Please explain the following stanza from "When I Heard the Learn'd Astronomer": "WHEN I heard the learn’d astronomer;/When the proofs, the figures, were ranged in columns before me;/When I was shown the charts and the diagrams, to add, divide, and measure them;/When I, sitting, heard the astronomer, where he lectured with much applause in the lecture-room"
It is important to realise that this poem is an example of American Romanticism. Romanticism as a literary movement started in many ways as a kind of backlash to rationalism and a period of history that resulted in many scientific discoveries and a feeling that scientific method could be used to unlock and penetrate even the most abstruse and recondite mysteries of nature.
The section of the poem you have quoted features the first four lines of the poem, and represents the triumph of the scientific method and of rationalism. It appears as if the heavens themselves have been scientifically understood, and almost seem to be chained in or encaged by the "proofs, the figures" that were "ranged in columns before me." Looking at the stars from this scientific viewpoint only makes the stars suitable objects to be quantified, as the diagrams and charts that the speaker is shown can be used to "add, divide and measure them." This of course shows the limitations of the scientific view, as it appears that this "learn'd astronomer," in spite of his great intelligence and knowledge about the heavens, has lost the simple human ability to marvel at what is beyond him. This section of the poem presents the universe as if it were some easily explained scientific formula or mathematical equation, which, if you read the rest of the poem, is what makes the poet feel sick inside.