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I think one angle a lot of people are overlooking is all the references to quantum mechanics, particularly Schroedinger's cat.
Let me quickly explain what all that stuff with the cat was about. No equations, just the "stories" that Larry said help illustrate the math. Intrinsically quantum mechanical objects can exist, before being measured, in a 'superposition' of seemingly independent states. For example, a radioactive atom, if left to its own devices, doesn't simply just 'decay' at some fixed moment. The way it works is that it starts out non-decayed, and it slowly reaches a superposition of the "non-decayed" state and the "decayed" state, each with different "amplitude" values associated with them. Once the state of the system is measured, it collapses to one or the other state, either decayed or non-decayed, with a probability dictated by the amplitude values that the two states had. Before the atom is observed, it is both 'decayed' and 'non-decayed.' It's tempting to see this stuff as just empty philosophy. But it turns out that this kind of behavior implies certain statistical properties for the behaviors of quantum mechanical objects, and these properties have been measured and confirmed with extremely strong accuracy. So this strange quantum behavior is a matter of scientific fact.
But a physicist named Schroedinger (one of he creators of QM) saw a paradox in this. Imagine that you put a radioactive atom next to a Geiger counter. Attach this Geiger counter to a hammer that breaks a vial of poisonous gas right next to a housecat. So if the atom decays, the cat dies. Now, enclose the entire system in an ideal box that closes it off from the rest of the world until the box is opened. To the external world, before the box is opened, the atom is in a quantum superposition of 'decayed' and 'non-decayed,' so the cat is in a quantum superposition of 'alive' and 'dead.' The cat is both alive and dead until someone opens the box to take a look at it.
In the movie we see a few examples of these 'superposed' states of affairs. The strange opening scene is an example. The dybbuk (if I remember the word right) who enters the house is both alive and dead, until the wife finally makes a measurement of the question.
**SPOILERS BELOW**
A bigger example is Sy Ableman. Even after Sy dies (in an event strangely "entangled" with Larry's life, to raise another bit of QM jargon) he's still showing up in Larry's dreams, he's still costing Larry large sums of money, he's still endangering his tenure, and he's still breaking up his marriage and forcing him to live at the Jolly Roger. Also, one thing that can't be a coincidence: the symbol that physicists conventionally use to denote a quantum state is the Greek letter Psi.
And there are other examples. There's the "culture clash" argument with the Korean student's father. Larry either has to accept a bribe or be accused of defamation for claiming that it happened. The father tells him to "accept the mystery." Rabbi #2 tells him the same thing. And Larry himself tells the Korean student the same thing (or words to that effect) with regard to quantum mechanics. It doesn't make sense that the cat is both alive and dead, Larry himself says he doesn't understand it. It's just the way it is.
EDIT: And now that I think of it, all this stuff with the doctor kinda fits into this interpretation as well. At the beginning of the movie, the doctor is making measurements with regard to Larry's mortality. Throughout most of the movie, these measurements are ongoing without Larry's knowledge. Larry is the cat, in this example.
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