Today’s post deals with a bit of technical magic. What I want to talk about today applies both to digital photography and to analogue photography. It’s just that the language of digital photography makes discussion simpler.

So the question of the day is: “how many possible photographs are there?” Well, an infinite number you say. Is that so? Let’s see?

You’ve probably heard about pixels. If you look at the detector chip of a digital camera you see that it looks like a graph paper. There are little individual detectors that form the “little squares” of the graph paper. These little squares are your pixels. The camera lens forms an image onto the graph paper (aka the pixel element array). Each little pixel measures how much light it gets. If you take a magnifying glass and look closely at your flatscreen TV or computer monitor, you’ll see a corresponding array of light emitting pixels. So there’s a one-to-one mapping. Pixels on the camera correspond to pixels on the computer or TV screen.

There are a whole bunch of fine points to be ignored right now, like what happens if your camera has fewer pixels elements than your display and what about color. We can deal with these fine points another time. Right now we need to just accept the observation that a high resolution digital camera takes pretty well resolved pictures that can be displayed in all their brilliance and sharpness on a high definition monitor.

So let’s say you have a 15 megapixel camera. A megapixel is a million right? Actually, not right. A megapixel is 1024 kilopixels or 1024 * 1024 pixels; that is 1,048,576 pixels. When did a thousand stop being a thousand and become 1024 instead? Let’s not worry about that now. OK, so let’s also recognize that your standard 8 bit camera does a pretty good job of imaging things. What does this mean? It means that for any scene we do a reasonable of imaging it by defining it in terms of 2^8 =256 intensity levels. (The symbol ^ mean raised to the power. So, for instance, 2^3=8) The intensity range (called the dynamic range) is divided into 255 evenly spaced parts such that every possible intensity level (grey level) is reasonably (remember this is a high definition image) represented by by an integer between 0 and 255.

If we stick to black and white images, every pixel can take on a value from 0 to 255. Suppose that you had a two by two array; that’s only a four pixel image. Each pixel has 256 grey level possibilities; so the total number of possible images would be 256#256*256*256 = 256^4. For our 15 megapixel camera there are (15X1,048,576)^256 possible photographs that you can take. This is a large number. But it’s not infinite. To allow for color we need only recognize that color images are typically broken down into three primary color images, say red, green, and blue. Each color plane can be represented by 256 grey levels so the number of possible color images is (15X1,048,576^256)^3; that is (15X1048,576)^768. A larger, but still finite, number.

If you had all of these images on a disk, then you would have every possible picture. And I mean everything – everything that ever was, everything that is, everything that will be, everything that can be imagined, and even everything that is beyond imagination. It is the nature of discrete information systems (such as our discrete number of pixels) that the seemingly infinite becomes finite.

But, but, but …, you may want to say. Let me remind you that the human eye itself has only a finite number of detector pixels. Indeed, the meaning of resolution, the fact that a 15 megapixel display is sufficient to present all the necessary information to describe a scene is ultimately because of the eye’s resolution. And similarly the acceptable dynamic range of a scene, the number of need gray levels depend ultimately on both the dynamic range and nonlinearity of the human eye.

So two things are clear. First, we’ve got a lot to talk about. Second, the answer to today’s question is no there are not an infinite number of photographs, just a very large number of them.