DOC TAYROC'S [UNSOLICITED] ECONOMICS HOT THOUGHT

---

Marx and the Death of the Author VIII: The Marxist Mathematician

---

One of my listed specialities, and a topic that I've spent no small amount of time thinking about is computational statistics. That is, the ways in which computers do maths. As such, I've taught modules on statistics, coding, econometrics (ugh), and calculus. When some of my colleagues find out I teach, and even (God-forbid) enjoy these topics (albeit not econometrics per se) they often ask, 'and how does a Marxist do maths'?

A big part of this question, of course, is the role of 'mathematics' in modern economics, which comes into the discipline by way of the 'marginalist revolution'. As has been previously covered on this proverbial programme, much of modern 'mainstream' economics comes from the Vienna School of economics. Like many other problematic Austrians from the early 20th century, many in the Vienna School tried to borrow certain tricks from the hard sciences and apply them to the soft, with the same unwavering mathematical vigour that one would expect from a physicist. You may think I'm exaggerating, but one of my undergraduate lecturers did refer to economics as the 'physics of the humanities', the logic being, 'you need not understand the law of gravity to be forced to follow it, same with the laws of supply and demand'.

There are, of course, more than a few places where that line of thinking is... over ambitious at best. First, of course, being that whilst the laws of physics have been determined long before man put the 'observation' into 'observable universe', the laws of economics are created entirely by humans, and can therefore be modified by humans. The 'invisible hand of the free market' is less an immutable primal cosmic force and more the result of a series of political choices made by all relevant actors in a marketplace. Capitalism is not, as it asserts, a natural conclusion to human behaviour, but a rather recent invention like feudalism before it. Like all social phenomena, it had to come, and so it can go.

Nonetheless, when one thinks of mathematics and economics they tend to think of one of two things, the dreadful little exercises in microeconomics ('assume a perfectly competitive, and somehow linear marketplace...') and if they did a BSc in Economics, their dreaded econometrics modules that were likely taught by the same or similar staff to who also taught them the more dreaded calculus module. (Assuming the programme still teaches Calculus, a lot of them are dropping it due to student feedback, because the customer is always right, even when they're paying to learn what 'right' is, smart). Both of these forms of mathematics in economics is, of course, rooted in the strand of economics that could be defined as neo-classicalism/neo-liberalism. Even if they weren't initially related, they grew up in the same proverbial cot(s) at Vienna, London, and Chicago.

There are many things, in my experience, that are glossed over when teaching maths to economists, but the two biggest ones that I will focus on today are thusly:

1. Marx also loved maths

2. Maths revolves around assumptions

Marx also loved maths

As discussed previously, a central part of Marxist thought and theory is around historical materialism (HM). The key focus of HM is that no economic phenomena occurs ahistorically, rather in response to previous measurable reality. Indeed, the key idea here of measurable is vital to remembering Marx's love of maths. As much as we like to belittle neoclassicist and neo-liberalist attempts to turn economics into a science, Marx was really one of the first to formalise the potential relationship between the two. The capitalist, Marx figured, needed to quantify everything in order to adequately charge so as to guarantee profit, and thusly anyone studying the capitalist must also be given to studying these quantifications with an understanding that the capitalist will always be given towards the productivity ratio:

P = £/(c+v)

That is, the capacity to produce profit given fixed cost (c) and variable cost (v), with 'fixed cost' also becoming variable over a long-run system as the capitalist seeks to cut costs everywhere, giving:

P = £/v

Further, the capitalist will also see this as a function of time, that is, they'd like to maximise productivity over as brief a time period as necessary, introducing our final 'player' into the equation:

P = £/(v)^t

Obviously, to the capitalist P is merely profit, whereas to the outside observer, namely the Marxist, P is profit and surplus value, surplus value, the Marxist argues is something only labour can provide. But capital, in its chase to be self-reproducing, obfuscates the difference between profit and surplus value. Think the difference between a work of art and AI slop. The something extra, personal, and intentional the artist adds is the surplus value, something that capital cannot comprehend, hence why when capital moves into a creative space it almost invariably will rob it of its authenticity as the capitalist, in an effort to remove c from the equation will seek to maximise profit by reducing the amount of labour, resulting in the good moving into the 'uncanny valley' that capital has a history of moving goods into until it loses profitability, and thus capital moves on to the next thing, giving artisans room to reclaim the space previously dominated by capital until capital notices and repeats the cycle.

