Levinas’ Three-Body Problem

Within Newtonian physics, there exists a seemingly intractable problem of motion that is described as the n-body problem. Simply described, it posits that in a system where three or more bodies (e.g., planets) exist in macro-space it will be impossible to predict the motion of each body even when accounting for their speed, initial position and constant gravitational forces. This is because there exists so many other variables—each of which may exert a significant influence on subsequent motion—that it becomes impossible to know what variables need to be accounted for.

An analogous problem exists within a certain branch of philosophy. Within the continental tradition, stands one thinker whose works are almost singularly associated with a single theme. The theme is ethics and the philosopher is Emmanuel Levinas. Described as a Jewish émigré who lived in Lithuania during the early 20th century1, Levinas lived through the two World Wars (he was imprisoned in a labor camp near Hanover, Germany for 5 years during WWII) and this profoundly shaped his conception of ethics. Drawing from the traditions of Judaism and phenomenology, Levinas’ main contribution to the latter was his nearly myopic (some would say traumatic) insistence on the primacy of the ethical relation to the Other before all other considerations.  The Other here is defined as an individual—outside of what we claim as our own self/sameness—whose singularity forms a point of absolute difference, uniqueness, vulnerability and venerability that must be regarded/defended/respected. Although a position of radically asymmetrical responsibility towards the Other seems impossible and even preposterous, Levinas insists on the primacy of this relationship as the only viable alternative to paths that ultimately lead towards fascism, totalitarianism and other forms of embodied and metaphysical violence.

The most persistent criticism of Levinasian ethics has been its utter ambiguity with regards to informing and guiding practical human behaviors. But, as I will argue for Levinas, that was beside the point. Nowadays, ethics has a uniquely pragmatic orientation (i.e., regulations, bylaws, codes of conduct, charters etc.) but this wasn’t always so. For most of Western history in fact, ethics was a branch a moral philosophy that was mostly concerned with largely abstract concerns such as God, Good, Bad, Truth etc. We can observe a parallel with early astrology; it was believed to have originated not from a desire to map precise geospatial relations between cosmological bodies in space but rather with an existential need to better predict variability in days, seasons and their impact on surrounding animal/plant life. Later however, astrology also became concerned with our unique place in relation to abstract cosmological entities (deities). As the world took a scientific turn in the age of reason or the Enlightenment, the philosophy of empiricism came to dominate areas of scientific and social thinking. Empiricism, for our purposes, can be thought of as a guiding principle that emphasizes direct experience as a higher authority than reason or revelation. Astronomy had to give way to the new science of physics and ethics—as a branch of moral philosophy—was grafted into a branch of legal scholarship which was concerned with the establishment of societal Laws and customs.

However, the genius of Levinas was that he recognized and anticipated this problem (i.e., of social practice) as an intractable issue—a form of violence even—that would forever contaminate his philosophy. You see, for Levinas’ ethical relation to the Other to be taken seriously, one would have to consider the reality that we live in a world of many Others. For example, how can I stand before You–an Other to whom I am affixed with the infinite responsibility of nonviolence, if not care–and simultaneously maintain my responsibility to the Other beside or behind you? Even if I take food meant for my mouth and give it to you, am I still not denying this other Other? Perhaps these seem like ridiculous or hyperbolic concerns for the pragmatic thinker. However, the problem that Levinas poses for us is greatly analogous to the n-body problem confounding modern physicists.

Just as it becomes impossible to predict the trajectories of three or more objects in relation to one another; it becomes infinitely problematic to discern the ideal way to orient to more than one thing/individual/concern at a time. You see, in a 2-body system in physics, motion can be predicted by setting a relative center point (i.e., the center of gravity in the system). In a three-or-more-body system, there is no relative center point and so their motions can only be predicted by accounting for all the unknown variables that may affect their motion (which appears mathematically impossible to do). In an ethical relation, the center point (i.e., of radical responsibility) between I and Other becomes destabilized through the introduction of an other Other. There are too many variables to account for in order to apprehend the influence our actions (or inactions) will have upon one another.

Physicists today have responded to this calamitous uncertainty by inculcating epistemic humility: no matter how advanced our instruments become, there will always exist chaos within the cosmological order. But what are we to do with chaos within our ethical order? For Levinas, the solution is ultimately a form of violence which he struggles to reconcile with his ethics; that is, he recognizes the need for institutions of justice and norms of behavioral reciprocity. The way that physicists generally approach n-body systems today is by “restricting” the properties of other bodies (i.e., because their mass is so relatively light as to be considered negligible). Predictions can then be made by modelling the behaviors roughly on a two-body system. In institutions of justice, we see a similar heuristic where the vagaries and nuances of Others are stripped away and the primary relation is between the Self and the Law. What can Levinas’ n-body problem then teach us, practically, about the ways we inhabit the Law?

  1. The law is only an approximation of our ethical responsibilities. It is meant to guide us but it is a form of justice that necessarily does violence by erasing the singularity of the others’ actual call upon us.
  2. We are expected not to fall short of our judicial responsibilities but we must accept that we will ultimately always fall short of our ethical responsibilities. How we live with this short-coming is up to us. Some will live in denial—a form of legal fundamentalism in which their responsibilities to all others cease where the letter of the law does. Others will live with epistemic humility, finding ways to redress the harms they may make (i.e., upon the unseen others) even as they fulfill their obligations to the law, family and the proximate Others in their regular lives. There are some relatively recent and stringent philosophical developments here that are worth considering because of their practiceability (if not practicality).
  3. Though flawed, our lived experience of others still demands a highly personal (theocratic?) view of order in the cosmos. Just as the average person is still concerned with predicting the length of days, weather and seasonal shifts in life; we are still people who are concerned with where we stand in relation to the others in our orbit. Although some may venomously rebuke the notion of absolute responsibility for the Other (especially if that other has the face of an abusive parent, enemy or jilted love); we are all principally concerned with finding meaning in our lives. Levinas proposes a cosmos in which we are never alone—always in relation to Others (who in turn “by the grace of God” are in relation to us). The other can never be totally erased; and it is from their affixture that all other institutions (e.g., Justice, Education, Government) must necessarily come into being.

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