It's Not Always About Arithmetic
I'm not sure if you've noticed or not, but there sure is a lot of math involved in photography. It's all very technical when you get down to it, and there's a formula for everything. But thankfully, some of the best parts have been left all up to you.
One of the first vocabulary words the aspiring photographer gets to learn is the "stop." As the basic unit of camera theory, it's the doubling or halving of light or time that governs exposure. Leave the shutter open for twice as long, and twice as much light will reach the camera sensor before it snaps shut again. That's one "stop" of additional light. Close down the aperture such that the opening has half the original area, and you will have affected exposure in the opposite direction. One "stop" less light will reach the sensor, assuming all other variables remain unchanged. That makes good sense, but here's where the math part comes in. The area of a circle depends on the radius measurement squared, so we are left shooting with apertures such as 1.4 and 2.8. But hey, what's a little "square root of two" among friends.
When you're first learning photography, it may seem as if improving is a matter of learning to follow more of the rules. It's just that there are so many rules.
They say the longest exposure you can safely handhold is one divided by the lens's focal length. Your mileage may vary, but there's a rule for it. Now you know what to blame when your images come out blurry. It wasn't your fault; it was on account of the math.
There are endless lists of formulas related to macro photography. The same is true for flash photography. Did you know that the light from any given source falls off relative to the square of the distance to the target? You're welcome. You may be able to avoid math if you stick with basic pointandshoot and fully automated photography, but venture any distance from that center, and you will invariably run into arithmetic.
All this used to be of great import when everyone shot with film. When shooting macro, the film photographer had to calculate the light lost through extension and mentally adjust what the camera meter told them. Long exposures back then typically topped out around 30 seconds because beyond that, it became increasingly critical to compensate for something known as "reciprocity failure." You had to know that you had to account for such things and how to do so. Not doing so meant you were flying blind, with no means of predicting what the results would be. Film had to be developed in the darkroom before you could see what it contained.
The shift to digital got rid of some of the math. Before then, we had to solve for depth of field with a formula or a specialized device that looked more like a slide rule than a calculator or computer. Today, you can work out the details with an app on your phone. But with a bit of trial and error, it's simple and safe to shoot a few test shots and look at the results. Just fire off a frame and zoom in on the LCD camera back. If you don't like what you see, make the necessary adjustments and try again. Skip the math altogether and just look.
And digital is nearly immune to reciprocity failure. I don't miss in the least having to calculate the time I needed to add to my nighttime exposures.
But for every technical arcana and mathematical equation we have been relieved of worrying about, digital seems to have added at least one new one. Now everything has been turned into numbers and math. There are only 256 shades for any 8Bit channel because there are only 256 possible bit patterns in an 8Bit byte. If you use Photoshop or any rasterbased editing program, be sure you work in 16bit mode to avoid banding caused by 8Bit truncation. Digital has ushered in entirely new backwaters of mathematics that lie at the heart of photography. Color management is merely a practical implementation of arithmetic.
Apart from this persistent math background, there is one aspect of photography where arithmetic rarely raises its head. Composition remains primarily the domain of esthetic and not formulas. Some guidelines like the "rule of thirds" help get beginners in the right ballpark, but it's ultimately about what looks good to you.
Arithmetic gets the last word on some matters. Physics is physics. But sometimes, we get to decide. Sometimes, all it takes is giving ourselves permission to jump off and explore.
