Humanities is a window in the epistemic jail of mathematics.



Engels once referred anglo-saxon economists as theory-less, referring to their tendency of abstracting human action to ahistorical rules such as human nature. Today, the theory-less barbarism is generalized as capitalism’s drive for reducing everything into fundamental units – such as the dollar, the worker, the commodity, and the automobile part in the assembly line – obfuscates the greater logics that these fundamental units submit to, such as capital accumulation, exploitation, patriarchy and white supremacy. In the world perceived by the theory-less, humans exist in isolation of greater logics, driven by simple, ahistorical rules such as “human nature” and rationality. In such a picture, then poverty, the criminal drive that emerges from certain marginalized individuals, obesity, drug addiction etc. are judged based on simple rules within the individual itself without taking into account systemic trends that maintain those in the lowest rung of society in that state. In other words, the drug addict, the gangster, and the minimum wage worker are seen as functions of their individual choices, without taking into account the greater logics that might animate them as well. This atomization is simply reflective of the scientific analytic of focusing in the most fundamental, individual unit of the system, and seeing the system as merely a sum of its components. Thatcher famously proclaimed that there is no society, only individuals and families.

In modern society, much of the theory done to study these greater “logics” that exist above the simple rules of individual human units is done within the humanities. A common attack on the humanities is that they are  qualitative and imprecise and therefore they counter the scientific spirit of precision and quantification. The sciences and the fields that try to emulate them (e.g. analytic philosophy and economics) construct their celebrated analytic clarity by starting from the study of very small, fundamental units or laws, and then construct more complicated concepts by using these units as building blocks. Gases are made of atoms. The economy is composed of rational agents maximizing utility. A particle field reduces to quantum harmonic oscillators. This tendency to reduce everything to a fundamental, quantitative unit is perceived as rigorous and precise. Yet, in contrast with the hard sciences, the humanities deal with more olympian concerns, such as society, the evolution of class society, or the systemic power asymmetries faced by women, people of color, and workers. Marx’s Capital studies the fundamental laws of motion of capitalism – a world system where billions of humans participate in complex and inter-connected ways. The scientifically and quantitatively minded individual may find these approaches as inexact, soft and sloppy – given that these approaches do not lead necessarily to well defined, mathematical laws that can be used to predict the behaviour of the system. In contrast, the scientist begins by studying a very small and precise part of the system, and then eventually builds up to the higher laws that govern it. However, many important systems, such as the world economy, do not simply behave as the sum of its individual components – the laws of motion that govern these systems cannot be reduced to the laws of the subcomponents. The humanities, then, offer us insights about systems that have behaviours that cannot be necessarily decomposed to the rules of simpler subcomponents. This article will attempt to bridge the methods of the quantitative, hard sciences, with the humanities, by showing the gaps left behind by the hard sciences.  I will use human society as an example for a system that remains epistemically elusive to the quantitative, giving a space for the humanities to operate. I will build my argument using a  language and conceptual constellation borrowed from the mathematical sciences, to show the inner limits of such approach.

The behaviour of society at large cannot be reduced to the behaviour of its elementary units – humans. Terms exist that explain this irreducibility of a system in the scientific literature: society is nonlinear and complex. It is nonlinear because the system’s behaviour is not simply the sum of its components. In mathematics, linear systems have a property called the superposition principle, where the behaviour of a system can be decomposed to the behaviour of its subcomponents. A very famous example of a linear system is the behaviour of waves. Waves, such as water ripples, can merge into one wave, whose properties are simply the sum of its parents’ properties: if a crest of a wave intersects with the crest of another wave, the amplitude of the daughter wave becomes larger, in contrast, if the crest of a wave intersects with the trough of another wave, they cancel each other out. Much of the theoretical work done in physics and engineering is done through the study of these linear systems because they are tractable and easy to understand.

However nonlinear systems are extremely hard to track quantitatively. One can’t simply break a nonlinear system into simple components that can be studied individually. Scientists either try to approximate these nonlinear systems into simpler linear systems or use powerful computers to simulate them. For example, the earth’s atmosphere is a nonlinear system and much of the evidence behind anthropogenic global warming was derived from very complicated computer simulations of the nonlinear equations that govern the Earth system. However, computer simulations can only offer an approximation of the behaviour of a nonlinear system, sometimes with large uncertainties. Another complication that arises in nonlinear systems is that many of them are chaotic. Even if chaotic systems are deterministic, i.e. once the initial values of the system are known, one may ideally be able to track its behaviour indefinitely – a very small difference in the initial values of the chaotic system leads to extremely different behaviours. In other words, tiny human or instrumental errors in the measurement of these initial values makes the chaotic system’s behaviour vary so much that it becomes intractable. Human society in both nonlinear and chaotic, and therefore epistemically opaque to mathematics. That’s the main reason why the best economists of the world, with the finest credentials from Harvard, Cambridge or Chicago, couldn’t predict the economic shock of 2007 – the precise trajectory of the world economy is muddled by chaos, nonlinearity, and also randomness.

Not only is human society nonlinear, and chaotic, but it’s also complex. By complex I mean that two humans that are spatially separated by thousands of miles can influence each other, sometimes even without being conscious of it. The speculation in real estate in Vancouver by some desk jockeys in Wall Street will affect the price of corn tortillas bought by some Mexican worker. Finally, complex systems have emergent properties; In other words, the collective behavior of the system’s components gives rise to global laws of motion that govern the system in its totality, and these laws of motions cannot be reduced to the simpler laws followed by each individual component. In physics, the random motion of gas molecules gives rise to collective properties such as pressure or temperature – properties that cannot be reduced to the individual motion of one molecule. Similarly, capitalism has has its own individual laws of motion that cannot be reduced to the behaviour of an individual worker or capitalist. Other emergent properties of human society are patriarchy and white supremacy. A racist cop that executes an unarmed, black man, may genuinely fear for his life, and may convince himself that he doesn’t really hate black people – yet, the emergent properties of white supremacy and class stratification animates the police to disproportionally target the poor and people of color. Although these emergent properties in human societies can be partially tracked quantitatively by looking at the empirical data – such as the statistics behind the wage gap between genders, sexual assaults on women and the queer, the number of people of color frisked by the police, the household incomes of marginalized minorities – the fundamental laws of motion that animate these power asymmetries are quantitatively obfuscated by nonlinearities, chaos and complexity. Therefore many of these emergent properties can only be unearthed qualitatively and heuristically – with tools and concepts developed by philosophers, sociologists and critical theorists – such as Marx, Fanon or Hegel.

While we may never have the computational resources to unearth the fundamental formula that leads to the abjection of specific demographics – the Newton’s Laws of capitalism – the humanities have developed conceptual frameworks to precisely study these things. Hegel’s world-spirit, or Marx’s historical materialism, are simply attempts to shed light to the truths that are quantitatively denied from us. Therefore, the theory-less barbarian that rejects the humanities due to their “lack of rigour” is trapped in an epistemic jail delimited by chaos, the nonlinear, and complexity.

2 thoughts on “Humanities is a window in the epistemic jail of mathematics.

  1. Your comments toward the end of your essay are excellent justifications for studying humanities. I’m going to add these to my already growing list of justifications. Thanks.

    Liked by 1 person

  2. “Engels once referred anglo-saxon economists as theory-less, referring to their tendency of abstracting human action to ahistorical rules such as human nature.” While, Engels did the same with the a-historical abstractions Hegel inflicted on his readers.


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