Some Like it Hoth or We Don't Need No Stinkin' Laws of Thermodynamics!
I have an idea that I think connects up several threads from last night's episode, but it might not be all that clear so feel free to add in or suggest changes.
It's coming out of the reference to the polar bear experiments--where Dr. Chang threatens to send Hurley to measure Polar Bear poop if he lets any of the secrets about the death and the transport of the body out of the bag (so to speak). And this was not the only reference to stinky stuff last night--there was the smell of the body which Hurley mistook for other bodily byproduct. And there was the idea of Miles changing his own diaper. Somehow all of this made me think of the second law of thermodynamics and entropy.
Basically the idea that everything is moving toward disorder, toward waste, and toward eventually the end of all existence (a good explanation of entropy from a story perspective is Asimov's short story "The Last Question" which DL linked on the site for the speculative fiction class). The idea that everything is moving toward increasing entropy is really the only concept in physics which necessitates a temporal direction--the arrow of time. But what happens in a place where time is loopy?
Connecting up entropy to mythic/psychological structures and to information technology:
A few other things I picked up about entropy from the wiki entry--entropy is also the measure of uncertainty of a system--it shows the uncertainty which remains after observable macroscopic properties are taken into account. Thinking in terms of a probability wave--a probability wave with a high peak indicating a system with a high degree of certainty--has low entropy. A more even distribution of probability means high entropy. If I'm following this then--there's a counter force to entropy--and that counter force is consciousness, the observer, the story-teller?
Interestingly--entropy has been used to describe something in the transmission of information like story-telling. The information that is lost between someone giving a message (telling the story) and someone receiving it is called Shannon entropy (an interesting coincidence).
And then going back to what I was writing about Lacan (or Freud, or Oedipus, or Osiris--pick your mythic framework :-)--we might think of the idealized function of language (the Symbolic) as perfectly capturing the Real as a kind of language without entropy, with no loss of information. Actually sort of what Horace is trying to enforce in his "Circle of Trust"--complete transparency within the circle--but only possible if trust is absolute and reciprocal. In which case there would be "no questions asked" (because understanding would be inherent to the system). Or another way to think of that is an idealized reconnection with the Father (no loss)--no inner emptiness (as Bram describes Miles having--and interesting that what fails to compensate for that inner loss is the material--filthy lucre). No Dad chopping off your hand due to familial misunderstandings.
OK--I'm short of time, but let me just give a sense of where I'm going and then leave this as a jumping off point (I'll come back and on to later as well):
Entropy>>movement toward disorder, death, non-existence
The exact opposite of Entropy would be Perfection--the perfect circle, complete transparency of language, the world and the word as the same ("In the beginning"--in other words).
Balanced between Entropy (Hoth--Ice--loss of energy ) and Perfection (Hot) is I think--story, artifice, "drag" or costuming (Some Like it Hot). Miles fills the emptiness inside left by the loss of his father. Simultaneously he "knows" that his father is gone and heals the pain of that loss with his father telling him a story.
Ok--let's see how much Shannon I generated... 
The third faction
On a completely different subject in relation to the episode--thought the "What lies in the shadow of the statue" crowd were established as a third faction last night, neither Widmore's nor Ben's. Miles, I think, asked Ben for 3.2 million to see if he were a member of this crew, and he wasn't. The guy who picks Miles up, Bram, is an allusion to Bram Stoker--which fits in with the whole dead but alive theme. I think the main work that the writers might be thinking of in connection with Stoker, though, is probably not Dracula, but Lair of the White Worm (aka The Garden of Evil). In that text, the monster (the white worm) is female--a being able to appear as either a woman or a gigantic snake. Stoker there was probably referencing Lilith--and the whole idea of the first woman going off to couple with monsters and create creatures, part human, part animal. Which might then tie back to the statue if it turns out to be Taweret. And then the shadow, I would bet, would be the shadow cast by Taweret's pregnant belly. I wonder if what lies in the shadow is Jughead? The belly of the beast? BTW does anyone know if "belly of the beast" is an allusion to Jonah?
Anyway, I'm thinking this third faction is female led so I wonder if this is Ms. Hawking's group.
ETA: "The Garden of Evil" allusions, etc. doesn't mean (to me anyway) that this third faction is evil. I don't think the show really works that way.
How does the island feel about children?
The fact that this group might be female led, and that the statue is female and representative of fertility and childbirth--it seems to me that that makes sense as a counterbalance for all the anti-fertility and anti-child stuff going on on the island. Widmore banished for having a child off island. Ben told that the Island wanted Alex killed. Alex's biological father trying to kill her and her mother. The whole pregnancy/conception issue. The only one I can think of so far that has represented this anti-child view among the characters is Richard--who talks to Locke about Ben getting off track with all of his focus on pregnancy and birth.
