Although a bit abstract, most of us are familiar with the idea of space in some capacity. Even young children have a rudimentary sense of direction and are able to grasp the concept of distance. Without this, it is practically impossible to make sense of any physical occurrence. When one tries to imagine absolute nothingness, the mind’s eye typically conjures the image of a dark, empty space by default.
Modern technology has had an immense impact on our everyday impression of spatial relations. The airplane and the World Wide Web seem to bring the most remote destinations closer than our proximal surroundings.
The earliest notions of space can be boiled down to a pure extendedness. In antiquity, space was thought of as a sort of container filling the area around an object. It had not yet taken on an explicitly mathematical form, but was instead characterized by a basic intuition about location and movement. Aristotle, for one, thought of space as a sort of limit to an object’s physical presence. He lists the essential aspects of this concept by remarking,
We assume first that place is what contains that of which it is the place, and is no part of the thing … that the primary place of a thing is neither less nor greater than the thing … that place can be left behind by the thing and is separable; and in addition that all place admits of the distinction of up and down, and each of the bodies is naturally carried to its appropriate place and rests there, and this makes the place either up or down.1
The place that any material object occupies is determined by what is directly around it. The place of a straw within a cup, for instance, is defined by where the surface of the cup touches that of the straw.
Every object is inclined towards its proper place on its own if it is removed from it. This was long before gravity was identified as a recognizable force, so the inclination of things to fall toward the Earth was interpreted as the maintaining of a divine order in a teleological sense.
Aristotle, like the pre-socratic thinkers we have discussed, surmised that the world was made up of four elements. He interpreted motion as the tendency of these elements to move back to their natural position. Rocks fall to the earth because their place is downward while flames, likewise, leap upward.
If all the places of all the things in the universe were added together, their sum would define space. Space itself has no place in relation to anything else since it is the totality of all places. The logical consequence of this is that there can be nothing outside of space as it is only the interconnection between the places of different objects. A patchwork model like this aims to preserve it as something irreducibly objective—an emergent property of things out there in the world.
But, is this the whole story? The way we experience space surely changes based on the situation. Optical illusions demonstrate how our brains, instead of being arbiters of unconditional truth, are constantly judging the sizes and positions of things through environmental clues. If these are manipulated correctly, the human perception of distance can be greatly distorted.
This understanding was brought to perhaps its most radical instantiation within the philosophy of Transcendental Idealism, devised by Immanuel Kant. He argued that space was an a priori feature of how we perceive objects rather than an independent part of the physical world. In his Inaugural Dissertation of 1770, Kant proclaims,
Space is not something objective and real, nor a substance, nor an accident, nor a relation; instead, it is subjective and ideal, and originates from the mind’s nature in accord with a stable law as a scheme, as it were, for coordinating everything sensed externally.2
Kant appears to assert that space is nothing more than a fiction, arising only because of how our brains organize information. Space, however, is not a later empirical intuition from sense data; it is a cardinal category of thought which we apply to our perceptions because it must be presupposed just as we must presuppose that 1 + 1 = 2.
What is the source of this modern interpretation of space?
Kant’s view is nothing more than the inevitable conclusion of scientific enlightenment progress. In order for the world to be understood mathematically through quantifiable experimentation, the location of objects had to be divorced from any innate significance; any place is just as valid as any other place. Space is thus reduced to a coordinate grid which we project upon nature.
The advances of modern science complicate this picture still further. Space no doubt acts as a background for all the entities in the universe. It cannot be touched or measured in its own right, but is made use of in all conceivable measurements.
General Relativity, nonetheless, indicates that space along with time can possess curvature. This curvature is an objective attribute of the manifold and cannot be brushed aside as a subjective fantasy. The form of the coordinate grid we choose is arbitrary, but whether it is geometrically flat or whether there exist gravitational radiation is a real attribute independent of our own minds.
Aristotle, Physics, Book IV Da Jonathan Barnes, editor, The Complete Works of Aristotle. The Revised Oxford Translation, Vol. 1, 1991
Kant, Immanuel, Kants gesammelte Schriften, edited by Königlich Preussischen Akademie der Wissenschaften, Berlin: G. Reimer, 1902