Renaissance artists particularly worked through the math when they discovered linear perspective, but much of what is written about their adherence to the Golden Section is over-analyzing on the part of modern critics. It's been shown that the Golden Section is divisible to such an extent that it can be mapped onto nearly anything. There's a fascinating collection of drawings in this vein in a book called "The Power of Limits," but it's mostly fanciful.
I don't think I've read anything about emotional composition, but I've read plenty about emotional response in the process of picture taking. The advice usually goes something like this: when something inspires you to take a photograph, acknowledge which emotion is registering, and then consider the "rules" to figure out how you might communicate that emotion as strongly as possible. I like the general outline of having an initial, subconscious response and then using a rational process to maximize the impact of the photograph. However, I find it difficult to reconcile "emotions" with composition", so I prefer to think of "energy" and "power" instead. How much energy or power does an image (or potential image) have? If it seems lacking, could a compositional rule help? That sort of thing. I most certainly do not advocate that rules should be primary in the process or that all good photos follow them.
Of course as an art historian, I've spent much more time analyzing images than making them, so the rational process looms large in my head, even if it does follow a subconscious response.
So, OK, Doylem, if you say you don't benefit in the field from a rational thought every now and then, I suppose I'll have to believe you. I'm just very suspicious about the idea that anyone who has read up on the subject of compositional rules can ever claim to be innocent of them.
