By Aji Kang

Recently I have been spending a lot of time talking with my mom, and we have been pondering together over what makes people into the people they are. Naturally, these discussions have made me wonder what makes me perceive people as the people they are.

I noticed that there is a clear difference between my perception of another person when I am giving my full attention to them in the moment, and my perception of them when my concern is towards something else. If someone is in front of me and I am giving my full attention to them, the things that become most visible to me are things that are harder to categorize: their idiosyncratic ways of caring and thinking, the particular way that they use words or their body in the moment, the details of their way of thinking, and their way of playing with identifying or not identifying as their age, ethnicity, or gender roles, in this moment. Meanwhile, if they are in front of me but I am concerned with something else, the things about them that become visible to me are restricted to the things that are easier to categorize: their character trope, habits, the social categories they technically fit into, the parts of their worldview which I can caricature in my mind, and the contexts I associate them with. It seems then that there are two different ways of perceiving people: one that is “up close,” which allows me to feel all that I have in common with another person, and becomes most visible in the moment of paying attention to them; and another that is “from afar,” which gives me a sense of the big picture of what issues this person’s life is mixed up with, and is most visible when my attention is no longer fully on them.

If other people also perceive me through these two different modes of perceiving, then I am very lucky to have people in my life, like my mom, who give me their full attention when I am with them. In those moments when I am perceived up close, I feel seen in some meaningful way, and I feel like I likewise see them in some meaningful way. But then… if we see eye-to-eye in those moments, why do I still feel that when we step back from each other, my dreams run counter to the desires of these people I love? And why do I feel a persistent imperative to justify, using our shared values, perspectives I have which are fundamental to who I am? Why do I feel deep anger at the injustices they have faced when they themselves are numb towards them? And why does communicating that these differences do not stem from my inadequate self-understanding feel impossible? In short, why does it become apparent to me that even when our view of each other “up close” is the same, the view that we have of each other and ourselves “from afar” is so different?

There is a story in geometry that involves a similar twist—two things that look the same from up close become very different from afar.* The story starts like this: suppose that upon a plane (also known as a flat surface), you drew three distinct lines, called l, k, and j, where k and j are both perpendicular to l—as in the image above. In geometry class, teachers usually say that this makes k and j parallel to each other, which means that no matter how far left or right you extend k and j, they will not intersect. It is tempting to believe that the way that the lines l, k, and j are arranged somehow contains the secret to why k and j do not intersect. Indeed, I want to believe that if two people can see each other in parallel from up close, surely there is no way for there to exist any kind of conflict in their view of each other from afar.

Imagine, however, that you and a friend are on a boat somewhere along the equator of the Earth—the surface of which, in our thought experiment, is purely ocean, so no land gets in your way. If you travel purely east (or purely west), you clearly will be traveling in as straight a line as you can. You also will not sway off the equator as you travel purely east. For this reason, the equator of the globe is called a geodesic, which is the same kind of thing that a line on a plane is—if a curve c on a surface is a geodesic, then given any two points A and B on the curve c, the shortest path from A to B is to travel along c, as opposed to stepping off of c.

Let’s call the equator of the Earth l. Say that your friend gets on a different boat that starts at a different point on the equator, and both of you begin traveling perfectly north. Call the path your friend travels along k, and call the path that you travel along j. If you both travel at the same speed, then you’ll meet up at the north pole; this means that k and j intersect. Note that the north direction is perpendicular to the east direction; for this reason, we can say that k and j are both perpendicular to l.

In the above image, I have drawn the geometric image that accompanies this thought experiment: on the surface of a sphere are three distinct “lines,” or geodesics, l, k, and j, where k and j are both perpendicular to l. In contrast with when I drew these lines on a plane, k and j intersect when drawn on the surface of a sphere. This tells us that the fact that k and j do not intersect when drawn on a plane has nothing to do with the way that l, k, and j are arranged with each other; it has to do with the space that they exist in—be it a plane, the surface of a sphere, or some other surface. Likewise, the fact that two people may or may not have a fundamental conflict in their perception of themselves from afar has nothing to do with how much attention they give when they are beside each other.

The surface of the Earth appears like a flat surface to us, and it would require us to do something incredibly difficult to intuitively see that the Earth as a whole is not flat: we must contemplate vast distances along the surface of the Earth, or go very high up into the sky. In the same way, it seems that locally—that is, when we both pay attention to each other and can see each other in a moment from up close—we inhabit a flat surface. We feel this when we can both be playful and feel like we share some crucial taste with each other, and when we can communicate our emotions and reasons in mutually recognizable ways. However, globally—that is, taking our attention away from the other to view them from afar—it is apparent that the space we inhabit has its own idiosyncratic curvature—be it the lack of curvature in the case of a plane, or what is referred to as “positive” curvature in the case of a sphere. Trying to justify myself using shared values would be like trying to demonstrate that the arrangement of l, k, and j is fundamental to the fact that k and j do not intersect, when in reality it is the curvature of the surface that makes k and j intersect or not.

In a previous post, I asked questions about the meaning of a quote by Simone Weil: “Every being cries out silently to be read differently.” In their own post, Duxy responded to these questions with a claim of their own: “I find Weil’s idea [of being read differently] to be of a more genuine understanding of a person than I believe empathy entails. I believe that understanding emotions is not enough; instead, every person’s desire to be understood differently goes as deep as their beliefs and desires.”

What I take away from Duxy’s claim now is that empathy gives us the ability to understand another person in the moment of paying attention to them from up close. Meanwhile, reading another person differently gives us the ability to perceive them from afar the way they are silently asking to be perceived.

Duxy also says about the difference between crying out silently and announcing one’s desire from the rooftops, “It is the difference between a mother making her child’s favorite meal when she notices they have less energy than normal, and making the meal upon request. While both of these actions mean a lot, there is a beautiful recognition in the mother being able to see her child’s silent cries. It is that beauty that we long for, for someone to understand us so well that we need not tell what we need, but for our needs to be recognized anyway.”

I think that my mom and I both try to respond to each other’s silent cries, but I will confess that it is very easy for us to unjustly assume that we reside in a plane, because that is what we see of each other from up close. However, I get a sense every now and then that somehow, unpredictably, we catch sight of the curvature in our relationship, and we can make the choice to continue traveling along a geodesic or to step off of it. And I imagine that our choices at these moments are a big part of what makes us into the people who we are.

* You can read more about this geometry story, and how this idea has raised questions about the shape of the universe, in chapter 1 of Geometry with an Introduction to Cosmic Topology, by Michael P. Hitchman (which can be found at this link: https://mphitchman.com/geometry/GCTscreen.pdf).

Aji Kang is a writer who, in college, majored in theoretical mathematics and minored in English and philosophy. You can also find Aji as A Well-Rested Dog on YouTube.