6 Assemblages and Realist Ontology

How does actualization occur in things themselves? Why is differenciation at once both composition and determination of qualities, organization and determination of species? Why is differenciation differenciated along these two complementary paths? Beneath the actual qualities and extensities, species and parts, there are spatio-temporal dynamisms. These are the actualizing, differenciating agencies. They must be surveyed in every domain, even though they are ordinarily hidden by the constituted qualities and extensities. Embryology shows that the division of an egg into parts is secondary in relation to more significant morphogenetic movements: the augmentation of free surfaces, stretching of cellular layers, invagination by folding, regional displacement of groups. A whole kinematics of the egg appears, which implies a dynamic . . . Types of egg are therefore distinguished by the orientations, the axes of development, the differential speeds and rhythms which are the primary factors in the actualization of a structure and create a space and a time peculiar to that which is actualized . . . [and] lived by the individual-embryo in its field of individuation.

Deleuze, Difference and Repetition1

In previous chapters we have not stressed enough the distinction between the concept of assemblage and the concrete objective entities that the concept helps us understand. But it is important to keep the concept, with its material and expressive variables and its territorialisation and coding parameters, apart from actual cases, with their material and expressive components, and the articulatory processes that select, sort out, link, and stabilise those components. The distinction is important for epistemological and ontological reasons. On the one hand, it forces us to confront the question of the cognitive relation between the concept and the actual cases. In particular, if we conceive of this relation as one of class inclusion, a relation in which the general category denoted by the term ‘assemblage’ gives us necessary and sufficient conditions to classify entities as assemblages, then we would be adding another reified generality to the long list already created by philosophers. This would, of course, make a mockery of the arguments against such reifications rehearsed in previous chapters. So how should we conceive of that relation? In the previous chapter we argued that the singularities that structure a virtual diagram have a relation of divergent actualisation with the states that effectuate them in concrete processes: a topological point is related divergently to the many metric forms (spherical bubbles, polyhedral crystals, geodesic light rays) that actualise it. A similar divergent relation should be established between the abstract concept of assemblage, its variables and parameters, and all its concrete actualisations. Just as there is no mechanical recipe to establish in advance how a topological point can be actualised, so the ways in which the variables and parameters of the concept are effectuated by actual material and expressive components and articulatory processes should be established one case at a time.

The distinction between the concept and its cases also has an ontological aspect. The concept itself is a product of our minds and would not exist without them, but concrete assemblages must be considered to be fully independent of our minds. This statement must be qualified, because in the case of social assemblages like communities, organisations, and cities, the assemblages would cease to exist if our minds disappeared. So in this case we should say that social assemblages are independent of the content of our minds, that is, independent of the way in which communities, organisations, and cities are conceived. This is just another way of saying that assemblage theory operates within a realist ontology. Realists have a harder task than philosophers with other ontological commitments because it is not enough to state one’s position: we must in addition specify what the contents of an autonomous world are, or at least, what should not be included among its contents. Many religious people, for example, are realists about transcendent spaces and entities, like heaven and hell, angels and demons. But a materialist philosopher can only be a realist about immanent entities, that is, entities that may not subsist without some connection to a material or energetic substratum. And while it may be simple for a materialist to get rid of angelic or demonic creatures, there are other forms of transcendence that are far more difficult to remove.

The most important transcendent entity that we must confront and eliminate is the one postulated to explain the existence and endurance of autonomous entities: essences. Essences have been part of realism for more than two thousand years. The most defensible version of this concept is the one due to Aristotle, who defined metaphysics or ontology as a science concerning itself with the study of entities capable of separate subsistence. Among these he distinguished between those that subsist according to accident and those that subsist essentially. In his ontological science it was not valid to speculate about the accidental, so it was the second kind of entities that constituted its subject matter. As he wrote:

Now, if there is something that is eternal and immovable, and that involves a separate subsistence, it is evident that it is the province of the speculative, that is, of the ontological, to investigate such. It is not, certainly, the province of the physical science, at any rate (for physical science is conversant about certain movable natures), nor of the mathematical, but of a science prior to both of these, that is, the science of metaphysics . . . Metaphysics, or the First Philosophy, is conversant about entities which both have a separate existence and are immovable; and it is necessary that causes should be eternal, all without exception . . .2

Aristotle’s world was populated by three categories of entities: genus, species, and individual. Entities belonging to the first two categories subsisted essentially, those belonging to the third one only accidentally. The genus could be, for example, animal, the species human, and the individual this or that particular person characterised by contingent properties: being white, being musical, being just. From this ontology assemblage theory preserves only the third category, since all assemblages are unique historical individuals. As mentioned before, the term ‘individual’ has become synonymous with the term ‘person’, but this is just a quirk of ordinary language. As an ontological category the term ‘individual’ has no preference for any one particular level of scale. It is perfectly possible to speak of individual communities, individual organisations, individual cities. Similarly, we can, without invoking any undesirable connotations, speak of individual atoms, individual molecules, individual cells, and individual organs. All of these entities are assemblages, their defining emergent properties produced by their interacting parts, and therefore contingent on the occurrence of the requisite interactions. The historicity and individuality of all assemblages forces us as materialists to confront the question of the historical processes which produced or brought into being any given assemblage. We may refer to these as processes of individuation.

