What does Hamlet mean to say "yeah, from the table . . . yes, by heaven!" in act 1, scene 5? Please mention literary terms used in these lines.

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Having received the command to avenge his father's death, Hamlet speaks these lines, committing himself to the murder of Claudius:

Yea, from the table of my memory
I’ll wipe away all trivial fond records,
All saws of books, all forms, all pressures past
That youth and observation copied there,
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Having received the command to avenge his father's death, Hamlet speaks these lines, committing himself to the murder of Claudius:

Yea, from the table of my memory
I’ll wipe away all trivial fond records,
All saws of books, all forms, all pressures past
That youth and observation copied there,
And thy commandment all alone shall live
Within the book and volume of my brain,
Unmixed with baser matter. Yes, by heaven!

Hamlet's mind is wonderfully imaginative, and he speaks in metaphors that show not only his wide range of knowledge but also his ability to place diverse concepts in relation to each other. Here, he compares his mind to a book, or a tablet, on which is written a range of experiences and thoughts. By wiping or erasing all his past thoughts from his memory, he is saying he can devote himself fully to one task: avenging his father. One way Hamlet's mind works—and it is a tactic we see in the sonnets as well—is that he sets forth a rather basic metaphor (the mind is a book), but then he continues to develop it, as we see each successive line do here. This both intensifies the metaphor (or poetic conceit, which is the extended metaphorical pattern found in verse) and shows that Hamlet is a character who speaks and then immediately reflects on or interrogates his own speech.

This metacognitive quality in Hamlet has often been noted as singularly powerful. Some readers even feel that Hamlet is the first truly modern character, not only thinking but demonstratively thinking about the mind and how it constructs its statements.

In addition to metaphor or conceit, which is the most powerful figure used here, we could say that youth and observation are personified. In the literal reading of these lines, they are agents who transcribed into the book of his memory the thoughts he is now displacing. This too is characteristic of Hamlet's mind. Thoughts are so vibrant in his intellect that even abstractions are suffused with the power to act.

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The lines you are interested in read in full,

    Yea, from the table of my memory
    I'll wipe away all trivial fond records,
    All saws of books, all forms, all pressures past,
    That youth and observation copied there;
    And thy commandment all alone shall live
    Within the book and volume of my brain,
    Unmix'd with baser matter: yes, by heaven!

Hamlet is speaking to himself (a soliloquy) after the Ghost of his father has told him of the treachery of both his uncle and mother.  He vows to forget his intellectual pursuits, and everything that he previously held dear in his life (like his mother's love) and instead will replace all of those things with a singleminded pursuit of revenge and justice for his father.

Hamlet uses metaphor, ie, "the table of my brain" to help him envision everything in his life that has transpired previously, thinking of his books and experiences as being laid out for him to see, and all is meaningless clutter compared to that which now dominates his life:  betrayal, murder, and revenge. 


 

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