The phase-shifted island and Hawking as oracle...
OK, let's consider this idea, then...
The island is in some kind of dimensional phase-shift, much like the one allegedly experienced by the USS Eldridge in 1943 (notice, in the linked article, the effect of the event on the crew), and this is evidenced by the "EM bubble" around the island. Thus the island is rendered invisible, although at specific moments in various places it becomes visible. Now, for your average person looking for the island, finding the location at which it will materialize is only half the battle. You also have to know the heading by which you must travel to the island in order to land on it in the time frame synchronous with your own. Failure to arrive on the island at a time-synchronous moment will result in a paradox that could cause you to suffer... well, again, just read what happened to the crew of the Eldridge.
So to say the island's motion... in space OR time... is what prevented rescue isn't entirely accurate even taking away the faked wreckage at the bottom of the ocean. Hawking made it sound as though the island is literally jumping around on the globe in... um... space or time or both, I guess... and to get to it you simply need to calculate where it will be and go there by plane, duplicating as much as possible the conditions that existed when you were there before. When the truth is that, yes, its location is variable but once you know when it will materialize you can travel to it by conventional means and be safe so long as you also approach with the proper heading. In fact, the most likely way that Widmore found the island was by a method similar to what Hawking did in the Lamppost, then he hired Hawking's son since he'd be able to calculate the proper headings, and then he sent a boat.
So why would Hawking make it appear as though a) only a very particular appearance of the island would do... they couldn't wait for the next one; b) they cannot just travel to the island by boat or air, they have to get into a plane traveling near the island and duplicate conditions of their previous arrival; and c) the vector of the approach to the island is irrelevant?
Of course, the only logical answer is that Hawking was lying about everything except where the island would appear. She must have known that when the island appeared it would be with the aid of John "turning the wheel". She must have known that the heading the flight was taking would cause Jack and the others to arrive on the island at a non-synchronous time. In fact, she must have known precisely where and when she was sending Jack and the others. But for obvious reasons, she couldn't tell any of THEM that.
She probably made up the whole notion of "duplicating the flight conditions" also. Probably because there's something important about those shoes. And the guitar. And the other two people who were on the plane (in first class with Jack and company).
Note how Hawking herself acknowledged how ridiculous her story was when she practically said to Jack, "Just shut up and believe it."
In all of this, Hawking acts as a classic oracle. Since an oracle knows what's going to happen, she or he is in a tricky spot in regard to everyone else. If I'm an oracle, say, and I know you're about to stub your toe, and I want to prevent that from happening, how do I know that warning you that you're going to stub your toe isn't the thing that will cause it? How do I know that NOT warning you is what causes it to happen? So your typical oracle winds up speaking in riddles and lies and "telling you what you needed to hear". I've always felt as though Hawking wasn't perfectly truthful with Desmond, and I'm feeling very confident that she's just sold a seriously huge load of cow manure to Jack.
The paradox she's creating by sending Jack and the others to the wrong time must be the thing that she believes will actually alter the time-line in the way Dan claims is impossible. So the question is, how will the paradox do that... what will make it "stick" when others don't... and does it mean that Jack and the others will never get back to their own time?
Phase Shift, Equinoxes, Character Roles
If I understand how phase-shifting works--then the island would be invisible not because it's in 1954 and you're looking for it in 2008, but because spatially-temporally it's on a slightly different but parallel wave so the light travelling between it and people on the other wave couldn't be seen? (What Faraday says about light on the island)
So bringing in what you were reminding us of about Equinoxes, the fact that the equinox (here I'm linking to Wiki rather than your post) is a day when every place on earth receives equal amounts of light would correspond to the two points in this illustration of phase shift in which the two waves intersect (vs. the rest of the time when they are parallel).
Interestingly this description of phase-shift sounds a lot like Des and Jack: "A phase difference is analogous to two athletes running around a race track at the same speed and direction but starting at different positions on the track."
I wounder if that means that one of them represents the island's wave and the other the wave off-island.
And Dharma being the one true way--did Dharma make an error in trying to bring the island into line with the wave off-island?
I think I can see the role of a couple of the characters in this narrative. Claire's ability to read the stars seems to indicate that something has happened in which the island is off-course and needs a navigator--that would be her role with Des as the pilot.
People turning the wheel as emblematic of larger roles:
Ben's turn causes skipping, chaos, disruption, death.
Locke, locks them back into place after Ben's disruption.
Des should eventually steer.
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"He walks among us, but is not one of us."
A further thought about phase-shifting. We see now that a number of the Losties are in some way connected to an earlier generation who was on the island.
What if these are people who should never have left the island? Is that the original mistake? I think with the word "incident" I've been focussed on something more like opening up the chamber rather than what happens to the people--they could all be part of the same thing.
