I would like to have a short analysis of "One day I wrote her name" by Edmund Spenser. What does this poem show us?

This famous sonnet concerns a theme which is explored
through many different sonnets by various authors, such as Shakespeare himself. The
subject of this sonnet concerns the speaker's attempts to immortalise the object of his
affections, his beloved. The sonnet starts with his early abortive attempts, that nature
seems to be set against, as he writes the name of his beloved on the sand of the shore,
but on the two occasions he does this, the waves and the tide wash it away. The beloved
herself is shown to remonstrate with the speaker, trying to make him sea that it is
foolishness and impossible to immortalise a mortal being, as she herself will die and
decay and be remembered no more. The speaker's response is to comment on how she will
live "by fame":

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"My verse your vertues rare shall
eternize,
And in the heavens wryte your glorious name.
Where whenas
death shall all the world subdew,
Our love shall live, and later life
renew."

Through this poem and
the art of the speaker, the beloved can defy her fate and never be forgotten, as through
poetry the speaker can write her name, just as he did on the sand, but this time in "the
heavens." This will immortalise their love and give it the power to outlive death. This
poem thus shows us that immortality can be achieved through
poetry.