The embryological operations mentioned by Deleuze in the opening quotation illustrate one kind of individuation process, the individuation of organisms, but any assemblage is individuated by the processes of articulation that establish more or less permanent relations between its components. Deleuze, however, uses the term ‘individual’ in a special way, not to refer to an ontological category but to any entity that is currently undergoing individuation. Thus, an embryo that is still suffering foldings and stretchings of cellular layers, migratory movements of cellular populations, and the progressive differentiation of a single cell type into many types would be considered an individual. The completed newborn creature, on the other hand, would not be. While the embryo is defined in intensity, by the chemical gradients driving the assembly processes, as well as by the experienced intensity of the foldings and stretchings, the newborn is defined by its extensive boundaries and its emergent qualities. As he writes: ‘Intensity is individuating, and intensive quantities are individuating factors . . . All individuality is intensive, and therefore serial, steeped and communicating, comprising and affirming in itself the difference in intensities by which it is constituted.’3 But once the process yields fixed extensities and qualities, the latter hide the intensities, making individuation invisible and presenting us with an objective illusion, the same illusion that tempts us to classify the final product by a list of spatial and qualitative properties, a list which, when reified, generates an essence.

A similar point applies to another term, which in its purely ontological sense is synonymous with ‘individual’, the term haecceity. In scholastic philosophy the term signified the uniqueness of a given entity, the characteristics of an entity not shared with other entities and, hence, not generalisable. Since no general category can be used to specify an entity as a haecceity, we can only do this is by ostension. Hence the term ‘haecceity’ is often defined as the ‘thisness’ of a thing. However, in his work with Guattari, Deleuze adds an intensive element to this traditional definition, affirming that there is

a mode of individuation very different from that of a person, subject, thing, or substance. We reserve the name haecceity for it. A season, a winter, a summer, an hour, a date have a perfect individuality lacking nothing, even though this individuality is different from that of a thing or a subject. [It consists] entirely of relations of movement and rest between molecules or particles, capacities to affect and be affected.4

The opposition the authors draw between individual and organism, or between haecceity and subject, is simply another instance of the opposition between assemblages (in the original sense) and strata. In what follows we will continue to avoid these oppositions, recovering them as qualitatively different phases of an assemblage (in the parametrised sense), while the terms ‘individual’ and ‘haecceity’ will be used exclusively with their traditional ontological meaning.

To return to the main argument, of the three ontological categories posited by Aristotle we will retain only the third: individuals defined by their contingent properties and dispositions. But is this enough to recover the rich metaphysics of the Greek philosopher? No. Something else needs to be added to perform the role that genera and species play, that of explaining the regularity and stability of the characteristics of individual entities. In the previous chapter we argued that these regularities can be explained by adding a diagram to the assemblage, that is, by conceiving of the space of possibilities associated with its dispositions as being structured by singularities. The latter, as we saw, define both recurrent stable states (attractors) as well as changes from one stable state to another (bifurcations). The appeal of singularities to Deleuze is derived from the requirement that explaining the genesis of individuals should not involve concepts that presuppose the concept of individual. Singularities meet this requirement because ontologically they can be considered to be pre-individual: ‘The highest generalities of life, therefore, point beyond species and genus, but point beyond them in the direction of the individual and pre-individual singularities . . .’5

Another difference between these two philosophers involves their respective conceptions of the genesis of individuals. Aristotle’s explanation of how entities come into existence, in both nature and art, uses essences acting as formal causes. He argued that in nature the operation of essences is self-evident, because a horse begets a horse, and a human a human, that is, because an animal species generates individual organisms by formally causing them. And similarly for art. In the case of building a house (or nurturing a patient to health), the formal cause is the idea pre-existing in the human soul. A house, or any other entity that ‘involves matter arises, or is generated, from that which does not involve a connection with matter: for the medicinal and the house-building arts are the form, the one of health, and the other of a house. Now, I mean by substance not involving any connection with matter, the essence or very nature or formal cause of a thing.’6 We can summarise this conception as one in which forms are imposed from the outside on an inert and obedient matter, a conception that Gilbert Simondon, a philosopher whose ideas were very influential on Deleuze, named the hylomorphic model. The hylomorphic model can be challenged in three ways: first, by replacing a passive matter with a materiality possessing its own active powers, like chemical substances with the capacity to affect and be affected by other substances, a capacity (or intensive affect) that leads to the spontaneous generation of new chemical forms; second, by replacing the notion of a formal cause resembling that which it causes to form by topological forms that do not resemble what they cause to form because they are actualised divergently;7 and third, by replacing the essential properties necessary to belong to a category with the emergent properties of a whole that are contingent on the interactions between its parts. These three replacements, of which only the first two are acknowledged by Deleuze and Guattari, should be performed in the case of natural forms as well as in cases of forms that involve human intervention, like the forms that a carpenter can tease out of wood:

But Simondon demonstrates that the hylomorphic model leaves many things, active and affective, by the wayside. On the one hand, to the formed or formable matter we must add an entire energetic materiality in movement, carrying singularities . . . that are already like implicit forms that are topological, rather than geometrical, and that combine with processes of deformation: for example, the variable undulations and torsions of the fibers guiding the operation of splitting wood. On the other hand, to the essential properties of the matter deriving from the formal essence we must add variable intensive affects, now resulting from the operation, now on the contrary making it possible: for example, wood that is more or less porous, more or less elastic and resistant. At any rate, it is a question of surrendering to the wood, then following where it leads by connecting operations to a materiality, instead of imposing a form upon a matter . . .8

