Ian, the rules of composition are merely a mathimatical statement of what has been found over a long period of time and cultures to be what is intuitively pleasing. Many pleasing images are based on intuition and can be explained by rules. Many dud images likewise are compositionally correct. And of course, there are examples of images that do not comply but are excellant, most often because the selected composition evokes a desired response. These compositions are often stricking because of the unexpected.
Have you ever tried to justify why a woman is beautiful by the fact that her features comply with given mathematical formulae of composition? Perhaps you have given us a new method for judging beatuy and we should all post a beatuy score as to how good we look. NB Didger get minus 100 to start with for the fluffy white beard (though could be construed as a bonus this time of year
I would agree that the golden rule provides a much tried and tested compositional framework, however, there are many non mathematical concepts (lead in lines, false symmetry, perspective, etc..). These provide a language for describing photographic technique which is helpful in describing concepts, but I would disagree that they are hard and fast rules. At the end of the day a woman is beautiful because she is radiant, glowing and intelligent, not because her nose is pi/4 from her upper lip and her eyes are equidistant between her ears. The same holds true for pictures.
It is good that we have this discussion between the need for formal and informal compositional rules. Cartier-Bresson was very much in the former camp (with Howard) and made the following statement with regard to a photographers education:"There should be a visual education emphasized from the very beginning in all schools. It should be introduced just like the study of literature, history or mathematics. With a language, everyone learns the grammer first. In photography, one must learn the visual grammar."
HCB's comment needs to be seen in the context that the French system is very formal in its educational techniques and creativity doesn't come high up the list of features - everything can be taught in France! On the other hand there are a group of photgrapher who believe that artistic creativity comes from within and cannot, as such be taught, these favour informal learning. An example of such a person would be Eliot Porter who said:"You learn to see things by practice. It's just like playing tennis, you get better the more you play. The more you look around at things, the more you see. The more you photograph, the more you realise what can be photographed and what can't be photographed. You just have to keep doing it."
There is also a third group which believe that photography should be a life enhancing holistic experience and that the photograper should become more concious of life through photography. Henry Holmes Smith said on this subject:"Somebody said recently that the best thing a student could do was to get in some shows and publish a book; but nothing about becoming a human being, nothing about having important feelings or concepts of humanity. That's the sort of thing that is bad education. I'd say be a human first and if you happen to wind up using photography, that's good photography."
In reality all positions are correct as it is necessary to have technical knowledge to master the tools, however, at some point it is necessary to transcend the technical knowledge in order to establish creative art. Once technical knowledge has been transcended then it is only left to master ourselves in order to become master of our art.