Easily the most complex of the Dharma Stations, arguably the most important, and infinitely the most confounding. The real trick to this Station is in grasping how much of it is psychological experiment and how much of it is an integral aspect of maintaining the electromagnetic anomaly. See, in principle, the Swan Station is actually very simple to understand save for one peculiar aspect to it. Allow me to explain.
The Swan Station was created, as the Orientation film explained, to study the electromagnetic properties prevalent at that particular point on the Island. You can imagine the Swan Station resembled more of a working laboratory and may have even been the location where the 'Orchid Rabbit Experiment' took place (a subject for another post). If the electromagnetic qualities were being studied for their capacity to warp time, or split universes, the Orchid and Swan connection makes sense and explains the original purpose for the Station.
Then, however, something happened. An incident.
The explanation about 'the incident' and the function of the computer, paraphrased from the mouths of the creators themselves, goes like this. Dharma, in their study of the source of the electromagnetism, drilled too deeply and lost control. I think of this like drilling into a water pipe, mainly because trying to imagine 'gushing electromagnetism' doesn't come easily. The computer system was set-up to therefore vent this gushing electromagnetism to stop it building up and causing serious damage the way you'd use buckets to toss water over the side of a sinking boat to stop it from becoming submerged.
I'm not going to deny this is certainly farfetched, but it's the official explanation so I'm afraid you're just going to have to wear it! Electromagnetism constantly leaks, building a charge, and if left unchecked creates a magnetic reaction (as we saw in Live Together, Die Alone). Thus the computer is in place to release this build-up at intervals to prevent the electromagnetism from becoming destructive. It just so happens that it takes approximately 108 minutes for the charge to build to sufficiently dangerous levels. So be it.
As I said, the Swan Station is actually very simple to understand, save for one peculiar aspect. Because it is here that Dharma, for me, reveal their perverse scientific nature. Now stuck with having to vent electromagnetism every 108 minutes by computer, the natural action to take would be automation. By that I mean the computer would be designed to vent electromagnetism at 108-minute intervals by itself. It would have to be monitored, the same way CCTV requires security guards to watch the monitors, but automation would be the most effective system.
Instead, Dharma choose to keep the computer operated manually. Dharma see an opportunity to conduct another experiment. It is here where the 4 8 15 16 23 42 code comes in. It is here where the Orientation film is made. The Swan Station is re-fitted to be a liveable habitat, with 'modern' furnishings to facilitate its function as a sustainable environment. Kitchen, exercise equipment, music and artificial daylight. Two unwitting Dharma guinea pigs are brought in, told to enter the code every 108 minutes for three months until their relief appears. Out of the 'incident' Dharma conduct psychological research in the vein of Skinner and Milgram.
Dharma didn't miss a trick, basically. They took a necessary task (venting electromagnetism) and made it a psychological study. Was it essential that the code was 4 8 15 16 23 42? I don't think so. I think the code could have just as easily been 1 2 3 4 5 - but making the code the Valenzetti equation adds to the illusion. If any of the Dharma guinea pigs had heard of Valenzetti the sense that they were part of a psychological test would have been diminished (even though, technically, it was not an entirely fake situation). Throw in red and black hieroglyphics at the timer's end and the illusion is complete. Put yourself in the guinea pig's shoes. Enter the code. Don't enter the code. What would you do?
The Fail Safe, by the way, served as a kind of 'cork' in the electromagnetism. It cut off the stream completely. The reason Dharma considered this the last resort, I presume, was because once the Fail Safe was turned the process was irreversible. This wonderful mine of electromagnetism they were studying was cut off permanently the moment the Fail Safe was turned; thus why it was only to be used in absolute emergency.
The creators have stated that Ben and The Others had no awareness of the Swan Station until after the crash of Oceanic 815. This means, at the time of The Purge, there were two Dharma guinea pigs in the Swan Station left down there whilst their colleagues were killed (there were also, at least, two Dharma guinea pigs left in the Pearl Station - but this is again material for another post). Two Dharma workers were left to enter the code to 'save the world' as part of a necessary experiment no longer being officially observed and the rest, as they say, is history.
N.B. My brief here was to explain the original purpose behind the Swan Station. I appreciate, however, that the above interpretation creates a black hole about how the likes of Kelvin (who almost certainly came to the Island after 'the purge') wound up there. Whilst it was my imperative to avoid sidelines, it would be remiss of me to ignore this. A simplified version of a much more complex chain of events posits a notion that, like the Dharma guinea pigs, other Dharma Initiative people survived 'the purge' and lived, hiding as best they could on the Island. Kelvin Inman's arrival, I feel, given his military background, was as part of an 'investigation squad' sent to the Island by Dharma to discover what had occurred after 'the purge' I envisage he was briefly part of a resistance movement. Losing the battle against "the hostiles", Inman, with Radzinsky, continued the task of pushing the button believing it was, above all else, the most important function to be maintained on the Island. (Let me emphasise that this is a massive simplification of a story that, I feel, Lost is yet to tell and I certainly do not wish for it to become a focus point here.)