1 (life) ÷ 0 (blackness) = ∞ − ∞ or ∞ / ∞: On Matter Beyond the Equation of Value

1. A thing, affair, concern
2. That which constitutes or forms the basis of thought, speech, or action
3. In purely physical application
4. The substance, or substances collectively, of which something consists; constituent material, esp. of a particular kind. [rare]
Contrasted with form:
22. Philos.
a) In Aristotelian and scholastic philosophy: that component of a thing which has bare existence but requires an essential determinant (form) to make it a thing of a determinate kind.
b) In scholastic philosophy: the result of the first act of creation, i.e. substance without form. Obs
c) In Kantian philosophy: the element in knowledge supplied by or derived from sensation, as distinct from that which is contributed a priori by the mind (the forms of intuition and the categories of the understanding).1

What if blackness referred to rare and obsolete definitions of matter: respectively, “substance … of which something consists” and “substance without form”? How would this affect the question of value? What would become of the economic value of things if they were read as expressions of our modern grammar and its defining logic of obliteration? Would this expose how the object (of exchange, appreciation, and knowledge)—that is, the economic, the artistic, and the scientific thing—cannot be imagined without presupposing an ethical (self-determining) thing, which is its very condition of existence and the determination of value in general?2 Black Lives Matter, as both a movement and a call to respond to everyday events of racial violence (the killing of unarmed black persons by police) that rehearse the ethical syntax that works through/as the liberal democratic state,3 signals a political subject emerging in the scene of obliteration through a sentence without a (self-determined) subject.

What I do in this text is activate blackness’s disruptive force, that is, its capacity to tear the veil of transparency (even if briefly) and disclose what lies at the limits of justice. With a thought experiment that I call the Equation of Value, designed to help the imagination break away from the enclosures of modern thought, this speculative exercise reaches for The Thing,4 which is the referent of blackness, or that which in it is exposed as the excess that justifies otherwise untenable racial violence.5

When taken not as a category but as a referent of another mode of existing in the world, blackness returns The Thing at the limits of modern thought. Or, put differently, when deployed as method, blackness fractures the glassy walls of universality understood as formal determination. The violence inherent in the illusion of that value is both an effect and an actualization of self-determination, or autonomy. My itinerary is simple. It begins with considerations of the role of determinacy—formal determination articulated as a kind of efficient causation—in modern thought, and closes with a proof of the Equation of Value, intended to release that which in blackness has the capacity to disclose another horizon of existence, with its attendant accounts of existence.

Installation view of Otobong Nkanga, In Pursuit of Bling, 2014. Courtesy Lumen Travo Gallery.

“Without Properties”

In her 2014 installation In Pursuit of Bling, Otobong Nkanga worked with mica and other minerals that glitter-image colonial violence, thereby making it impossible not to see the hole in the Green Hill (the site of a German mining operation in Namibia)—especially when I think about the minerals used in everything around me regardless of where they come from, precisely because they come from another “place of obscurity.”6 Listening to the artist’s comments on these minerals, I wonder about the many ways in which her intention activates blackness’s creative capacity, which at first manifests as a disruptive force. I find this in her distinction between what she terms “space of shine” and “places of obscurity,” which comes through in images, artifacts, and movements—exhibitions and performances—and which exposes obvious but frequently obscured linkages between spaces of plenty and places of scarcity. Much like blacklight, Nkanga’s intention seeps through In Pursuit of Bling, illuminating that which must remain obscure for the fantasy of freedom and equality to remain intact.7

In Pursuit of Bling, however, inhabits an artistic scene still framed by what the postcolonial literature scholar and critic David Lloyd calls “Western aesthetic culture,” which not only produces the “disposition of the subject,” as figured in Kant’s disinterested “subject of judgement” or “the Subject without properties,” but also provides the very condition of possibility for the notion of a “common or public” domain that holds the Kantian rendering of humanity as an ethical entity.8 When describing In Pursuit of Bling, Nkanga notes that its chapters do several things, including to “look at the notion of power” (by which she means colonial and imperial power as well as capitalism) “through the notion of shine.” Reading the work with her intention, I find that it does more than comment on power. For In Pursuit of Bling, like other works in her portfolio,9 performs both as an item in the anticolonial arsenal and a site of confrontation; that is, it works for the exposure of how colonial violence remains active in the global present. In doing so, it punctures the presumed transparency of the subject of aesthetic culture, whose whole ethical framework rests on a formulation of universality held by our modern formalized syntax. For the most part, what I do here is try to emulate Nkanga’s artistic intervention into Western aesthetic culture with an analytic formal artifact—that is, the proof of the Equation of Value—which might implode the basis of the ethical grammar that cannot but provide a negative answer for the never-asked question for which Black Lives Matter demands a different answer.

