When you do something quixotically, you act in an unrealistically hopeful way. Despite the impossibility of your plan, you quixotically continue trying to build a treehouse for your dog, complete with running water and electricity.
The adverb quixotically applies best to deeply impractical actions taken on in a spirit of romantic idealism. An activist who protests a logging company's clearcutting by remaining for weeks chained to the last redwood tree is acting quixotically, with noble but unattainable goals. The word comes from the impossibly idealistic hero of Cervantes's 1605 novel Don Quixote de la Mancha.