There is no ratio or particular number for division of the frame or placement of points which has any demonstrated special power. That includes both the rule of thirds and the golden ratio. However, the basic idea that centered subjects tend towards a more staid composition while off-center provides dynamic interest is fundamentally sound. Just don't get caught up a certain number. I've written extensively on this at:

* http://photo.stackexchange.com/questions/521/what-is-the-rule-of-thirds/9239#9239
* http://photo.stackexchange.com/questions/8965/what-is-the-golden-ratio-and-why-is-it-better-than-the-rule-of-thirds/9312#9312
* http://photo.stackexchange.com/questions/11060/what-is-the-diagonal-method-and-should-i-use-it-instead-of-the-rule-of-thirds/11067#11067

The golden ratio was invented by minor landscape artist John Thomas Smith in 1797, and his reasoning for it is incredibly weak — it seems mostly that he wanted to become famous for inventing an artistic concept. While the math of the golden ratio was known to the ancient Greeks, the idea of using it in aesthetics dates to around 1854, put forth by German intellectual Adolph Zeising. (The Parthenon isn't based on the golden ratio, nor is any other ancient art we know of, and despite repeated claims, there's no evidence that it was used in the Renaissance either.) And, if you look at  http://photo.stackexchange.com/questions/15298/what-historic-reasons-are-there-for-common-aspect-ratios, note that 5:8 never became popular, while 5:7 certainly did — if the golden ratio were more appealing, you'd think we'd naturally gravitate to it.

All of this comes about, I think, because art feels difficult and mysterious. It would be very comforting for their to be secret yet repeatable mathematical rules which, when followed, would lead to beauty. But, the world just plain doesn't work that way.