Having established the main differences between traditional realism and the realist ontology of assemblage theory, let’s explore some concrete examples of individuation processes. A good place to begin is the atomic scale, that is, the case in which the genus is ‘atom’, the species is ‘hydrogen’ or ‘oxygen’, and the individual is this atom here or that atom there. A modern Aristotelian approach would begin by giving necessary and sufficient conditions to belong to the general category ‘hydrogen’, such as possession of a single proton and a single electron. This is a perfectly reasonable way to specify the identity of this chemical species, given that if we added another proton to a hydrogen atom we would change its identity: two protons implies two electrons, and the latter give the resulting atom of helium entirely different chemical properties. The belief that the essence of any atomic species is given by its electronic structure is still quite common among modern realists, even if they do not go as far as positing it as playing the role of a formal cause.9 The composition of the outermost shell of electrons of an atom is indeed important. Whether the shell is missing an electron, or has an extra electron, or is exactly full does determine how many bonds an atom can form with other atoms: carbon atoms can form four; oxygen ones two; and hydrogen atoms only one. The properties of the outer shell, and the bonding capacities with which these endow an atom, however, should not be taken as given – the first step towards reifying them into an essence – but as emerging from the interactions between the components of an atom. And instead of focusing solely on those components that remain constant (protons), we should always stress those that act as sources of variation: neutrons. Depending on the number of neutrons a hydrogen nucleus possesses, several variant isotopes of this chemical species are generated: protium, deuterium, and tritium. The number of neutrons in a nucleus has very little effect on an atom’s chemical properties, but it does affect its physical properties: some isotopes are more stable and enduring, while others decay much faster. When we consider not one atom but an entire population of individual atoms, the relative abundances of isotopes, or more exactly, the statistical distribution of isotopic variation, contains information about the historical processes that produced the members of the population.

Let’s briefly sketch what is known in astrophysics about these historical processes. Although large populations of individual hydrogen and helium atoms were produced under the most intense conditions, those prevailing at the birth of the universe, atoms of other chemical species had to wait hundreds of millions of years for the formation of stars. Today the nuclei of most atoms are assembled in stars, a process of assembly known as stellar nucleosynthesis. The extensive and the intensive properties of stars (their size and their temperature gradients) define their capacity to act as assembly factories for atoms of different species: the larger and hotter the star, the heavier the atoms it can put together. The smaller stars, like our sun, are only hot enough (10 million degrees Kelvin) to burn hydrogen as fuel and produce helium as a product. At much higher temperatures (over 100 million degrees), helium itself can be burned as fuel and yield as products carbon, oxygen, and nitrogen. At even higher intensities (a billion degrees) carbon and oxygen become the fuel, while the products are atoms of the species sodium, magnesium, silicon, and sulphur. As intensities continue to increase silicon is burned as fuel to produce iron, and finally a maximum of intensity is reached in the process of explosive nucleosynthesis, in which the heavier species are created during the violent events known as ‘supernovae’.10 In this individuation process neutrons play a crucial role, because only highly stable isotopes can last long enough in the extreme stellar environment to serve as a platform (or intermediate step) for the assembly of more complex nuclei.

We can imagine that, confronted with this information, Aristotle would be unimpressed, since he could argue that the details of how a house is built, or a patient healed, or an atom assembled are less important than their formal causes. In particular, he could argue that regardless of what happens in stars, only a certain number of atomic species exists, a number that can be considered to have been fixed for all time. There is, in fact, some truth to this objection which is why we need to add to an ontology of individual atoms the singularities that structure the space of possible atomic species. Let’s first consider the regularities exhibited by these species as given in the Periodic Table. The table itself has a colourful history because several scientists had discerned regularities in the properties of chemical species (when ordered by atomic weight) prior to Mendeleev stamping his name on the table in 1869. Several decades earlier, for example, one scientist had already seen a simple arithmetical relation between triads of elements, while others noticed that certain dispositions (like chemical reactivity) recurred every seventh or eighth element. These rhythms were so compelling that when gaps in the arrangement were found, rather than taking these as indicating that there was something wrong with the Table, gaps were left in it, acting as daring predictions that as yet undiscovered species had to exist. Mendeleev predicted the existence of germanium on the basis of a gap near silicon. The Curies later on predicted the existence of radium on the basis of its neighbour barium.11 What accounts for these underlying rhythms at the chemical heart of matter?

To answer this question we need to bring back some of the mathematical ideas recruited in the previous chapter to make sense of the concept of the diagram of an assemblage. We saw that an actual process of progressive differentiation, like the differentiation of ancient hydrogen and helium into many chemical species, has as its virtual counterpart a cascade of broken symmetries. When we characterise a mathematical entity by the number of transformations that leave it invariant, the larger the number of transformations, the more symmetry the entity is said to have. A symmetry-breaking transition is an event changing an entity from one with more symmetry to one with less, a cascade being a series of such events. Let’s imagine a series of events that generates a family of forms starting with a sphere, a figure that remains invariant under any number of rotations. First, we can imagine the sphere losing rotational symmetry, becoming a two-lobed figure, invariant under only half the number of rotations. Then, as this figure loses further rotational symmetry it becomes a four-lobed figure, which, finally, becomes an even less symmetric six-lobed figure. If we imagine these geometrical figures as the shapes that the ‘orbits’ of electrons surrounding the nucleus can adopt at different levels of intensity, we can explain the different rhythms characterising the Periodic Table.

