What do the lines "And yonder all before us lie / Deserts of vast eternity" from "To His Coy Mistress" mean?

When the speaker says, "And yonder all before us lie / Deserts of vast eternity," he means to say that life is short and is followed by death, which lasts forever.

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In "To His Coy Mistress," the speaker is trying to convince a woman to have sex with him. The speaker's main argument seems to be that the woman needs to take advantage of her youth and beauty while she can, before time takes both away from her.

In the opening section of the poem, the speaker says that he would, if he had all the time in the world, spend years and years simply admiring and wooing her. He would spend "an hundred years" admiring her eyes, and "thirty thousand" years, or thereabouts, admiring the rest of her.

In the second part of the poem, the speaker tells the woman that he unfortunately does not have all the time in the world to woo and admire her. He says that he can hear "time's winged chariot" behind him. The speaker then says that "yonder all before us lie / Deserts of vast eternity." The "deserts" here metaphorically represent death. They stretch on for an "eternity," just like death does. The speaker's point is that life is short and death waits for all of us, and that it is silly, therefore, not to make the most of life and enjoy it while you can.

To emphasize his point, the speaker says to the woman, "Thy beauty shall no more be found … in thy marble vault." In other words, the speaker is telling the woman that her beauty will be no good to her, or to anyone else, when she is dead. She should, therefore, as he has said before, make the most of it while she can. Making the most of it, from the speaker's perspective of course, means having sex with him.

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