The mathematical bridge between the totality and consciousness.

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Recently in the american media, various articles discussed the social mobility barriers that mathematical prerequisites represent in higher education. Much of the discussion centered around remedial algebra in community college. Statistical evidence indicates that intermediate algebra is the main culprit that prevents many workers from graduating from highschool and community college.  Some of the writers and technocrats cited in these articles suggest scrapping  many of these mathematical pre-requisites.

Polarization arose in websites, social media, and comment sections. In one side, some people  argue that removing these mathematical pre-requisites would contribute to the cretinization of the general populace- akin to removing writing and reading classes from curricula. The other side of the debate pretends to take the pragmatic side, by arguing that these requirements are empirically holding back social mobility for the underclasses.

I find these debates often infuriating, informed by the theory-less barbarism of technocratic bean-counters. The pragmatists that want to cut the mathematical requirements do so because some “expert” with a fake master’s degree fitted a line through a scatter plot that somehow signaled that mathematics is insurmountable for black people. Yet, the other side of the debate is also very simplistic; it reacts out of conservatism because it conceives of an already established body of vetted knowledge – in this case, mathematics – that will be diluted by the administrative paper-pushers. I do agree that the admins and their lackeys should be opposed; they are willing to throw anyone under the bus in their fanatic drive for metrics and vulgar empiricism – as they have done so for countless of students, adjunct professors and teachers.  Furthermore, at least superficially, there seems to be a very problematic schism between the humanities and the hard sciences, as diagnosed by C. P. Snow almost 60 years ago, which  diminishes the creative potential of humanity at large.   Yet,  mathematics, as it is currently taught is deeply alienating – for it is not the mathematics of the visionaries that unfolded the symmetries of the universe – but the mathematics of accountants and assorted paper-pushers. Therefore, I will try to describe in this post why mathematics is important  outside the sphere of commodity circulation and technocracy – within the realm of leisure, art and creativity.

Innumeracy constricts thinking, as it blocks a path to the totality. In the same way illiteracy denies the individual access to  accumulated thoughts, memories, and disciplines, innumeracy denies entrance to a whole gradient of human experience: from aesthetic considerations about symmetry and beauty, to the laws of motion that regulate both the physical and human universe. Not only innumeracy closes a window to large wells of human knowledge, such as the natural sciences and mathematics,  but also constraints the ability to synthesize thoughts about the world. In the same way sociology, history and the arts immerse people in a rich context that will affect how they vote and relate to humans from different creeds and ethnicities, the abstractions of mathematics influence how individuals  navigate fundamental aspects of reality such as space, time, inter-connectedness, and change. For example, an idea that I frequently explore in my writings is the complexity and non-linearity of human society –properties that have deep implications in our ability to conceive ourselves as political beings. For instance, the mathematical volatility of human society and the nonlinear, economic coupling  that connects spatially separated humans across oceans and continents calls into question the philosophical foundations of nationalism and borders. Another example of the conceptual power of mathematics is how mathematical physics connects different natural qualities through minimalistic equations, such as newton’s second law, which relates force, mass and the rate of change of velocity (acceleration) into a differential equation.

Yet, the current pedagogy of mathematics is driven by the necessities to produce technical workers or professionals. The lesson plans for calculus and algebra in universities and high schools are designed as pre-requisites for STEM; the imperatives of professions such as engineering or finance dictate the content of these lessons. For example, fluency in number crunching is necessary in many of the hard sciences – where solving non-trivial algebra and calculus problems is business as usual.  However, such facility is only achieved by alienating  problem sets and repetitive grinding. which discourages the uninitiated. Yet the deeper dimensions of mathematics as a bridge between consciousness and symmetry, beauty, and change are not explored – it’s only the mathematics of balding men in cubicles and spreadsheet theorists that make their way into curricula.

The answer is not removing higher mathematics from the curriculum – unless one wants to shrink the consciousness of marginalized individuals. Nor it is keeping the mathematical pre-requisites as they are – which are the pre-requisites of accountants, engineers and bankers. As it stands, much of higher education is  a means to social mobility, and it’s obvious that the current spiritually draining approach to mathematical pedagogy is acting as an obstacle to achieve that function. Perhaps, the answer is to have alternative classes of mathematics for non-STEM students that highlight conceptual reasoning over computational fluency. A mathematical pedagogy that describes how  the symmetries sketched by artists are the same symmetries found in the movement of the heavens and in the interior of an atomic nucleus, will do much more good than emphasizing how to compute the cubic root of a function. Much of mathematical innovation and inspiration arose from observing the natural and human world – perhaps that same inspiration can awaken in unmotivated students when teachers and pedagogues bridge the relationship between mathematics and the totality.

Imperialism is the world-monster that ties all our destinies.


