From "The Poet" (1844)—
If the imagination intoxicates the poet, it is not inactive in other men. The metamorphosis excites in the beholder an emotion of joy.
The use of symbols has a certain power of emancipation and exhilaration for all men. We seem to be touched by a wand, which makes us dance and run about happily, like children. We are like persons who come out of a cave or cellar into the open air. This is the effect on us of tropes, fables, oracles, and all poetic forms. Poets are thus liberating gods. Men have really got a new sense, and found within their world, another world or nest of worlds; for the metamorphosis once seen, we divine that it does not stop. I will not now consider how much this makes the charm of algebra and the mathematics, which also have their tropes, but it is felt in every definition….
… Here is the difference betwixt the poet and the mystic, that the last nails a symbol to one sense, which was a true sense for a moment, but soon becomes old and false…. Mysticism consists in the mistake of an accidental and individual symbol for an universal one…. And the mystic must be steadily told,— All that you say is just as true without the tedious use of that symbol as with it. Let us have a little algebra, instead of this trite rhetoric,— universal signs, instead of these village symbols,— and we shall both be gainers.
See also Weyl on the use of symbols (in coordinate systems) and today's previous posts Birth of a Poet and Symmetric Generation Illustrated.