Valenzetti Equation/Theories
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Significance and Resolution
 The Valenzetti Equation may have some sort of physical meaning. For example, the numbers may be the predicted date of the end of the human race, and as the final moment nears, they become increasingly common in the most unexpected places. (Maybe 4/8 15:16 2342  3:16 PM on April 8th 2342 or 4+8 15+16 23+42  12/31/65, December 31st __65)
 As there are six "core values" and six hatches, perhaps each hatch is devoted to the attempt to manipulate one specific factor apiece.
 Each factor, or number, represents one of the DHARMA Initiative fields of study, such as electromagnetism and psychology. Each research field is relevant to what is inputted to the Valenzetti Equation, and therefore it would me most effective to focus on these areas.
 In the Sri Lanka Video, Alvar Hanso mentions six specific ways that would lead to the end of Humanity, mentioned in order just before he mentions the Numbers in order. The specific numbers may refer to the amount of time there is left before that particular form of extinction occurs. 4 corresponds with 'nuclear fire', 8 with 'chemical warfare', 15 with 'biological warfare', 16 with 'conventional warfare', 23 with 'pandemic', 42 with 'overpopulation'. Also, in the Sri Lanka Video, we hear Thomas Mittelwerk talking of a virus with an optimal mortality rate of 30%, which sounds like they may be trying to kill off a certain percentage of the human race, to ensure the remaining 70% can survive. That solution would correspond to 42  'overpopulation'.
 The Hieroglyphics from the Countdown Timer may be part of the Valenzetti Equation, as hinted by Dr. Armand Zander in Rachel Blake's first Iceland video.
 When looking at the maps he stole from Rousseau's dugout, Sayid says, "These equations are like nothing I have ever seen before." The equations he is referring to may be related to the Valenzetti Equation.
 The Hanso Foundation perhaps works with the equation for honest reasons. If they can work out all the variables necessary for 'the end of human life' they can actively try to manipulate the variables so that it will never occur. In this way, perhaps they are taking the 'greater good' approach and that is why they are willing to be corrupt/scandalous (as Rachel Blake and DJ Dan's research suggests)  as they hold human life itself as the highest priority, and are willing to do anything to preserve it.
 Perhaps the date of the apocalypse had already been prophesied by an ancient race (say, the people who built the fourtoed Statue) and Alvar Hanso was looking to the Valenzetti Equation to provide a scientific confirmation for this ancient prophecy.
 The concept of predicting the future with mathematical models may be inspired by "psychohistory" found in the Foundation Trilogy of Isaac Asimov.
 A chalkboard is seen in the background of one of ABC's sneak peak scenes as a woman is talking to Jack, presumably on the island. This could imply that certain parts of the DHARMA facilities may be educational as opposed to implemental and that the equation was taught to new recruits in such locations. (More likely the chalkboard is used for research, this is a very common practice in equation based research)
 Perhaps the Island is an attempt to prove or disprove or modify the Valenzetti Equation. The inhabitants are "the human race", only smaller, and the equation is applied to them to predict when their existence on the island will end. The Dharma Initiative is trying to modify the core factors to actually speed up the demise of the inhabitants, to prove the validity of the equation in a more easily measurable timeframe.
 Perhaps the above theory is true, and in addition, the numbers also represent specific people (or apecific people represent the specific variables and what they correspond to in the Sri Lanka video. Perhaps the six numbers each refer to members of the Oceanic Six, or perhaps each character's seat number on the plane corresponds to the number they represent. The attempt to change the equation could then account for the Ajira flight, as characters on this flight could then correspond to a new set of numbers. remember that Daniel Faraday said something to the effect of, "the variables are us." Also keep in mind that characters from the island such as Jacob, Richard, and Ethan (as well as Eloise and Matthew Abaddon) have been interacting with the survivors throughout their lives as if to influence, change, or shape what they will and will not do.
 The system failure and subsequent fail safe activation may have changed one or more of the core values of the equation, changing the fate of the human race.
 The Hawthorne effect: By studying the numbers, the Dharma Initiative managed to change the equation. The equation became a self fulfilling prophecy and the end of humankind would not happen if they had never tampered with the numbers in the first place.
