What insight is offered by Matthew Arnold about how an individual's interactions with nature may help define his or her character in "Dover Beach"?

Arnold lived in the Victorian Age, a time when industrialization and science were undermining traditional religious faith. Published in 1851, "Dover Beach" expresses his concerns about the belief in evolution and the loss of faith in traditional religion. Certainly, his interactions with Nature at the coast of Dover reflect his feelings of uncertainty about the changing world in which he lives.

Transcendentalist Ralph Waldo Emerson once wrote, 

...the lover of nature is he whose inward and outward senses are still truly adjusted to each other.

For the speaker of "Dover Beach" there is such an adjustment, and such a communion of feeling, as expressed in the first stanza:

The sea is calm tonight,...
Glimmering and vast, out in the tranquil bay,
Come to the window, sweet is the night air!

However, this harmony with Nature is interrupted in the fourth stanza of the poem:

But now I only hear
Its melancholy, long, withdrawing roar,
Retreating,...

In other words, faith that once encircled the world (a "Sea of Faith") is threatened by the new theories on evolution. Now, the poet, who bemoans this loss of faith, only hears the melancholy sounds of the waves as they leave the world with "naked shingles"; pebbles that no longer represent the beauty of creation.

And we are here as on a darkling plain...
Where ignorant armies clash by night.

For Arnold, who is a poet of his time, theories on evolution have sent shock waves to established and traditional religious beliefs, and these shock waves have disrupted the harmony with Nature in which he has lived. For, now, Arnold feels the human misery that "Sophocles long ago/Heard," as well as the loss of faith. This disruption of nature certainly defines Arnold's despondent nature.