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An Introduction to a Fractal Ontology

By A.T. Kingsmith.

All of my propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when we have used them—as steps—to climb beyond them. [We] must, so to speak, throw away the ladder after [we] have climbed through it.
-Ludwig Wittgenstein, Tractatus Logico-Philosophicus, 1921: 6.54.

All relations are founded upon the simple yet indispensable truth that in the beginning there was noise, not silence. Even the simplest words arrive much later—and at any rate, words are still noise. In his illuminating work on The Parasite, philosopher Michel Serres reminds us that the primary grounding of noise is chaos: the pure multiplicity behind things, without any pre-existing order or organisation. The indefinite presence of noise means no system is without turbulence for very long, that there is always chaos, multiplicity and deviation—in short, ontology is always parasitic, always a background noise, always a depth and darkness beyond the flows between order and disorder.

All knowledges are an attempt to bring order to noise—to forcefully organise the chaos continually fixing everything together in an asymmetrical block of concurrent becoming. We can call this instantaneous zigzag a fractal ontology—a set of concepts and categories that show the properties and relations between them. The following is an introductory exploration of some of the phenomenological implications of such an ontology—of the vital mutations of becoming that operate as a material intensification of existentialism, a thorough going-beyond of Martin Heidegger, an exploration of Friedrich Nietzsche’s maps, as well as declaration of war on Aristotle, Descartes, and Kant.

We will deploy a number of over-simplified examples to clarify these points. Importantly, these shouldn’t be taken as arguments, rather they are tools that will help us think about the terrain upon which a fractal ontology is situated. One of the biggest challenges here is that a fractal ontology is an attempt to write in a space beyond analogy—far past what Franz Kafka refers to as the ceaseless constraints of the metaphor—and against the smooth categorisations of language. In other words, a fractal ontology does not give examples (A is like B), or define terms cleanly (A is any X that has such and such properties) because that would defeat the purpose. Like Wittgenstein’s ladder, these examples are merely tools to move us to a space where they are no longer necessary.

The Problem of Demarcation

Imagine that you’re eating a pear. This seems like a simple ‘event:’ you, the subject, are eating, verbing, the pear, the object. There are two things, you and the pear—thanks to the laws of syntax, the verb ‘eating’ quickly tells us who’s dictating the relation.
When we try to define these things further, we quickly run into some difficulties: where’s the ‘cut off’ for the pear, as in, where does the pear end and begin? In everyday life we tend use the notion of geometrical space occupied by the (transparent) flows of oxygen as a convenient measure for demarcating objects. So the pear ends at the yellow skin, and the bite mark. However, this is obviously just a pragmatic and intuitive short hand at the macro level—Gilles Deleuze and Felix Guattari refer to this level as molar. Surely we can find a more ‘objective’ edge by zooming in to this edge and drawing up a line.

As we zoom in to the edge of the pear, though, a nice clear line doesn’t reveal itself— like a fractal (ontology), the edge becomes more and more ambiguous. We discover that other things are eating the pear too, that the skin is porous, that chemical reactions are exploding off it. We find that our bodies (hands) are effortlessly transferring energy as heat into the pear, which is causing other imperceptible (macro) chemical shifts.

Now that we are ‘zoomed in’ these tiny transformations in the pear are huge. Around the bite mark there’s even saliva, containing our DNA, bubbling and transforming the sugars in the pear and reacting with the acid, with particles flaking off and floating through the air in a cloud being sucked up through our noses—so now even the supposedly simple question of ‘where does the eating begin and end’ is beginning to get really blurry.

We can call this problem the demarcation problem. And while you might think that this ambiguity (of the object) is essentially meaningless (uninteresting?), for all pragmatic intents and purposes we have no trouble defining where the pear ends and we begin—we’re doing metaphysics, so it is interesting and problematic, and, more importantly, where a pear ends and begins in a geometrical space indeed isn’t a problem very well suited to cause us worry, but where a person begins and ends in a political space is.

