Metamodern Mathematics

/ April 2023

Within the vastness of things lies an order, the study of which is mathematics. This fabled field has propelled me on a mad quest to understand the ways of numbers. After so many thousands of hours, I can mumble about schemes, sheaves, and stalks, automorphic forms, cohomologies, adjoint functors, chaotic dynamical systems, maximal abelian unramified extensions of number fields, and other otherworldly terms of the trade. But this essay is not an ode, but a lament; for my beloved field which seeks to grasp the stars has had its soul stolen by the machinery of power.

Mathematics commands near-universal respect as an intellectual field, but among the many, it is recognized not for the feat of having smuggled secrets out the gate of heaven. No, the respect given to the number-chasers is due to their economic potential. It is understood that understanding math, though few have any idea of the form or substance of a university-level math education, enables one to participate in the inner workings of the quantitative technocracy which rules our lives. The modern mathematician can sell their labor writing algorithms or software, predicting economic trajectories, optimizing transit systems, and much more.

But these intellectual labors do not wield the celestial secrets which enchant the eager student. The magnificent truths, the crowning achievements of the human spirit, are left by the wayside. The mathematician’s true magic, of having been trained for grueling years in the craft of structural aesthetic thinking, is no longer necessary. What is most valued in the standard white-collar mathematician job are not the grand insights into the order of things, but the mundane quantitative experience which lets one design systems and models, the underlying math often incredibly simple relative to the worker’s education.

Math is so respected in our world not for its beauty, but for its central role in legitimizing the entire technocracy. Organization of society is no longer justified by the rationalizations of priests or even the state, but rather by the calculations of an amorphous class of number-crunchers. Our incomprehensible numerical lives of infinite products with ever-shifting prices, daily fluctuations in oil and flight networks, rate-changing loans and so much more, is only acceptable under the pretense that someone, somewhere, has run the numbers and assures us that this is the best of all possible worlds.

Both our decisions and our agency to achieve them are outsourced to allegedly-optimized systems: the market-competitive (and thus self-justifying) Product, to guide our (consumptive) free time; the narrativizing Advertisement, to guide our desires; the Algorithm, to guide our intellectual actions; the Machine, to guide our physical actions. Then there are the behind-the-scenes systems, like the Supply Chain and the Mass Media (having replaced art or mythology as our collective narrative), to disguise and manage the postcolonial violence necessary to maintain the whole thing.

We are neither to question nor participate in these systems, because that is for those with economic, or at least educational, capital. Our agency is subsumed by number-optimizing bureaucrats, planners, designers, investors, and the grand knowledge-apparatus which, downstream, produces the material conditions of our lives. It is a class-gated and alienated crew which cannot envision better futures without increased consumption of industrial products. And thus we have the new fascist reaction sweeping the rich countries. The masses, excluded from power structures while watching their communities be annihilated by capital, have their anger redirected towards ethnic divisions by the right-wing narrative machine. The much-bemoaned distrust of expertise associated with this movement is only natural when people’s lived experiences of suffering contradict what they are told by numerical models. Unsurprisingly, it is bad politics to tell someone to believe your graph showing that their lives are better rather than their actual experience of increasing economic precarity. Fascism, along with general alienation and discontent, will continue to grow as long as those in power view technical reports as the only legitimate form of knowledge.

The ringleaders of this grand numerification are our latter-day priests, those who can commune with capital and transmit its wishes to us unworthy masses: the economists. Like the priests of old, macroeconomists have convinced us that they do not speak from their personal biases, but merely reveal to us the objective will of the Lord (the Lord now being finance capital). How sad that in place of priestly poetry as their tool of justification, the economists rely on high-school level math to provide a flimsy pretense for the exertion of raw power.

But this priesthood is held in such high regard that politicians, too, are praised for their ability to mediate between capital and the masses. Euphemistic phrasing about “promoting growth” and the like signals that a politician is skilled in the art of divining capital’s desires. The cosmic force of capital remains mute, just as God is silent; and so we must fill our ears with the adulations of its bishops, the professional-managerial and political class. Their claim to power runs through their supposed ability to translate between the number-world which encodes the objective truth of capital, and the human-world of dreams, hopes, loves, and desires.

