In "1984", why does Winston, mumble the word ''Shakespeare'' when he awakens from the dream about the naked girl?

Good question! I'd say Winston awakes muttering "Shakespeare" because of three reasons. First, Shakespeare is a representative of that old culture that the Thought Police are trying to stamp out. Second, his language is the complete opposite of Newspeak, making many things possible. Third and most specifically, there is a line in "Hamlet" that sums up the attitude of this new society: "Why then 'tis none to you; for there is nothing either good or
" This society claims they can rework the world by controlling what people think, as the "mad" Hamlet suggests.