Mathematics and the Question of Human Rights

By Priyanka Menon 12/30/16
https://www.aaas.org/news/mathematics-and-question-human-rights

Priyanka Menon graduated from Harvard College in 2016 with a B.A. in Mathematics and a secondary in History. She is currently a Humanities Fellow at the Dumbarton Oaks Research Library and Collection at Harvard.

The study of mathematics is, seemingly, the practice of becoming transparent. To take part in a conversation extending from Archimedes to Andrew Wiles, one must necessarily allow particularities to give way to universals. The art of mathematics lies in the way mathematics appears to exist independently of mathematicians, so that it seems as if the subject were engaged in an eternal game of hide-and-seek with its practitioners. The willingness to think in universals, to forget oneself, is the apparent cost of participation in this pursuit.

It is tempting to think that such an abstract discipline has little to do with questions of rights and justice. Within the scientific disciplines, mathematics–more specifically, pure mathematics–seems to evade intersection with issues of human rights. The study of ideal objects takes place in an ideal world; worries concerning human rights are simply misplaced.

Such a characterization of mathematics (and its relationship to human rights), however, is mistaken. On a practical level, mathematicians themselves live in this world, rather than an immaterial realm of pure abstraction, thus making them subject to the consequences of political structures. Among the most famous examples of this fact are the lives of Alexander Grothendieck and Paul Erdös. Both of these brilliant mathematicians experienced the dark repercussions of political turmoil, subjected, respectively, to unjust imprisonment and expulsion.

The theoretical aspects of mathematics are grounded in worldly reality as well. Even at its most “useless,” it is a deeply human enterprise, representing the creativity of the human mind at the limits of abstraction. The ethereal discipline of Euclid and Galois does not consist solely of disembodied observations of the truth, nor of activity removed entirely from the realm of the physical. As Gödel’s groundbreaking incompleteness theorems demonstrated, a sufficiently complicated mathematical system cannot rely on logic alone to justify itself via consistency. Rather, such a set of axioms must be connected to something illogical, some remnant of the earthliness of mathematics.

Owing to this disciplinary “Achilles’ heel,” one finds that contact between mathematics and human rights is not as rare as initially expected. Applications abound: in everything from the dissipation of technology such as computers and cellphones to the use of more productive agricultural methods, mathematics appears. Even in issues pertaining to international human rights law, mathematics appears in the form of assessments of risk and the interpretation of scientific evidence.

Conceptually, too, mathematics is deeply intertwined with issues of human rights. The theoretical frameworks with which one approaches the structure and development of human rights can be thought of as congruent to those utilized in mathematics, though the problems that occupy the respective fields may seem wildly different. While the content of the solutions to these problems is different, there is a way in which their structure is similar.

For example, human rights claims, at their most fundamental, are claims as to the equivalence of seemingly disparate subjects. The argument that one is entitled to the same basic rights as a stranger located oceans away is an assertion as to the correspondence between the properties of two like entities. In appealing to the discourse of human rights, one can be seen as constructing a bijective relationship between each individual on earth. As in theoretical mathematics, the impact of such a bijection is profound. One’s own rights are inextricably linked to those of another; to ignore this fact would be to ignore a fundamental characteristic of one’s own existence.

Admittedly, there is a way in which such a connection between mathematics and human rights can appear strained, even artificial. By reducing mathematics and human rights to such a great degree, is one simply making an argument about the pervasiveness of human reasoning and rationality? The description of a human rights claim as a mapping between two sets seems somewhat forced, with little substantive usefulness.

However, despite its seeming affect, this very relationship engages directly with a debate at the core of human rights and political theory. The German legal theorist Carl Schmitt resisted such accounts of measured political reasoning, arguing instead that rights and justice are solely products of human decision, unconstrained by the exacting requirements of rationality. On Schmitt’s account, political decisions are simply made; the attempt to understand them through or bind them to pre-existing norms is a hopelessly artificial and potentially harmful task. [1]

Schmitt’s legacy has persisted in discussions concerning both science and human rights. Philosopher and historian of science Alexander Koyre argued in his book From the Closed World to the Infinite Universe that the rise of Cartesian reasoning was linked with the alienation of man from his fellow members of society. [2] A mathematical outlook of the world is to blame for the deterioration of the state. Similarly, Hannah Arendt, a prominent political theorist of the twentieth century, advocated for Schmitt-esque models of political interaction in her discussion of science. In her book The Human Condition, Arendt singles out the moment at which mathematical reasoning permeated social and political discussion as the beginning of the decline in political community. [3] She advocated instead for a politics rooted in immediate circumstances. All three saw mathematics and the form of universal reasoning used in the discipline as the particular enemy.

In all honesty, the similarity between the two fields is not one of full completeness. The study of human rights cannot be reduced entirely to applications of mathematics. At some point, political and scientific questions diverge. But, to deny the connection between mathematics and human rights would be to deny underlying attributes of the fields, eliminating entirely the possibility of using such a connection to respond to issues in both. After all, both disciplines must grapple with similar, sometimes paralyzing, questions. An oft-made inquiry in the field of human rights is the foundational one: where do rights come from? Similarly, set theorists and philosophers of mathematics are preoccupied with understanding where mathematics comes from. Moreover, both fields are continually subject to pragmatic worries. What are rights practically useful for? What is mathematics practically useful for? Understanding the intersection between the two subjects is key to answering these questions.

The recognition that mathematics and human rights can be thought of as asking questions in similar ways is a practically useful idea. As disciplinary segregation becomes the norm in universities and educational institutions across the world, there exists a tendency to relegate the arts and humanities, social sciences, and natural sciences to separate ends of a campus, to the extent that the deepest form of interdisciplinary collaboration occurs at annual faculty meetings. Acknowledging the connections between disciplines, and the subsequent responsibilities these connections generates allows for the growth of interdisciplinary research and discussion, increasing the potential for generating novel knowledge.

Mathematics is not a transparent discipline; neither, for that matter, is the field of human rights. Speaking to either Andrew Wiles or Archimedes entails the encountering of the other in one’s full specificity, in the same way the realization of human rights is contingent on the recognition of the equality of worth of a billionaire and penniless street vendor. The study of the universal is at its most robust when it embraces the particular, when it engages with the tangible circumstances that shape one’s understanding of the universal. One cannot, and must not, deny this.

References

[1] Carl Schmitt (2010), Political Theology: Four Chapters on the Concept of Sovereignty, (Chicago: University of Chicago Press), 31.

[2] Alexander Koyre (1991), From the Closed World to the Infinite Universe, (Baltimore: The Johns Hopkins University Press), 90.

[3] Hannah Arendt (1998), The Human Condition, (Chicago: The University of Chicago Press), 264.