Commentary:

The explanation of the Heart Sutra will be divided into two sections: a general explanation of the title, and an explanation of the meaning of the text. The general explanation of the title will be further divided into a discussion of the sutra title and a discussion of the translator.

Seven categories of titles have been divised for the three treasuries (tripitaka) and the twelve divisions of the sutras spoken by the Buddha:

1) The first kind of title refers exclusively to persons. The Buddha Speaks of Amitabha Sutra is an example, since both Shakyamuni Buddha and Amitabha Buddha are personages. 

2) The Nirvana Sutra is an example of a title which is determined exclusively by reference to dharma. Nirvana, which signifies a dharma (dharmalaksana), is used for its title. 

3) In the third category are titles comprised of analogies. The Brahma Net Sutra is an example of this kind of title. The text of the sutra employs in its discussion of the precepts (the rules of moral conduct taught by the Buddha) the analogy of the cylindrical net-curtain belonging to the king of the Great Brahma Heaven; the curtain is a manifestation of his adornments. All through the net-curtain are holes, and in the empty space of each hole there is a precious pearl, each the brightest and most valuable of all pearls. All the way around, the precious pearls illuminate each other with light, and the emptiness interpenetrates. This precious pearl illuminates that precious pearl – back and forth. That is what is meant by their "illuminating each other." 

Your light illuminates my light and my light illuminates yours. However, the lights do not oppose one another. One of them is incapable of saying, "Keep your light out of my light," or, "I don't want my light to shine on you." There is none of that; they illuminate each other and the emptiness interpenetrates. 

In other words, then, the precepts are like the light of the precious pearls; they illuminate each other. If you keep a precept, that is, if you obey a rule of moral conduct without fail, it emits light. Each precept you keep has light. Each of the ten major and forty-eight minor Bodhisattva precepts, which are explained in the Brahma Net Sutra emits rays of light, just like the pearls in the Brahma net-curtain.

Why are the precious pearls embroidered in the holes? It indicates to us that originally, before we keep the Bodhisattva precepts, there are holes. How do we know there are holes? Because there are leaks, also called outflows (asrava). Yet the leaks can be transformed into precious pearls. If you keep a precept, a precious pearl shines. If you break a precept, there is a leak. "The lights illuminate each other and the emptiness interpenetrates" represents the Buddhadharma, the minds of the Buddhas, the minds of the Bodhisattvas, and the minds of all living beings – every mind responding to every other, mind with mind.

How did the Buddhas realize Buddhahood? It was through the cultivation of the precepts. And Bodhisattvas as well must cultivate the precepts to become Buddhas. Living beings must also keep the precepts; then they can cultivate and become Buddhas. All this represents transformation, endless transformation. Thus the title of the Brahma Net Sutra is comprised exclusively of analogy.

The first three of the seven kinds of sutra titles are called the unitary three, while the next three kinds are called the dual three: 

4) The first of the three kinds of dual title makes reference to both persons and dharmas. The Manjushri Asks about Prajna Sutra is an example, since Manjushri is a person and prajna is a particular dharma. 

5) The next kind of title refers to both persons and analogies; the Lion's Roar of the Thus Come One Sutra is an example. The Thus Come One (tathagata) is a person, and the lion's roar is an analogy. The Buddha's exclamation of the Dharma is likened to a lion's roar: "When the lion roars, the hundred beasts are terrified." 

6) The sixth kind of title is established by reference to dharma and analogy. In the Heart of Prajna Paramita Sutra, prajna paramita is the dharma and heart is the analogy. 

7) The one remaining variation combines all three unitary elements: person, dharma, and analogy. The Sutra of the Flowering Adornment of the Buddha of Great Expanse, commonly known as the Avatamsaka Sutra, is the example here. This kind of title is said to be "complete in one." Great Expanse symbolizes the substance of the dharma, and Flowering Adornment represents its function. The dharma of great expanse was cultivated by the Buddha in order to realize Buddhahood. He cultivated the six paramitas and the ten thousand practices and used the flowering of those causes to adorn the attainment of the supreme fruit, which is Buddhahood.