Number and numbness: Data journalism, the rationality community, and the misuse of mathematics
When the data journalism website FiveThirtyEight launched in March of 2014, founder Nate Silver introduced the site’s Information Age take on news as follows: “our approach […] will be quantitative–there will be plenty of numbers at this site. But using numbers is neither necessary nor sufficient to produce good works of journalism.”1 The caution evident in that last sentence was unfortunately warranted. The proliferation of charts, figures, and tables in online media reinforces the idea that the use of numbers is required to have an informed opinion about the world. Meanwhile, FiveThirtyEight’s own reporting offers plenty of evidence that a focus on data is hardly correlated to deep insight.
Numbers increasingly rule our lives. “Big data” is both a Silicon Valley buzzword and the reality of our online existences. Thanks to the efforts of whistleblower Edward Snowden, we now know that as part of its mass surveillance regime the NSA has been keeping digitized records of millions of Americans’ phone calls and electronic communications. Of course, the private sector practices mass data collection on a scale rivaling if not surpassing the United States government; and while we may be intellectually aware that we “trade” our data to companies like Google and Facebook for the use of their social media services, we rarely reflect on the ways in which that data is used against us. Numbers and data are in no way morally neutral objects. As Rachel Goodman points out in a recent blog post for the ACLU, even “unthinking” data algorithms can have discriminatory impact.2 Strings of zeros and ones are already tools of our oppressors; we are perhaps not far off from the day when these strings are our oppressors.
But the emergence of data journalism sites like FiveThirtyEight and the similar New York Times venture The Upshot highlights a different danger of the increasing prevalence of numbers in our daily lives: it is more and more common to treat numbers as constitutive of truth. FiveThirtyEight promised to provide a new kind of rigorous, data-driven analysis of politics, economics, science, life, and sports. In assessing its realization of this promise it is hard not to agree with blogger and Nobel Prize-winning economist Paul Krugman that the site has become “something between a disappointment and a disaster.”3 Most FiveThirtyEight articles treat their subjects with the superficiality of a BuzzFeed listicle, and with less humor. See for instance this article4 responding to Republican presidential candidate Marco Rubio’s soundbite “Welders make more than philosophers. We need more welders and less philosophers,” by challenging the assertion that those who graduate with a degree in philosophy have it bad financially, and not whether the market is the proper tool for evaluating life choices. Or this article5 entitled “Everything Donald Trump’s Immigration Plan Gets Wrong” which somehow elides the obvious “it is immoral to deport eleven million people.”
Political reporting was supposed to be the site’s forte. But while Nate Silver has often criticized traditional media outlets for horserace election coverage that “proclaim[s] every dubious poll or every minor campaign stumble a ‘game changer’ ”6, the vast majority of FiveThirtyEight’s coverage of the 2016 presidential election has consisted of reaction to the latest polling789, as well as some appraisal of the parties’ admittedly undemocratic nomination apparatuses 10 and discussion of the demographic breakdown of support for various candidates.11 Apparently less important, because they have yet to receive any coverage at FiveThirtyEight, are the issues at stake in the current election, who we should vote for and why, or even an assessment of why so many Americans are (maybe rightly?) apathetic about the voting process in this country. In 2015 in particular we might have expected at least an attempt at a higher-level explanation of the apparently significant support in America for a candidate as openly fascist as Donald Trump; but instead we were repeatedly told why, statistically, his candidacy is doomed.12
The 20th century saw amazing advances in science, technology, and engineering, advances which rapidly changed the world and society. With this legacy in mind we revere and respect science. The rise of the personal computer and the Internet at the end of the 20th century and into the 21st shone particular prominence on the science of numbers: data science, computer science, and mathematics. Numbers have come to signify the beginning and end of rational man. But to quote Walter Kaufmann in the introduction to his translation of Martin Buber’s I and Thou:
Man’s world is manifold, and his attitudes are manifold. What is manifold is often frightening because it is not neat and simple. Men prefer to forget how many possibilities are open to them.
