breadth, thickness, as if space could, like a triangle made of three sticks, be divided into three parts. To imagine three lines meeting in one point at right angles to one another [construct such lines], would convey no meaning of our space to any one who had been acquainted with only those three lines. The notion of a point, of breadth, of crookedness, of form, that is to say, of space as it is given, would be hidden from him. He would know those three lines and nothing beside. Any added line, say one at an angle of 45° or any thickening of the lines, would open a new world to him. To the normal adult there exists an indefinite number of lines, points, shapes and directions. If he sums these up in a formula, that is merely for convenience.
The fact that space is regarded as tri-dimensional has suggested a mountain of absurdities to those who have not asked themselves the pertinent question as to what is the nature of space. It is as though it were said that since a perpendicular line may be drawn in two directions — up or down, therefore there could be in such a line three, or four, or more directions ; or one direction only. Men have also reasoned from a tri-dimensional world to a two-dimensional and a four-dimensional one. Let us accordingly assume a one-dimensional being who is part of a straight line. Now does it make sense to think of a line that shall have no breadth and no depth? It certainly does not. Every imaginable line exemplifies every direction at once. A perpendicular line without breadth or depth is a monstrosity, and cannot be conceived. Hence all the arguments about one-dimensional or two-dimensional beings which are to illustrate the existence of four-dimensional beings are based on bare abstractions. Though men are supposed to be three-dimensioned, yet they neither live in the third dimension alone, nor are they aware of taking advantage of any two-dimensioned or one-dimensioned being. Why, then, assume beings who live in a fourth dimension and play tricks on those who live in three other dimensions ? Why not imagine a being which lives and moves (?) and has its being in a mathematical point ? Why not have beings for every kind of direction ? Why are we three-dimensional beings unaware of any two-dimensional beings ? How could beings of four dimensions escape detection as regards their three dimensions ; and how could a being of one dimension, a fourth dimension, interfere with beings of dimensions to which it does not belong? The three-dimensional doctrine of space must be regarded with suspicion ; for such a division merely selects certain few factors which are not what they appear to be. We know nothing of a space less than three-dimensioned, as ordinarily understood, and the conception of three bare dimensions, is empty. Thus also the notion of a four-dimensional or five-dimensional space is a barren play upon numbers, arising from the handling of misunderstood formulae.
We may turn now to more general considerations. We look upon a piece of land, and we remark that there is space to build twenty houses on ; so, too, we glance into our purse, and say that it is empty. Now note, not only is vision three-dimensional, but its field is unbroken by any points of no vision. Hence we never see nothing, never really gaze into vacancy. What do we mean, then, by an empty purse ? There is but one answer. Certain lines are observed, where certain other lines or complexes are imaginable. Instead of the worn lining, sovereigns might be seen ; instead of heaps of refuse, houses might be seen. It is not that a full purse is an empty purse plus coins ; it is a purse the lining of which is made of gold and not of leather.
What, then, is meant by space and empty space ? Are they a mysterious somewhere where lines are placed, a hole without walls where things are situated ? One fails to catch the sense of these phrases, except in terms of lines. If the nearest row of houses which is within the view were pulled down, I could see the exterior of the next row behind it. So, too, the exterior of the row to be pulled down could be made to vanish, by building in front of it, by changing the lines. Similarly, since only one line in one position can be seen on a smooth two-dimensional plane, two things cannot simultaneously occupy the same space. Again, most tines may be displaced by others ; and hence men speak of latent lines, of space. Infinite space, except as meaning infinite expanse, or infinite endeavour to see, is infinite nonsense: you might as well say that you could imagine a room without boundaries. If we could stand on an overhanging promontory of a flat world and look outwards, we should have the immediate environment of the eyes, and around us, perhaps, some grey expanse. This expanse might be imagined indefinitely retreating as we advance into the gloom ; but wipe out the lines, wipe out sight, and not space but nothing is left. Assume that we are beings of but one sense, that of vision, and there can be little doubt that by space we mean certain line relations and details ; and that apart from these relations the word has no meaning. Thus space, being a relation between systems, cannot exist prior to systems, nor can it survive them. Large, small, round, square, are visual terms. When we are once convinced that space is not a glove into which the world fits, our difficulties are soon overcome.
SOURCE: Spiller, Gustav. The Mind of Man: A Text-Book of Psychology (London: S. Sonnenschein & Company, Lim.; New York: The Macmillan Company, 1902), Chapter VIII: Systems as Unified; 182: Space (336-347), pp. 342-343.
Gustav Spiller (1864 - February 1940) was a Hungarian-born ethical and sociological writer who was active in Ethical Societies in the United Kingdom. He helped to organize the First Universal Races Congress in 1911. (Wikipedia)
Gustav Spiller is referenced several times in Jorge Luis Borges’s Selected Non-fictions:
Joyce’s Ulysses (1925)
An Investigation of the Word (1927)
Time and J. W. Dunne (1940)
Book Review: Edward Kasner & James Newman, Mathematics and the Imagination (1940)
A New Refutation of Time (1944-47)
Prologue: Charles Howard Hinton, Scientific Romances (1986)
Borges references Spiller’s psychology on matters of perception, syntax, pain, vision, bodily injury, and space. In his book review of Edward Kasner’s & James Newman’s Mathematics and the Imagination (1940), Borges itemizes Spiller’s book as one of the five he has most revisited. In “Blindness” (1977), Borges mentions that his father, a professor of psychology, had a keen interest in Spiller. In his prologue to Charles Howard Hinton’s Scientific Romances (1986), Borges mentions Spiller’s refutation of the notion of four-dimensional space.
First Universal Races Congress, London, July 26-29, 1911: Selected Bibliography
Book Review: Barnetts Universe
Homage to Martin Gardner
Non-fictions: Table of Contents
by Jorge Luis Borges;
Eliot Weinberger (ed.,tr.), Esther Allen (tr.), Suzanne Jill Levine (tr.)
Jorge Luis Borges: Selected Study Materials on the Web
Enrique Gaspar y Rimbau: El anacronópete — The First Time Machine
H. G. Wells’ The Time Machine: Selected Bibliography
Science Fiction & Utopia Research Resources: A Selective Work in Progress
Gustav Spiller - Wikipedia, the free encyclopedia
Edwin Abbott Abbott - Wikipedia, the free encyclopedia
Flatland - Wikipedia, the free encyclopedia
Charles Howard Hinton - Wikipedia, the free encyclopedia
Fourth dimension in literature - Wikipedia, the free encyclopedia
Johann Karl Friedrich Zöllner - Wikipedia, the free encyclopedia
: A Romance of Many Dimensions
with Illustrations by the Author, A SQUARE [Edwin Abbott Abbott]
Gardner | The Church of the Fourth Dimension
Giulio Prisco, October 13, 2012
C4D | The Church Of The Fourth Dimension
Llull, Bruno, Borges, and the fourth dimension
Borges on Hinton
Charles Hinton and His Cubes by David Auerbach
Blindness (1977) by Jorge Luis Borges
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