The Joker in The Dark Knight reminds me of Dostoevsky's underground man in Notes from the Underground. The underground man declares that sometimes one wants two and two to equal five, that a person can take pleasure even in a toothache. He asserts that humans don't behave according to reason, that our behaviors and our motivations are often irrational. And the Joker wants chaos, anarchy, anything but a plan. He seems to take pleasure in his own pain, and he takes pleasure in the entirely irrational.
But it's more than that: at an aesthetic level, Heath Ledger's twitchiness seems to me a physical representation of the underground man's writing style. The sharp bursts, the halting movements, the dark laughter, the sneering, the cynicism in the stare, in the comedy. It's all unexpected exploding, chasing down tangents, a bitter mockery.
Then there are the political overtones, which were not perhaps so ham-fisted as they seemed to me (waiting months to see the movie and thus hearing others talk about it). Briefly, the film tells us this: Terrorists are illogical and lack motivations; they only want destruction. The only way to defeat them is to sink to their level, and thus all the excesses of the war on terror are justified, including torture, illegal spying, and lying to the public.
To fit this theme, nothing is truly known about the Joker's past and background--he has no origin story (he keeps lying about his scars). His motivations are not practical (he burns a giant wad of cash) but based on a psychotic love of disaster, destruction, anarchy, and chaos. He makes demands and targets defenseless civilians and institutions (like hospitals). He also achieves his ends by not valuing his own life; he regularly behaves with suicidal recklessness, daring death.
I'll be rewatching the Michael Keaton Batman soon to re-appreciate Jack Nicholson's Joker. I realize I probably haven't seen the movie in over a decade; however, I watched it so many times when I was a kid that several lines and images are still ingrained in my memory.
As I've been reflecting on Nicholson's Joker, I've thought how at the end, he becomes something more like Ledger's Joker. Throughout the film he's a clever, scheming, smooth-talking Joker. But in the big tower scene, he becomes completely unhinged in a very hilarious way. He starts pulling out silly gags when Batman beats on him (like putting on glasses and asking whether Batman would really hit a man with glasses). He laughs maniacally as he hangs on the verge of death. He becomes a silly, giggly, irrational mess: his voice and his facial expressions are all over the place: unpredictable, unexpected, chaotic.
addendum: I just rewatched Batman; sadly for my tainted memory, the late '80s were not exactly a zenith for film-making.
Nicholson's Joker is goofier throughout than I remembered: he's always laughing, giggling, cackling. He's frequently doing silly gags, and his outbursts are always unpredictable. But something distinguishes him from Ledger's Joker: rhythm. Nicholson is often dancing about the screen, clownishly prancing to music (he frequently brings music with him). There's a rhythmic performance to his movements, whereas Ledger's movements are herky-jerky, unbalanced, twittery. Though while the music and dancing in Batman give the Joker a greater sense of control, it also somehow foils or grounds the Joker's erratic behavior. It's controlled mayhem.