The Numbers Are Shifting Theory
Next time you are watching Lost, see how many times the number 7, and other numbers are used. Due to the implosion of the hatch, The Valenzetti Equation may have changed due to a huge factor disappearing, the electromagnetism. Since the numbers are changing, the luck is changing for the Islanders and for the Others, hence potential rescue, life (not death) and Hurley not having the curse.
The Valenzetti Equation Turns Back Time Theory
We saw that Desmond had to type in the numbers every 108 minutes. This could be a microcosm for what had happened to the characters who caused the incident
 At the end of 108 minutes, typing in the equation turned back the clock 108 minutes: this occurred at the same location that several people were supposed to have died when the bomb exploded (according to Richard he saw them die in the Season 5 Finale)
 If Daniel was correct that people are variables, then some survivors of Oceanic 815 can correspond to the variables ... perhaps the Oceanic 6 specifically correspond to the 6 variables of the equation, or perhaps some who caused "the incident"
 If either the Oceanic 6 or other characters represent the variables, then causing "the incident" was a reenactment of the Valenzetti equation  this reenactment could be specifically what the Dharma Initiative feared, but perhaps they feared it on a much larger scale and they merely witnessed a microcosm of what would occur.
 After the the Incident, Dharma Initiative started focusing their attention on changing the variables of the valenzetti equation on a larger scale and used the hatch they were building that caused it all.
 Perhaps reenacting the Valenzetti equation rewinds the people involved  the variables  to a specific moment that will repeat at an interval of 108 ... in this case 108 days; the variables/people involved (such as Jack and Kate) will have to relive the 108 days that caused them to reenact the equation in the first place, leaving them with nothing to do but try to undo mistakes that they made the first time around.
 They will be trapped in Samsara
 This explains why Sun protested Claire leaving Aaron in season 2, saying "A mother should not leave her child" even though Sun had not yet had her baby ... this is because she misses her child that she has not yet given birth to.
 When the clock in the hatch winds down and displays the hieroglyphs, which are meant to represent important members of the Dharma Initiative, they are commemorating those who died where the hatch was being built. They died reenacting the equation, so an important part of the project of changing the variables took place where they died, so that everyone will remember how important their work really is and so that everyone will remember what those characters are going through every 108 days
The Numbers in the Alternate Timeline
 The difference in Jack's seat number (23 in the original timeline and 24 in the alternate timeline) suggest an alteration to the core values of the Valenzetti Equation in the parallel universe.
 Hugo used these new numbers to win the lottery, which in turn resulted in his apparent good fortune.
A Change in the Numbers
 There has been a lot of speculation on if there is or is going to be another number. People for years have been trying to point out one of these numbers but it hasn't recieved to much attention from other viewers. One other number that may or may not be important is the number 9. You can see a list of the occurances in the show HERE, or the theories for the number HERE.
 Just as the flight number of Oceanic 815 contained two of the Numbers, Ajira Airlines flight 316 signifies a change in the core values of the Valenzetti Equation. Two of these numbers are embedded in the flight number, or alternatively, 316 represent the sum of the new core values, similar to 108 before.
 By leaving the Oceanic Six accomplished what the DHARMA Initiative was never able to do: alter the core values of the Valenzetti Equation. However, by leaving they have served to accelerate this disaster, not postpone or circumvent it. Thus their presence has had a strongly negative ripple effect on world events, albeit so subtly that few individuals (such as Eloise Hawking) have been able to rightfully observe this effect and discern its source. Their overall objective in returning to the Island will be not only to undue the damage which they have done, but to end the threat of Armageddon once and for all.
 As mentioned many time before on this site the numbers seem to have some geographical significance in that they can be split into coordinates, maybe by for the numbers of the Valenzetti Equation to be different the island needs to be somewhere else and the purpose of some of the DHARMA Initiative stations is to try to move the island but because of the electromagnatism of the island it is difficult to move and so the numbers will always stay the same.
 As of "The Substitute", a change in the numbers means a change of people (external), or, speculating in a more religious/philosophical way, a change in people (internal).
