The Other's Mirror

The Other's Mirror

I had already written a blog post about this phrase, and after finishing it, I remembered I had a book that alluded to the mirror. I went looking for it, and indeed there it was, so here comes this new entry. If anyone would like to see the previous post, it is at this link: https://reuniendoletras.blogspot.com/2026/01/seeing-oneself-from-others-perspective.html

 
A phrase that seems simple

«For me, the ultimate agreement would be trying to put yourself in the other person's shoes. Even if just for a little while. And in that way, manage to see oneself from the other's perspective. I hope that I have been able to do it at some point».

Jorge Schussheim's quote seems to propose a form of understanding: trying to occupy, even if provisionally, another person's place. But there is something in it that goes beyond empathy. It does not merely say to understand the other person, but to see oneself from the other.
That slight shift changes the problem. It is no longer just about knowing what someone thinks, but about imagining what happens when one ceases to be the center of their own gaze.

The mirror that seems to reflect us back to ourselves

In The Ambidextrous Universe (published in Spanish as Izquierda y derecha en el cosmos), Martin Gardner begins the chapter dedicated to the fourth dimension with Immanuel Kant. He does not do so because Kant discovered a better way to look at others, but because he found a philosophical problem in something we all believe we understand: mirror images.
Gardner recalls Kant's example: what could look more like our hand or our ear than its mirror image? And yet, we cannot place that image in the location of its original.
The image appears to be us. But we cannot make it coincide with us.

Kant's problem

Kant is interested in what are called “incongruent counterparts”: objects that possess the same geometric properties, yet cannot be superimposed on one another.
Two hands can have the same measurements, the same angles, and the same general shape. However, one is left and the other is right. Simply moving or rotating them within our space is not enough to make them coincide.
And here something strange appears.
It is not that one hand has a property that the other lacks.
It is that they are identical in certain respects, yet they cannot occupy the exact same space.
Kant finds a philosophical difficulty in this: what does this impossibility tell us about space and about our way of knowing things?

The mirror that does not reflect exactly what we think

In The Ambidextrous Universe, Martin Gardner begins his exploration of symmetry and asymmetry with a deceptively basic question: what exactly does a mirror do?
We are used to saying that it reverses left and right. However, Gardner shows that this way of speaking can confuse us: the mirror has no preference for our sides, but rather reverses the axis perpendicular to its surface. What we believe we see as a left-to-right reversal also depends on how we are positioned in front of it.
The image appears identical to us, but we cannot make it coincide with our body through the movements allowed by our space. It is our image and, at the same time, it is not our body.

The unexpected leap

Here is where the connection appears.
Schussheim proposes changing positions in order to see oneself differently. Gardner shows that one figure can be identical to another in its properties and yet not be superimposable upon it within the space we inhabit. In both cases, the difficulty lies not necessarily in what we are looking at, but in the position from which we try to make it coincide with ourselves.
The mirror gives us back an image that we recognize, but that we cannot occupy.
He proposes something that, read alongside Kant, acquires a different resonance:
What happens when I try to make my own image coincide with the image the other person has of me?
It is not exactly the same geometric problem. But there is a similarity in structure.
In Kant, a figure can be equal to another in its properties and yet not be superimposable on it.
In Schussheim, one can try to understand the other and, at the same time, discover that the image one has of oneself does not coincide with the image that appears from the other's gaze.
The difference is that, in one case, the limit lies in geometric space; in the other, in our perspective.
The other returns an image of ourselves that we can recognize, but that we cannot fully occupy either.

 

The mirror as a question about knowledge

Gardner does not stop at the problem of the hand. He explains that Kant came to relate mirror images to a deeper question: do we know things as they are in themselves, or only as they appear within the conditions of our experience?
And here the connection with Schussheim becomes more interesting.
Because perhaps the other is not just someone who helps us know ourselves better. Perhaps they are also someone who shows us that our own image of ourselves is built from a particular position.
I may believe that I am a certain way. But when I try to see myself from another perspective, I discover that there are things I had not considered. Not necessarily because the other person is right, but because I was looking from a place that did not allow me to see them.

What if the other were a dimension?

Gardner explains that, in a higher-dimensional space, an asymmetric figure could be made to coincide with its mirror image through a movement that our three-dimensional space does not allow. It is not that the figure is different: it is that the space available to move it is different.
So we can formulate a question that does not literally belong to Gardner or Schussheim, but is born from both:
What if putting oneself in the other's shoes were a kind of fourth dimension of perception?
Not because empathy is a spatial dimension, but because it demands imagining a movement that our habitual position does not spontaneously allow us to make. One tries to step out of one's own perspective to discover what one looks like from another.
As if to say:
I cannot make my image coincide with myself from here. Perhaps I need to change my position.

The limit of the comparison

But the connection must also preserve a difference.
In Gardner, the problem is geometric: two figures can be mirror images and non-superimposable within a given space. In Schussheim, the problem is human: the other is neither a figure we can move at will nor a position we can fully occupy.
That is why the comparison does not prove that empathy is a fourth dimension. The comparison serves to reflect on the limit of our gaze, not to resolve it.
And that limit is important: we can try to understand the other, but we cannot become them. We can imagine how they see us, but we cannot guarantee that this image is true. We can step out of our position, but we cannot cease to have a position.

Returning to the mirror

Perhaps that is why Schussheim's quote ends with a doubt:
«I hope that I have been able to do it at some point».
He does not claim to have succeeded in seeing himself perfectly from the other's point of view. He says I hope that I have been able to do it at some point. There is an interesting modesty in that ending: empathy does not appear as an ability acquired once and for all, but as an attempt that may or may not have occurred.
And Gardner, in a way, had prepared us for that modesty. The mirror seems like something we understand until we try to explain what it actually does. Then we discover that our everyday gaze also has its conventions, its limits, and its ways of confusing us.

The remaining question

Perhaps the unexpected connection between both texts is not that the other functions as a mirror. That would be too simple.
Perhaps it is this: The other is that which forces us to discover that our own space of understanding has limits.
And so, putting oneself in their shoes does not mean abandoning one's own, but trying to imagine what movement would allow us to see what we cannot reach from where we stand.
As if empathy were, for a moment, a form of impossible geometry.
And as if knowing oneself consisted not merely in looking at oneself, but also in discovering from where one is looking.

Written with mate and a bit of artificial intelligence.