Hence, I do not engage with what Sylvia Wynter claims to be the core of racial subjugation, namely, the hierarchical division of the human between rational/irrational, or “selected/dysselected.”10 My critical move here is not about ideological unveiling (as in exposing how European Man “overrepresents” the human, thus disavowing all other modes of being human); nor does it attempt to delineate an outside space from which to expose that “other” side of the “color line” dividing white/European (human) from nonwhite/non-European (nonhuman). For I am not interested in a transcultural (transcendental or physiological or symbolic) human attribute that would be both the condition of possibility for what is activated in Western European being and all other modes of being, and that which has already been mapped by anthropology, cognitive science, or neurology. My attention to Nkanga’s intention immediately takes me away from the usual analytical path. It takes me further in/down/through but beyond the observed divisions, beyond what the artist has already offered in the minerals which in her work expose the links between “places of shine”/“spaces of obscurity,” after and against that which gives meaning to the “/” that signals it. More particularly, I am interested in the ethical indifference with which racial violence is met—an indifference signaled by how the obvious question is never (to be) asked because everyone presumes to know why it can only have a negative answer. For this reason, I move to expose how determinacy, which along with separability and sequentiality constitutes the triad sustaining modern thought, operates in the ethical syntax in which this indifference makes sense as a (common and public) moral stance.11

When considering the “Subject without properties” it is always helpful to recall its genealogy, in particular how it emerged in efforts to answer another question that very few thinkers explicitly formulated: How to describe the world in such as way as to make it possible to establish that the human mind can know the truth of things in it without the need for divine revelation? This genealogy usually opens with Francis Bacon and René Descartes as crucial players in assembling tools and scientific programs intended to ensure just that. What interests me in their attempts is the account of causality they compile through a selective appropriation of Aristotle’s famous four causes, namely, material, formal, final, and efficient.12

Frontispiece of Francis Bacon’s book Sylva Sylvarum: or, A natural history, in Ten Centuries (1669). 

Bacon and Descartes emphasize efficient causality—that is, the idea of cause and effect—in modern knowledge. Though each grabs onto efficient causality for different reasons—or, to put it better, in the effort to address different issues—both do so in the preambles to knowledge programs devised to break through the mold of medieval scholasticism held together by authority, syllogism, and an image of the world governed by Aristotle’s final and formal causes. Like his contemporaries, Bacon postulated that scientific knowledge should deal with what was known as “secondary causes,” through which the divine author performs his work in/as nature. In the New Organon (1620), Bacon, advancing an ambitious knowledge program intended to replace Aristotelian orthodoxy, claims that material and efficient causes are all that matter for understanding the book of “God’s Work,” i.e., for understanding nature. Drawing from pre-Socratic philosophers such a Democritus, Bacon describes the elements constituting the world as “corpuscles” (atoms), which carry in themselves the force—or what he calls “form”—imprinted on them by the divine author. Nevertheless, while celebrated for introducing the inductive and experimental methods into Western science, Bacon does not occupy the same position as Descartes, precisely because, in addition to providing an acceptable ground for the claim that the human mind alone can decipher the book of nature, Descartes successfully demonstrated that the mind itself was such a ground when he established its existence and essence as the formal (thinking) thing, or res cogito.

Not surprisingly, formalization is the most evident contribution Descartes made to modern knowledge. For Descartes locates efficient causality in the very movement of thought that establishes I think, therefore I am as the ultimate ground for ontological and epistemological statements.13 He was not the first or the only one to make a case for replacing syllogistic logic with mathematical necessity; Galileo had done the same. Nevertheless, effectivity, or efficient causality, was central to his claim that the mind has direct access to truth because it is supported by how adequately its workings are captured by mathematical tools and reasoning. Effectivity also governs Descartes’s investigations of nature. For instance, in “The Treatise on Light,” Descartes, like Bacon and other philosophers of that era, privileges the investigation of nature from the point of view of the examination of what Galileo called “local motion,” that is, the spatial dislocation of bodies:

Someone else may if he wishes imagine the “form” of fire, the “quality” of heat, and the “action” of burning to be very different things in the wood. For my own part, I am afraid of going astray if I suppose there to be in the wood anything more than what I see must necessarily be there, so I am satisfied to confine myself to conceiving the motion of its parts. For you can posit “fire” and “heat” in the wood and make it burn as much as you please: but if you do not suppose in addition that some of its parts move or are detached from their neighbors then I cannot imagine that it would undergo any alteration or change.14

In sum, the emergence of modern science can be described as a shift from a concern with forms of nature, which prevailed in scholastic thought, to an inquiry into the efficient causes of changes in the things of nature. For Descartes, as for Galileo and later for Newton, change (as motion in space and alteration) results from the operation of efficient causes, the effects of which can be mapped mathematically. Resting on the two onto-epistemological components of effectivity and necessity, the “Subject without properties” (i.e., the Cartesian cogito) began a trajectory that would extend beyond the confines of knowledge to become the ruler of modern economic, juridical, ethical, and aesthetic scenes.