Historically, the first periodicity to be noticed was that the properties of elementary substances recurred every eight species. Later on, however, as more substances were isolated and purified, chemists realised that the rhythm was more complex than that: it repeated twice with a cycle of eight; then it repeated twice more with a cycle of eighteen; then twice more with a cycle of thirty-two. Adding to this the ‘lone’ ancient species, hydrogen and helium, the series becomes 2, 8, 8, 18, 18, 32, 32. How can the symmetry-breaking cascade just mentioned explain this series? Electrons do not move along sharply defined trajectories, since they behave like waves, but rather they inhabit a cloud or statistical distribution referred to as an orbital. But although these fuzzy clouds are not rigid spheres, they can still be assigned a degree of rotational symmetry. The set of possible orbital forms may be unfolded by injecting increasing amounts of energy into a basic hydrogen atom. The single electron of this atom inhabits an orbital with the symmetry of a sphere. Exciting this atom to the next level yields either a second larger spherical orbital, or one of three possible orbitals with a two-lobed symmetry (two-lobed figures with three different orientations). Injecting even more energy, we reach a point at which the two-lobed orbital becomes a four-lobed one (with variants oriented in five different directions), which in turn yields a six-lobed one as the excitation gets sufficiently intense. In reality, this unfolding sequence does not occur to a hydrogen atom but rather to atoms with an increasing number of protons in their nuclei, boron being the first chemical species to use the non-spherically symmetric orbital.12 Coupling this series of electron orbitals of decreasing symmetry to the requirement that only two electrons of opposite spin may inhabit the same orbital, we can exactly generate the series 2, 8, 8, 18, 18, 32, 32. Thus, we can confidently affirm that the symmetry-breaking cascade correctly represents the structure of the space of possible orbitals, and hence an important component of the possibility space of chemical species. (The latter would also need to include the space of possible combinations of protons and neutrons, structured by singularities of the minima and maxima type.)

Let’s summarise the argument so far. In assemblage theory there is no such thing as atoms in general, only populations of individual atomic assemblages. The kind and number of some of the components of the assemblage (protons, electrons) ensures that properties are shared by all atoms of a given species, while the kind and number of other components (neutrons) set those properties in variation. The electronic structure of an atom does determine its chemical capacities (as well as its place in the periodic classification) but it should not be treated as the essence of a chemical species. This manoeuvre takes the finished product of an individuation process, a fully assembled atom, and makes one of its properties (the number of electrons in the outer orbital) into a necessary and sufficient condition for its belonging to an eternal category. This eliminates the historical process that produces the atoms, rendering invisible the role played by intensities – the higher the stellar intensity the more complex the synthesis – as well as the role played by isotopic variants, the stability of which determines the actual production pathway from one species to another. In addition, it fails to reveal the deeper connection that exists between the electronic structure of different species, a connection captured by an analysis of the possibility space for electron orbitals. In place of an essentialist metaphysics, in which the world is already segmented by logical categories, some more specific, others more generic, we need a metaphysical approach in which the world begins as a continuum of intensity that becomes historically segmented into species. In the case of atomic assemblages, the intensive continuum is embodied in stars, balls of plasma possessing a minimal segmentation but not entirely undifferentiated, since stellar bodies have an intensive structure defined by differences of temperature, pressure, and density. The possible ways of segmenting this continuum are not given by a logical subdivision of a genus into species, but by a virtual structure that can be captured mathematically.

Let’s move on to tackle a more complex case of individuation, the one we need to replace the genus ‘animal’ and the species ‘human’. Today it is widely accepted that a biological species is as singular, as unique, and as contingent as an organism: species are born when their gene pool becomes closed to external flows of genetic materials through reproductive isolation, and they can suffer an equally historical death by extinction. This implies that species are individual entities, ontologically speaking.13 Moreover, reproductive isolation is a variable parameter. Human beings are strongly isolated from other primates, because our sperm is not capable of fertilising their eggs, and vice versa. Animals like horses and donkeys display a lesser strength, since they can fertilise one another but their offspring, mules, are infertile. The gene pools of many plants are even less strongly isolated, the plants retaining a capacity to hybridise throughout their lives. Finally, many microorganisms are so promiscuous that they do not even form stable species, but more transient strains. This variability results in very different forms of biological segmentation. The genetic materials of the earliest bacteria were not encapsulated within a nucleus, a condition that still allows their descendants to transfer genes horizontally, as opposed to vertically across generations, a transfer that allows them to rapidly acquire capacities they previously lacked (such as resistance to antibiotics). The ancient predators of those bacteria, on the other hand, encased their genetic materials into a nucleus, losing their ability to exchange genes freely, but acquiring the capacity to become reproductively isolated and hence to undergo a progressive differentiation into distinct species. The evolutionary histories of these two types of micro-organisms (eukaryotes and prokaryotes) was therefore different: the former went on to form a plurality of gene pools more or less segmented from each other, while the latter generated what is basically a single unsegmented gene pool spanning the entire planet.14

We may conclude from this that the relation between organisms and species is not one of membership in a general category. Rather, species are assemblages of organisms, or more exactly, of reproductive communities composed of organisms. The anatomical resemblances we use to classify the latter are not necessary but contingent, the result of a common history in which similar challenges were faced from predators and parasites, scarce resources and climatic changes. Selection pressures tend to homogenise a species’ gene pool over time, allowing us to infer that its composing organisms will tend to share more genes in common with each other than with organisms of other species. But as in the case of atoms, we must consider not only what stays the same but also what varies. Without a constant production of genetic differences by accidental mutations or sexual recombination, selection pressures would have no raw materials to operate on: no low fitness variants to filter out, or high fitness variants to promote. In addition, we must add to this account that biological species not only encapsulate genetic materials but also capture and envelop mineral nutrients and energy. This other territorialisation is what makes one species a reservoir of edible flesh relative to another species, creating the gradients of biomass that drive flows across the food webs that compose an ecosystem.

