Introduction:
In Shakespeare's play "The Tempest," Caliban compares Miranda with her mother Sycorax in various ways. Caliban, a deformed and savage creature, has a complex relationship with both Miranda and Sycorax. While he resents Sycorax for her oppressive rule over him, he idolizes Miranda for her kindness and beauty. Let us explore the comparison in detail.

Similarities between Miranda and Sycorax:
Despite their differences, Caliban draws some similarities between Miranda and her mother Sycorax:

1. Benevolent nature: Caliban sees both Miranda and Sycorax as inherently kind-hearted individuals. Miranda's compassionate nature is evident in her interactions with Caliban, while Sycorax's benevolence is implied through Caliban's description of her as "a freckled whelp, hag-born" (Act 1, Scene 2).

2. Isolation: Both Miranda and Sycorax have experienced isolation on the island. Miranda has been isolated since childhood, while Sycorax was banished to the island and left alone to practice witchcraft. This shared experience of solitude creates a sense of empathy in Caliban.

Differences between Miranda and Sycorax:
Caliban also highlights several stark differences between Miranda and Sycorax:

1. Physical appearance: Caliban describes Miranda as a "goddess" and "fair," emphasizing her beauty and purity. In contrast, he describes Sycorax as a "blue-eyed hag" and "damned witch," portraying her as ugly and evil.

2. Parental influence: Caliban acknowledges that Sycorax has been a negative influence on him, stating that she taught him nothing but "hateful graces." Miranda, on the other hand, has a positive impact on Caliban, teaching him language and treating him with kindness.

3. Colonization: Caliban resents Sycorax for her oppressive rule over him, as she imprisoned him and enslaved him on the island. Miranda, however, represents a different form of colonization through Prospero's control over Caliban. Despite this, Caliban still sees Miranda in a more favorable light due to her treatment of him.

Conclusion:
Caliban's comparison between Miranda and her mother Sycorax reveals both similarities and differences. While he sees benevolence in both women, he idolizes Miranda for her beauty and kindness, while resenting Sycorax for her oppressive rule. Caliban's complex feelings towards Miranda and Sycorax reflect the power dynamics and relationships explored in "The Tempest."