For the number of nothing, everything began with the definition of an empty quantity. Before this type of emptiness was officially used as an indispensable element of the algebraic structure, it was referred to in various ways, mainly as some kind of boundary, specific space of being-in-between, the horizon. The Egyptians had a symbol for zero: NFR = a hieroglyph that represented the heart or, to be more specific, the sheep heart or esophagus, i.e. the ciliated epithelium on the esophagus. It was basically a symbol for perfection or wholeness, with the additional meaning of good, pleasant, and beautiful. nFR was used (in drawings on tombs and pyramids) and understood as a homaloid that separates what is above the line from what is below it. Here, the void was the unifier of the separated.
It appears that the zero’s “=” asymptote, infinity, and emptiness do not exist in the “real” world. There are no entities we can observe that constantly approach but never reach.
If everything that exists has a place, place too will have a place, and so on ad infinitum.
The (non)existence of a void suggests that there are spaces in a certain infrastructure, in a certain relationship, in adaptation. Infrastructure of liminality and liminal spaces. But where can we click on NOCLIP, how do we travel through spaces, through the interstices that build?
How can a liminal space be a landmark which stands between two things? Liminal spaces are an unnatural void, they are interfaces, usually a place of transition, a state of change—in reference to the concept of liminality. The original etymological meaning of the word “liminal” is “harbor”, the place where land and sea meet. Harbors as cosmopolitan intersections of various cultures and languages, where material goods and artefacts, ideas, religious practices, etc. are exchanged. Cultural anthropologist Victor Turner explains the concept of the liminal through the distinction between structure and anti-structure. Structure, for example, belongs to the domain of hierarchies, status, politics, economics, and the legal system, whereas anti-structure, or “communitas” as Turner calls it, is its indispensable part. Structure can therefore only exist if there’s an anti-structure, which is a vessel. Turner distinguishes between three forms of anti-structure: marginality, inferiority, and liminality. Anti-structure is the force that constantly renews structure. “Communitas breaks in through the interstices of structure, in liminality; at the edges of structure, in marginality; and from beneath structure, in inferiority.”
This is the stage where new structure is born, the stage of pure potential. For Turner, in liminality all structural differences, from wealth and property to power, are dissolved, resulting in a flattening of all hierarchies, where there is no status, no property, no identity. Liminal entities appear to possess nothing.
The term liminality comes from the same root as the word subliminal, where the boundary is directly tied to the subject’s perception of a safe space, necessarily immersed in danger. In liminality, however, this boundary is not exclusively psychological: Turner does refer to a certain degree of rituality, where a change of state/transformation takes place, but what we are interested in here is the threshold, which is, in fact, construction of the new. We are interested in crossing the boundary into a completely new way of being, in structures that are in a constant, continuous relation of motion, which is also Heraclitus’s river.
Liminal entities are neither here nor there; they are betwixt and between.
The attributes of liminality or of liminal personae (“threshold people”) are necessarily ambiguous, since this condition and these persons elude or slip through the network of classifications that normally locate states and positions in cultural space.
In the ambiences where “liminal personae” and, might we add, “liminal objects” reside, ambiguity is the main attribute of liminality, that which constantly evades recognition but is also a necessary point of growth. Liminal objects occupy a spatial and temporal position, they are anchored in its fluidity of constant renewal and creation. It is therefore essential to create objects in networked spaces, in places where adaptation is expected. Where the created and brought object elements imply a relation into the brought space to complete both the object and the space. Where they can exist in relations, necessarily interconnected, out of which a distinct relationship is built. This is no mystical magical fiction that has failed to finally transform into reality, this is not a script, this is the main reality. We live in an infrastructure of systems, but the closer we get to liminality, the more this structure begins to dissolve, and the function of dissolution seems to be the rebirth of a system that mirrors its basic infrastructure.
Are atmospheres created violently, adapted violently, are objects neophytes, innovations that are brought in and kill everything in their sight? In botany, a neophyte is a plant species that is not native, is invasive, and displaces the native species in its new habitat. Such species are introduced through human activity, mainly freight transport. Movement of commodities allows neophytes to become unintentionally displaced and mount a biological invasion. Neo-biots shine in their high capacity for adaptation. Some have a major negative impact on the biodiversity of their new habitat and are extremely violent towards the environment and other organisms. Their adaptation does not remain within the adapted, they devour everything around them. There are also non-biotic species that do not cause any noticeable negative effects, they are a novelty and create new types of habitats.
An object is forcibly altered due to an atmospheric change, forced to adapt for an extended existence but trapped, and all the elements involved in the relationship begin to adjust.
The object is brought in, it does not pretend that it has always been there or that it is yet to be created there, it is a neo-biot. It is not exclusively built for a single space, yet it is built specifically for an environment. This environment is statically mobile, which means that it addresses a relation that cannot but exist. The relation becomes a space, it becomes a surface. It is built in layers, it is elementary in its multiplicity. The layers are constantly pushing each other out, falling into each other—these are the created contacts of reactions. This is both a dichotomy and Aristotle’s “mutual substitution”, where through repositioning entities we can explain that different spaces exist. When two bodies swap places, the space in which they were is transformed and is therefore simultaneously fundamentally different from what is displaced, whereas what is displaced already contains its own space, which is also always transformed. I offer my interpretation and add: here, we are talking about six types of entities or atmospheres, regardless of their solidity or phenomenological nature. The first body constitutes atmosphere A with its own space A1 and atmosphere B with its own space B2, which are both in atmosphere C, which also has its own space; the point here is that when atmospheres are displaced, they leave behind comprehension of spaces in layers that may or may not create interreactions.