There are many sources of truth beyond science. Some of these sources include history, morality, aesthetics, and emotion. Science certainly has a liberatory potential. Environmental science tells us how capitalism has damaged our planet and may suggest what steps we can take to mitigate or even reverse this damage. Recent efforts to create a searchable database of police killings in America1314 emphasize the particular role data science can play in making our world more just. Yet when we limit ourselves to bare empiricism as a truth protocol, numbers leave us numb: we end up with the vapidity of data journalism. Or worse: we arrive at the insular, reactionary politics of the online “rationality community.”
The rationality community is a loose collection of “skeptics” whose members coalesce at blogs such as Scott Alexander’s Slate Star Codex15, websites like RationalWiki16 and LessWrong17, and pseudo-academic organizations including the Center for Applied Rationality.18 In the community’s belief system we find ample proof that reverence for numbers is no substitute for proper moral and political thinking. The demographic of LessWrong, according to its entry on RationalWiki,19 is “the standard set of predominantely male, middle-class Internet-libertarians” and this description surely applies to the rationality community in general. These sites are rife with vile racist and sexist comments, of which the following is representative:20
People always assume that acknowledging a trait in a person requires you to have an explanation for it. And then they note that all possible explanations are politically controversial, so they conclude that the trait does not actually exist. This is bad logic, as far as I can tell.
One imagines that the rationality community attracts a great number of people for whom “The Bell Curve”21 was truly revelatory in its mixture of mathiness with a defense of the social status quo. In its own conception, the rationality community stands principally for two things: an epistemic program, the elimination of cognitive biases, and a moral program, effective altruism.
Modern psychology, the rationality community tells us, has uncovered all manner of fallacies of thought. On LessWrong we are warned about mental traps like the affect heuristic whereby “subjective impressions of goodness/ badness act as a heuristic–a source of fast, perceptual judgments.”22 The theory of knowledge adopted by the rationality community is not far from the common sense position of the data journalist described earlier; it sees deep truth in Bayes’ theorem23 (a statistical formula for updating our beliefs in light of new evidence24) but not necessarily in the philosophical literature of Dostoyevsky or Elena Ferrante. It is easy to find tensions inherent in this epistemic program: vigorously rooting out pseudoscience, while simultaneously basing one’s epistemology on cognitive science and psychology, which, at a minimum, have a very short half-life of knowledge25 and lots of trouble reproducing findings;26 attacking creationists and conspiracy theorists, but prominently developing a theory about artificial intelligence as loopy as the loopiest of conspiracy theories (please read this RationalWiki entry on “Roko’s basilisk”27); adopting a “skeptical” outlook while believing that one weird trick can make you think twice as good. Some of the promises made by rationality community groups (“We teach math- and science-based techniques that are actually useful. Learn how to evaluate evidence, make more accurate predictions, be more efficient using economics, understand your motivations using thought experiments, and much more.”28) are hard to distinguish from those you might find in a cult pamphlet. However, the worst aspect of the community’s understanding of truth lies not its contradictions but rather in the way in which it underpins a milquetoast, bourgeois morality: effective altruism.29
Effective altruism is a philosophical and social movement popularized by (in)famous Australian moral philosopher Peter Singer that stresses doing good in the world via a continuous scientific appraisal of one’s actions. In practice this means researching charities and donating to the most effective one, which, at least according to Singer’s no-frills utilitarianism, means the one that causes the most alleviation of pain per dollar spent. We can see how casting morality in such starkly reductionist and quantitative terms would appeal to someone who wants the world to be “neat and simple.” We can also see how this moral program would appeal to anyone who does not really want to challenge the structures that perpetuate injustice. Matthew Snow’s recent article for Jacobin30 does an excellent job explaining how effective altruism fails to call for radical change in the world, and utterly fails to challenge the global neoliberal consensus. The result is a “flawed moral and structural analysis that aspires to fix the world’s most pressing problems on capital’s terms.”
The rationality community is a marginal group whose members do not threaten society in the way that, for example, Donald Trump’s supporters do. Nevertheless in this community we see the dangers of a numerical, monolithic, masculinist approach to truth.
