If you are trying to look for spirals and ratios when composing you aren't really looking at your subject.
Aye, but that's assuming the subject has any importance. And to be honest, for me it doesn't have all that much. The subject may be a trigger of interest, but I am too much a Modernist/Formalist to care about genre if I can achieve the same kind of result in a landscape, or a still life, or a nude.
The disadvantage of 'rules', whether of thirds, the Golden Mean, or whatever, is that they are reductions; a shorthand conclusion of mechanical principles. That's not to say they don't work, they do, but they don't allow for the wider variety of possibilities. That's where Arnheim's book is helpful, or for that matter many of the others, like Ernst Gombrich, who have tried to analyse psychological impact in the visual arts.
What I find key is the frame, the break point between reality and illusion. The challenge in composing is to fill the frame in a visually meaningful way, whatever the format. This why I find the square most appealing - rather like the structure of a sonnet it is creatively demanding, as at first there may be no obvious way to fill the space. It hardly matters whether you make that decision in the viewfinder or in Photoshop.
With street photography, while I'm always going to size up the subject, as far as composing is concerned I look at my subject as if it were a cardboard cut-out, and shoot when I have it fitting into the background as I would like. My concern might be the lines made by the subject within the field of view, or it might be the relative weights of tones and their position within the frame.
One little trick you might like to try, as it tends to emphasise form over content: turn your image upside down and see if the composition still works for you. I think it helps show up the weaknesses.
