Divine Madness, Divine Mathematics: note towards a black philosophy of math
There is a lot about math that is veiled beneath its secularization that leads not only to a philosophical resistance to the metaphysical and epistemological questions posed by mathematics but also to a limitation of the pedagogical and practical investment in math itself. If the universe speaks through the language of mathematics then the study of mathematics need not necessarily be understood as antithetical to the historical, political, theological, mystical, spiritual, esoteric and/or divine. The history of mathematics is full of moments where such a notion was understood as common sense. An interesting book on parts of this history is titled, Equations from God: Pure Mathematics and Victorian Faith. There are many other pre-Victorian accounts of math and the divine that precede its secularization from both within and external to the Western historical tradition. Here, I am thinking of the mathematics of the Egyptians, the mathematics of ancient India and China, the mathematics of Pythagoreanism, the mathematics of the Islamic Golden Age and even the mathematics of the Medieval theologians who studied math as part of their theological training. (More book suggestions: Ron Eglash, African Fractals; Dirk Struik, A Concise History of Mathematics; George Lakoff, Where Mathematics Comes From; Peter Rudman, How Mathematics Happened)
This brief little note about the history of math is important because the secularization of mathematics is tied up with a mythological history of mathematics that centers a Platonic philosophy of mathematics as the only true philosophy of mathematics. Mathematical symbolism is viewed as a Platonic form opening up to the truest abstraction of the real available. Math is therefore divorced from the material realm, except for its instrumental application in physics, and imagined as a kind of Platonic ideal for measuring and mapping the language of the universe. The institutional education of math through an epistemological disavow of mathematical history gives credence to this philosophy of math, which gives mathematical symbols and ideas the appearance of having had come from nowhere. The truth of the immanence of mathematics rest in the fact that mathematical experience is always languishing in the unconscious of a subject, conditioning the possibility of its space and time and yet, if not for the process of education, this language can remain all but unknown and unthought to us. Thus, regardless, if mathematics is discovered or invented, anamnesis or intuition, the same fact remains: math must be taught. This teaching tells us the story of its history.
The hypothesis of this note as that: the mathematical nihilism of Black students is preconditioned by this Platonic historicization of math which presents an account of the ideas of mathematics as if they had occurred from nothing and apply to everyone. This history of mathematics, which rest on a philosophy of mathematics that conceptualizes math as a math-without-events, turns out to be a logical justification for the transcendent nature of mathematics. It is this caricature of mathematics that lends it an aesthetics of meaninglessness for those who are experiencing exorbitant meaningless violence on the daily. This mischaracterization of math caricatures the history of pure mathematics and its practitioners battles with madness, war and thought, which are necessarily entangled into the very conclusions that become the foundations of mathematics. This is to say that it is equally important for an immanent account of mathematics that we teach the war of discovery between Isaac Newton and Gottfried Leibniz at the moment that modern calculus came into the world as it is that we teach about Newton’s occultic investment in alchemy and theological investment in Arianism. In this way, the full context of theological, mystical and mathematical history can come to bear on the immanent truth of modern calculus.
Put plainly, I want to imagine the pedagogy of mathematics as a course on metaphysics. For it is math which grounds the ontology of Western physics, regulating its aesthetic of logical form, meta-measuring the laws of nature. This Platonic ontology becomes mathematical pedagogy. Yet, it misconstrues the various ways in which the application of mathematics within the immediate reality of the world facilitates, calculates and operationalizes mathematics into a violent production of an auto-poetic series of events. In this sense, math matters. Math maps the patterns of the possible. Math measures the limits of the real. Math models the linguistics of the divine. It is not just the way that math is used in the West that makes it a problem for Black thought, but it is the way math is thought that makes it a problem for Black being. In the paradox of mathematical abstraction is an ontological immanence flooded through all things: down to and including black death and dying. Therefore, when we talk about an ocean of violence or an accumulation of flesh we are also talking about equations from the perfection of slavery. To understand how deep we are in this monster, a sea of anti-Blackness, is to unveil the ways in which, at every scale of abstraction, the numbers are moving to make Black living more difficult and anti-Blackness more efficient. Until we think what is impure about pure mathematics, mathematics will be a secularized tool in a metaphysics of war, whereby ontological resistance to the very meaning of math will be thought as completely and utterly meaningless.
Georg Cantor went mad refuting an Aristotelian principle which for nearly 2400 years went unquestioned in the history of mathematics. Despite the fact that modern calculus required the use of the concept of the actual infinite as the limit of an infinite series of real numbers, mathematicians, under the influence of the Aristotelian principle (which argued that the concept of a ‘real infinity’ amounted to a logical contradiction) refused to provide a theoretical basis for an ‘actual infinity.’ The logical contradiction can be simplified as a question: How can something be both infinite and bound? Being both would be a ‘logical contradiction.’ Cantor’s discovery of transfinite numbers resolved this issue by affirming that the infinite is bounded by itself. [ ] The infinite set, if it exists, exist with bounds that are its own whole. Cantor devised a mathematical schema with set theory that provided a ‘rational’ explanation for the existence of an actual infinity as well as infinities of different sizes. 19th century mathematicians reacted emotionally and antagonistically to Cantor’s “discovery.” This was not because Cantor did not produce a mathematical proof or a logical account of his ideas, but because accepting Cantor’s notion of the transfinite would have required a shift away from the Aristotelian model of mathematical philosophy that had reigned supreme for over 2400 years. The pressure from having his ‘life’s work’ disdained by his peers contributed to Cantor’s consistent hospitalization towards the end of his life. He died poor and in a sanatorium. His theory of set theory is now fundamental to the foundations of mathematics. Cantor was thought to believe that his theory of the transfinite contributed to a proof of God. God was thought as the actual infinite. (Recapitulated from: https://apeironcentre.org/theology-of-georg-cantor/)
Cantor’s proof provided a model for thinking God without ‘logical contradiction.’ And thus, we find ourselves in the same territory, we had always been. Metaphysics. For even if mathematics is not ontology, as Alain Badiou would have it, mathematics is a door to the metaphysical question. Why is there something rather than nothing? How can something be both infinite and bound? If math is the language of the universe, is God a pure mathematician? If one is willing to ask, if others are willing to allow the question to be asked (without censor or coercion), if one is willing to see in the meaninglessness of the question itself, a bridge to the blackest curiosity, the blackest philosophy of mathematics, maybe, just maybe,… everything could be rethought.
Mumble Theory 