The Numbers/Theories
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Numbers as Specific Roles/Jobs
The numbers represent a specific role or job to be fulfilled on the Island  much in the same way a telephone extension in an office represents a specific job rather than the individual doing the job. For example, imagine someone holds the job/position of “Widget Adjuster” at Company X. The telephone extension of the Widget Adjuster at Company X doesn’t change when the person doing that job quits, is fired, or dies – it is inherited by the new Widget Adjuster.
The numbers in aggregate represent the combined mission of these roles/jobs to complete some large task.
Values Related to the Field or Device That Keeps the Island's EM Field Contained
The Island's exotic EM radiation is contained with the use of a magnetic bottle (as is the field near the Frozen Donkey Wheel). Each number in the sequence is a value corresponding to size of the iris opening of the magnetic bottle through which the energy build up can be dissipated. First 4 microns, then 8, then 15, 16, 23 and concluding with 42 microns and then closing shut. The numbers must be entered by hand because if conditions change (resulting from a change in the time line?) new numbers can be input based on the new conditions.
Related to the Oceanic Flight 815 crash survivors
According to Enzo Valenzetti the numbers present "numerical values to the human factors" Sri Lanka Video. Those human factors can be attributed as a kind of symbolism to the characters:
4  Locke: Faith (and/or hope)
8  Reyes: Compassion (and/or good will)
15  Ford: Change (and/or character progress)
16  Jarrah: Common Sense (and/or law and order)
23  Shephard: Science (and/or rationality)
42  Kwon: Family (and/or Love)
All these factors are essential to the survival of mankind, but the question remains which factor requires enhancement or reduction to accomplish the goal. The DHARMA Initiative had focused on the environmental factors but overlooked the human ones. With Locke and Jacob gone, the Man in Black has already altered the Valenzetti equation by crossing out faith and hope, which the Others and in particular Richard Alpert lost, once they learned that Jacob is dead.
Kate Austen and Frank Lapidus might represent and/or replace human factors and/or numerical values (deliberately) kept out of the equation for the time being.
While Lapidus hints compassion (for Locke's body), common sense (not burning the cabin as the fire may spring to the jungle vegetation) and change (he was a former alcoholic), Kate may represent regret and/or repentence (returning to the island to bring Claire home and to reunite her with Aaron), eventually replacing faith.
 An alternate interpretation of "human factors" through the lens of the MyersBriggs Type Indicator terminology:
4  Locke: Intuition
8  Reyes: Perception
15  Ford: Feeling
16  Jarrah: Judgment
23  Shepard: Thinking
42  Kwon: Sensation
Related to Psalms
According to the Man in Black, Jacob associated each number with a person. For instance:
Psalm 4 says "Offer the sacrifices of righteousness, and put your trust in the LORD," describing Locke, a man of faith.
In Psalm 8, "You made him a little lower than the heavenly beings and crowned him with glory and honor" refers to Hurley and his communication with the dead, especially Jacob.
Psalm 15 references behaviors to avoid in order to "never be shaken," and Sawyer has done them all, repeatedly.
Sayid's ressurection is addressed by Psalm 16 in the line "you will not abandon me to the grave, nor will you let your Holy One see decay."
23 represents Shephard. Psalm 23 begins "The Lord is my shepherd..."
42 is Kwon, and Psalm 42 contains a line which reads "Why have you forgotten me? Why must I go about mourning, oppressed by the enemy?" which seems to allude to Jin and Sun's separation.
It is not unreasonable to assume that a man who calls himself Jacob would have an affinity for biblical references.
Transmission
 The numbers may be a "safe code" sent via the underwater cable. This safe code may let the DHARMA network off the island know that everything is ok, and to proceed with the Periodic Resupply Drop (DL/CC have said they will also be visiting this in future episodes). When the Swan imploded, the numbers ceased being transmitted, and the listening station was alerted to this. Naomi's team (via DHARMA) was sent to investigate, ergo the importance of the numbers (see Enter 77). This would also imply that Penny is part of DHARMA. (We know that Widmore and Hanso are connected, so even this part is not wholly implausible).
