Revolutionary Mathematics

Artificial Intelligence, Statistics and the Logic of Capitalism

Justin Joque

• Verlag: Verso
• Jahr: 2022
• ISBN:
  9781788734028
• Thema: Economics
• Thema: Political Economy

Our finances, politics, media, opportunities, information, shopping and knowledge production are mediated through algorithms and their statistical approaches to knowledge; increasingly, these methods form the organizational backbone of contemporary capitalism. Revolutionary Mathematics traces the revolution in statistics and probability that has quietly underwritten the explosion of machine learning, big data and predictive algorithms that now decide many aspects of our lives. Exploring shifts in the philosophical understanding of probability in the late twentieth century, Joque shows how this was not merely a technical change but a wholesale philosophical transformation in the production of knowledge and the extraction of value. This book provides a new and unique perspective on the dangers of allowing artificial intelligence and big data to manage society. It is essential reading for those who want to understand the underlying ideological and philosophical changes that have fueled the rise of algorithms and convinced so many to blindly trust their outputs, reshaping our current political and economic situation.

PART I

Ghosts of Departed
Quantities

So may be Henry was a human being.

Let’s investigate that.

… We did; okay.

He is a human American man.

That’s true. My lass is braking.

My brass is aching. Come and diminish me, and map my way.

—John Berryman, “Dream Song 13”

Chapter 1

Automating Knowledge

In 2004, with Hurricane Frances charging toward the coast of Florida, Walmart’s chief information officer, Linda Dillman, asked her team of data scientists to forecast the effects the hurricane would have on sales. Based on prior data, the team came up with a number of insights. In addition to predictable consumption increases like canned food, water and flashlights, they discovered that strawberry Pop-Tarts sales increase to seven times their normal rate immediately prior to a hurricane.¹

The data Walmart used in its model was derived from Hurricane Charley, a storm that had struck the peninsula only a few weeks prior. Using this as a test case, Dillman’s team was able to contrast consumption patterns between stores in the path of the hurricane to stores not in the path of the hurricane. And indeed, sales of many of the items they stocked prior to Frances based on these insights sold as expected.²

While Walmart’s knowledge proved profitable in the near term, its statistical correlations offer little insight into underlying causal mechanisms. And, even if Dillman might claim otherwise, such correlations offer us little meaningful understanding of the world. Walmart’s model, built from data and algorithmically produced patterns discovered in that data, centers knowledge production on correlations. Their epistemic relationship to causality is irrelevant: the model cares little about why Walmart consumers prefer strawberry, so long as a mathematically modelable relationship exists.³ Ultimately, what is produced by Walmart is particular, local only to the conditions of the given data, and therefore unable to express any enduring principles. The irrelevance of Walmart’s model beyond a very specific and immediate problem demonstrates a certain limit of algorithmic knowledge, even if it is one with which engineers and researchers are rather comfortable.

All the same, these limits do not undermine the importance or value of machine learning models, because they are often designed to update themselves over time, offering up-to-the-minute predictions as new data comes in—a procedural analog to the realities of a dynamic, capricious society of capitalist consumption. With this self-correcting design, the algorithm generates not some ideal, universal understanding, but instead a local and constantly shifting set of predictions.

While Dillman and her team may have played some role in setting up the model and selecting the data, when it comes to the knowledge produced, their role is that of an envoy: they know only what a statistical model tells them. And that model can only suggest, with a given probability, that consumers will likely buy more strawberry Pop-Tarts prior to a specific hurricane. Due to its complexity, it is the computer-run model that in the end understands, rather than the researchers. It is in this sense a nearly automatic production of knowledge; even if humans are involved, they appear not to add intellectual labor to the production. Machine learning operates by taking a large set of inputs and computationally determining a way to map those inputs to outputs. Machine learning techniques most often work by running through a set of training examples, evaluating the output, and updating themselves in order to best match the training data.

We witness here, in miniature, a larger turn toward statistics, and probability in particular, in the management of contemporary capitalism. The use of probability to predict the most likely set of outcomes has become central to everything from logistics to advertisements to the stock market and beyond. But, probabilistic analyses are notoriously bad at dealing with systemic change. Frank Knight, one of the founders of the mid-twentieth-century neoclassical Chicago school of economics, used the terms “risk” and “uncertainty” to bring to light one critical challenge to this type of probabilistic knowledge.⁴