We are asked to transfer our intellectual discourses into a world of models, charts, approximations, and tabulations. The terms of quantified administration have come to dominate our entire imagination of how we can live. Everything must be assigned a value – and so desperate climate economists try to justify conservation by pricing a forest in United States dollars, since somehow our inhuman discourse precludes even mentioning that it is simply wrong to kill said forest and life on our planet alongside. The only lens through which a thing or creature may be understood is that of its price. Capital the divine renders judgments through its pricing, deforestation for industry being able to produce more dollars than letting the trees be.

Fool that I am, I do not price the beings of the world. Thus I am doomed to the curse of “irrationality,” the gravest sin for the pricing priests. For it is not my place to judge what lives and dies; it is that of Capital. If I refuse to name the price of the bird I hear singing, I am incompatible with the cold logic of our postmodern utopia. And that logic will crush me, because we are evermore only allowed to interact with the world transactionally, as more public space is destroyed or privatized, more human interactions mediated through algorithms, more consumption expected as one’s way of life.

Above all, the public discourse of political imagination is so totally captured by quantification that we have lost any sight of a more noble path. Our highest-minded utopias are those of optimized tax credits and tariffs, fine-tuned carbon pricing, electric cars externalizing environmental destruction to African mines instead of American roads, marginally faster trains – there is no vision. The logic of quantification demands ossification, stagnation, as each victim absorbed into its numerical structure further entrenches the legitimacy of existing prices. Slowly the whole globe is absorbed into a new way of life, a new daily ritual of price-assignment and self-commodification to join in the grand game. But the game is not for us to win: we lose our souls when we concede to the logic of the numerical world. We should not live our lives as machines of price and cost evaluation, self-entrepreneurship replacing personal development.

To transform a real thing into a collection of numbers is a weird and violent thing to do. My favorite area of math, number theory, studies many things, but it centers around understanding prime numbers. Prime numbers are irreducible. They are unique. They are irregular; it is difficult to determine if a number is prime. In these ways, prime numbers are like the things of the world (in fact, there are enough prime numbers to uniquely associate one to every thing). Each is self-justifying for its irreducibility, none deserve to die. But rather than looking to the numbers as a source of beauty and wisdom, we have enslaved them towards evil ends. They are mere tools of computation and gimmicks of storytelling to justify transfers of wealth towards finance capital.

The quantification of things gives capital a pretense at omnipotence: since everything is priced, the logic of the system should naturally unfold, the rational decision played out. Given that this never happens smoothly, and that macroeconomists seemingly never make correct predictions at critical junctures, it is hard to understand how this mythos has endured. But indeed, our entire discourse remains shaped by the strings of numbers which we are to accept as replacement for the complexity of society.

The great danger of allowing public discourse to take place in the number-realm is that the decisions produced are number-maximizing instead of being beneficial for real living things, such as humans. This is why those trying to price the value of protecting a forest or the like are doomed to fail: they are defending things which cannot be priced, like life and dignity. The number-discourse tells us that as long as we increase output, growth, and above all, consumption, our other problems will go away. Some innovator will make solar panels cheaper, and electric cars more efficient, and everything will work itself out.

Our most noble technological imaginations will not save us from overconsumption. If solar panels were free, we would cover the earth with them to power more machines. If electric cars are produced more efficiently, it will be an excuse to produce more without exceeding the “carbon budget” (the very idea of which shows how much we have conceded – as if there really exists some massive positive number of carbon we can safely spew).

The problem of our era is not technical, but aesthetic. We cannot imagine a world not centered around consumption. So entrenched do we find ourselves in a matrix of rationalizations that there is little room left to take stock of the inhuman madness of the situation. Producing more to get higher numbers, consuming more with our higher numbers – a sad game of shifting around capital, globally, to benefit the top while giving an illusion of agency to workers.

We will not mechanically innovate our way out of climate destruction. Already have our machines become vastly more efficient and skilled in the past decades, but we simply use that to produce more, not to expend less energy. The problem is consumption. We understand our agency in the world to be that of consumers, we understand the rewards of our labor to be industrial products, and so we are meant to organize our lives around consumption.

We will not escape the apocalypse with some fiddling of efficiency and expenditure numbers. We must reimagine the way we interact with and move through the world. An ever-growing army of machines to move and think for us is not sustainable, no matter how “green” their particular factory is. Nor is an ever-growing torrent of disposable products to pass the time, or a food system completely reliant on long-distance international shipping, ever going to be sustainable.

The innovation we need is not mechanical. We need to consume less. We need to live simpler but richer lives. We need to retake political control away from capital. Numbers have much to teach us, but let us not allow them to drive us to such violence.