 The special importance turned out to be their leading to the Looking Glass.
Effects
 When used for personal gain, they appear cursed.
 According to one of the Exec. Producers, they may have no meaning whatsoever.
 Its true that most theories of specific meanings of the numbers, and anything to do with the Valenzetti equation is probably mere conjecture compared to the thought they have put in. Whats more important is their impact, and they appear to be cursed since the numbers did originate from the island, all the way to Hurley. What comes out of the island such as the numbers appear to have a huge effect on people's timelines (such as the bad luck and the numbers appearing wherever they go) which shows that the island has an intrinsic connection to the fate of people. The flashsideways timeline shows evidence of when the Island does not affect the world with the numbers  Hurley is lucky.
 The numbers themselves are not significant. The people who use them are significant. People like Jack, Kate, Hurley and Sawyer have certain extrasensory powers (see Bea Klugh's List). In their hands, the numbers could appear significant when it is the people themselves who are influencing events. Walt was shown to have unusual powers. He would have been on Bea Klugh's list if she didn't have him already. Average people have no influence over the numbers.
 Of Bea Klugh's list, Hurley was sent back to the Losties with a message, Jack was needed to perform the operation on Ben, and Kate and Sawyer were needed to emotionally manipulate Jack into actually performing the operation. This list is a symbol of the twisted and devious way that the Others think, not of psychic powers or Island connections of the people on the list.
 The numbers are part of the Valenzetti Equation, but that is only one of the many meanings they have. They have intrinsic, possibly sinister, magical and metaphysical properties that connect them specifically to the Island and bring people to it. The Valenzetti equation itself may even be completely false, but what is important is that belief in the numbers brought the DHARMA Initiative to the island. The link between the numbers and the island is also why they were used as the code for the button, because they resonate uniquely with the electromagnetic anomaly. Their sinister nature also explains the effect they have on Hurley and Sam Toomey, at first helping them, but then bringing bad luck. With Hurley, this bad luck eventually brings him right to the Island. The Others, who according to Mikhail Bakunin lived on the island long before the DHARMA Initiative, may have their own ideas about what the Numbers represent.
 The DHARMA Initiative was ultimately successful in slightly changing the numbers. The radio tower on the island (with its automated calculation and broadcast of the numbers) was replaced with the distress message to keep anyone on the outside from finding out as they should have. All the bad luck and other problems associated with the numbers are related to the universe coursecorrecting as a result of the numbers (and the the Valenzetti Equation) actually having changed.
 The island may have been sent into the future when the hatch imploded. The numbers being broadcasted from the tower let the outside world know when the Valenzetti equation has been altered by events on the island.
 If you make the distinction between occurrences of the numbers where they appear "transient", i.e. on a shifting dashboard display ("There's No Place Like Home, Part 1"), a constellation of people or similar  as opposed to permanent like engraved (e.g. on the Swan hatch) or in print you will find (or prove this wrong) that the numbers only appear on the island in the latter form. The theory being, is that the Numbers in the fleeting form are signs of the influence of the island, a calling or something like that which shows up offisland in certain situations and/or to certain people. The numbers appearing in these cases are either intentional for the island (as in Jacob) to make its presence known, or a byproduct to some kind of direct influence e.g. when it stops Michael from killing himself ("Meet Kevin Johnson").
 The numbers not only relate to the Valenzetti Equation but also the key Candidates of Jacob's will, so because these numbers are so incredibly important for the protection of the Island and perhaps beyond, acquiring significant awareness of them plagues the individual with ill fortune in an effort to stop them interfering or investigating with the sequence of events the numbers are required for. For example Sam Toomey was driven to suicide, and Leonard Simms was incarcerated in Santa Rosa Mental Health Institute and the Danielle Rousseau lived a life in fear and isolation. Hurley overcame the bad luck because he was one of the key candidates, number 8.
Equations and Codes
 Hold the ALT key in notepad/wordpad (font type must be "System") and type the numbers 4 8 15 16 23 42. Release ALT, and you will get the Greek symbol µ (Mu) which is the name of the lost continent Lemuria, which is similar to Atlantis.
