"It would be kind of silly to walk to the middle of the island and there's a kind of a big large refrigerator box sitting there and Kate's horse comes trotting out and Sayid's little cat and Jack's dad ... that would be kind of the worst idea in the history of ideas."
This is the first time executive producer Damon Lindelof connects the magic box that Ben talked about to Amira's cat, but the clues were there from the beginning. When Amira, a former torture victim of Sayid's, tells Sayid about how she found a cat in a box filled with fireworks, it must be a reference to Schrödinger's cat, a famous thought experiment. Not only was Amira's cat trapped in a box and surrounded by lethal materials, but the scene that plays out has a possible reference to the thought experiment: You really can't predict what's going to happen with the scene, but then Amira forgives Sayid, an outcome that seemingly sprang from nowhere. Just like the seemingly paradoxical cat (a bit of a stretch on that last, but it makes a nice symmetry). (Please see Schrödinger's cat summary at the bottom of this post if you're not familiar with it)
Maybe this gives us a clue as to what the magic box is. Could it have something to do with quantum theory? The magic box, as Ben describes it, seems to be a metaphor for some force on the island that provides a specific thing--like a memory or a memento--that a character needs. Sayid is the character most connected with cats (Mikhail's cat in Enter 77 is named Nadia), and Sayid's story also has connections to Schrödinger's cat if we see the thought experiment as a theme in fiction. He doesn't quite know if he's good or bad; it's up in the air--either possibility could end up as the result--so he seems to be good and bad at the same time. This is a common theme throughout Lost, and I'm sure there are many more parallels to be drawn between Schrödinger's cat and Lost's characters.
WHAT THE CAT EXPERIMENT IS ALL ABOUT In 1935, Austrian physicist Erwin Schrödinger conducted a thought experiment: Quantum mechanics says that until a conscious observer observes a particle, the state of that particle cannot be accurately known. "Every particle has a probability of being in any state. It does not exist in a particular state until an experimenter observes it" (PBS). In the thought experiment, a cat is locked in a steel chamber with a small amount of radioactive substance linked to a Geiger counter. The Geiger counter is hooked up to a hammer poised above a flask of toxic acid. If the Geiger counter detects that one of the radioactive atoms decays, it will trigger the hammer to smash the flask and unleash the acid, killing the cat. But if no atoms decay, which is also a possibility, the cat will live. Until an observer sees whether an atom has decayed or not, both possibilities are present--it has and it hasn't. So the cat is both dead and alive.
Schrödinger used this scenario to try and prove that quantum mechanics couldn't work on a large scale, but the idea of the living and dead cat is still defended today. There's also the many worlds interpretation, which seems to have particular relevance to season six of Lost (depending on your view). The branching possibilities create two split realities, one in which the cat lives and one in which it is dead. The realities are both real, but they cannot interact.
Can anyone think of more parts in the show where the writers may have used these ideas?