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The inspiration behind the numbers, and many other things Lost, comes from the Small World Problem, an essay in Psychology Today written in 1967 by social psychologist Stanley Milgram.
In it Milgram describes how he conducted an experiment to estimate the probability of two randomly chosen individuals to know each other. He picked a random "target person" in Boston and several other random "starting persons" in other parts of the US. He sent letters to the starting persons describing the experiment, giving a few details about the target person (occupation, residence), asking them to send the letter to a friend, relative or acquaintance of theirs which they believed could possibly know the target person. The next link in the chain should do the same and they all should inform him of the selection. He found out that, on average the "paths" starting from the starting persons, managed to find the target in just six steps (or 5 persons between the starting point and the target). This finding later came to be known as the "six degrees of separation".
The text is abundant with Lost related details: the name Ben and Tunisia, even a reference to an isolated island (which would render the process impossible). The striking detail is that he found that most paths, just before reaching the target person, passed through a single individual. His name was Jacobs! Really! There is also an illustration of the network thus created with numbers assigned among the links of the paths!
Note that J.J. Abrams himself has a thing for the six degrees of separation theme. He made an appearance in a 1993 film of the same name and of course produced the 2006 Abc series "Six degrees". My guess is that he not only instructed Darlton to play with the themes of Castaway and Survivor but also with the six degrees.
To come back to Lost: it is obvious that Jacob has the ability to shorten the degrees of separation (via lighthouse style time travel manipulation) of the 6 chosen individuals in order to bring them gradually closer together and onto Oceanic 815. To keep track of this process he assigns numbers to the nods of the network, just like Milgram, related to the "crossovers" each character has.
And now to complete my theory: Jacobs is not the protector of the island, but the protector of the world. His job is to keep the MIB dark force contained in the island and thus avoid the spreading of the "disease" to the world. This involves finding eventually a replacement (like Kelvin Inman did in the hatch) through a candidate system. The next one will of course continue the process through another set of numbers and that is when the numbers change. Or something along these lines, anyhow.
This process somehow permeates the reality of the island and this is the reason, microcosmically that Dharma Initiative wants to save the world by changing the core values of the Valenzetti equation and Inman/Desmond input the numbers to "save the world". Maybe, again, if the island is destroyed, the MIB is unleashed to infect the world.
I would appreciate your thoughts on this. --Harisg 13:35, February 25, 2010 (UTC)