What would correspond to the intensive continuum within which plant and animal species would appear as segmentations? First of all, as in the case of stars, the term ‘continuum’ does not imply an absolute absence of segmentation. Stars may not be segmented into chemical species – except those that they produce and burn as fuel – but they certainly are segmented at a smaller scale by sub-atomic particles. Similarly, when we imagine an ecological continuum, we should treat it as pre-segmented physically or chemically, but not biologically. Prior to the advent of living creatures our planet already possessed physical gradients, differences in temperature driving energy flows, as well as chemical gradients created by the coupling of materials with different Ph (some acid, some alkaline) or of materials with different capacities for oxidation and reduction. These chemical gradients were capable of driving not just flows of energy but also flows of matter. The first biologically discontinuous segments to emerge, flat layers of motionless bacteria inhabiting the interface between ocean water and the sediment at the bottom, had to tap into those gradients to survive, proliferate, and evolve.15 The earliest forms of life fuelled themselves by fermenting available minerals, but after a billion years they evolved the capacity to tap into the solar gradient. After another long period of time they evolved the ability to tap into the gradient of concentration of oxygen that had formed as a by-product of their own activity. Compared to fermentation, photosynthesis and respiration brought about an enormous increase in productivity, and the surplus of biomass that resulted became another gradient that could be tapped into by the ancestors of today’s amoebas and paramecia. The addition of these ancient predators generated a simple and barely differentiated food chain, but one that had the ability to progressively differentiate into many species as new ecological niches opened up and novel species came into being to occupy those niches.

The addition of an intensive component to the basic evolutionary picture, while not as uncontroversial as the latter, is also widely accepted today. But this feeling of familiarity begins to dissipate when we add the next component of an assemblage: the virtual structure of possibility spaces constituting its diagram. Metaphysically, this involves a proper conceptualisation of a topological animal that can be folded and stretched into the multitude of different animal species that populate the world. As Deleuze and Guattari put it:

A single abstract Animal for all the assemblages that effectuate it. A unique plane of consistency or composition for the cephalopod and the vertebrate; for the vertebrate to become an Octopus or Cuttlefish, all it would have to do is fold itself in two fast enough to fuse the elements of the halves of its back together, then bring its pelvis up to the nape of its neck and gather its limbs together into one of its extremities.16

Topological transformations like these cannot, of course, be performed on adult animals: only the embryos of those animals are flexible enough to endure them. A well-studied example, one already recognised by Darwin, is the tetrapod limb. We can think of this component of an animal assemblage as an undifferentiated virtual limb that can be actualised as a bird’s wing, as the single-digit limb of a horse, or as the human hand with its opposable thumb. It was identified early on as an example of adaptive radiation, leading to the search for an ancient homologous limb pattern that could be the ancestor of all of today’s limbs. More recently, however, it has become clear that comparing adult forms for similarity is not the correct way to conceptualise this phenomenon. Rather we need to look to embryology, that is, to an individuation procedure, to identify homologies of process.17

The first problem that we encounter when trying to clarify the concept of a topological animal is that we cannot just imagine the foldings and stretchings that a human hand must undergo to become a wing or a hoof, like the lengthening of the digits or the inhibition of their growth. In addition, we must explain how these transformations can be inheritable. In the terms we have been using, we need to conceptualise an assemblage in which not only the settings of the territorialisation parameter are important but also those of the coding parameter. Unlike the former, which in many cases can be conceived as a continuous parameter space modelled using differential equations, the space of possible genes is entirely discrete and has no intrinsic spatial order. We do not know of any general way to approach these combinatorial spaces, nor do we know how to conceptualise their virtual structure. So let’s begin with what we do know. The genetic code is by now well established and used routinely in industry. Both genes and the proteins they code for are linear sequences of molecules differing only in their components: nucleotide molecules in the case of genes, amino acids in the case of proteins. The genetic code is simply a way of mapping one type of molecular sequence on to another, three nucleotides corresponding to each of the twenty amino acids used by biological creatures, the correspondence itself being arbitrary, a kind of frozen evolutionary accident.