 It should be noted that only the last 8 digits (15 16 23 42) produce Mu (µ) it doesn't matter what precedes them.
 In relation, holding in the ALT key in notepad/wordpad, typing in 15, then releasing ALT reveals an 8spoked wheel. This could be connected to the Frozen Donkey Wheel.
 They may be related to the Valenzetti equation
 According to information about the Equation, specific causes for the destruction of humanity were cited, and each subsection of DHARMA ostensibly worked at changing the relevant variable. The numbers may represent a timeframe or number of years/decades to destruction based on that variable. If so, the actual time to destruction would rely on a function of those numbers, since several of such "deadlines" would have already passed.
 They are the current solutions/roots of the equation, and the purpose of the DHARMA Initiative is to change these roots of the equation, as stated by Alvar Hanso. Since the solution to the equation is supposed to predict the end of mankind, then Hurley, Leonard, Danielle etc. espousing these numbers as 'cursed' are spreading these numbers around with a negative connotation, causing death & suffering through their belief in the fatal character of the numbers. When Hurley chooses hope over the 'curse' of the numbers & starts the car, he has effectively overcome the curse of the numbers, is changing the numbers of the valenzetti equation simply by choosing to ignore their power... IMHO this is the purpose of the Island as it is now, get a bunch of people together (Flight 815 survivors) who unwittingly will overcome the despair accompanied with the numbers and to build a society based on hope, thus changing the numbers of the equation & eventually bringing about a better future for mankind.
 The implication of changing the numbers isn't just that end of the world can be avoided. If the numbers can be changed even slightly, it opens the door not just to saving the world, but reengineering the world into a utopia. The discovery of the Valenzetti equation opened a "window" into the workings of fate. DHARMA's task was to find even the slightest weakness in any part of the equation as a springboard from which an allout attack on the equation could be made.
 The numbers can correspond to letters.
 When you write out the numbers using letters (FOUR EIGHT FIFTEEN SIXTEEN TWENTYTHREE FORTYTWO) There are exactly 42 letters (not counting the dashes). If you count off the 4th, 8th, 15th, 16th, 23rd, and 42nd letters from the beginning you get the letters: R H E N N O respectively. "Rhenno" could have some meaning.
Binary
Binary 
Numbers are binary to the following:
 Machines
 People with 4 toes per foot
 The syntax of the Dharma octagon logo
 Anyone needing the simplest expression of numbers
Binary notation is the least complex notation and thus is not needlessly complex. Six digits is the fewest, thus simplest, # of binary digits per number. Three palindromes is the fewest possible from these binary lost numbers with only 1 possible combination.
So, the most basic possible, thus natural, loop of binary palindromes is 101, 00001000010000 and 0111101000001011110, exactly equal to the loop 4,15,16,32,42 in six digit binary. In this example, the 3 digit binary number "101" is pointed to by the arrow at the octagon's top.
This "101" top of the octagon is also the eighth of the octagon that is in the direction to escape or find the island when the octagon is used as a symbol to indicate North. Per mapping convention, the longest continuous line pointing away from the center designates North. North, both binary "000" and base10 "000," (3 digits because bearings are stated that way) would be the eighth of the octagon at 1:30 (o'clock), and to it's immediate left at the top of the octagon is the eighth section containing the binary "101" and also containing both island escape bearings of 305 and 325 degrees, with the arrow pointing at the exact midpoint of both. Whether the escape bearing varies, or whether magnetic North varies is unknown, but in all cases, "101" is the direction sector of both escape and return.
Scientists generally view a short binary radio signal, which can be viewed in even rows and columns, on a loop, as the simplest possible way to communicate information when there is an expected and unknowable language barrier. This is what scientists now send into space in search of other life forms, because it meets the test of Occam's razor, yielding the most simple possible interpretation.
