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 diagrams, to add, divide, and measure them,
When I sitting heard the astronomer where he lectured with much
applause in the lecture-room,
How soon unaccountable I became tired and sick,
Whitman is shown these results, but in a way that can only be examined externally. The “charts and diagrams” parallel “the proofs” and “the figures” in the line above. However, the only way Whitman is shown to understand these concepts indirectly through displayed calculations. 

When I Heard the Learnd Astronomer