If you did microeconomics, and even half-remember this equation, you might already be headed off to the comments section to point out that this equation that Marx had written about has indeed made its way to 'mainstream' economics, and indeed it has, as has Marx's word for the system, 'capitalism'. Turns out Marxists have been infiltrating all along. But you likely weren't explained this equation and this phenomenon this particular way, and that's because:

Maths revolves around assumptions

I mean, I've already given away the plot in one of my above asides,'assume a perfectly competitive marketplace', of course the commonality of this phrase likely means that I am wrong in saying this is historically glossed over by my colleagues. To that I say, you've assumed that you've appreciated the depth of the assumptions, and my friend, this well goes so much deeper, and that's what is glossed over.

For multiple people in multiple disciplines and industries, and indeed in modern computing with all our talk of 'large language models', it is tempting to treat mathematics the way that some denominations of Christianity treat the Bible, as infallible language handed down unto us by the gods of nature themselves. I'm not here to debate Christian theology (today) but with mathematics this is intellectually lazy at best, and intellectual malfeasance at worst.

As Rojas and Joques [YEAR] have both pointed out, mathematics is a mere extension of language, a way of quantifiable ideas in an allegedly efficient way. Some of these statements are non-controversial: pi is the ratio of the diameter of a given circle to its circumference, being just over three times the length of the diameter. Others of these are considerably more controversial: the price a good reflects both producer supply and consumer demand at any given moment in a competitive marketplace. The latter, Marx himself would point out, is impossible, given the inevitable time-delay and information asymmetry, and that's before pointing out inevitable market distortions by cartels, governments, retailers, etc.

These assumptions go to the very roots of all the data you see in and around economics. First let me get this out of the way, there is no such thing as an apolitical economist. Economics is about the distribution of resources, which invariably links economics to power and with power and the distribution of power invariably comes politics. Like with internet discourse when an economist claims to be 'apolitical' further interrogation of their assumptions and assertions almost always reveals their preference for any manner of 'centrist' and right-wing ideologies. Anything to maintain the current status-quo which is often identified as being 'flawed but still fine', or if you're an American academic between 2000 and 2016, 'it may be flawed but it's the best we got, I must go and watch some Sorkin drivel now which assures me how smart I am and how unquestionably great America is, but from a sensible centrist perspective that lets me pretend I'm progressive without actually having to be'.

First, let us talk about the data. In most countries, the principle data collectors are the very people that the centre and right love to hate, the tax collectors. In order to effectively govern, a state requires resources, in order to effectively collect these resources, the state must quantify them. As such, your employer reports to HMRC (or your local equivalent(OLE)) a few key facts, first, you exist and work for them, second, you have a right to work in the United Kingdom (or local equivalent, either because you're an outright citizen, or your visa allows x number of hours of payable labour. Third, you've been paid £xyz, and of that payment, such and such a percentage has gone to National Insurance (OLE) such and such has gone to payroll tax, such and such to the union, and such and such to pension, and finally whatever's left goes to the employee, or rather their bank as this payslip also functions as a BACS (OLE) remittance acknowledgement.

From this, the government statistician can extrapolate the following data: how many people are working in the country, how many dependents they declared when they filled out their employment tax forms, how much a given citizen makes in a given year, where they live (from above form), and what level of education they have (from above form) as well as what the average Briton is paying in various forms of tax, what the average Briton is putting in their pension, what demographic breakdowns exist amongst income earners in the UK (above form, again), and many other data points. In the UK, anonymised versions of these data points are made available to the public via the Office for National Statistics (ONS) who also grab data from the second largest form of data collection in most countries, the once-a-decade give or take Census.

The census is a survey, that's all it is. Typically the largest survey run in a country, but a survey nonetheless. Questionnaires are sent out to every house in the nation-state and a percentage of the population will fill them out (as one statistician put it once, more than you'd think, but less then you'd hope). Of these, a certain percentage are chosen, based on how much money is left, for more in-depth interviews and surveys during the period between national censuses, these are typically referred to as 'household surveys'.

There's a couple of flaws with these data collection schemes: first, in the neo-liberal era, both the HMRC and the National Census are critically underfunded and understaffed. The reason HMRC seems to go after small infractions on tax rather than the big corporations is because they simply lack the resources necessary to go after corporations with massive legal budgets. This wasn't an accident. Second, people lie. People always lie.