The existence of place is held to be obvious from the fact of mutual replacement. Where water now is, there in turn, when the water has gone out as from a vessel, air is present. When therefore another body occupies this same place, the place is thought to be different from all the bodies which come to be in it and replace one another. What now contains air formerly contained water, so that clearly the place or space into which and out of which they passed was something different from both.
Space is a body or, rather, space is an atmosphere, which requires a different infrastructure of a given place, meaning that two bodies can be in the same place, which excludes the possibility of there being only one place. It is built in layers or, so to speak, on homaloids where several atmospheres “reside”.
Further, if body has a place and space, clearly so too have surface and the other limits of body; for the same statement will apply to them: where the bounding planes of the water were, there in turn will be those of the air. But when we come to a point we cannot make a distinction between it and its place. Hence if the place of a point is not different from the point, no more will that of any of the others be different, and place will not be something different from each.
Aristotle insists on the everyness of space, where space can be shape and matter, is neither shape nor matter. Space is that which originally surrounds each body, the boundary is not mutually separable from a thing, matter or space. It confines to two points: 1 ) space separable from things: i.e. that which is within matter, 2 ) space inseparable from things: that which surrounds matter.
- Space is therefore that which surrounds = the shape and image of each individual body, for this is precisely the limit for each thing. Space is the shape of each individual thing.
- Space is an extension = when space is an extension or, rather, a spacing, space is matter. Bodies being reduced to matter.
If the place is in the thing (it must be if it is either shape or matter) place will have a place: for both the form and the indeterminate undergo change and motion along with the thing, and are not always in the same place, but are where the thing is. Hence the place will have a place. Further, when water is produced from air, the place has been destroyed, for the resulting body is not in the same place. What sort of destruction then is that?
This kind of destruction is adaptation. It is not about annihilation, space does not disappear; rather, it adapts to every infrastructure of every space, the process is networked, homaloids interwave. There is no established intermediate space between two homaloids, only the constant of the new space, nor is this a case of perfect adhesion or an inseparable whole, although the whole of course comprises components that are indivisibly mobile … they are equal atmospheres, brought together by contact. In adaptation, the new is constantly being built, in interconnectedness. The contact is infinitesimal, a process that approaches zero, that manages to flirt with infinities. It is a paradox, Zenon’s aporia of the construction of motion that seems to stand still.
The arrow argument states that if the composition of time is assumed to be atomic, then motion is atomic as well. Atomic motion, however, is at rest. In one atom of time, everything is at rest, because if something were different at the beginning of an atom of time from what it is at the end, this would no longer be an atom, but could still be divided, as it would lack unity. Atoms of time can be thought of as frames on a filmstrip. In each frame, the figures are at rest, so motion itself also consists of atomic leaps from one stationary image to another. Atomic motion is therefore nothing more than the sum of different rests. And the sum of rests cannot constitute motion.
What we have here, then, is a kind of sameness, connectedness to the same place, being in oneself and being in the other, what is and that in which it is are both part of the same thing and are at the same time Zenon’s infinite spaces, because if space exists, there must also be space in another space.
If space is neither matter nor shape, it is something completely different, it has no material definition. Space is that which envelops the thing whose space it is, and space is nothing the thing itself is in possession of. Connectedness is key here. Aristotle speaks of the how water and air are connected as they exchange places in a vessel, where their boundaries are not explicit and perceptible, where there is no material tangibility, and where connectedness is the option of using the same space. Distance from a thing, i.e. the space that can be separated from matter or shape, is not key here. What is key is that a thing in that which surrounds it is thus at the extreme boundary of that which is surrounded and that which surrounds it, the boundary is not a constant but is constantly being created, it is not created by contact but in the presupposition that each thing already has its own space. It is not only intangible things that are non-corporeal; in this infrastructure, everything is corporeal and everything is spatial. The Pythagorean air is a boundless void that the principle of life (both divine and mortal) inhales and thus transforms into a perceivable and finite being. Invisible atmospheric air is not just a void but something as real as earth and water. Emptiness came into the world from the infinite air, as the Pythagoreans suppose emptiness to be something that divides a succession, where emptiness aims to be a dimension of the body.
Aristotle argues that if there is some expanse next to the body that is displaced and into which any number of bodies that are displaced can enter and come into contact, this is only the case if there are infinitely many spaces in one and the same place. And what is most interesting is that at the same time the space also changes, as does another space, and so many spaces are together at the same time. But if space is none of these, then all that is left is time in motion, which seems to stand still.
Well, then, if place is none of the three—neither the form nor the matter nor an extension which is always there, different from, and over and above, the extension of the thing which is displaced—place necessarily is the one of the four which is left, namely, the boundary of the containing body at which it is in contact with the contained body. (By the contained body is meant what can be moved by way of locomotion.)
It is therefore not only the boundary that is a void—the boundary of a boundary is also a void. Space is a space within spaces, an encompassing surface where the boundaries of what delimits are together with what is delimited. When thing B moves, thing A, which is in thing B, moves as well, so thing A also changes, adjusts, and moves. Space, however, wants to be immobile, so space is the whole river, which as a whole is immobile. Leucippus was able to explain motion by asserting that nothing exists—if the void exists, then motion does not exist. He accepted Zeno’s arguments against infinite divisibility and affirmed the existence of finite particles or atoms, where everything consists of atoms and voids in various arrangements.
Nothing happens at random, but all things for a reason and of necessity.
There is no dimension distinct from bodies, nor separate, nor residing in reality that dismembers the cosmic body so that it no longer continues. These are the responses of spatial sequences; a detail or an atmosphere is highlighted to array a given relationship, based on the construction of what has adapted successfully.
Is it acceptable for two bodies to be in one and the same place? If so, that in itself does not show that the void exists or, as Aristotle suggests, each body is necessarily void and grows in all directions, and does so because of the void.