A caveat: what follows is pure speculation.
In the Wool and Water chapter of Lewis Carroll’s Through the Looking-Glass, the sheep says
“Are you a child or a teetotum? You’ll make me giddy soon, if you go on turning round like that.”
The word “teetotum” piqued my interest. A teetotum, as Martin Gardner explains in Annotated Alice, is a small top used as a device in children’s games in Victorian England. Dom Cobb’s “totem” (as it is called in most internet discussions) in the movie Inception is, in fact, a small spinning top: essentially a totum. The purpose of a totem, in the movie, is to differentiate the dream or reality of one’s own creation from those of others. This had me wondering about how similar — in theme, setting and ideas — Inception and Through the Looking-Glass are. Ariadne’s totem, a chess piece, only served to strengthen this speculative thought. The two basic premises of the movie — the possibility of multiple layers of dreams and the problem of differentiating one’s own dream from that of another — are present almost exactly in Through the Looking-Glass. The Red King sleeps and dreams throughout the dream narrative of the novel. And the fundamental ambiguity of Alice’s dream — who dreamt it, the Red King or Alice? — is almost equivalent to that of the movie: whose dream or reality is it?