Balance
Miyagi has modeled his entire practice and method of Karate after the concept of balance. He believes in the Buddhist idea of Yin-Yang, two opposite forces -- chaos and order -- which work together to balance the universe. In his approach to life, Miyagi teaches balance to his students. He lives what he preaches, so he embraces suffering and joy to the same extent. This practice gives him a special measure of peace at the end of his life after WWII when he becomes terribly depressed. Even in the grips of mental illness, he maintains balance in his thoughts, words, and actions. After almost a full lifetime of learning from Miyagi, Ota remembers this one belief the best. It has become his mantra as well.
Defense
Miyagi seems to constantly rest in defense mode. The Karate method which he teaches is one of combat. Contrary to the Hollywood depiction of Karate, Miyagi's actual methods are terribly violent, designed to kill and protect against death. It's a style of combat which Miyagi has perfected as a defense. His defensiveness continues, however, in the form of reserve. He never utters three words when one suffices, which leads to a rather intimidating teaching style for poor Ota. Finally, Miyagi is thrown into the midst of an external defense when Japan enters WWII by bombing Pearl Harbor. Ota is actually in charge of defending the Island of Okinawa from the U.S. attacking forces. All of Japan is braced for a seemingly un-winnable fight. In his old age, Miyagi retreats even further inward, trying to preserve his life's work of peace in such troubling times as those that followed the war.
Legacy
Ota devotes his fictional narration to Miyagi's legacy. In fact he has dedicated his life to finishing Miyagi's work. It was always Miyagi's dream to establish Goju Ryu, his method of Karate, in Japan and then even further. To him Karate was a method by which to live, more than an art. Training under him for years, Ota witnessed firsthand how important Karate was to his master. After Miyagi dies, Ota determines to realize his dream by taking Goju Ryu various places. Already a Karate master, he teaches his practice to the younger generation and anyone who is willing to listen and take matters seriously. In the end, Ota inherits all of Miyagi's life's work in the form of knowledge, which he is able to pass on to the next generation as well. He is participating in Miyagi's legacy, ensuring his master's name will be remembers for centuries to come.