What does the rainbow symbolize in the poem "my heart leaps when I behold a rainbow"?

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The search for truth has often been a tension between reason and emotion.  Many feel that reason by itself can bring us to knowledge, but not to truth.  For Wordsworth, nature speaks to us of the Divine without the intervention of reason; it is, in the Transcendentalist's sense, intuition rather than tuition.  When he beholds the rainbow, Wordsworth doesn't see the droplets of water breaking down sunlight into its spectrum of colors; he perceives the Divine in what he sees.

I have always thought that the closing lines of "Ode on a Grecian Urn (Keats) best summarizes the Romantics' search:

'Beauty is truth, truth beauty,—that is all      

Ye know on earth, and all ye need to know.'

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