Literature is often a rather difficult matter to approach in pure theoretical terms, being highly symbolic and metaphoric. Poetry, with its often considerable reliance on, or rather use of complex literary devices, such as metonomy and synecdoche, can be even more daunting. Mathematics, in particular higher dimensional mathematics, can be a useful tool in assisting to analyze the literary concepts. We are proposing that mathematics be used as a tool in the teaching and understanding of subtle or obtuse literary manifestations. Let's look at how this method can be practically applied. We take allusion as an example. Merrian Webster's collegiate dictionary, Tenth Edition, defines allusion as "an implied or indirect reference especially in literature." Of course the literary definition is more rigorous, but for purposes let us be content with the aforementioned explication. In these terms, allusion is a tangible manifestation of an intangible reference, meant to make some comment or reference with the referent. This is not dissimilar to the basic concept of mathematical shadows. In terms of mathematical shadows, allusion can be viewed and perhaps better understood. the element being referred to, the referent, is the intangible element, much as a, say, hypercube is an intangible element. But by studying the two dimensional shadow of the hypercube, or the literary reference, we can understand and appreciate certain aspects of the hypercube itself. Although we can not visualize the four dimensional cube, its shadow can reveal its basic shape and symmetry. A literary allusion, a shadow, also is limited in what information it can relay, concerning the original referent, the hyperube in our example' but nevertheless, succeeds in providing the reader a further grasp of the concepts. Let's now consider one of Shakespeare's sonnets to see how this can really work, and specifically:

How like Eve's apple doth thy beauty grow,
If sweet virtue marry not thy show?

The allusion here is fairly explicit and straightforward, but that is really preferable to aid expliation. "How like Eve's apple," simile aside, is a clear allusion to the garden of Eden and the parable of man's fall from grace. The allusion must be understood for the couplet to have any meaning, but that story is really inaccessible. What is needed for clarification is the 'shadow' of the reference. The story then is the hypercube, and the shadow is its germane meaning in the sonnet, that is, the aspect of the parable that is directly relevant and approachable, not the myth as a whole. The apple as forbidden temptation is discussed elsewhere and is relevant rally only to the simile involved. It is with the allusion of the fall from grace that the speaker or author of this sonnet concerns himself, for that would be his eventual fate if in fact he did pursue this belle. But understanding that meaning is perhaps made more accessible from the perspective of a shadow of its meaning.