Connecting the Numbers to The Lighthouse Dial
Theory:
The story behind the numbers is a Strange Loop, and acts like the Bad Wolf motif in the Dr.Who episode: "The Parting of the Ways". The numbers arose because the user of The Lighthouse was seeking candidates. These candidates corresponded to numbers on the dial, and had no significance other than these were the lighthouse orientations needed to view them. When he began to interven in their lives, to affect their future destinies, coincidences and correlations between these people began to echo down the timeline. In 1963 Valenzetti discovered that such correlations exist, and was able to use mathematics to determine values underpinning these correlations. By broadcasting the numbers from the island in 1972, the numbers acted as a selfreplicating virus which enhanced the original intervention effects, and thus became a selffulfilling prophecy.
Facts and indisputable Logic:
The numbers on the dial as shown in the Lighthouse, are a clear attempt at 'trial and error' in seeking out possible candidates. At the end of this process, we appear to be left with the names corresponding to the six Valenzetti numbers (plus the additional value of 51 (Kate), which has not been crossed off). This means that whoever has been using the Lighthouse to view and select candidates, has, independently, arrived at the same six core values that Valenzetti did using his equations. The numbers on the dial appear to give the user views (whether of past, present or future is uncertain) of specific locations connected to the named person. This would imply two things:
 The lighthouse user cannot have been aware of the Valenzetti core values, otherwise he (or she) would have saved themselves a great deal of trial and error, in trying to determine which of the 360 names on the dial would be suitable as 'candidates'
 The lighthouse dial numbers are either 'independent discoveries' of both the lighthouse user and Valinzetti, or one "preceded" the other, and there is a causal link between the two.
The Numbers had been broadcast on the island since 1972, and were known much earlier (evidence from the Lost Experience would put their discovery around 1963). The Lighthouse user would therefore have known about the values from at least 1972 onwards, and possibly as early as 1963.
Now, here is a dilemma: Since Kate (#51) was not born until 1977, Hugo (#8), was not born until 1982, the lighthouse user must therefore have known about the existence of these Losties prior to their actual births. In other words, one of the functions of The Lighthouse is to view the (possible) futures of (possible) candidates. In addition, because of point (1) above, the use of the lighthouse to determine the candidates, must have taken place prior to 1972.
Thus we are left with two propositions, one of which MUST be true: (A) The Lighthouse user and Valenzetti independently discovered the numbers at around the same time (between 1963 and 1972), and they result from the same underlying factor (B) The Numbers on the Lighthouse predate the Valenzetti equation, and Valenzetti's equation is simply reporting "observational" values related to the end of the human race.
Conclusion:
(B) Offers a clear explanation of what happened. The Lighthouse user was able to see the future, and intervene in the lives of those candidates indicated by the numbers on the lighthouse wheel. These interventions were across time and space, and not limited to any one time. We have distinct evidence that such interventions occurred, via the Jacob flashbacks in The Incident, Parts 1 & 2. Note that it does not matter whether or not the interventions occur before, after or at the same time as, the discovery of the Valenzetti equation, as this equation is a prediction of the future. In making these interventions, changes to lives have occured which have echoed down through time, causing "coincidences" in the lives of those affected (e.g. Locke's father being rersponsible for the death of Sawyer's parents). When Valenzetti worked on the equation, he simply discovered the effects of the interventions, which showed up as correlations within the equation, and was therefore reporting a 'fact', that the numbers existed and were embedded in the history of humankind. When he began to broadcast the numbers, like a virus, they then began to selfreplicate, so much so that the Original Timeline became "infected" with the Valenzetti numbers which then appeared everywhere.
If (B) is incorrect, then an explanation is required of why the association of names & numbers on the lighthouse would coincidentally be identical to those signalling the end of humankind. This is not impossible, but in the face of the explanation resulting from (A) it is rendered unlikely in the extreme.
Theory (C)
Jacob (the previously mentioned Lighthouse user), has a thing for numbers and has been seen off the island. Therefore it is possible for him to have directly influenced the Valenzetti Equation (maybe under the guise of a research assistant or fellow scientist). He may've even hijacked Valenzetti's work in order to help identify the most likely candidates which could replace him.
This would explain the link between the lighthouse and the equation, and eliminate any need for coincidence in their relationship.