For Knight, “risk” describes a set of knowable probabilities that can be managed—for instance, the probability that someone will win the lottery, the survival rate for various diseases, or the chance that a drug will produce a certain side effect. Correspondingly, “uncertainty” describes elements whose probability one does not know—or those one chooses not to include in their calculations. For example, when calculating the odds that a single ticket will win the lottery, the equation normally does not include the probability that the state or organization running the lottery will go bankrupt. While risk can be calculated, uncertainty cannot. Uncertainty threatens every model, because there are always dangers that lie outside the closed space of the system. While historically, capitalism has excelled at integrating newfound uncertainties into its social and economic processes, the powers of machine learning threaten to upset this stability. For the more efficiently systems manage risk, the harder it becomes to imagine and prepare for uncertainty. By definition, efficiency comes at the expense of redundancies and the type of double-checking that could make it easier to handle unexpected situations. For an example of this, one need look no further than capitalism’s privileging of short-term profits blocking any real response to climate change.

Since at least 1876, statisticians have been aware of the effects, in calculations of probability, of their choices about what data to include. John Venn, the man whose intersecting diagram made his work famous to grade-schoolers, describes the origin of this problem: “Every individual thing or event has an indefinite number of properties or attributes observable in it, and might therefore be considered as belonging to an indefinite number of different classes of things.”⁵ This problem is now known as the reference class problem, and describes the challenges of how this “indefinite number” is narrowed down, and thus defined, into something more manageable. It is at its base an ontological question about what something is and what else falls into that category.

The reference class problem directly challenges the supposed objectivity of statistics and machine learning. For example, if a patient is diagnosed with cancer, how that patient is defined—such as what stage their cancer is—determines their calculated probability of survival. Just as there is no “true” patient demographic, there is no “correct” way to define the world, only decisions that frame that world in potentially disparate ways. While some approaches, especially Bayesian ones, claim to avoid the reference class problem, they too choose what data is relevant to a given problem.⁶ Whoever defines the reference class—or selects the relevant data that is included in an analysis—wields extraordinary power over the seemingly “data-driven” neutrality of statistics. A statistical model like Facebook’s News Feed algorithm, for instance, weds users to the variables Facebook employed to construct that model. The conditions of possibilities are prefigured according to Facebook. In this way, probability is always political.

Statistics can only operate within the closed world of the reference class or the data it is given to operate on. Correspondingly, as an enclosed world develops and new statistical models describe that world with increasing accuracy, it becomes harder to imagine that anything might exist outside it and upset it. The greater one is able to manage risk, the more unlikely and unimportant uncertainty appears to be.

One of the great challenges to machine learning is that often, a wide variety of factors can explain any measured difference. In the Walmart model, for instance, geography, the time of week, or even the internal temperature of each store may have an effect. All algorithmic systems of knowledge production are relative only to the data that is put into the system. This was precisely what doomed Google’s attempt to predict flu activity based on search results: the model worked well for the first few years, but in 2011, something likely changed in how people searched for flu information, because the model predicted a number of doctor visits for flu that was more than double the figure reported by the Centers for Disease Control and Prevention.⁷ Again, the problem here was that algorithmic models are only able to assess risk (the probability that something will happen) relative to the input data, while remaining perennially vulnerable to uncertainty (the inability to know everything).⁸ While this is, to an extent, true of all knowledge, the use of theories and the discovery of causal mechanisms help buttress our trust in predictions and extrapolate beyond the data at hand; in Walmart’s model, the fact that the correlation discovered applies only to prior data means there is even less guarantee that some unforeseen uncertainty will not intervene to disrupt its predictive power.

While statistical modeling has been used since at least the 1700s to facilitate mathematical descriptions of relationships between phenomena for purposes of prediction, machine learning goes further, allowing for the modeling of significantly more complex relationships based on vast fields of data. By design, it also largely abandons the hope that one could extract some universal understanding from observed relationships. Traditionally, statistical models were built on relatively simple formulas for relating input variables to output variables. For example, in 2004 it was reported, based on data from the United States and United Kingdom, that on average, each additional inch of a person’s height correlates with a $789 increase in annual salary.⁹ While the study does not tell us why this happens, we nonetheless learn something about the relationship between height and income. The relationship is a simple, linear one. Given only two individuals’ height, the expected income difference between both can be easily calculated with pen and paper.

In contrast to this ease, machine learning models generally rely on massive numbers of calculations—so large it would be impossible for a human to do them in a reasonable amount of time—in order to train an algorithm. Furthermore, these algorithms frequently account for nonlinear relationships (wherein a change in one variable does not correspond to a constant change in another) between an immense sea of variables. For instance, the predicted strength of a hurricane could significantly relate to Pop-Tart sales, but the amount of those sales drastically increases between Category 2 and 3 hurricanes, levels off at 4, and then declines prior to a Category 5 storm.

