Over at The Online Photographer, Ctein has a great essay about the difference between science and mathematics, and why you confuse the two at your peril. And how this relates to photography, which must concern itself with real physical phenomena:
Mathematics is fundamentally an intellectual exercise. You start with a set of postulates or axioms and you see how far you can run with them, creating an extensive and self-consistent (more or less) system of theorems and proofs. It's all in the logic and it's all internal to that system. The system you create doesn't necessarily relate to the real world nor to any other mathematical system you create. It's a beautiful entity unto itself. ...
Science is all about the real world. You can construct the most elaborate and apparently ironclad logical analysis, based on indisputable first principles, and if a laboratory experiment (properly done, of course, and that's a lot harder than most photographers realize) disagrees with that analysis, you have to toss the analysis out. It doesn't matter that you can't figure out what's wrong with it, the real world has told you something is wrong with it.
Here's how this ties into photography: lots and lots of would-be photographic experts treat photography as if it were mathematics. You see this most especially in discussions of the "quantitative" aspects of the craft like sharpness, resolution, diffraction, depth of field, exposure ranges, etc. I call them "would-be experts" because they never subject to their analyses to testing. They then issue pronouncements about how digital cameras cannot match the resolution of film, or how you simply can't stop down a lens beyond a certain point without obvious and visible degradation, or that depth of field does this that or the other, or...you get the idea.
Top image via Ctein.
The whole thing is well worth reading. [The Online Photographer]