Rei.
The beginning and end of all things.
Have you ever wondered why Shotokan karate involves so much bowing? I know I did when I first joined a dojo. The reason is really quite simple. It is all about courtesy, and respect. Today, of all the Twenty Precepts left to us by Master Gichin Funakoshi, my personal favourite is precept number one, to me it says it all. "Karate-do begins with courtesy, and ends with rei". Now rei means a lot more than just bowing at the beginning, and at the end, of each kata. Rei also means having respect for yourself, as well as for others.
The art of Shotokan karate first came to life in Japan. A country where bowing is an integral part of everyday life. Everyone does it, everywhere, and often. In fact not bow properly whenever you meet, greet, thank, or have an interaction with another person for any reason whatsoever, would be considered extremely rude. This is especially true in the Japanese work place. Here how an employee bows depends on their rank, and their status, within the corporation. The lower a person's rank the deeper, and longer their bow is to their superiors. On the other hand, the higher a person’s rank within the company the higher, and shorter their bow is to their juniors. Often it could be likened to a simple nod of the head.
Since a dojo is also a very structured environment, it is only natural that here too how we bow is also based on rank. Even in the smallest karate dojo. After all is not the ultimate aim of karate is to use courtesy, and respect to help all student seek perfection of character? If so then whenever you have cause to bow in the dojo, be sure to do so with honesty, and true intent.
For without this underlying ideology of courtesy, and respect, karate would be a very hollow thing indeed.
Remember: "To bow well physically, you must first bow well in your mind."