So the island is drawing back to itself people who should never have existed off island? The children, or other people from this next generation (Sawyer) who either exist, or whose lives were altered by people going back to the world who should never have been there (Paik, Widmore, Hawking, Christian, Cooper--would be my guesses). And somehow there has to be a course correction of the changes wrought by their leaving.
The Whispers are all of people who died and these people all are connected to someone on island. They shouldn't have died and wouldn't have if it hadn't been for that original group leaving.
Then the fact that the next generation--Aaron, Ji Yeon, Charlie, Walt is still off island as far as we know--don't know how it fits, but it seems part of the pattern.
That's Electrifying!!!
I like the idea of the phase shifting. Just a little background on how this idea is used in everyday life. Electricity is generated by running a coil of wire tightly spun in two directions(usually one will be spooled clockwise and the other counterclockwise) over a magnet. As the spool passes over the magnet it creates a charge that when graphed looks like the diagram Jaz was showing. Most of the electric in your house is DC (direct current) and is primarily single phase wiring. Larger power hungry gear like a refrigerator or an air conditioner often uses 3 phase 220 or 440 voltage. To achieve that higher voltage a triple wire is run instead of a single wire (forgetting about the ground and neutral wires for the moment). The two extra wires are set at even increments from the first but are running slightly off phase of the magnet while the first wire is lined up (or in phase) with the magnet. By setting it up like this it allows one magnet (or set of magnets) to generate the additional power - thereby reducing the equipment needed to generate an equal amount using a single phase set up. An added benefit is that it also allows for a modest economy of scale - meaning you actually get a slightly higher yield in combination than you might through multiple single line wiring.
When running the calculations for 3 phase wiring you would actually multiply the peak voltage from the phase diagram by the square root of the number of wires. Let's take an example of 440 Volts. To reach 440V the diagram chart would show the phase peak at 277 Volts (with another 277V in the negative range.) So the equation would be 277 times the square root of 3. When using 3 phase wiring it doesn't matter what voltage we want we will always multiply by the square root of 3 (or 1.732) which is the constant in all of the equations.
One last point about 3 phase electric. Jaz is speaking about the point at which the diagram phases intersect. That never actually happens because each of the phases is shielded from the others -- except at the equipment location.
Let's mix our metaphor with our show. We looked at 3 phase wiring and said that each is on it's own wave and when combined in the equipment cretes a sum greater than it's parts. I'll suggest that the island serves in the role of the equipment. We know that there is a high level of magnetism on the island. What if each person who is brought there is considered a wire. They're interaction or exposure to the magnets "charges" them until they begin to cycle on their individual phase. They need to be in the equipment to make use of the charge - so once they leave the island they are no longer beneficial hence the need for all of them to come back. The question is what is the end goal for each of them and to what purpose? Is Jacob just another wire that is out of phase with everyone else? Is he the result of years of exposure?
Recreating the original flight
Something else that doesn't make sense...
in her story.
If we take it that Locke's turning the wheel caused the flash which not only took them back to Dharma days but also brought Jack, Hurley and Kate (at least) onto the island--then how does the story of this "window" of opportunity fit and all the mathematical equations?
ETA: Heh, this is what you were saying above--took me a while to figger it out.
Oracles
This makes a lot of sense to me primarily on the basis of the "this is how Oracles work" notion. What I mean is that especially for Ms. Hawking, one cant' really base speculation on what she has said as the truth of what's going on. And really what I was trying to say about Dan as well. Maybe a clearer way of saying it in regard to Dan is not just that he might change his mind, but that he might just be wrong. Anything we're getting from a character's perspective is not wholly reliable.
I'm not sure about the duplicating the flight details stuff--whether it's all going to be malarkey or not. This seems like a lot of malarkey for the viewers to swallow. Like if later on something reveals that that whole story was BS--my feeling is you'd lose a lot of viewers on a trick like that, but who knows.
So the non-synchronous--that's why they just wake up at a place on island instead of experiencing a crash?
Hmmm, going back to "The Pilot" doesn't this make it important again that Jack woke up in a very similar fashion--so that maybe everyone else on the plane actually crashed, but he came onto the island in a different way. I think the Jack we see in the Pilot--though largely forgetting what's been before--is not just the Jack who was on the plane. So maybe he'll be the only one who gets back to his own time.
Manipulation--I don't know what it is yet, but I think Ms. Hawking's manipulation involves leaving Ben outside of the conversation with Jack. And her connection to Des also being a surprise to Ben. Whatever dynamic was going on between them--I think she'll have wound up playing Ben--which will just be...cool...
Hmm...