Hi Anton,
I found some interesting info on the golden section (as used in architecture and art)
here.
As far as I understand it, the rule of thirds is basically a simplification of the golden number (a rounding up if you like) to give a meaningless justification as to why photos look better with the subject not in the middle (sometimes only). You may as well multiply the mass of an electron by e for all the help it can give. Having said this, it does seem to obsessed many finer minds than mine for many centuries, and in some disciplines maybe some kind of heavy internal structure can be desirable, even if not recognisable in the end result (music and architecture for example). Not in photography though.
cheers, David