Detail of the installation Otobong Nkanga, In Pursuit of Bling, 2014. Courtesy Lumen Travo Gallery.

The Ethical Scene of Value

Negroes are enslaved by Europeans and sold to America. Bad as this may be, their lot in their own lands is even worse, since there a slavery quite as absolute exists; for it is the essential principle of slavery, that man has not yet attained a consciousness of his freedom, and consequently sinks down to a mere Thing—an object of no value.15

The call for Black Lives (to) Matter hides the question it answers: Why don’t black lives matter? More precisely, it exposes how this question already contains the Kantian program and its equation of the universal and the formal—through articulating determinacy as efficient causation, or effectivity—which guides modern ethical, economic, and juridical formations. For, as a tool of modern knowledge, the category of blackness figures the operation of efficient and formal causes (that is, anatomic forms and organic processes) in the production of a racial subject destined to obliteration. Efficient and formal causes are conjoined in Kant’s account of knowledge and the figuring of reality, which is putatively a philosophical presentation of Newton’s natural philosophy. In it, the world becomes an effect, that is, the result of determination—of judgements or decisions reached by the pure intuitions and the categories of the understanding, that is, the tools available to the mind to access the Truth of the things of the world. This is so because, when he repeats Galileo’s and Bacon’s rejection of final and formal causes—in the famous statement that science is not interested in the Thing-in-itself (essence)—Kant defines the limits of knowledge as that which in things—now objects—is available to the senses (movements and alterations). Furthermore, repeating Descartes’s assertion that the mind can only know with certainty that which is akin to it—that is, the abstract or the formal—Kant consolidates modern thought when he elevates the formal (as the pure or transcendental) to that moment that is before and beyond what is accessible to the senses. Only there, as Descartes had stated about a century before, is the mind comfortable dealing with the sort of objects—numbers and geometrical forms—which it can handle without reference to space-time. For only objects exhibiting such attributes can allow for the kinds of statements Kant considers proper to knowledge, that is, statements that add to what is known about something without drawing from experience. My objective in rehearsing this argument in this context is simply to highlight how, while formalization remains central to modern thought, effectivity constitutes the main descriptor of the world, as knowledge becomes interested in what happens (events, movements, and alteration). More importantly, effectivity refers both to the senses’ access to the things of the world (being affected or moved by them) and to the mind’s capacity to resolve the manifold into the basic tools (categories) that the understanding has available for the “higher” moments of cognition—that is, abstraction and reflection—as well as for the task of knowledge—that is, determination.

Among other things, in Kant’s account of knowledge Descartes’s formal thing (the cogito) not only knows itself (its existence and essence) without the aid of its body, but also envelops Bacon’s material and efficient causes, and takes the lead in the task of classifying and measuring nature. For instance, in his Lectures on Logic we find Kant employing the categories of the understanding in a description of Bacon’s method for producing his tables; in this description, Kant subsumes Bacon’s method into his own rendering of Descartes’s “formal I” as a transcendental (a priori, pure, or formal) condition for knowledge.16 Of course, the reference to Bacon’s program is more evident in what is called Kant’s “pre-critical” work. However, determination—that is, the attribution of one, and just one, predicate to a subject—remains central in his rendering of knowledge as a matter of judgement (that is, of decision), as well as in the very definition of the critical task, which privileges the exposure of grounds. In any event, as noted before, determination is crucial to Kant’s notion of synthetic judgements a priori, as it is the term he uses for what Descartes called the “nexus” of consequences that the rational mind follows when attempting to establish something with certainty.17 There is no question that determination is a task of the mind.18

In sum, determinacy as deployed in Kant’s knowledge (scientific) program remains the core of modern thought: it is presupposed in accounts of the juridical and ethical field of statements (such as the human-rights framework) which (a) presume a universal that operates as an a priori (formal) determining force (effectivity), and which (b) produce objects for which “Truth” refers to how they relate to something else—relationships mediated by abstract determinants (laws and rules) that can only be captured by the rational things’ (including the human mind/soul) “principles of disposition.”

