Mathematics and Photography

by Todd Smith on July 25, 2008

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.

{ 3 comments… read them below or add one }

Kaz Maslanka July 25, 2008 at 8:35 pm

It is interesting how you formulate your thoughts on mapping 3D to 2D … I think more in terms of projecting the three dimensional world on a two dimensional surface. Hmmm geometry or numbers?
Cheers,
Kaz

Todd Smith July 25, 2008 at 10:38 pm

Thanks, Kaz! I think they are the same concept.

Projecting a 3D world onto a 2D surface in topological terms would be called a mapping of a 3D space (or set, or field) onto a 2D space (or set, or field).

What is interesting about photography is that I can choose what to bring over from the 3D world onto my camera sensor’s plane.

It’s not possible to bring everything I experience in three dimensions into a world of only two dimensions. So I am challenged to find the essence of what I see in the world.

By the very act of photographing, I am forced to distill my experience to its most essential elements and project only those that fit into my tiny two dimensional rectangle.

In this way, photography can be said to be a means of transcending the everyday experience of the world and seeing something deeper.

Because of this basic challenge in photography, of mapping 3D on to 2D, it makes me slow down enough to really look at what I’m seeing.

Todd Smith July 25, 2008 at 10:42 pm

P.S. Nice blog Kaz! For everyone reading, check out Kaz’s blog on mathematical poetry: http://mathematicalpoetry.blogspot.com/

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