If we just use pragmatic ‘edge-marking’ techniques we haven’t problematised the issue of who is marking these edges, and for what pragmatic function. We mark the edges of the pear like this so we can coordinate our bites, and not eat our hands, which is obvious enough, but when we mark the edges of something like ‘woman/man,’ ‘normal/abnormal,’ ‘sane/insane,’ ‘permissible/perverted’ these demarcations can have huge consequences. This is doubled when we consider that the demarcations are merely a method for creating regions on a cloud of molecular elements distributed chaotically for some pragmatic ends (again, what ends?) and then begin to use the demarcation as primary, mistaking the map for the territory, as it were: ‘here is, naturally, the binary of men and women, and they are all such and such; you’re either one or the other, etc…’

Thus a fractal ontology begins against the modes of thinking that mistake the map for the territory, and don’t question the political, social, cultural, and administrative aims for which these maps are expedient. Anyone who has realised that a country is more than geopolitical lines on a map, and that lines on the map signify nothing but a specific set of ideas, not a permanent geographical feature, has intuited this demarcation problem.

Yet it is important to point out that mistaking maps for territories isn’t some special or deficient case. We’re always dealing with and manipulating maps because language is a cartography. Thus maps, once drawn, are not merely sterile descriptions of the world (as is), they are also ontologically performative upon the ‘molecules’ they organise.

Have you ever met someone who eats the core of a pear? It makes a difference to the genealogy of the pear whether the core is eaten or composted or discarded. We can see this in the history of agriculture and cultivation: pears have been getting bigger and sweeter over millennia. It’s not, strictly speaking, the pears’ collective concern or desire to continue becoming bigger and sweeter, it’s the concern of the (socio-linguistic) maps we have drawn that pears have become ensnared by and thus subsumed under.

The Tree Yellows

How do we think beyond maps with their static regions (being)? According to Deleuze’s The Logic of Sense, the trick is to start thinking of verbs as primary. Verbs are often seen as less substantial than nouns (or adjectives) because their mapping is more chaotic. If you’ve studied a foreign language—French perhaps, with its 20 or so different verb tenses for conjugating the past, present, and future—you’ll know this all too well.

We can transform the proposition ‘the tree is yellow’ to ‘the tree yellows.’ The process of yellowing is more fundamental than yellow—referring to an unfurling event from which we derive the static theme ‘yellow.’ Making this shift renders certain metaphysical problems about objects and their properties less problematic. By A Thousand Plateaus Deleuze and Guattari have gotten to ‘a-treeing yellows.’ That is, they are turning static ‘beings’ (regions on the map with their properties allocated by definitions that demarcate their edge points) to ‘becomings,’ ‘doings,’ ‘transpirings.’ In other words, we are confronting the molecules squiggly shifting under the molar territories on the map.

There are no people, only ‘personations’ that begin and end (this beginning and ending are transformations), with the in-between—a life lived—being some sort of ‘semi-stable’ state representing the crossing of some threshold at some critical point. The transition from ice to water to steam is a useful analogy here because we can grasp these transformations but they are anything but smooth or linear—the properties, capabilities, and possibilities of ice, steam and water differ drastically, and they can change rapidly (sublimation, evaporation, condensation, etc.) depending on the state they occupy.

Billions of personations bumbling and stumbling around, persistently personating before deadening and then decomposing. All around this giant cloud of personating we draw a region of best fit, call it ‘person,’ and develop various methods for describing and reaffirming this line—methods such as our DNA convergences, commonalities of phenotypical expression, commonalities of commercial function (i.e. occupation), commonalities of stances towards (this is how to properly say ‘hello’), legal jurisdictions (private property, state boundaries), etc. Obviously such maps have nothing to do with personhood, or with the a-personating that’s a-going on around here-ish. The definition ‘person’ is static and dead. This map has to do with personation—a process that is persisting in a semi-stable state underneath the fixed definition of ‘person’ and thus it can find a new semi-stable state (evolution) or destruct (extinction).

In The Genealogy of Morals, Friedrich Nietzsche reminds us: there is no ‘being’ behind doing, effecting, becoming; ‘the doer’ is merely a fiction added to the deed. Things only seem like things (discrete objects) because we have some pragmatic interest in treating and demarcating them as such in a given context (field/map), and this is mirrored in and enforced by language. What’s more, though ensnared by the methods with which we demarcate them, things aren’t really concerned with the maps we have drawn—they blur and bleed out of the borders. A person is a person until the critical threshold of the transformation into inert flesh and static organs. Our name for this threshold is death.

Thus things (being), are just features of maps we draw. Beneath them are transforming, semi-stable processes of becoming (Doing! Effecting!). In these transformations, our semi-stable states (person) are book-ended by critical points these processes stumble into, over, and out of—representing a fundamental transformation in that things/persons only seem like things/persons (discrete objects/subjects) because we have a pragmatic interest in treating and demarcating them as such within a given context (field/map).