And then the only powerful female leader I think we've seen has been Ms. Hawking--I'm not sure it even makes sense to think of her in opposition to either Ben or Widmore. Widmore seems to direct Des to find her. Ben seems to need her help and she's not letting him know everything about what's going on (takes Jack off to talk to him separately).
"What lies in the shadow of the statue": Hurley's revision of TESB involves having Chewie (who along with Han is hiding from a bounty hunter) take out a surveillance camera. Illana is a bounty hunter. At the moment the shadow of the statue is pretty short--somehow this reminded me of Raiders--the fact that Indy has to construct a pole of the right height to get light passing through the jewel to show him where to dig for the Ark of the Covenant. So I think Illana's job is to reconstruct the height of the statue to find out where the shadow points. (Maybe Charlotte was there for that reason too?) And I wonder if this is all somehow connected to making the island permanently visible.
Adding some more details
In case it wasn't clear what the polar bear experiments might have to do with entropy--was thinking that they seem to be measuring physically observable properties like mass in order to gauge what is leftover, the uncertainty, the entropy.
Entropy and more than one quantum state: Entropyis a measure of the different possible quantum states, and they have somehow opened the door on how many quantum states are in existence (or can be "seen") at once. This would be the Many Worlds theory--they've opened the door (or opened the lid to the box--Pandora's box) that allows for more than one state of the same being to exist at once. Schrodinger's cat both alive and dead at the same time. Or Miles both an adult and a baby at the same time. This is why it is important for bodies to be burned on the island (and why the Others wanted Paul's body)--the island can use the physicality of the body--it is no longer just "waste"--things are not being directed by the arrow of time to more disorder or to decay. Alvarez's body being removed--are the DI trying to duplicate the revival process?
Also Alvarez is a brand of guitar--seems to be a Charlie reference. So what's the importance of the items that symbolize people (like Kate's plane, Sawyer's letter, Charlie's guitar)? Are they constants? Are they also connections to that person that allows the island to make a connection to that person from a different time line? What about Christian's shoes?
Re-visions: There was a lot going on about being defined by being seen--or that being seen results in the story going in a particular direction. So Many Worlds opens up to many story lines (the Dharmacakra)--but vision (especially limited, or tunnel vision--as alluded to in Aaron's watching the cartoon)--might define which story line you are on.
So Hurley's revision of "The Empire Strikes Back" begins with Chewie getting to the Empire's surveillance droid in time (to perhaps prevent even the need to fight off the Empire on Hoth?) whereas in contrast Sawyer and Kate's surveillance tape is not destroyed by Miles and this is going to send them down a path which I would imagine means leaving the DI (or even this time period).
Hurely's revision rests on open communication between father and son. But what's happening in the "circle of trust" is open communication defined by factionalism. Complete openness within but guarding against any leaking of secrets to anyone outside the circle. And that's also what Hurley is imagining in his revision--that the Empire doesn't learn the secret of the Hoth base location. As long as there are these binary oppositions of Empire/Rebel, good/evil, Ben/Widmore, Miles' mother/Miles' father, black/white (Gray was a character in this episode)--then you can't really have openness or trust or faith. An expanded vision is necessary that sees both sides at once (God doesn't see the island?).
What happens with the binary opposition is that there are always incursions from one to the other and those incursions are deadly--like Alvarez's tooth exploding from the inside to the outside. Like the inner emptiness Miles feels.
Nobody's Perfect: That's the last line of "Some Like it Hot." The treatment of gender in that movie might be a model of the kind of inclusiveness that overcomes opposition. The main male character in the movie played by Tony Curtis is, at the beginning of the movie, a fairly typical womanizer. Through cross-dressing he both learns to identify/empathize with women, and also experiences the fact that femininity is an act-a cultural fiction. I'd argue that the way Marilyn Monroe's character is portrayed in the movie--her exaggerated voluptuousness, breathy voice, etc.--means that she's just as much in drag as he is. And then the Jack Lemmon character actually becomes what he wears. This all reminds me of the kind of artifice that is a big part of what the Others do. I also think about how uncomfortable Hurley was with the "Lie" and how happy and at peace he seems to be now that he's back on the island (compare his relationship with food to his earlier reaction to being put in charge of distributing food from the Swan). Happy because he's figuring out how to revision, how to tell the story. Even the fact that his story was at first presented as "personal"--as a journal--but then turns out to be a script for a movie--I think Hurley's learning to connect up to the collective unconsious. The universal story IS the personal story. Hurley, jumbotron of truthiness.