Imperialism is real. The core economies use financial, political and military means to enforce asymmetric economic relationships between the global north and the global south to maximize profit. Imperialism has long been identified by the left as a dynamic in world capitalism– however a coherent political economy has yet to emerge. This notes, which are heuristical and not academic, are my attempt to bring some coherence to the political economy of imperialism. Much of this discussion will be based off ideas I explored in previous posts  – mainly, that capitalism is a global, nonlinear and complex system, with emergent properties that arise from the non-intuitive coupling of different parts of the system. Therefore, linear approaches to imperialism, e.g. core economies’ wealth is proportional to the plunder and rape of the peripheries, or in the opposite case, that imperialism simply doesn’t exist, contrast to the spirit of this article. These vulgar approaches to imperialism also lead to questionable political conclusions, as I will show in the following paragraphs.

Some leftists, especially those outside the marxist tradition, either identify imperialism merely through the military adventures of the global hegemon – The United States – and its allies, or don’t even talk about it. Their silence then suggests that the only class and power dynamics that matter are national – within the sovereignty of the nation-state. In this simplistic picture, the rich and politicians hoard a national GDP that they refuse to redistribute  to the hard working american or canadian workers. This is the picture of mainstream social democracy. This limited view of class exploitation and wealth redistribution, where the relevant economic agents lie within the nation’s borders, can devolve in some cases to national chauvinism – with slogans such as “british jobs for british workers”.

The opposite argument, which is equally vulgar, simplifies the core-periphery relationship by posing a unidirectional flow of value from the periphery to the core, implying that the global north’s wealth is a function of the global south’s pauperization. Some of them, such as the followers of J. Sakai, argue that most of the white working class is in the core economies is a “labor aristocracy”, and therefore  exists in a parasitical relationship with the periphery (and oppressed minorities). In its more extreme variants, this argument implies that white workers are not exploited at all, and are just beneficiaries of imperialism. Often the political implications of these arguments boil down to a moralism or orientalism – “revolutionary consciousness” as a function of the degree of pauperization faced by a demographic, and a fetishization of the armed peasant movements that bubble up in faraway peripheries, such as the ones in India, Nepal, or Peru.

In order to to correct the vulgar models of imperialism (and capitalism) as delineated above, I will sketch a more complex picture. Imperialism emerges from the nonlinear and complex coupling of all the workers of the world. A global division of labour arises that sustains the world-hierarchy of states. The production of an airplane in a factory in Seattle couples agents that exist thousands of miles from each other: a child worker collecting cobalt with his bare hands in a Congolese mine, the Engineer credentialed by some prestigious american or european university, the unionized wielder that owns a mortgaged house in some american suburb, a bolt produced in a Mexican firm with lax safety regulations. The core economies enforce the smooth functioning of this global assembly line through financial and military means. Predatory loans, NAFTA, the World Bank, and the IMF, are some parts of this imperialist machinery. This imperialism creates feed-back effects in the global south, retarding the progress of certain parts of peripheral society, while accelerating the development of its profitable parts. Furthermore, the business cycle is displaced downward into the peripheries through the intensification of imperialist policies that  extract a surplus. This surplus then is used to dampen the economic crises in the global north. Due to the secular trend of diminishing rate of profit experienced by the core economies since the 70s, imperialism intensifies in order to keep producing even more marginal  returns. Imperialism is necessary to maintain the competitive edge of core economies, since a refusal to engage in predation will lead to the competitor states gaining the upper hand. Because social democracy is based on capitalist growth, rather the restructuring of society to serve human needs – it can only be maintained through the intensification of imperialism. In other words, the social-democrat that sees its task as merely the redistribution of the national GDP to its compatriot citizen-workers is either a chauvinist or an idiot.

However, the other extreme side of the debate, which sees the global north’s wealth as merely proportional to the exploitation of the periphery is also vulgar. A large bulk of the global north’s economic growth is based in capital intensive industries and the transformation of society into a productive,  well-oiled machinery. Advances in science and technology due to centuries of  capitalist competition leads to machinery and logistical apparatus that produce more fuel, cars, and computers per unit of labor time. In other words, a second of labor in the core is worth more than a second of peripheral labor, due to the accumulated and enormous mass of dead labour in the form of technology, institutions, and capital, which younger capitalist countries lack. Furthermore, capitalism in the core economies has domesticated society into an aggregate of cogs and springs that produce value: the well maintained roads that transport workers and commodities across firms, the rule of law that cracks down on criminality and enforces business as usual, the social peace supported by economic growth. This domestication of an amorphous human mass into well defined workers, capitalists, and technocrats contrasts to the chaos of peripheral societies, where kinship ties, fealty and honor, criminality, and fragmented institutions hamper the dominion of capital. This two properties of the system – domestication, and technological innovation, are tightly coupled, and feed off each other, causing much faster economic growth in the global north than in the peripheries. Therefore, the global north isn’t simply wealthier because of imperialism, but it legitimately produces more value per unit of labor time.

