According to this report from the Guardian, someone claims that the golden ratio pleases the eye because of scanning ratios, i.e. how fast the eye scans things horizontally versus vertically. The actual paper is supposed to be free access (with a little digging) but you need to sign up for an account, and presumably some amount of spam mail.
I used to give talks about the golden ratio, mainly because I see it appearing everywhere. Over the years, I started to remove connections that seemed spurious, or added disclaimers, like for example the dimensions of the parthenon. Generally, I’m not as excited as before. Of course, the mathematics remain beautiful, perhaps I’m just getting a little old and a little jaded.
I’ll end with something not so spurious, according to mashable twitter was designed with the golden ratio. But how many people actually uses the twitter client?