Mathematics and Photography

I recently reconnected with an old friend from college. We were both math majors. Amy’s now a lecturer at Princeton University and she asked if I still use any of my math skills.

I realize that I do use the math I learned all the time in my photography. I’m not talking about arithmetic or even differential equations. The math I loved in school was abstract. My favorite class was topology: the study of what changes when you map one abstract space onto another.

In photography, I do this all the time. I take a multi-dimensional space (the world around me) and map it onto a two dimensional plane (my camera’s sensor). What is interesting is finding out what changes when I do this.

There is no way to compress everything I see onto a 28.7 x 19.1 mm sensor (in mathematical terms, we’d say the mapping is not “onto”). But this limitation is what makes photography an art form. Every photograph is an interpretation of the world, not an identical copy it.

In reality, because of the limitations of the medium, a photograph is more a description of the person taking the picture and the decisions he or she has made than it is a representation of the object that was photographed.

What should be included and what should be left out? Not everything can come along. It’s up to the photographer to choose what to map over from the world onto the camera frame.

There are 360 degrees of angle from which to photograph, but only one can be selected. There are another 360 degrees of vertical angle, and again only one can be chosen. Choices, choices, choices. What lens to use, what shutter speed, what depth of field. Black and white or color? What about the lighting? Not to mention the basic question on setting out to photograph, “What subject matter shall I choose”?

Basically, the choices are infinite. It’s up to the photographer to map the world onto a tiny rectangle. It is a challenge, no doubt. But it is also where the power of the art form can be found.

Good photography distills the essence of the world and makes it fit inside a picture frame. An aphorism or a line of poetry accomplishes the same feat: to hold the ocean in a drop.

Through the choices of the photographer, the world is mapped onto the camera’s sensor. What results is not a replica of the world but a miniature version of what’s important to the artist.