No doubt many of you will want to dismiss my whole argument as a futile exercise in bogus mathematics. I don’t accept that.
—Edmund R. Leach, Rethinking Anthropology

In some places, the surface of the world is smooth. Everyday life unfolds and existence is affirmed. In others, it is riddled with gaps, loops, and insurmountable blockades. Just being in the world feels like a full time job, and at some point, it becomes impossible to cope. At this limit, existence itself is threatened. This essay asks: What if, using topology (and a little bit of calculus), this limit could be represented mathematically and transposed, universally, onto any landscape containing humans in order to localize existential crisis.

To pursue that possibility, we reduce the world to a topological surface. Depending on how a being is positioned, the surface will be experienced as smooth, rough, unpassable, or somewhere in between. Our provisional formulation can be represented thus, where f is a smooth function and x and y are the coordinates of a surface:

\[ z = f(x,y) \]

Figure 1. A smooth surface.

The surface \( (z) \) is smooth at a point \( (a,b) \) if there are tangent lines in any direction at that point. \( f \) varies across ethnographic contexts, i.e., what makes a surface smooth will be different, depending on who you are. The surface will not be smooth at point \( (a,b) \), i.e., it will have a kink, if at least one direction fails to have a tangent line. In nonmathematical terms, a tangent line is a trajectory, on which forward motion in some direction is possible. A kink, then, is a trajectory along which forward motion is not possible. In DeafBlind communities, where Terra Edwards has been conducting anthropological research for more than a decade, the surface of the world has many kinks (Clark 2017). For example, Sarah K. McMillen (2015), a DeafBlind graduate of Gallaudet University, says that it is not possible to exist at Gallaudet. She cites many reasons: sneeze guards, individualism, long commutes on public transit, immovable chairs, bad walking conditions, people who resist touch, and so on. None of this, in isolation, is enough to precipitate existential crisis. Indeed, discourses of “individual responsibility” and “self-advocacy” relentlessly demonstrate the feasibility of every little thing. But existence is not composed of individual tasks, nor is it simply the sum of all tasks in a life. More complex concepts and calculations are needed.

For Heidegger, “existence” is the human mode of being, which involves comporting oneself toward oneself in some way while going about one’s business (Heidegger 1962, 32–35). The being of humans (which we are), the being of “substances” (which we study and think about), and the being of “equipment,” (which we use “in-order-to”) are holistically related and together, they comprise the world (63–107). Effectively going about one’s business presupposes a temporal alignment with the world. On a topological surface, we can think about those alignments as “tangent lines,” which become kinks when equipment is damaged or unusable. Too many kinks leads to existential crisis. We therefore distinguish between a kink (which involves the absence of a single tangent line along which movement is enabled), and an existential kink (which is defined by the absence of any viable tangent line such that existence is no longer possible).

In order to localize this moment of existential crisis in a limitless range of settings, we begin with a being, going about their business (i.e., existing) on the (topological) surface of the world. A being moves on the surface \( z=f(x,y) \) along the path represented in Figure 2. The various shapes the world might take (i.e., specific cultural worlds)—are irrelevant. What matters is whether or not the surface of the world is smooth. Existence can therefore be represented thus:

\[ y(t) = (x(t),y(t),z(t)) \]

Figure 2. Existence.

where \( z(t) = f(x(t),y(t)) \). Since \( (t) \) is time, and \( f(x, y) \) is a surface, \( f(x (t), y(t)) \) represents movement on a surface. We are concerned with the moment at which existence is slower than the speed of life (Figure 3). Appealing not only to topology, but also to calculus, we represent the speed of life as:

\[|y'(t)| = { \sqrt{x'(t)^2+y'(t)^2+z'(t)^2} }\]

Figure 3. The speed of life.

where \( x'(t),y'(t) \), and \( z'(t) \)denote the rates of change of existence. In response to the presence or absence of kinks, a being will either speed up, slow down, or continue at a constant speed. The speed of life is an objective temporal construct that governs such things as the back and forth of conversation, the workweek, transit schedules, etc., and which captures the fact that existence must unfold at a pace that does not preclude participation in society. I am moving with the speed of life if:

\[ | y'(t)| \cong \overline y \]

Figure 4. I am moving at the speed of life.

where \( \overline y \) is the speed of life, which falls within a range \( [r,R] \); \( (t) \)is time, and \( \cong \) means approximately equal. A human being approaches existential crisis at time \( t_0 \) as its speed moves away from the speed of life towards \( 0 \) and falls below \( r \). Movement on the surface of the world ceases if \( | y'(t_0)| = 0 \). When the speed of existence \( | y'(t)| \), at time \( t_0 \), moves toward \( \infty \) and increases above \( R \), (blows-up), existence gets out of control. In either case, we say an existential kink has occurred. That is, in either direction—too slow or too fast—there is a limit, beyond which, existence is no longer feasible.

In the spirit of Edmund R. Leach (1966), we offer this concept: the existential kink—and its mathematical formulation—as immediately applicable for purposes of comparative generalization. As our readers, we invite you to transpose these equations onto disparate ethnographic landscapes. In doing so, we will, together, build a universal framework for anticipating (and preventing!) existential crisis.


Clark, John Lee. 2017. “Distantism.” Notes from a DeafBlind Writer.

granda, aj, and Jelica Nuccio. 2018. “Protactile Principles.” Seattle, Wash.: Tactile Communications.

Heidegger, Martin. 1962. Being and Time. Translated by John Macquarrie and Edward Robinson. New York: Harper and Row. Originally published in 1927.

Leach, Edmund R. 1966. Rethinking Anthropology. New York: Athlone. Originally published in 1961.

McMillen, Sarah K. 2015. “Is Protactile Habitable at Gallaudet University: What Does It Take?” MA thesis, Gallaudet University.