The Lostpedia website explains:
According to the 1975 orientation film in the Sri Lanka Video, the Valenzetti Equation "predicts the exact number of years and months until humanity extinguishes itself." During the video, Alvar Hanso also states that the radio transmitter on the Island, will "broadcast the core numerical values of the Valenzetti Equation." The numbers, 4, 8, 15, 16, 23 and 42, are explained in the Sri Lanka Video, as the numerical values to the core environmental and human factors of the Valenzetti Equation. Alvar Hanso also states in the video that the purpose of the DHARMA Initiative is to change the numerical values of any one of the core factors in the equation in order to give humanity a chance to survive by, effectively, changing doomsday. However, Thomas Mittelwerk reveals that as of 2006, they have failed to change the values through manipulating the environment, as the equation continues to arrive at the same six numbers.The equation, therefore, is a mathematical prediction of the end of days, and Dharma is part of the experiment to change the equation. So here are my questions: (1) Why hasn't the show explained either the Valenzetti Equation or Dharma's purpose? Having just finished season 5, I would think the Cuse and Lindelof would have incorporated this background information into the story by now. Changing the equation explains why Dharma is experimenting with polar bears in tropical climates, electro-magnetism, and time-travel (the bunnies). (2) The purpose of the numbers 4, 8, 15, 16, 23, and 42 are still being depicted on the show as coincidental. When they were etching the numbers into the Swan's door, why wasn't there an explanation as to why those numbers were chosen? And (3) the show is heavily invested in this idea of variables. If the following theory is correct (which I attribute entirely to my mother), then why hasn't the Valenzetti Equation been mentioned?
If the show does not incorporate the Valenzetti Equation into the last season of the show, I will be very disappointed. The following explanation of the show has allowed me to accept and appreciate the characters, their ridiculous circumstances (and even more ridiculous decisions), and to embrace the tone of the show rather than merely criticize the reality of it.
The End-All, Explain-All Theory (that makes Lost better than it actually is)
If we assume that changing the Valenzetti Equation is in fact part of Lost's mythology -- and I really hope it is because it explains so much (for a show that explains so little) -- then we can connect Jacob and Esau's "game" to the equation as well. Let's say that Jacob and Esau are god-like characters (not necessarily the Judeo-Christian God, but some sort of metaphysical beings), who are engaged in an eternal debate concerning the quality of humanity. To borrow the over-arching question of Battlestar Galactica -- Is humanity worth saving? Season 5's finale began with Esau stating, "They come, fight, they destroy, they corrupt. It always ends the same." It refers to the cycle of destruction in humanity's history, and cyles are traceably mathematical in nature, so Esau could be representative of the Valenzetti Equation. He predicts and awaits for humankind of destroy itself. (I will ignore, for now, what the loophole is and why Esau is intent on killing Jacob. Perhaps Esau isn't interested in saving humanity.) Jacob's duty, therefore, is to prove to Esau that humanity is worth saving -- that the outcome of the equation/cycle can be changed -- by choosing randomly selected individuals to represent the human race.
The random selection is important. Sure, Jacob could have chosen Buddhist monks or philanthropists to come to the island, but the point is that humanity is flawed. Our heroes are flawed. Our heroes make mistakes. Our heroes are not incredibly intelligent. They are average people who are conflicted between their hearts and their heads, between doing what is right and doing what is necessary. And as Daniel Faraday mentioned before he died, our characters are the variables. Not variables in time travel, but variables in the equation. Faraday noted that free will is what changes the course of history. Our heroes were chosen to save humanity through their choices.