Assemblages of the Unconscious

When we look at a person’s teeth—remember, teeth are ‘teethings,’ that is, the sucking up of calcium and deployment into a semi-stable tooth shape/state that is itself engaged in a constant process of decaying and resisting decay—we can only understand them by looking at what a person eats. Those pearly whites are rapidly yellowing. But why are they ‘teething’ like that? Too much black coffee and red wine? Not enough brushing?

Teeth are teething like that in the same way that flesh is ‘fleshing.’ The tooth and the skin of the pear blend and bleed into each other in the ‘biting.’ The biting is another becoming, another thing we’ve mapped (separated) out. But the biting only makes sense when taken in conjunction with tooth and pear skin (and stomachs, hunger, food, supermarkets, pear trees, etc.). So people have teeth and stomachs and hunger and prey with skin and seeds and sugars in orchards with hills and grass and wind and smells, and in different maps we can create a myriad of regions to demarcate all of this in a myriad of different ways. But underneath all such maps these (fractal) entities bleed together and hold each other in semi-stable states between thresholds—a temporary assembling of particles (teeth, seeds, hills, wind, etc.) that form into an assemblage.

If it is still necessary to talk about structure (being) in relation to an assemblage—which is not self-evident—we could say that it is structured like an unconscious machine fuelled by a multiplicity of modes of semiotisation (of which linguistic enunciation is by no means the most important). It is on this condition that one can remove the shackles of the subjective, consciential, and personative limitations through which desire and the unconscious have been imprisoned. An assemblage is neither individual nor collective, and they exist everywhere that a labour of significations bears on reality in such a way so as to constitute or demarcate a vision/map/productive perception of the world.

Why are snow leopards fast? Because jackrabbits are fast. Why are jackrabbits fast? Because snow leopards are fast. The leg muscles of the snow leopard and the leg muscles of the jackrabbit are both a single ‘becoming-fast’ resonating in a semi-stable state (assemblage), but they are also connected up, obviously, to a ‘becoming-prey-becoming-predator,’ a bit-ing, a hunger-ing, a flee-ing and a chase-ing (the leg muscles mean nothing unless there is chasing and eating). Using one map we can demarcate this semi-stable state as ‘the cynegetic process,’ using another we can demarcate it as ‘an ecological balance,’ and using another we demarcate it as ‘Planet Earth, S01E03.’

It is also important to note that even though the legs of the snow leopard and the legs of the jackrabbit are a single interconnected assemblage of ‘becoming-fast,’ the snow leopard and the jackrabbit obviously have different quantitative speeds. It is too simple to say that the jackrabbit is as fast as the snow leopard and the snow leopard as fast as the jackrabbit—the relationship is asymmetric and multifaceted. Thinking about this should help us appreciated how many disparate elements, geographies, temperatures, protein fibres, hormones, neurones, behaviours, tendencies, causes and effects, all get tangled up in this one assemblage of ‘becoming-fast.’ What’s more, we must remember that all of these entangled ‘things’ are not static objects or properties ‘belonging’ to the snow leopard or the jackrabbit, they too are becomings, resonating in semi-stable states between thresholds, entangled together in a chaotic myriad of intertwined assemblages.

Not Imitation But Transformation

In Civilization and its Discontents, Sigmund Freud’s great innovation was the discovery of tunnels underneath our maps connecting disparate (unconscious) regions, whereby a snow leopard, for example, can simultaneously connect the subject to a father, while at the same time concealing that connection. Yet Deleuze and Guattari claim Freud hasn’t gone beyond the assumption that regions on a map are beings, and their connections (through the subconscious) are lines of signification. They want to flip this picture upside down, where signifying a snow leopard becomes a becoming-snow-leopard.

Now as we have said, becoming-snow leopard is not the same as imitating (signifying) a snow-leopard, but bringing the particles that constitute one’s body—what one merely is—into arrangements with the assemblages that make up becoming-snow-leopard: the semi-stable states/processes humming along in the region we have loosely demarcated as ‘snow-leopard.’ We’ve already pointed out that a person’s (or a snow-leopard’s) tooth forms an assemblage with a prey’s skin and a biting, and a (…), so imitating a snow-leopard on the plane of resemblance (maps) (i.e. filing my teeth down to points so they look like snow-leopard teeth) is not the entirety of ‘becoming-snow-leopard,’ that would be just me (region a) signifying a snow-leopard (region b), not becoming-snow-leopard.