With the consolidation of the Kantian knowledge program starting in the nineteenth century, knowing and all other activities of the mind are reduced to determinacy: namely, the assignation of value that refers to a universal (scale or grid), while the object of knowledge becomes a unity of formal qualities (properties, variables, etc.), that is, an effect of judgements that produce it through measurement (degree) and classification (position). Precisely this notion of effectivity lies at the core of the modern ethical program and accounts for how difference plays into it. For there too the assignation of value results not from direct comparison—the juxtaposition of two or more things—but from the operation of a universal (formal or transcendental) mediator—the universal unit of measurement or the universal basis for classification. That is, the assignation of value results from the operation of something which shares in the attributes that universal reason acquired in the late eighteenth century.

Let me briefly elaborate on this by situating blackness in the Kantian design of the modern ethical scene of value.19 Here, as we know, the guiding ethical entity is humanity, which Kant describes as the sole existing thing possessing dignity, that is, possessing intrinsic value. Among existing things, humanity is highest in the figuring of determinacy because it alone shares in the determining powers of universal reason, since it alone has free will, or self-determination.20 Though humanity, in Kant’s formulation, already refers only to Europeans, the closing of humanity’s ethical boundaries occurs in the nineteenth century, both in Hegel’s revision of the Kantian program and in the deployment by scientists of man and society of the tools of scientific reason to account for human difference. In Hegel’s version, this happens in an ethical account that transforms World History into a scene of development (the self-actualization of universal reason), which culminates in the mental and social (juridical, economic, symbolic) configurations found in post-Enlightenment Europe.21

Both the scientific and ethical figurings of determinacy would enter into nineteenth-century scientific accounts of human difference, which produced the notions of racial and cultural difference. Both notions are manufactured in knowledge procedures that produce physical and social configurations as effects and causes of (explanations for) mental (moral and intellectual) differences. Further, these procedures deploy the European/white mind as the universal gauge, since it alone shares a key quality with universal reason (or with Hegel’s “Spirit”), namely, self-determination. In this way, this earlier moment of racial knowledge yielded indexes of human difference—i.e., the naming of racial collectives such as the Negro, the Caucasian, the Oriental, and the Australian—that transformed economic differences resulting from conquest, colonization, settlement, and enslavement into presentations of (Hegel’s self-actualizing) universal reason, identifying spatial and bodily configuration that, in their turn, produced the mental (intellectual and moral) forms that caused the differences in social configurations found in the European continent and its colonies.22

My point here is that the very arsenal designed to determine and to ascertain the truth of human difference already assumed Europeanness/whiteness as the universal measure, that is, as the bodily, mental, and societal actualization of universality. This has several consequences, the most relevant (to my argument here) being the occlusion of the latter as a term of comparison. More explicitly, economic differences resulting from hundreds of years of expropriating land and labor were attributed to racial and cultural difference. In racial knowledge, they become the effects of particular bodily arrangements, which are established as the causes for particular mental (moral and intellectual) traits, which are themselves expressed in the social configurations found across the globe. Put differently, both the anthropological and sociological versions of racial knowledge transform the consequences of hundreds years of colonial expropriation into the effects of efficient causes (the laws of nature) as they operate through human forms (bodies and societies). In sum, as a category of racial difference, blackness occludes the total violence necessary for this expropriation, a violence that was authorized by modern juridical forms—namely, colonial domination (conquest, displacement, and settlement) and property (enslavement). Nevertheless, blackness—precisely because of how, as an object of knowledge, it occludes these juridical modalities—has the capacity to unsettle the ethical program governed by determinacy, through exposing the violence that the latter refigures.

A United Nations image used to illustrate an article on migrant deaths in 2016 on the website World Maritime News. 

The Equation of Value

To explore this potential of blackness to unsettle ethics, I will now tackle the unquestioned question reiterated by the disregard for lives lost in the streets of the US and in the Mediterranean Sea: Why don’t black lives matter? To do this, I use that which grounds the modern knowledge program—mathematical reasoning—to devise a procedure that unleashes blackness to confront life. Using what I call the Equation of Value, I describe blackness’s capacity to unravel modern thought without reproducing the violence housed in knowledge and in the scene of value. My proof of this equation is designed to sidestep the hegemony of the Kantian subject and to make it possible to expose the disruptive/creative capacity that blackness hosts/holds.