With enough data, machine learning algorithms are able to detect incredibly elaborate interactions between variables. But these interactions often become so complex that while the algorithm may find strong correlations and thus “learn” them, humans, for all intents and purposes, never can.¹⁰ Unlike scientific theories that offer elegant mathematical descriptions of universally valid causal processes, we ask machine learning systems something much more epistemically complex: to calculate the probability of a set of outcomes over a circumscribed field of examples. In response, those systems generate a set of probabilistic knowledges from which one can, in the aggregate, act. To allude to the epigraph from John Berryman, we initially determine probabilistically that Henry is a human being, then, with more data, that he is a human American man. With that, we may claim to begin to map his way. Because these models are only as effective as the data input into them, the solutions and models that have been developed in the past decade tend to work well only in the relatively limited domains for which they are intended. Machine learning algorithms have effectively classified images, predicted purchasing behavior, turned audio into text, and even allowed digital assistants (such as Amazon’s Echo) to provide an increasing array of voice-activated functionality. But the utopia (or perhaps dystopia) of an artificial general intelligence that can carry out abstract and complex general tasks remains far afield.¹¹ Moreover, the data on which these models are trained—and the biased social reality that the data represents—build into their algorithmic outputs simple replications of extant systems.¹²

Because all data is mediated through our social world, biases cannot but saturate the closed worlds of algorithmic knowledge production. Consider, for example, the COMPAS (Correctional Offender Management Profiling for Alternative Sanctions) algorithm, designed by software company Northpointe, whose results are regarded by courts and prison systems as predictive of an individual’s likelihood of recidivism. In 2016, investigative journalists from ProPublica determined that the algorithm was demonstrably racist. Based on a series of questionnaires and demographic data, COMPAS identified Black defendants to be at a significantly higher risk for reoffending while identifying white defendants at a much lower risk.¹³ While the above Pop-Tarts example challenges how we understand knowledge in the abstract, COMPAS’s racism makes the challenges of algorithmic knowledge much more concrete: algorithmic bias in predicting recidivism rates can have a significant impact on pretrial, parole, and sentencing decisions.¹⁴

The algorithmic logics that both Walmart and Northpointe use represent a new epistemic version of the world, one that is private and particular. And Walmart is far from the only company attempting to predict their customers behaviors: Target famously predicts when customers are pregnant;¹⁵ Canadian Tire discovered that individuals who bought felt pads to protect their hardwood floors never missed credit card payments—while those who bought chrome skull accessories for their car were almost guaranteed to default.¹⁶ Each of these companies builds their own private databases of sales or arrests (and buys databases from other vendors) to create microcosms of the world where they can continually compute the probability of various events.

While techno-futurists have sold a world of untold wonder in which computers and machines will predict our every need, both collectively and individually, the reality is much more constrained and disappointing. This is, in part, because many of these systems excel at interpolation (the process of filling in holes in given data), while progress on extrapolation (the prediction of future, completely unknown situations) has been limited.¹⁷ We will explore the social implications of these technologies soon enough, but in order to better grasp what is at stake, it is worth explicating, first, what machine learning is and how it works.

Artificial Neural Nets

Many machine learning systems are built using the powerful, yet relatively straightforward artificial neural network. An ANN consists of multiple layers of artificial “neurons” that are connected to each other, in a structure that mimics a very simplified model of the human brain. In biology, at the distinct risk of oversimplifying things, human beings “learn” when synapses connecting their networked neurons fire between each other, increasing the ease with which similar signals can travel, and thus remembering, those pathways. In machine learning, the basic idea is similar: training data is fed through a network, and the network attempts to discover the best way to transform input values into outputs. ANNs are made up of multiple layers, where each neuron in a layer connects to each neuron in the following layer. A simple ANN can have an input layer, a single “hidden” layer and an output layer; more complex networks can have multiple hidden layers and complex divisions inside layers. In either case, each neuron tries to learn how to evaluate the information coming from its input neurons. In this way, every neuron—and the network as a whole—remembers its history in abstracted form, maintaining a trace of the values of what it has seen before, in order to create a model that can make predictions based on new data.

Imagine we create our own Pop-Tarts ...

Inhaltsverzeichnis

• Cover Page
• Halftitle Page
• Title Page
• Copyright Page
• Contents
• Acknowledgments
• Introduction
• Part I: Ghosts of Departed Quantities
• Part II: The Promise of Frequentist Knowledge
• Part III: Bayesian Dreams
• Conclusion: Toward a Revolutionary Mathematics
• Notes
• Index