When everything exists within your big mind, all dualistic relationships drop away. There is no distinction between heaven and earth, man and woman, teacher and disciple. Sometimes a man bows to a woman; sometimes a woman bows to a man. Sometimes the disciple bows to the master; sometimes the master bows to the disciple. A master who cannot bow to his disciple cannot bow to Buddha. Sometimes the master and disciple bow together to Buddha. Sometimes we may bow to cats and dogs. –Shunryu Suzuki (Zen Mind, Beginner’s Mind)
While the point of training is to persuade your dog to bow to you, in my book I discuss the fact that genuine masters also bow, in a manner of speaking, to their dogs. Among other things, doing so acknowledges the mutual respect that is part of being friends.
In the examples Suzuki chooses, the roles are also reversed, so that the one who bows becomes the one bowed to. Reversing the roles undermines distinctions and thereby brings us within the nondualistic big mind. Thus, for example, I bowed to my dear (and sorely missed) Kestra whenever I relinquished control—dissolving a boundary—and let her lead the way and set the tone of our rambles.
Generally speaking, bowing is a gesture which acknowledges that another being has earned a place of respect in our world. Again, “big mind” teaches that ultimately all beings deserve a bow, inasmuch as all beings are connected in the cosmos. Bowing thus indirectly acknowledges the interdependence of beings.
The Buddha taught how to meditate on the interdependence of all beings, and this remains a fixture of Buddhist practice. Besides being regarded as a metaphysical truth capable of being directly experienced, meditating on interdependence also offers yet another path to compassion—for reasons I’ll leave to your speculation.