What is the significance of the lines "Miracle, bird or golden handiwork, / More miracle than bird or handiwork" in "Byzantium"?

The significance of these lines in "Byzantium" is that they relate to one of the poem's central themes, the immortality of great works of art. As the bird is mechanical, because it is a work of art and not a real bird, it achieves a state of immortality that contrasts with the "common bird or petal" which will eventually die.

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Among a number of other themes in the poem, Yeats's “Byzantium” deals with the immortal nature of great works of art. We can observe an illustration of this theme in the third stanza, when the speaker's eye is caught by what appears to be a miracle. In actual fact, it's a golden mechanical bird, and yet so impressive is it that it puts all real birds in the shade.

The bird may not be real, but it appears to be crowing like the cocks of Hades, the kingdom of the dead in ancient mythology. This work of art, this masterpiece is more than just a bird or a piece of handiwork, it is a veritable miracle:

Miracle, bird or golden handiwork,

More miracle than bird of handiwork.

As with all great works of art, the bird is truly immortal. And because it is immortal, because it is made of “changeless metal,” it can look down upon the “common bird or petal” and all the other aspects of the physical universe, each of which will eventually die.

What Yeats appears to be expressing here is the belief that art, because it is immortal, transcends the here and now, the world of space and time, the material world that we all inhabit. That world “of mire or blood” is scorned by the simplicity of the golden mechanical bird as it remains untouched or unscathed by the ravages of time.

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