There is a strain in feminist thought, going back at least to Derrida’s “phallogocentrism,” which sees the Western conception of rationality as essentially colonial. According to this understanding we would be right to cede the term “rationality” to the rationality community for they are its true heirs. But we should push against this impulse; rationality is worth saving. Let me quote Yale Professor of Political Science and Philosophy Seyla Benhabib in an interview conducted by George Yancy for the New York Times’ philosophy forum The Stone:[*31]
G.Y.: I think that it is important to mention that within the Western philosophical tradition, the mind, coded as white and male, is privileged over the body, coded as female or a signification of blackness, creating a false, disembodied practice.
S.B.: Of course, I agree with you. The master also shows “mastery” over his own feelings and emotions, where domination over the other means domination over the otherness within. As Adorno and Horkheimer argued brilliantly in the “Dialectic of Enlightenment,” in Western philosophy reason is understood as “ratio,” as instrumental reason, which in Descartes’ famous words intends to render us “masters and possessors of Nature.” Such ratio is an instrument for the social domination of others. And the slave, whether black or not, is always represented as part of the order of nature that needs to be mastered and subjugated. Such an understanding of rationality brings with it the dualism of mind/body.
Yet we also have to remember that there is a different view of the relation of reason to the emotions, and of body to soul which is more one of education and formation and shaping – not domination. I would argue that from Aristotle to Hume to Smith and even the early Hegel, we find another model of rationality as “embodied intelligence,” as the shaping of emotion by reason rather than its domination. John Dewey is the most articulate philosopher of this alternative understanding of rationality.
Rationality as constructive, embodied discourse is valuable. What needs to be challenged is the common sense theory of truth implicit in both data journalism and the rationality community.
What is this common sense account of truth? It is a generic, unsophisticated empiricism; although probably unaware of its roots it goes back to the Vienna Circle and is later developed in the work of Karl Popper and W.V. Quine. As Professor Benhabib says, its adherents enthusiastically view rationality as rendering us “masters and possessors of Nature.” When pressed, these adherents might justify their position as follows: we ought to believe our best theories and only our best theories; our best theories are our scientific theories; the goodness or badness of a scientific theory depends first of all on its ability to be experimentally falsified, and secondly on whether it has yet been falsified. Here are some major issues with this account of truth:
- It employs a basic metaphysical swindle: The notion that there is an external world subject to physical laws is extremely convincing. We constantly experience this world and we are all taught at least an approximate version of its aesthetically appealing laws. In light of this convincingness we judge it true that such a physical world exists. But upon our acceptance of this very plausible proposition (the existence of the physical world), the empiricist turns around and says that the physical world is the source of truth, that all facts correspond to physical entities, and so on. This last move is an unsupported metaphysical leap of faith. It ignores our role as adjudicators of truth. In particular it reverses the relationship between truth and the physical world: rather than truth being a property we have granted to the physical world, it sees truth as generated by the physical world. The idea that there is a physical world is convincing; but there is no reason other ideas could not be convincing in the same way.
- It conflates science with the scientific method: Certainly empirical evidence is important to science. But it is sophomoric to treat falsifiability as the complete extent of our evaluation of scientific theories. Great theoretical progress is often made in science, especially physics, without any empirical work. If we are to believe the legend, Albert Einstein developed a lot of special relativity from thought experiments alone. And of course the cutting edge of current theoretical physics research (e.g., string theory) is far removed from experimentation. Asserting that string theorists are not doing science is nonsensical adherence to dogma. Consider even the most representative and essential scientific theory: the theory of evolution. The theory of evolution is praised because it is testable and because it aligns with observation, yes, but it is praised also because it is explanatory. What it means for a theory to be explanatory is obviously a complicated question but in any event “explanatory” is not coextensive with “falsifiable.” If science really reduced to bare empiricism, why do we train our scientists the way we do? Why do we spend classroom time discussing the elegance and symmetry of Maxwell’s equations? Clearly scientists, if not philosophers of science, think the development of scientific taste is important.
