Why did prospero punish Ferdinand by facing him to carry logs?

Prospero punished Ferdinand by forcing him to carry logs as a test of his character and worthiness to win the love of his daughter, Miranda. This laborious task was meant to demonstrate Ferdinand's perseverance, strength, and dedication, qualities that Prospero valued. Additionally, it served to establish Prospero's authority and control over the situation, while also allowing Ferdinand to prove his intentions were sincere. Ultimately, the punishment was a means to ensure that Ferdinand was truly committed to Miranda before granting him her hand in marriage.