As one of the main themes of the series is the duality between coincidence and fate, I think members of the DHARMA Initiative make experiments on chance (which on the island, instead of -like fate):
Instead of automating the entry of the same code every 108 minutes in a computer (which would be simpler and less expensive), they are dependent on human intervention , and observe what happens: Desmond support behind the button, and it causes the crash of Flight 815 (with aboard, survivors whose past "overlap ")...
What are the chances that a plane stranded finds himself trapped in an electromagnetic field accidentally released at some point in the middle of a desert island in the middle of the Pacific? This phenomenon defies all laws of probability! And I think that's just it of interest to members of the DHARMA Initiative! Of coincidences occur regularly on the island, and the Others are trying to establish experimentally the existence of what might be called "fate" (the absence of chance) on the island ...
We also note that the powers of Walt fit perfectly within the framework of this type of experience! The bird that crashed against the glass when Walt is reading a book on birds, is a phenomenon typical of what parapsychologists call "synchronicity" ... Such as Walt playing backgammon with Hurley, and he gets the numbers he wanted whenever he rolls the dice!
So if you follow my suggestion, Walt was kidnapped by the Others to consider his ability to "defy coincidence", or technically, to cause phenomena synchronicity! They try to understand how it is possible to establish heuristics (ie d, new knowledge)! Dharma also means: Department of Heuristics And Research on Material Applications Initiative ... So, in my opinion, DHARMA is a department of the Hanso Foundation, which seeks to establish a new knowledge (heuristics) of chance, from concrete observations on the island ...
Note: When Walt told his father (a prisoner in the "wrong" side of others) they make him take tests, I think there is any simple tests that involve chance (Example: they ask Walt to name a card, then they ask him to draw one in a game .. of course, Walt pulls the right card! And they try to understand where this phenomenon ... That's probably why they have taken a blood sample to Michael to see if it's genetic)
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