What do we know about the spaces of possible genes and possible proteins? We have solid insights about their size, because the number of possible sequences of a given length can be calculated by taking the number of available components and raising it to the number representing the maximum possible length. If, as we just said, proteins can draw from a repertoire of twenty possible amino acids, then a very short protein five amino acids long can exist in over three million different combinations (the number twenty raised to the fifth power). For more realistic lengths, like the 300 amino acids composing an average enzyme, the number of combinations becomes practically infinite. The number of possible genes is smaller, because genes are formed of only four components, but their lengths tend to be larger since each amino acid demands three nucleotides to be specified. Thus, in either case we are considering combinatorial spaces that grow explosively as the length of the sequences increases. But how can we study the structure of these infinite spaces if they lack any intrinsic spatial order? One strategy would be to impose on them a non-arbitrary order, that is, an order that has some connection to the actual dispositions of the molecular sequence in question. In the case of genes the most important dispositions are their capacity to replicate, as well as their tendency to undergo copying errors (mutations) during replication. Hence, a reasonable spatial order can be imposed if we arrange each sequence of nucleotides so that it has as neighbours all sequences that differ from it by only one mutation. If a gene were in direct contact with all its one-mutant neighbours, that is, with all the genes into which it could be transformed by a single copying error, then the imposed connectivity on the space would make sense: a connected path starting at any one gene would be a path that evolution could follow.18

This arrangement may seem much too complicated: the space must include every variant that can be created by varying each nucleotide along the full length of a given gene, and each variant must get its own dimension. Yet other possibility spaces have a similar problem. The state spaces examined in the previous chapter can have very high dimensionality if the phenomenon being modelled can change in a large number of different ways. On the other hand, a complex phenomenon is extremely simplified, since the state in which it can be at any moment becomes a single point, and its history a single trajectory. A similar idea applies to the space of possible genes: however complex it may be in terms of its many dimensions, the spatial arrangement simplifies how genetic evolution is visualised since it becomes a single trajectory from one neighbour to the next, driven by events producing one mutation at a time. To capture the selection pressures guiding these evolutionary walks we can superimpose on the combinatorial space a set of fitness values, one for each possible sequence. This yields a distribution of singularities in the form of a distribution of maxima and minima of fitness.19 We can imagine the singularities as the highest points of peaks, and lowest points of valleys, in a fitness landscape. The simplest landscape would be one possessing an easy-to-reach single peak (a global maximum), a peak that evolutionary walks could simply climb and then inhabit. This is the case captured by the misleading slogan ‘survival of the fittest’. More realistic versions should possess a plurality of local maxima, each standing for an adaptive compromise to conflicting selection pressures. While the landscape with a global maximum seems to deny a role for history – we could identify the maximally fit species with the form it necessarily had to adopt – the one with multiple local optima has the opposite consequence, since the peak a given species happened to climb is a contingent historical fact. In this case, once a peak of fitness has been climbed a species is literally trapped there, because genes below the peak are by definition less fit, so descending from it to climb a higher peak is prevented by selection pressures. Genetic drift, on the other hand, may help species break away from a local trap by providing a random source of variation not subjected to the filtering effects of natural selection.

This is a simple but rigorously defined way of constructing a possibility space for genes. It is too simple because only one source of variation is included (mutation) and because the notion of fitness is well defined only for the immediate products of genes: proteins and their catalytic capacities.20 Using this possibility space we could explore the process of progressive differentiation of proteins that led the earliest unicellular organisms to discover photosynthesis and respiration. But it would not be very useful beyond that for several reasons. One is that, unlike mutation, sexual recombination involves producing new genomes from sequences that are separated in the possibility space. If we imagine a nucleotide sequence belonging to the mother’s chromosome perched on one local fitness peak, and a sequence belonging to the father’s on another, combining the two may very well produce a sequence located at an intermediate fitness minimum. There are some proposed solutions to this problem, such as requiring that the peaks and valleys of fitness form a ‘rugged landscape’, in which there are no deep valleys between tightly clustered peaks, but it is too early to say whether this solution will work.21 Another problem is that once we move from proteins to multicellular organisms, the fitness of each possible molecular sequence is much harder to define. Finally, unlike proteins, the bodies of large animals are not produced directly from genes but involve a complex embryological process that progressively differentiates a single cell (a fertilised egg) into the several hundred different cell types of a newborn, and through foldings, stretchings, and migrations, makes organs out of those cells.

Let’s tackle the third problem. To understand how to transform a fertilised egg into an organism we do not need to model the effect of every gene but only of a small subset, that is, we can forget about genes performing routine housekeeping tasks on every cell and focus on those that cause the differences between different cell types. Given that all the cells that compose a multicellular organism have the exact same DNA, there must be special genes that turn other genes on or off in different cell types as required. These special genes code for proteins that have DNA itself as their target, binding to a portion of it to determine if another gene ‘downstream’ will or will not be expressed. This type of gene can itself be further differentiated into those that control nearby downstream genes, and those that, in addition, are controlled by upstream genes. Producing a protein that switches other genes on or off, while simultaneously being capable of being switched on or off, gives these genes the ability to form circuits and networks of switches. If we consider that the central processing unit of a desktop computer is just such a network of switches (And-gates, Or-gates, Not-gates), the power of this type of genes becomes obvious.

The switches themselves are non-coding regions of DNA to which proteins attach, and are typically between six and nine nucleotides long: this yields between 4,096 (46) and 262,144 (49) possible permutations. The genes that code for proteins performing the switching are relatively few in number. Assuming that only 500 of the 20,000 coding genes in the human genome are involved gives us 250,000 possibilities for two-gene circuits; over twelve million possibilities for circuits of three genes; and more than six billion possibilities for circuits of four genes.22 Thus, focusing on regulatory genes alone leads us to consider possibility spaces of a different kind: not the space of possible nucleotide sequences but the space of possible circuits. We can restrict the size of these other spaces by concentrating only on genes for which there is evidence of direct involvement in the specification of body form during embryology. These are the so-called Hox genes. The phylum to which vertebrates belong, for example, has four Hox clusters (thirty-nine genes) while the one to which insects belong has two Hox clusters (eight genes).23 As before, we need to superimpose on the space of possible circuits a set of fitness values. The selection pressures determining these values, however, should not be the traditional external ones (predators, parasites) but rather internal selection processes that maintain the coherence of existing circuits by selecting mutations that preserve it and eliminating those that do not.24