- It completely overlooks mathematical truth: It would be a tragedy if the increasing visibility of numbers online and in our day-to-day lives were to cement an unimaginative empiricism as the default epistemic position because mathematics is a prime example of truth which is not derived from experience. Mathematical truth follows rather from abstract, a priori reasoning. Of course empiricists are well-aware of the apparent contrast between empirical and mathematical reasoning. They have canned responses like the “Quine-Putnam indispensability argument” which says that mathematical statements are true because mathematics is indispensable to empirical science. But if you asked a mathematician why the Gaussian curvature of a surface is a geometric invariant that does not depend on how the surface is embedded in Euclidean space, she would begin presenting the arguments Gauss offered for his Theorema Egregium. She would presumably not discuss the indispensability of math to science. It seems totally reasonable to think that the arguments mathematicians present for their claims are in fact the reasons we should believe these claims. We conclude that there are multiple, varied sources of truth.
A holistic approach to truth, one which accepts many different sources of truth, is not “neat and simple.” But maybe the world is not neat and simple.
Here is Nate Silver’s explanation of the FiveThirtyEight logo:31
Our logo depicts a fox (we call him Fox No. 92) as an allusion to a phrase originally attributed to the Greek poet Archilochus: “The fox knows many things, but the hedgehog knows one big thing.” We take a pluralistic approach and we hope to contribute to your understanding of the news in a variety of ways.
FiveThirtyEight’s approach, which could be summarized as “view from nowhere” journalism32 plus statistics, has been far from pluralistic. Honest pluralism would accept the obvious fact that there is truth in a theorem and truth, of a very different sort, in a poem. Data journalism comes close to denying this fact and to processing literature in the same way as the computer program, imagined by Italo Calvino in “If on a winter’s night a traveler,” that “can read a novel in a few minutes and record the list of all words contained in the text, in order of frequency.” Observe FiveThirtyEight’s obsession with ranking33 and indexing34 media. Apparently the rationality community has no more nuanced a perspective on art: the entry for “aesthetics” on RationalWiki redirects to an article entitled “argument from beauty,” an anti-theist screed which loudly proclaims “the perception of beauty is a psychological phenomenon that is easily described in terms of evolutionary principles and neurological models of sensory processing […] there is no absolute standard of beauty and the idea of beauty is entirely subjective.”35
In this essay I have so far dismissed the application of numbers to art and politics as either uninteresting (in the case of the data journalism) or reactionary (in the case of the rationality community). In order not to come off as wholly negative, let me conclude by noting that there is room for numbers to be genuinely inspiring when we seek analogies between mathematical reasoning and reasoning in other fields. Alain Badiou, more than any other contemporary philosopher, has accepted the many and varied truth procedures in the world and has tried to understand their connections and intersections. His mathematical analogies are the kind that make physicist Alan Sokal (of “Sokal hoax”36 fame) cringe; but I would not immediately dismiss Badiou’s invocation of mathematics as crackpottery.
Let me briefly present one example of a mathematical analogy suggested by Badiou in his magnum opus “Being and Event.” The mathematics concerns set theory. Recall that in 1874 Georg Cantor famously proved that there are multiple sizes of infinity. Cantor showed in particular that the set of all counting numbers (one, two, three, and so on) is strictly smaller in size than the set of all real numbers (which includes negative numbers and fractional numbers, but also more importantly irrational numbers like π ≈ 3.14159… whose digital expansions go on forever without repeating). The continuum hypothesis, a conjecture which Cantor put forward in 1878 and spent the rest of his life working on, asserts that the real numbers are bigger than the counting numbers in a minimal way; it asserts that there is no set whose size is strictly between that of the counting numbers and the real numbers. Questions about sets like the continuum hypothesis are often resolved by constructing models of set theory: collections of sets obeying all the axioms we think the universe of sets should obey. Kurt Gödel showed in 1940 that a kind of highly structured, minimal model of set theory (called the constructible universe) obeys the continuum hypothesis. Thus the continuum hypothesis is at least consistent with our other beliefs about sets. On the other hand, in a tour-de-force in 1963 Paul Cohen showed that there are models of set theory that violate the continuum hypothesis. Cohen did this by developing the method of forcing, which takes a model of set theory and, subject to certain forcing conditions, adds a generic set to this model. This generic set is importantly “indiscernible” in that it cannot be picked out by any formula or property. Cohen showed that one can choose forcing conditions so that the new model with this extra generic set violates the continuum hypothesis.