Actors can help us think about this. When an actor needs to play the role of an alcoholic father, despite being neither, it’s not merely enough to read a few articles about the two topics. Better to find one (an alcoholic father) and imitate their gait, their tone of voice, their flush, and their way of holding their body. Yet better still is to go within oneself and find those particles that already are part of the assemblage of ‘alcoholic father beats their children,’ the disappointment, the aggression, the sadism, the masochism and surplus enjoyment, literally become the becoming-alcoholic father, raising the intensity of these points over thresholds to create a new organisation (assemblage) of the body.

Imitating a given example, or set of given examples, will always be confined to the demarcated map regions, resulting in pantomime, gestures, and movements that signify the alcoholic father through the logic of the mapping procedures (region a signifies region b). Becoming one doesn’t mean literally becoming an alcoholic and having children—it’s about making the particles one is resonate in semi-stable states in the site of the assemblage alcoholic-father. Acting is not at all about imitation, it is about transformation. Growling like a snow leopard is different from growling as snow-leopard.

“Do not imitate a dog, but make your organism enter into composition with something else in such a way that the particles emitted from the aggregate thus composed will be canine as a function of movement and rest, or of molecular proximity, into which they enter,” Deleuze and Guattari, (1987:302).

Think of the becoming-animal of the warrior. The fighter jet is not supposed to resemble or even imitate the snow leopard, but is painted in line with the becoming-snow leopard, becoming-animal, of the soldiers flying it. It’s one outward symptom, or trace, of the transformation they are trying to enact on themselves, on what they are becoming. Making oneself a snow leopard doesn’t necessarily mean ‘go into the tundra and stalk and eat jackrabbits.’ The field of molecules we map into the region ‘snow leopard’ enter into all manner of assemblages: biting, killing, terrifying, running, sleeping, hunting, bleeding, becoming-invisible, becoming-explosive, nightmares, horror movies, etc.

To say ‘the soldiers desire to become snow leopards’ is also inaccurate, because this is always going to be an imitation, because we have already expressed two distinct beings (soldiers and snow leopard), two distinct map regions. But if we remember the map is secondary, that ‘soldiers’ and ‘snow leopards’ are a pragmatic distinction we make upon a chaotic distribution of particles, we see that the two regions, sharing particles between them in any given map (field), can enter into subterranean singularities and alliances.

To take up an ontology that is fractal in nature we must accept that there are no soldiers or snow leopards, just particles forming various assemblages in semi-stable states of becoming that we then use some method or other to demarcate into regions: this bunch of stuff is a soldier, and that bunch of stuff is a snow leopard. For example, we can write a poem charting a new map, one where a snow leopard stares at a photo of its sweetheart back home and a soldier tracks the smell of blood over half of a mile. This is what Deleuze and Guattari mean by ‘becoming-other,’ this slipping beneath the maps and seeing the multitude of assemblages that compose the ‘beings’ on the map’s surface, and thus realising they are fractal and can be formed and blended together.

Locating our Metamorphosis-Machines

As any political engagement with the concept of becoming-other is only ever going to be a territorial approximation, we need to look at a fractal ontology in relation to our ability to obliterate and to reconstruct maps. For Deleuze and Guattari, war machines—engines of differentiation that we will instead refer to here as metamorphosis-machines—are the processes through which we expunge and reassemble maps. We should also remember that ‘machine’ in Deleuzo-Guattarian thought simply refers to a combination of forces or elements—it does not have any overtones of instrumentalism or of mindless mechanisms. A social group, an ecosystem, a knight on horseback are all ‘machines.’

By initiating a process of deterritorialisation—a Deleuzo-Guattarian term for the means through which something departs/breaks from a given territory or map—metamorphosis-machines function as a form of social assemblage directed against the ways of thinking in terms of stasis, sovereignty, and being. The way such machines undermine traditional understandings of ontology as static is by exercising diffuse power to break down concentrated power through the replacement of ‘striated’ (i.e. regulated, marked) space with ‘smooth’ (i.e. fractal) space. For example, think of how street gangs communicate to resist subordination by rival gangs, or how autonomous social movements—such as the European squatters’ movement, the Zapatistas, the networks of protest against summits or the everyday practices of indigenous groups—resist concentrations of political power.

