Do I dare to eat a peach?
Prufrock’s concern here is a very real consideration for many people. For example:
Would you be embarrassed to eat heavily sauced chicken wings on a first date?
Would you be embarrassed to eat messy BBQ ribs on a job interview that included a lunch?
Would the risk of cracking a tooth scare you away from eating pitted fruit?
Prufrock’s getting on in age; he doesn’t want to lose a tooth, or eat the “wrong” thing as part of his diet, or be seen with delicious peach juices running down his chin: in other words, he’s going crazy troubling himself with mundane concerns. The line also functions more subtly as a metaphor for the girl he desires, who appears to be a younger woman. Think of the peach as a kind of stand-in for Eve’s apple. (And if you’re seeing some sexual innuendo in the line, you’re not wrong.)
The peach is also a metaphor for taking a bite out of life, as if taking the bite will justify his existence and renew his vitality. The fruit is juicy as hell and drips all over. It’s real; sweet and sour, hard and soft, smooth and fuzzy, ripe and unripe. It’s delicious, but you can’t let it rot.
Hamlet, to whom Prufrock feels inferior, contemplates things like murder and the secrets of the universe. Prufrock, though equally fraught with existential malaise, is more pathetic, as his contemplative nature lacks any of the dramatic interest of Hamlet’s. The simple act of eating a peach is something that consumes his conscience in bitter inner debate.
In the end, too, unlike Prufrock, Hamlet actually did something. Though it took the prospect of his own death to spur him into action, he got decisive and killed his uncle Claudius. Prufrock sees himself as a coward who will never find the courage to act no matter what.
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