Several characteristics set Hox genes apart: they are extremely old, predating the differentiation of multicellular organisms; they are clustered together in the animal genome; they display striking similarities across body plans (such as those of vertebrates, molluscs, or insects); and more importantly in a discussion of the segmentation of an intensive continuum, their spatial arrangement has intriguing correspondences with the distribution of body parts, and body part segments, that characterises an adult body. The first set of correspondences is that between the symmetries and broken symmetries (or polarities) of the adult form, and the axes that, like longitude, latitude, and altitude, define the geography of the embryo. All adult vertebrates have bilateral symmetry, the right and left sides being roughly invariant under the transformation mirror-imaging, but head and tail, as well as front and back (top and bottom in horses) break this symmetry. The population of cells that constitutes an early embryo develops an east–west and a north–south axis, corresponding to these two broken symmetries, by activating certain genes on stripes of cells. In effect, what used to be a continuous cellular population becomes segmented along longitude and latitude, at progressively finer scales.25 The details of the segmentation vary across species. Thus, while the body plan common to all vertebrates specifies a stiff vertebral column, the way in which it is segmented (the number and type of vertebrae) depends on the species.26 Correspondences also exist between the modular construction of the adult form and a modular use of Hox genes. Animals are assemblages of components, many of which are repeated modules differing only in kind and size. For example, limbs are made of parts (thigh, calf, ankle; upper arm, forearm, wrist) and their extremities are also made out of variably repeated modules, like the different bones of fingers and toes. A limb begins its actualisation as a small bud that projects out of the embryo at a specific location along the east–west axis. Then the growing bud is segmented by its own sets of local longitudes and latitudes, each segment containing cellular sub-populations in which specific genes are switched on. The extremities of these limbs are, in turn, further segmented through a set of finer subdivisions, prefiguring the future digits.27 Although strictly speaking the process of embryogenesis refers to the individuation of organisms, all organisms of the same species share the same space of possible circuits of genes, so a diagram of this possibility space should be considered a virtual component of the individuation of species.

Let’s now compare the two processes of individuation. The individuation of atomic species is comparatively simpler to describe because it involves only one parameter, territorialisation, while the individuation of species needs a second parameter: coding. The assembly and final form of atoms can be derived directly from their diagram (symmetries of electron orbitals, minima of energy in proton–neutron interactions), but the assembly and shared form of conspecific organisms involves a very specific coding by Hox genes. Moreover, while in the first case territorialisation is measured in its most basic form, distance from thermodynamic equilibrium, the organisms composing a species at any one time encapsulate not only matter and energy but also genes, so the first parameter involves the creation of discrete boundaries between species playing different ecological roles (predator, prey, parasite, host, symbiont) as well as barriers to the flow of genetic materials (reproductive isolation). A second difference is the nature of the matrix within which the process of individuation takes place. The medium formed by the stellar environment contains all the raw materials needed to assemble atoms, as well as the gradients to drive the assembly process. The matrix for the individuation of species, on the other hand, is not as tangible as a discrete ball of plasma floating alone in space. It consists of flows of energy and mineral nutrients on planet Earth, one driven by the solar gradient, the other by chemical gradients. At human timescales of observation these flows are invisible, but at temporal scales long enough to encompass several births and deaths, organisms would seem like temporary coagulations in these continuous flows. In addition, there is the equally invisible flow of genetic materials – vertically across generations and horizontally across strains – a flow which was at first more or less continuous in unicellular organisms without a nucleus. After the three basic strategies to tap into energy gradients had been developed within this continuum, they did not have to be invented again: the creatures that followed, with their encapsulated nucleus and their capacity for speciation, simply absorbed those organisms as functional modules, trapping them within their membranes and establishing a more permanent symbiosis with them.28 They still exist inside every plant and animal cell, as chloroplasts and mitochondria, reproducing on their own but separated from the global prokaryote gene pool. Thus, in a very real sense, the lightly segmented gene pool of the original bacteria was an intensive continuum from which crucial pieces of metabolic machinery could be extracted and incorporated into more rigidly segmented creatures.

These two individuation processes give us a sense of what happens at the birth of atomic and biological species, but to conclude this chapter we should add a few observations about how they go on to live their lives. A batch of recently produced hydrogen atoms, for instance, has a variety of possible histories ahead of it. Some of these atomic assemblages may go on to exist autonomously, their state determined by the distribution of singularities in their diagrams. The latter may determine that the state in which two atoms are bound together corresponds to a lower minimum than the two atoms on their own, the state being therefore more energetically favourable. Given this inherent tendency, we will be more likely to find atoms of hydrogen as diatomic molecules, existing in populations in a fluid state, segmented only by convection cells or turbulent eddies. But other hydrogen atoms may forgo autonomy and go on to form parts of larger molar entities, such as water molecules. Atoms have the capacity to form covalent bonds – extremely strong bonds formed by the sharing of a pair of outer shell electrons – with other atoms. This is the kind of bond holding together water molecules, so in this case the hydrogen atoms become part of a larger, more rigidly segmented whole. But although in this bound state the atoms have become more territorialised, they can still play a deterritorialising role. In addition to their ordinary bonding capacity, hydrogen atoms possess a singular capacity to form weaker bonds, appropriately called ‘hydrogen bonds’. This ability can only be exercised if the group of atoms that is the target of the bonding operation is electronegative, and if the hydrogen atom itself is covalently attached to a group of atoms that is electronegative. But if these conditions are met, hydrogen bonds allow the formation of less rigid wholes, some of which can use the added flexibility to store information. This is the case with chromosomes: their identity is preserved through time by covalent bonds, but their capacity to self-replicate is determined by hydrogen bonds, because the two strands of the double helix must be easily unglued, and new nucleotides easily glued to each strand serving as a template.29

