The Balrog Theorem

[Witch-King]

My fellow Barrow-downers, I present to you the Balrog Theorem, proving mathematically that Balrogs do not have wings.

First, some derivative information using quotes:

"His enemy [the Balrog] halted again, facing him, and the shadow about it reached out like two vast wings... The fire within it seemed to die, but the darkness grew. It stepped forward slowly onto the bridge, and suddenly it drew itself up to a great height and its wings were spread from wall to wall."

Now, my theorem:

If shadow=wings, then wings=shadow. If the wings spread, then the shadow spreads. Concordedly, vis-a-vi, ergo, when the wings stretch from wall to wall, the shadow, which is the wings which are the shadow, does so as well. It's a paradoxyl simile. Thus there are only figurative wings, and no literal wings.