Some of the lies are 'protests', 'I don't like organised religion, so I'm going to tell the underpaid workers of the secular nation-state that I'm a Jedi, that'll show the organised churches that have nothing to do with this survey'. Some of these lies are delusions, some of them are out of paranoia, the underlying assumption that an organisation like GCHQ needs the Census or the delusion that multiple departments of the British government are actually capable of meaningful data sharing. The lies all do the same thing, they undermine the reliability of the final dataset. Datasets that academics are increasingly reliant on ourselves as cuts to education budgets mean we're increasingly unable to run our own surveys for people to lie to us on (more on that later). With tax data, one of the reasons we have such a hard time measuring wealth inequality is also simple, the poorest don't pay tax, and the richest lie to the tax man. (A lie by omission is still a lie). Indeed, in both census data and tax, the poorest tend to go entirely unrecorded, affecting both population statistics as well as wealth inequality statistics.

And so far, we've only been working with continuous variables. Discrete variables are problematic mathematically, but even more problematic when we apply them to any given population. Pick any given British colony, almost invariably one of the more problematic and controversial things the British did there was (amongst other things) introduce a census. Of course, part of the reason the census was controversial is the British often used the census to do terrible things. For example, as IBM, Nazi Germany, and the US State of Virginia can all tell you, a genocide is much easier to commit when you know how many people need genociding, and which demographical groups are most vulnerable. After all, a key part of demonstrating your capacity for violence is to never pick on someone your own size, as they say. As such, a vital tool in the toolbox of the fascist is to make sure a minority knows exactly how small, other, and isolated they are so they know that no one is coming to save them. Censuses are extremely useful for this, especially if before the British arrive, you already have a highly hierarchical society, through caste, for example.

Of course, the British did not invent caste, there are records of caste in what is now India dating back to the earliest traders travelling along the Silk Road centuries before the majority of Britons had even heard of the Tudors. What the census did do, however, was create a far more formalised, discrete variable, which when applied alongside British racial 'science' of the era created the highly racialised version of caste we see in modern India.

The problem with survey data, especially in the era of 'big data' is the sheer number of discrete/categorical variables, which we want to treat like continuous variables, but unlike continuous variables we define everything about them. The poverty line? We defined that, and our definition, frankly, isn't very good. Race? We defined that, and our definition, frankly, isn't very good. Age groups/generations? We defined that, and as you likely guessed by now, our definition isn't very good. Quite a few of these artificially imposed boundaries between groups were chosen by personal preference of a single academic without much thought or justification. The British census of Indian caste groups? Done with little to no consultation from anyone who wasn't a Brahmin and/or a Mughal administrator. Age groups? Largely defined in relation to proximity to the Second World War. Race? Well, I've already written more than a few posts about how bullshit race is. Gender and sexuality? Let's not even get started. Poverty line? What makes capital feel comfortable (quite literally, as it is defined by none other than the World Bank).

Worse, when we deal with discrete variables we no longer deal with 'regular maths' where we can get a fairly consistent and easily measured relationship between x and y, rather the instant we hit discrete variables we cross into 'probability of y occurring given x', or other expressions of probability, and the vast majority of people who will read and make decisions based on those reports do not understand how probability actually works, treating the outcome, mentally, the same as they would for a continuous variable. In slightly more mathematical terms, they'd like something like an R^2 value to denote 'goodness of fit', and instead are given an AIC or BIC score, and don't fully grasp how many, many more assumptions are being made once we cross the threshold into Bayesian inference and its cousins. (Again, I recommend Justin Joque's work on the matter).

And of course, all of this is missing the blatant and continuos tendency of modern academics, capital, journalists, and tech-bros to ignore the golden rule of mathematics and science:

CORRELATION DOES NOT EQUAL CAUSATION

Because, we forget that ultimately mathematics is just an extension of language, and therefore the problems persistent in the rest of the spoken and written word persist in mathematics, people will always choose the bit that reinforces what they want to believe and sod the rest. You can lie by omission when speaking the King's English, and you can do it in your regression analysis just as easily, and many do. You can do wild extrapolation with in the vernacular, in ecclesiastical Latin, and in scientific notation. For the same reason you can't always assume 'good faith debate' is occurring, you can't assume 'good faith statistics and maths' is occurring.

The Marxist way to do maths is to do it with a critical eye towards other mathematicians, and an apprehension to capital's fetishisation of 'the science' of economics. Who does the statistic benefit, and why might they twist it to benefit them?

As Terry Eagleton put it, Marxism can only exist for as long as capitalism exists, for Marxism is a critique of capitalism, and once capitalism ceases to exist, the need for Marxism will cease with it, and the academics involved can move on to other problems (and indeed, there will always be other problems). Similarly, Marxist mathematics need only exist for as long as capitalist mathematics needs to be critiqued.