If the lives of hydrogen atoms can be this eventful, it is not hard to imagine that a biological species has many more adventures available to it, since it can follow movements of deterritorialisation and decoding. A species typically exists in the form of several reproductive communities inhabiting distinct ecosystems. The role played by the members of these communities in a food web, the niche they occupy, is more or less rigidly determined. But historical events that increase or decrease the availability of niches can open or close opportunities for a species to change. This effect is easier to visualise if we consider not single species but classes of species, like mammals and reptiles. About 60 million years ago, most niches were occupied by highly differentiated reptiles, while mammalian species were mostly undifferentiated: a few nocturnal species of furry, rat-like creatures that gave a pale picture of the fantastic variety that we see today, including giraffes and rhinoceros, dolphins and whales, chimpanzees and humans. It is as if the latter had been there virtually, but repressed by the absence of niches within which their differences could be expressed. Then a contingent event, a mass extinction caused by a meteor striking the planet, emptied many positions in the existing food webs and created opportunities for mammalian differentiation. This is only the simplest of deterritorialising possibilities. A more interesting case involves relations between different niches. Predators and their prey, for example, can enter into ‘arms races’ in which any inheritable improvement in the ability to evade predators or capture prey acts as a selection pressure for the development of counter-measures. When this mutual stimulation is maintained over many generations, predator and prey species can force each other to adaptively modify their genetic identity, and to be carried away by a mutual line of flight. Other ecological relations, like symbiosis, can also lead to deterritorialisations. As Deleuze and Guattari note in the case of plants and the insects that pollinate them:

The orchid deterritorializes by forming an image, a tracing of a wasp; but the wasp reterritorializes on that image. The wasp is nevertheless deterritorialized, becoming a piece in the orchid’s reproductive apparatus. But it reterritorializes the orchid by carrying its pollen . . . a becoming-wasp of the orchid and a becoming-orchid of the wasp. Each of these becomings brings about the deterritorialization of one term and the reterritorialization of the other; the two becomings interlink and form relays in a circulation of intensities pushing the deterritorialization ever further.30

Biological species also follow movements of decoding, best illustrated by the emergence of behaviour not rigidly coded by genes. The progressive detachment of learning from inherited patterns can be followed by comparing the different forms of learning in the sequence classical (Pavlovian) conditioning, instrumental conditioning, and complex skill acquisition. The first form of learning uses as its basis a rigidly coded reflex – such as the licking behaviour of bees that follows the contact of their antenna and a sugary solution – and adds associations with various ecologically meaningful stimuli. Thus, a honey bee can be trained to associate the presence of nectar with a variety of stimuli that are natural signs (indices) of such presence: floral aroma, expanses of floral colour, and symmetric petal arrangements. The second form of learning is more decoded, involving the acquisition of habits through the association of rewarding experiences and existing behavioural patterns that occur spontaneously but with low probability. The kind of novel behaviours this can produce are easy to observe in the case of circus animals. Finally, we can go beyond learning through habits into the acquisition of skills. In many cases this involves not just rewards, but the presence of an animal that has already mastered the skill and can serve as a model to the learner, with repeated practising leading to mastery. The song of territorial birds like the nightingale or the blackbird, with their elaborate stylistic variants and endless flourishes, is a good illustration.31 But as we have already pointed out, knowhow – knowledge taught by example and learned by doing – reaches its maximum expression with the human species. There seems to be no end to the number of skills that human beings can master, ranging from productive abilities – the proliferation of which is attested by the progressive differentiation of labour into many specialities, blacksmiths, carpenters, potters – to unproductive abilities that nevertheless express the human body’s potential for decoded behaviour, as illustrated by the skills of jugglers, tight-rope walkers, and trapeze artists.

Finally, we should consider the various interactions between movements of deterritorialisation and decoding, the first liberating some anatomical components (at the expense of others), the second making their behaviour more versatile. Such was the adventure of the human hand: the erect posture of early humans detached it from the function of locomotion, simultaneously depriving the feet of their prehensile abilities, while the advent of stone tools connected it with a cultural line of flight that generated an increasing variety of manual skills. To conclude with the words of Deleuze and Guattari:

Not only is the hand a deterritorialized front paw; the hand thus freed is itself deterritorialized in relation to the grasping and locomotive hand of the monkey . . . [There were also] correlative deterritorializations of the milieu: the steppe as an associated milieu more deterritorialized than the forest, exerting a selective pressure of deterritorialization upon the body and technology (it was on the steppe, not in the forest, that the hand was able to appear as free form, and fire as a technologically formable matter). Finally, complementary reterritorializations must be taken into account (the foot as a compensatory reterritorialization for the hand, also occurring on the steppe). Maps should be made of all these things, organic, ecological, and technological, maps one can lay out on the plane of consistency.32

Notes