The Cuban Missile Crisis may have been the first time we humans came close to world oblivion. Let’s take that as a timeline starting point for the Dharma Initiative’s quest.
In the real world, there is a mathematical series by Minkowski (around time of Einstein), often referred to re: Minkowski Space. He identified mathematical coordinates for each of our Four Dimensions (including Time), i.e., he devised a "mathematical representation" of the universe. Could this be related to the Valenzetti Equation? Might the Dharma Initiative have envisioned "human coordinates" for predicting future events?
The Losties on the Island comprise a "lab" in which individual PEOPLE (the main characters) represent Variables or Constants, where their actions (via free will, ability to grow/change) become a kind of "living equation" to determine the future of mankind.
The Composite of their actions is what matters. Live together, die alone.
When Charlie kicks the heroine, when he later redeems himself via sacrifice to help others, he reveals himself to be a certain kind of Variable – and his change alters the equation. Likewise, the actions of each Lostie. Jacob, in his search for a non-corrupt human being, is actually searching for the Necessary Human Equation that could sustain life on earth without intermittently inciting nuclear war.
The Losties are the future of the human race. They are living variables being plugged into the Valenzetti Equation in which numbers are coordinates for human traits. Jacob and the MM represent "Project team captains" of the outcome, each trying to guide (or corrupt) the human test subjects towards different desired outcomes, i.e., is it possible to populate a human society that will not ultimately destroy itself?
Further thoughts:
Was the "crash" of Flight 815 the first time Jack was on the island?
What if he had worked with the Dharma Initiative….maybe all the Losties had.
Maybe the reason that bird called Hurley’s name is that the bird had been trained to repeat his name years earlier and recognized his old friend from the DI Aviary.
What if the beginning (pilot episode) wasn’t a beginning at all?
The DI was formed to "study material applications." Material applications of what? The strange effects of the island? Or maybe the material applications of a pending world catastrophe. If the Valenzetti Equation offered a way to accurately predict the end of human life on earth, why did the writers bother to connect it to the era of the Cuban Missile Crisis?
Maybe the equation had been around before that – maybe some people predicted the Cuban M.C. to be the date of the end of the world. So why didn’t it happen? How did the "miracle" of political forces manage to avoid that nearly unavoidable nuclear war? Was it the result of great minds that anticipated the war/end and worked to prevent it?
Did those minds then form the Dharma Initiative – to prevent the next "perfect storm" of a nuclear war waiting around the corner (and derived from potential new variables in the Valenzetti Equation)?
DI might have been working frantically on two tracks:
1. How to prevent a world catastrophe?; or…
2. If unavoidable, how to repopulate earth so that humans don’t just blow themselves into oblivion again and again.
They chose the Island because of its extraordinary magnetic force. Insert short physics course here (theoretical physics’ focus on gravity as the missing link to discovering a “theory of everything,” potential of slowing down time ala Einstein’s "traveling twin" experiment, etc.)