I've been coming up with theories about this show for a long time, and the one force I keep coming back to is electromagnetism. I think it's very possible that at this show's center, electromagnetism is really what the show is all about.
Here's what we know, either from the show, or from history:
-The Dharma Initiative came there because of the unique EM properties of the island.
-Studying the EM was the original purpose of the Swan bunker.
-The concrete wall has a heavy EM force behind it, meaning the EM source is very close to the Swan bunker.
-The human brain generates electromagnetic fields.
-EM is one of the 'building block' forces of the universe, and is theorized to be what powers human consciousness.
My theories:
About the island...
It seems to me that the island contains a natural anomaly in the Earth's
magnetosphere, generating a "false North Pole" on the island, causing nearby equipment to believe that it's north. This is a known phenomenon. There is one in the
South Atlantic Ocean, and there are several around the Earth as well, some more or less powerful than others. There are a couple in the western US if I'm not mistaken. The island may just be a particularly strong one. This is how everything crashed there.
It may also explain why the island wasn't detected; EM interference keeps satellites from picking it up. If it were over a city, people might notice EM satellite interference. But it's likely that in the middle of nowhere South Pacific, nobody who maintains satellite pictures of Earth ever thought to look there, to see if anything that small were obscured by interference.
This natural condition of the island may be a combination of the magnetosphere and/or the geology of the island, for example if the island contained a lot of magnetic rock (if it is volcanic in nature, this is even more likely, since metals would be thrown up to the Earth's crust from below). This explains why Sayid's compass doesn't work. It also explains why Locke continued using his compass when he was trying to find the hatch, even after Sayid told him it didn't work - he was trying to find the source.
Now, read about
Electromagnetic Theories of Consciousness on Wikipedia. It's a short entry.
If this theory is true, isn't it also possible that an
extremely powerful EM force could potentially cause people nearby it to hallucinate? This would explain why the fuselage survivors are seeing things, yet the tailies haven't experienced any hallucinations. It would also explain why there is a "parapsychology" bunker elsewhere on the island, and it would explain why the hallucinations are things out of people's own pasts. So are the whispers, for that matter, as we saw with Sawyer hearing "It'll come back around".
About the 'incident', the 'sickness', and the computer...
Say they built a reactor around the source of the EM force, near the Swan bunker. A reactor meltdown, of an energy force that permeates
everything, would be disastrous to its surroundings. So they set up a satellite that could detect this island that is invisible to other satellites. The satellite orbits Earth every 108 minutes, and the pressing of the button tells the satellite that the island is still there, and that nothing has gone wrong with the remnants of the reactor. Packaged with that, they also get their results for social conditioning experiments, by having someone press a button just because they're told to. If nobody presses it, the blast doors come down just in case, and then they send someone into the hatch to make sure another meltdown isn't in progress.
Danielle's "sickness" could be a type of insanity, caused by prolonged exposure to an EM force that strong, which would create interference with your own mind. That section of the island is contaminated with the EM equivalent of radioactive reactor leakage, which is why the safe bunkers have "quarantine" written on the inside. You go outside, you start seeing things. But only when you're in that area.
About the 'monster'...
It has been theorized that the 'monster' is a cloud of electromagnetic dust, held aloft by the EM properties in the air. This theory comes about when you watch the Dharma film, and see that Gerald DeGroot is suspending bits of metal in midair when Dr. Candle mentions "electromagnetism" as one of the Dharma Initiative studies. If that's what the security system/monster is, the flashes of Eko's memory in the cloud very well could've had a scientific explanation of "EM interference" from Eko's brain. If EM is part of everything, and it's particularly strong on this island and especially in that area, you could make a case for "psychic" phenomenon, under the right circumstances, being a scientific possibility.
About 'fate', the 'numbers', and the meaning of "good people"...
Through the back stories it seems like the passengers of flight 815 were "drawn" to the island. This could be because they have special properties in the EM fields generated by their brains. Walt would apparently have the highest EM properties. Maybe what Goodwin meant by "good people" was people with higher or more useful EM properties in their brains.
Dharma would likely have all kinds of scientific formulas drawn up for this. The famous 'numbers' could be what is accurately plugged into their formula to create the results they were looking for. Having those numbers and these circumstances permeate reality outside of the island, especially through "EM Consciousness", may very well make it seem like "fate" brought you to the island. That's how this show could be both "pseudo-science" and "destiny" at the same time. Just make it a pseudo-scientific explanation for fate.
About 'the others'...
They're all that's left of the Dharma experiments, and they're continuing their studies with new guinea pigs however they can. I don't really have enough information about them to say whether or not they're all working together or independently of each other, so I'll leave that idea alone for now. But I will say that I think they're trapped there, with only their research. They may not
want to leave the island, but I think they couldn't even if they wanted to, which is why they reach out and try to draw specific, useful people in.
And finally, another character name significance:
Lord 'Kelvin' and
Ernest 'Rutherford' were both
geophysicists. Kelvin worked primarily in geology, and his theories about the age of the Earth were debunked by Rutherford's work in nuclear physics and testing radioactivity.
This theory, I'll admit, doesn't explain EVERY question on the show, but I think it's a good start to putting the pieces of the puzzle together. The one common theme to answer most of the questions, is the force of electromagnetism.