Prepare for a rant, people. Over my thirty years of writing about photography, I've spent an unfortunate amount of time having to argue with people who think arithmetic is a substitute for reality. I can't say whether photographers are more prone to this delusion than other folks; it's just that I have to deal with it in the world of photography. If you are not guilty of the following misjudgments, then this is not aimed at you, so please don't take umbrage.
There is nothing mystical about the craft of photography; it does reduce to physics and mathematics. But that doesn't mean that short, high-school-level algebra equations reflect that reality. They are born of insufficient assumptions, inadequate experience, and some outright error, backed by a strong human inclination to find some way to rationalize whatever one believes, no matter how many mental hoops one has to jump through to do it.
For your edification, I present diverse examples. What they have in common is that they're all born of that irrationality that Simplicity=Truth and that what one has always believed must be True.
The equation that relates luminance, exposure, and film ISO is very clean. The real world is very messy. Many photographers have made pronouncements about how film manufacturers lie about film speeds. They do not understand how errors in exposing and processing compound; collective errors greater than one third stop are the norm. Second, they rarely know what their meter is doing. They read 18% gray cards without realizing that a properly ISO-standard-calibrated light meter's going to give them an exposure recommendation based on an assumed 12% equivalent reflectance. (Yes, true, according to both the written specs and the scientists at Kodak who know more about this subject than any of us! Don't argue!) Even those who do know that don't know how closely their meter's manufacturer followed the standard. Some are scrupulously good; others not so much.
I've written several columns about this, explaining how the simplistic assumption that one should have a blur circle equal to the size of the physical pixel just plain doesn't work well in the real world. That nice simple Rayleigh limit diffraction equation is so seductive. Problems? The theoretical blur circle isn't what you really get in the sensor plane ,and a 1:1 match between pixel and blur circle doesn't produce optimal image quality.
Need I belabor this one after several recent articles? The nonsense adamantly spouted by some people about how depth of field "should" work inspired this post. Even when faced with correct math, and computational and experimental evidence, some still insist upon hanging onto their simple and erroneous rules of thumb. Rarely does one see such clear-cut evidence of errancy.
This one is a perpetual problem. In the course of recommending (or dissing) a particular piece of equipment, someone will announce that "on average" Category A is better than Category B equipment in some aspect. That's if they're being scrupulous. Many folks don't even bother to include the phrase "on average."
This is completely useless advice when you're shopping; you don't buy an average, you buy a specific piece of equipment. That particular product may or may not perform better than one in a different category, no matter what the average says. Further, those "average" assertions are often based on some erroneous theory rather than real data.
A full frame camera does not necessarily provide better image quality than a smaller-sensor camera. An ƒ/2 lens does not necessarily provide usefully shallower DoF than an ƒ/2.8 lens. It depends on the two cameras/lenses you're considering. The variance is not ignorable.
If you've got real-world knowledge about to specific products, then you're making a legitimate comparison. Otherwise it's just hot air, devoid of any useful information. Save your breath, and save us having to listen.
Okay, that felt good!
If you're thinking about trying to write a rebuttal to the facts, don't bother. You will be wrong. This is my field of expertise! If you're a surgeon, I wouldn't argue the fine points of your surgical specialty with you. I know what I'm talking about. Class dismissed.
Featured Comment by MBS: "'Reality is not arithmetic.' —Ctein, The Online Photographer
from The Quest for Certainty,
later works volume 4, page 174.
"Of course, Ctein is more succinct."
[*Latin for "worthless remains," although fans of the Grateful Dead will be pleased to know that the literal translation is "dead head." —Ed.]