Well, this got complicated.
If I may step back for a minute, did Wayland refer to binary math as a rhetorical, geeky inside joke, or as a legitimate suggestion that photographers should know it? I strongly suspect it was the former.
The technical/artistic topic has been raging forever and will never be settled. When have art and science ever gotten along? Though I won't kid myself about settling anything, as I see it, there are three types of knowledge (approaches, mindsets, skillsets, or whatever your preferred term may be) involved in photography. They're listed below, but the sequence does not represent a progression or any kind of ranking. Every photog will blend these three (consciously or not) as they see fit.
- Aesthetic insight (The What): This is the class of insight that tells you a photo is too blurred, undersaturated, poorly cropped, underexposed, need flash, etc. Everyone has it, and every opinion is valid. While aesthetic insight can tell you what's wrong or right about a photo, it doesn't tell you how to attack it. Aesthetic insight tells you when you see a good photo, where to stand, which perspective you want. It's separate, but inextricably linked to things like knowing how to set up your tripod and which lens to use.
- Technical Insight (The How): Once you know that a photo needs more depth of field, greater sharpness, less noise, etc., as informed by your aesthetic insight, you apply your technical knowledge and fiddle with your camera. Change lenses, stop down, get a more stable support, slow down the shutter, program flashes... However, technical insight can also predict aesthetic results - this is what a photographer does when determining their settings and equipment before pressing the shutter. It's your ability to adjust white balance, crop, use a grey card, archive your work, clone, color correct, etc. Technical insight is the collision of aesthetic targets and equipment setup and use, which derives from scientific knowledge.
- Scientific Insight (The Why): This, I believe, is the crux of this thread. Scientific knowledge is probably the least necessary of the three, but it's the driving force behind the actions (technical insights) we use to achieve our aesthetic goals. Chromatic aberrations appear on heavily backlit subjects, since light dispersion is dependent on its wavelength. Narrowing your aperture only works to a point because of diffraction, as predicted by optics. Certain glass compositions produce higher-quality images, as predicted by materials science. Photoshop's Bicubic Sharper reduction algorithm can produce an oversharpened image because of the pixel-averaging mathematics. To get a good photo, you don't necessarily need to know any of these mechanisms, but their effects affect our aesthetic judgement, and they are dealt with by our technical knowledge.
I hope that clarifies some of what I think people are talking about.
Personally, I can count in binary on my fingers (up to 1,023), so it's probably obvious where I stand. At the end of the day, more knowledge of any kind will not hurt your photography.