The complexity of imperialism raises some important political points. First, social-democracy, which is designed to coexist with the global market, can only be sustained by imperialism, simply because refusing imperial mechanisms would make the social democratic state less competitive. Furthermore, if the secular trend of diminishing rate of profit continues in the core economies, the returns from imperialism will decrease, as the purchasing power of workers and firms in the periphery lowers due to imperial policies, making the whole social democratic project unsustainable in the long run. Finally, The global coupling of the division of labour implies that socialism cannot be simply sustained in one country – simply because a sole country cannot develop the whole intricate division of labor necessary to sustain a modern society within a small, isolated geographic area. Thus, the fevered dreams of building socialism in an isolated third world country are empty – such socialism will be based on the export of raw resources, never unshackling it from imperialism. Greece, Venezuela, and arguably the old USSR, are testament to the bankruptcy of anti-capitalism in one country.

The existence of imperialism and the global coupling of all the workers of the world, require international socialist organization with transnational material ties – ties that don’t just reduce to the lip-service that we see in current anti-capitalist movements. Today’s socialists have the almost unsurmountable task of finding the complex nodes of the global assembly network in order to disrupt them. Finally, by uncovering the global couplings of the division of labor, socialists can begin dreaming about a global, socialist society that eschews unbounded growth in favor of human needs.

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.

The productive human cannot love.

Technocrats defend the current power structures in the West by the real or perceived imperatives of productivity and efficiency; they say that a society organized in a different way would limit capital growth and therefore cause more poverty and precarity. The Left is often accused of having visions that will lead to economic ruination and inefficient allocation of resources, for privatization and wage-labor ensures that the land, hospitals, and energy companies remain productive and efficient. The ruling class portrays history as driven by a linear development of technology and optimization- a straight line from the discovery of fire to the splitting of the atom.

Many twentieth century writers have disputed this naive conception of history. Most of human history was alien to the privatization of the Earth for the sake of growth and optimization. The glory of the warrior and fealty to the King organized the hierarchies and structures that regulated many ancient societies. Some human groups remained in cultural and technological equilibrium for centuries, worshipping the northern lights and sustaining its members through the bones, blood and muscles of the Caribou they followed through the frozen tundra. The scientific manipulation of space and time solely for the unbounded growth of agriculture, industry, and war is a modern logic that radiates from the cores of global capitalism, and crawls into the periphery.

Present life in the Global North has been thoroughly optimized and hacked for the purpose of capital valorization. Humans are dispersed into a division of labor based on the scientific evaluation of test scores, credentials and work experience. Human activity is regulated through laws, paperwork, and carefully directed violence so that people go to work, the streets remain clean, and the flux of humans through roads, cars and public transport doesn’t reach an unacceptable bottleneck. This synergy between the State, capitalists, and workers ensures that maximum value is created per unit of labor-time for the purpose of capital growth. The State and the commodity erodes older forms of social cohesion – such as the clan and the agricultural household – in order to replace them by institutions, consumer groups, and the workplace, all for the sake of a more efficient unit of labor time.

We rarely consider the psychological consequences of productivity and optimization. If the mind is saturated with calculations on how to optimize every parcel of space and time, then something must give in. An anxiety develops as our problem solving brain tries to navigate the increasingly more abstract and complex decision-trees of a civilization in disequilibrium – from ruminating about that off-color remark done in a workplace meeting, to the fevered delusion of a West destroyed by terrorism and refugees. The noise increases inside the skull; an assonant song that lists everything that could go wrong if the citizen gets a a B- in a class, or they don’t stay in the office after 5:00 PM. The efficient citizen of the Global North resents those that do not practice the same rituals of optimization. Newspapers and pundits justify the homelessness and poverty of millions of people by claiming the latter doesn’t work sufficiently hard. The latino that waves their hands too much in front of a  powerpoint presentation is deemed as unprofessional, in contrast to the anglo-saxon suit whose words and body movements are optimized and focused.

Interpersonal relations are eroded by the imperatives of optimization; there is nothing more infernal than the dating market of thirty-something professionals. Future partners are judged for their potential as mortgage companions, where the tension between how interesting their personality is versus the respectability of their career plays out. Everyone wants to date the good looking engineer that is also a musician, yet optimized society selects some traits against the others – a person that spent all their bandwidth grinding through the math homework, job searching, and acquiring the right work experience for a fruitful career, will have no energy left to cultivate a deep taste in music, art or literature. Emotional labor is allocated into the three or four potential spouses in order to find the intersecting point between the supply and demand curves of the most desirable partner. The domesticated impulse that makes us think about our date’s career prospects, equity, and how interesting their personality is, leads to the death of romance.

A softer and brighter world wouldn’t be governed by the imperatives of efficiency and optimization. A young socialist society would use time saving technologies and processes to immediately decrease the work week, with a long term goal of eventually abolishing work. Psychological and existential cost will be considered when implementing a new regulation or time-saving process, in contrast to the current society that considers workers as infinitely optimizable and regulated machines, as another commodity alongside computers and tractors. Late capitalism considers efficiency and productivity as almost axiomatic, given that capital growth is treated as unbounded, as something that always requires innovation, productivity and more efficient labor-power. Therefore, it follows that socialists should fight for slowing down the world. The healthy human relates to space and time in an often inexact and spontaneous way, while the anxiety ridden professional sees time and space as something that can be parcelled and optimized.