In the finale, Jacob is reading Flannery O'Connor's Everything that Rises Must Converge collection of short stories outside of the hospital where Locke's father pushes him out the window. Wikipedia describes the collection as follows:
In the story after which the work is titled, human weaknesses are exposed and important moral questions are explored through everyday situations. Critics view the story as a prime example of O’Connor’s literary skills and moral views. [...] Through irony, the blindness and ignorance of the characters are exposed. The title Everything That Rises Must Converge refers to an underlying religious message central to her work: aiming to expose the sinful nature of humanity that often goes unrecognized in the modern, secular world.My mother, having a PhD in Southern literature, explained to me that Flannery O'Connor's works are about a moment of grace, where a character, despite their moral turpitude, may be redeemed. Patrick Galloway expands on this in his essay, "The Dark Side of the Cross: Flannery O'Connor's Short Fiction":
O'Connor is compassionate to her characters in that she gives them the opportunity of receiving grace, however devastating that might be to their fragile self-images, as well as their fragile mortal frames, for in O'Connor, grace often comes at the moment of grisly death.In "The Incident: Part I and II," many of the characters have a moment of reaching grace -- hence the significance of Jacob's flashbacks. (Earlier I mentioned that I didn't like the flashbacks, but considering that Jacob was present for each character's moment of grace, I now appreciate their relevance to both the characters and the mythology of the show.) Kate promises to near steal again, but we all know that she chooses to rob a bank later in life (which leads to the death of her childhood friend). Sawyer's decision to write a letter to the man who killed his parents is thwarted by an inkless pen. Jacob gives him a new pen, allowing him the choice to continue writing the letter. A friend of the family tells young James Ford not to finish the letter, but we know that he chooses to finish it later. Locke is essentially killed by his father but is revived from Jacob's touch. This is the moment where Locke is given a second chance at life. He can go on being pathetic and miserable (a failed relationship, daddy issues, etc.) or he can choose a life of adventure. His infamous line -- "You cannot tell me what I can and cannot do" -- places the decisions of his life solely in his hands. Despite being in a wheelchair, he chooses to do a walk-about. When faced with killing his father, per Ben's instructions, Locke chooses to ask Sawyer to do it (which is arguably Sawyer's moment of choice as well). Sun and Jin, our resident couple of institutional love, get married and vow to honor and love one another. But we all know that Jin chooses to work and murder for Sun's father and that Sun chooses to have an extramarital affair. Their moment of grace comes through their separation in time. Three years after the time split, Sun and Jin refuse to let go of the idea of finding one another. (Love, my friends, love is what will save humanity.) With Jack and Hurley, they are both at a crossroads -- Jack with quitting his job and Hurley with being released from prison. They can continue moving forward, or they can change direction altogether. As Jacob points out to Hurley, he doesn't have to get on the Ajira flight. He could have chosen to walk away.
In a letter written to Winifred McCarthy, Flannery O'Connor writes, "There is a moment in every great story in which the presence of grace can be felt as it waits to be accepted or rejected, even though the reader may not recognize this moment." [...] Critic Carter W. Martin notes, "Most of the short stories are constructed in such a way as to dramatize the sinfulness and the need for grace..." and goes on to delineate two different kinds of grace normally received by the characters: "prevenient grace-- which moves the will spontaneously, making it incline to God--and illuminating grace, by which God enlightens men to bring them nearer to eternal life." That is to say either a kind of spark that ignites a low smolder of realization, or full-blown revelation. Usually the character "recognizes his need for repentance and either accepts or ignores the opportunity.
And most importantly, Ben has the choice to kill Jacob. Perhaps it is because Jacob knows how Ben will choose -- Ben does have quite the history of killing people (let's not forget about The Purge) -- that prompts him to tell Ben, "You? What about you?" He says it with such sadness, not because he knows that he is about to die but because Ben represents everything that is greedy and immoral about humanity. Ben could have walked away. But he didn't. He chose to kill Jacob, hence Esau's victory burial of Jacob in the fire.
The entire series of Lost has been about choices. Originally it was about the choices of Jack versus Locke, but when you consider all of the flashbacks throughout the series, it makes a lot of sense that these flashbacks serve to illustrate not simply the type of character each individual person is, but also how they come to make choices. What outside influencing factors help determine their path? What do they choose to ignore, what do they choose to embrace? And most importantly, how is their moment of grace significant to the Valenzetti Equation? Sawyer sacrificed himself by jumping out of the helicopter. Kate returned to the island to find Claire. Jack and Juliet, the rational characters, are willing to "reset" history for love. Charlie sacrificed himself for Desmond and the others. Michael died as a means of redeeming himself for leaving the island. A majority of these deeply flawed characters have already had their moment of grace, that moment where they undoubtedly answer the question -- Yes. Yes, humanity is worth saving.