In the modern Western imagination, blackness has no value; it is nothing. As such, it marks an opposition that signals a negation, which does not refer to contradiction. For blackness refers to matter—as The Thing; it refers to that without form—it functions as a nullification of the whole signifying order that sustains value in both its economic and ethical scenes.23

The crux of this exercise is to provide an account of opposition that figures nullification instead of contradiction. This is crucial for distinguishing a radical engagement from a critical one—because the latter cannot but assume the Kantian forms when it seeks to expose their conditions of possibility.24

Let us first see how the figuring of opposition as contradiction would work in relation to black life. Life is the form; the positive position vis-à-vis life is figured as “1,” and the negative position is figured as “-1”:

i. positive life = 1
ii. negative life = -1

If blackness occupies the place of negative life—that is, life that has negative value, that does not matter—then

iii. blackness = -1

Let me now figure the relationship between life (1) and blackness (-1) using basic mathematical procedures: addition, subtraction, multiplication, and division. Addition in this case becomes subtraction because of blackness’s negative value:

a) 1 (life) + -1 (blackness) = 0

When simply combined with life, blackness brings about nullification (0); when added to the positive form of life, blackness obliterates it.

As discussed previously, value, because it is both an effect of determinacy (Kant’s account of knowledge) and is equated with determinacy (Kantian and Hegelian ethical scenes), it is (a) determinate, resulting in relations marked by effectivity (efficient causation), that is, relations marked by power differences insofar as one element effectively acts upon another; and it is (b) determinant insofar as it is the effective element—that is, it is the form which is applied to matter (content).

To express the relation between blackness (0) and life (1) in terms of effectivity, I use multiplication (×) and division (÷):

b) 1 (life) × -1 (blackness) = -1
c) 1 (life) ÷ -1 (blackness) = -1

When blackness multiplies or divides life, it remains in its negative expression, as blackness (-1)—that is, as lack, as a symbol of an absence (of life).

My next move is to take blackness’s power to annihilate life (a) and deploy it to multiply (×) life. If

iv. life = 1
v. blackness = 0

then we find that

d) 1 (life) × -1 (blackness) = -1
e) 1 (life) × 0 (blackness) = 0

The movement in both cases is unmistakably violent; it refigures dialectics. In (d), negativity (blackness) engulfs value, and in (e) it destroys it. Put differently, in (d), life without value—that is, blackness (-1)—disappears with life, and in (e), blackness as a figuring of the absence of form (blackness = 0) disappears with the form (life = 1) and releases matter itself (0).

Taking this a step further, it might be possible to move away from dialectics and its deployment of effectivity, which cannot but reproduce violence, by dividing life by blackness:

f) 1 (life) ÷ 0 (blackness) = ∞ − ∞ or ∞ / ∞

Instead of the sublation (d) or obliteration (e) of the form, this procedure has no result because it is impossible to divide something by zero. I have chosen ∞ − ∞ (infinity minus infinity) or ∞ / ∞ (infinity divided by infinity) to picture the result because it is undeterminable, it has no form: it is ∞ minus itself or ∞ divided by itself. It is neither life nor nonlife; it is content without form, or materia prima—that which has no value because it exists (as ∞) without form.

In equating blackness with ∞ and capturing the rare (“of which something consists”) and the obsolete (“substance without form”) meanings of matter, I claim a radical praxis of refusal to contain blackness in the dialectical form. Though Frantz Fanon’s refusal of dialectics is the most celebrated, I find this refusal also in Cedric Robinson’s tracing of the black radical tradition; in Hortense Spillers’s figuring of the flesh as zero degree of signification; in Saidiya Hartman’s refusal to rehearse racial violence as the moment of black subjectification; and in Fred Moten’s descriptions of blackness in the scene of violence which refuse a simple reconciliation with the categories and premises of modern thought.25 When blackness’s oppositional power refers to matter—or, in Fanon’s words, in the “night of the absolute”—it is possible to avoid the principle of contradiction and the accounts of self-determination it sustains; it is possible to avoid, that is, a return to Hegel (or Marx) via the shortcut of racial eschatology. What I hope this move against determinacy—the very notion presupposed in the question that Black Lives Matter sets out to challenge—makes possible is an appreciation of the urgency of bringing about its dissolution. For the work of blackness as a category of difference fits the Hegelian movement but has no emancipatory power because it functions as a signifier of violence which, when deployed successfully, justifies the otherwise unacceptable, such as the deaths of black persons due to state violence (in the US and in Europe) and capitalist expropriation (in Africa). That is, the category of blackness serves the ordered universe of determinacy and the violence and violations it authorizes. A guide to thinking, a method for study and unbounded sociality26—blackness as matter signals ∞, another world: namely, that which exists without time and out of space, in the plenum.