In other words, the metamorphosis-machine—the force through which we can fractalise ontology—is a space characterised by pluralities, multiplicities, and differences, which escape traditional-coding by eschewing binary structures. On the ground, we might even say schizoanalysis is the political embodiment of such processes. For as Serres reminds us, the metamorphosis-machine is the noise—whatever escapes capture, a cross-signal or lawless irruption witnessed in the chaotic permutations introduced by becoming-other.

Metamorphosis-machines help us think in terms of a theoretical terrain characterised by conceptual openness to plurality and difference that eschews stable identities, essences and conceptual unities that form fixed assemblages. Such machines are what make possible the transformation of the soldier into snow leopard, the pear into teeth, the tree into yellow, the actor into alcoholic father, or the living into dead. Such a becoming-other involves a return to what Deleuze and Guattari call a ‘fibroproliferative unground’ that allows us to begin a project of strategic affirmation of any becoming whatsoever: becoming-woman, becoming-child, becoming-animal, but also other even more strange becomings: becoming-machine, becoming-molecular, becoming-cosmic, etc.

One only need to think of the intensity and of the self-obliterating passion at the opening of, for example, a new romantic affair to grasp these ‘too great a diversity of conjugated becomings’ that are brought into play through the metamorphosis-machine of love. Out of the intensity of a new relationship, semi-stable identities form in the wake of the destruction, and in the end you have a new assemblage that we refer to as ‘love.’

The very passion that founds the relationship also works to destroy these stable regions of gender organisation by creating a myriad of unexpected assemblages (loving-arguing- living-dying-going-thinking-becoming-animal-becoming-pear-becoming-metamorphasis-machine). Once again, the demarcation problem comes to the fore as the members of the relationship obliterate each other in a cloud of molecules—bleeding out and over and under any map that tries to fix and impose upon them static, individuated mode of being.

In politics—as in loving, eating, playing, etc.—we can rebuild maps that determine our unfolding however we wish (of course, these constructions and re-constructions always exist in relation to the specific material conditions of socio-economic life). Hence why it’s utterly monstrous when, as under newly-minted President Trump, the traditional political, social, cultural, familial, biological, and metaphorical maps that have kept us imprisoned in false categories of power (by subjugating genders, races, classes, etc.) are restored unchanged, imported wholesale from somewhere extraneous to the present moment.

From problems of demarcation and personation through to assemblages of animality and gender, the world exists in/as a fractal ontology. Of course, this cursory introduction shouldn’t be taken as a static argument so much as an assemblage of tools to help us to start building new metamorphosis-machines in order to confront and reassemble in a political space beyond the limits of tradition, being, and analogy—far past the ceaseless constraints of the metaphor and against the smooth categorisations of language. From here, the task of augmenting logics and mutating binaries to move through the current configurations of power is now (and has always been) yours to take up (as well).

“We don’t know yet what the multiple entails when it is no longer attributed, that is, after it has been elevated to the status of the substantive,” Deleuze and Guattari, (1987:04).


Félix Guattari. Chaosmosis: An Ethico-Aesthetic Paradigm. Indianapolis: Indiana University Press, 1992.

Friedrich Nietzsche. On The Genealogy of Morals. London: Vintage Books, 1887.

Gilles Deleuze. The Logic of Sense. New York: Columbia University Press, 1969.

Gilles Deleuze and Felix Guattari. Anti-Oedipus: Capitalism and Schizophrenia. Minneapolis: University of Minnesota Press, 1983.

Gilles Deleuze and Felix Guattari. A Thousand Plateaus: Capitalism and Schizophrenia. Minneapolis: University of Minnesota Press, 1987.

Kafka, Franz. The Metamorphosis. London: Wordsworth Classics of Literature, 1915.

Ludwig Wittgenstein. Tractatus Logico-Philosophicus. New York: Routledge, 1921.

Michel Serres. The Parasite. Minneapolis: University of Minnesota Press, 2007.

Pierre Clastres. Archaeology of Violence. Cambridge, Mass: The MIT Press, 2010.

Sigmund Freud. Civilization and Its Discontents. London: Penguin Books, 1948.



A.T. Kingsmith is a PhD Candidate at York University, where he studies and teaches political theory. He lives in Toronto and writes at adamkingsmith.com.

First published in 3:AM Magazine: Friday, February 17th, 2017.