I spent more than half my life in the Orient. In Thailand, they bow but slightly different from the Japanese. When I was stationed in Okinawa I did my time in the karate dojo and that included a formal class in bowing, because we gaijin didn;t know how to bow properly. A common theme is the person of lower rank bows lower; how low he or she goes depends on the relative rank of the other person.
There is a whole dynamic going on with Obama’s bow- the President of the United States is equal (if not superior) to the Emperor of Japan. If Obama wanted to execute a courtesy bow, a slight bend forward at the waist followed by a slight nod of the head while maintaining eye contact would have been appropriate.
Westerners are not accustomed to bowing, and we are generally ignorant of the nuances of this custom. It’s not that we’re considered rude for not bowing- we’re considered savage hairy barbarians to begin with, the fact that we don’t bow or don’t know how to bow just compounds the issue.
There is a right way and a wrong way to do it. What Obama did has the Japanese (and the rest of East Asia) rolling in fits of laughter, because it is the bow an employee gives to his boss, or a child gives to parents. He went WAY too low; it is only one step above a kow-tow.
Compare Obama’s bow with how he conducted himself in the company of the Queen of England, and then contrast this with the way he leaned forward to bow and scrape before the King of Saudi Arabia; this certainly leaves a lot of room to wonder about which direction this man’s sentiments lie.
I am an American. The only King I bow and pay homage to is Elvis.