Here comes the analogy. Badiou wants to identify the notion of a generic set with Rousseau’s notion of the “general will.” Recall that, according to Rousseau, the general will is the will of the people as a whole; it is this will which the law ought to reflect and which gives the law its legitimacy in a truly representative democracy. Crucially, the general will is not the individual will of any particular person, nor is it any “function” of these individual wills. For instance, Rousseau (at least sometimes) wants to distinguish the general will from mere majority opinion. In this way the general will is, like a generic set, indiscernible– it cannot be picked out by any formula, it cannot be “constructed” out of the wills of individuals, but it is representative of the universe of wills that it inhabits. Badiou’s writing is dense. I am not sure exactly what his point is in identifying the general will with the generic set. Nevertheless, the general will is an important idea. In practical terms, society already recognizes that certain laws (e.g., changes to the constitution) require more than just majority support to be enacted. When it comes to issues like minority rights we find a tension between the goals and methods of democracy, one which a better understanding of what makes laws legitimate in a democracy could resolve. It is not totally crazy to imagine that analogies of the sort Badiou is proposing could be useful in this regard.
I conclude this essay with my own attempt at a scientific analogy. It is about what might be called the paradox of progress, namely, the observation that social progress is continuous, significant, and insufficient. In 1866, 1916, 1966, and 2016 Middle America could be heard to exclaim, that things were bad“wow, we were really barbarians fifty years ago. Blacks and women had it so bad! But ain’t it great now that society is just and fair.” Of course anyone with their eyes open should be aware of American society’s contemporary injustices: mass surveillance, drone warfare, mass incarceration, rampant police killings, massive income and wealth inequality, and seething white resentment, to name a few. It seems accurate, at any moment in history, to say that we have come far and have far to go. Now for the science, which involves statistical mechanics. The second law of thermodynamics states that the entropy of a closed system constantly increases. Entropy is, roughly, the amount of disorder in a system. The character of Thomasina in Tom Stoppard’s “Arcadia” explains the second law like this: when we stir jam into rice pudding, the jam and the rice pudding mix, but if we then stir backwards the jam and pudding do not separate. The second law could be taken as a physical axiom. However, one could also try to deduce this law from more basic physical laws such as the laws of classical, Newtonian mechanics. This is exactly what mathematical physicist Ludwig Boltzmann attempted in 1871 with his celebrated but controversial “H-theorem.” As Johann Loschmidt objected, Boltzmann’s H-theorem seems paradoxical because the laws of classical mechanics are time-symmetric whereas time is directed in the statement of the second law. Taken to its logical extreme, Boltzmann’s reasoning would suggest that the past is also likely to be a time of much higher entropy than the present. A way around this paradox is by considering the second law to be a boundary condition– under this view the second law is the assertion that the entropy at the starting-point of our universe (the Big Bang) was extremely low. We should view progress as subject to a boundary condition in an analogous way: social progress is always possible (and always required) because the level of justice at the starting-point of our moral universe was extremely low. Martin Luther King Jr. encapsulated this view in his deservedly famous quote, “The arc of the moral universe is long, but it bends towards justice.” Of course, a good analogy must admit its limitations. As Noam Chomsky reminds us, the arc of history is bent towards justice not by the inexorable laws of nature and probability, not by bouncing particles, but by “courageous people, often under severe duress, refusing to bow to illegitimate authority and persecution, others devoting themselves to support and to combatting injustice and violence, young people who sincerely want to change the world.”37
Sam Hopkins is a PhD student in the MIT mathematics department.