The fact that major characters can often move both ways in time and remain intact, like a binary palindrome, is clearly integral to this multiverse. A sequence of binary palindromes would survive better, moving back in time, than the frequent whispers, which are backwards and thus unintelligible. Hieroglyphs, like the one on the countdown timer, can be read in either direction and the meaning may vary. This is why this sequence does not have a normal probability distribution when in proximity to time displacement, meaning it defies probability by coming up so often. The lost number loop is not bound by linear unidirectional time distributions, as are other natural sequences, because it is not unidirectional, but megadirectional. Time misdirection anomalies could cause an inordinate number of random outcomes of the lost number loop, since that loop would be more enduring through backwards time travel and thus more likely than other random outcomes. This cumulative breakdown of the quantum physics probability distribution balance, widens the gap in spacetime continuity, so that the number loop can become increasingly more prevalent in realized reality. As the lost number loop continues to, ever more, disrupt continuity, the disruption, ever more, allows the lost number loop to proliferate into the past. If one doubts that some integers could possibly ever be more prevelant in reality, note that the first digit in a truely random baseten number is much more likely to be a "1" than a "9", and that is without time travel manipulation.
This perhaps disrupts the whole multiverse via the third palindrone containing an odddigit "hinge" palindrone with it's middle digit split as the mirror, and this hinge palindrone "1000001" existing within identical outer palindrones of "011110." The perpendicular reach of this pattern, with enough power, manipulation and repetition, could extend a feedback loop so that it warps from a particle into a wave. Thus if it acted upon time, it would leak into the dimension of probability, like the improbability drive from "Hitchhiker's Guide to the Galaxy." So the signal can go back (negative), perpendicular (square) and wavy (root). The square root of a negative is an imaginary number, which taken literally could explain some things. :)
A "fate" interpretation of quantum physics thus collapses the multiverse into a single predetermined path, per Locke's quest. But the numbers must need some deliberate push to gain such a critical mass. Such critical mass would require exotic matter from a particle accelerator with various stations in a circle, so that each "1" or "0" bit would be a quantum wave/particle, for economy of scale. This could cause magnetic effects on local matter along and above the underground loop. Of special interest would be the impact on the life force that caused the event, should there be a time paradox.
The cat is not dead until you open the box, unless you train it to leave the box, go back in time and swap the poison gas with the clean air before getting in. Then it can be niether dead nor alive, it just vanishes and takes you with it. Where might "free will" hide under this emerging determinism?
If these 2 larger binary palindromes were ever detected in the past by a NASA subatomic listening station in space, they would be transmitted back to Earth in normal base10. Note that the "Ulysses" Virtual Energetic Particle Observatory reported an event "528" at etime "249950," which was on March 9, 2002. This is around the times of the first and third time shift and when Juliet came to the island. This translates the lost numbers into a vector "101", an exact etime "249950," and an exact subatomic event type, "528." The lead investigator in charge of that detection module spoke in 2009 on "New Spaceflight Mission To Study Earth's Radiation Belts."
Was this planned by the writers? No, but it remains the only logical explanation for the show's greatest riddle.
Stations
 The numbers were some sort of coded instructions that told a computer program to discharge the Swan Station generator. This can explain why the discharging is not automated or why the Losties couldn't just press "Execute" instead of typing in the numbers and then pushing the button.
 The numbers may be a nod to the realworld phenomenon of the numbers station
 The numbers may reference field strength increases in the "anomaly." The fourminute warning alarm is the "last chance" warning to input the numbers and push the button. The implication is that the numbers may "activate" in reverse order. At 42 minutes past the button push, the first field jump occurs, then 23 minutes later the next, 16 minutes later the next, fifteen the next, eight the next. The alarm goes off  the level is getting too high. The final field jump, four, occurs four minutes later at a total of 108 minutes elapsed. The supporting evidence for this fieldstrength hypothesis is the readout in the listening station during the system failure  the notice is headed with the number 7418880, the product of the numbers and the "full strength" field discharge.
 The DHARMA stations could be researching the numbers for the Valenzetti Equation. One number could research a particular field as in "Station 3 or The Swan could be studying #15, the third number in the equation order, 15 could possibly refer to Electromagnetism" and the rest for all the 6 research stations. station 1 = 4/ station 2 = 8/ station 3 = 15/ station 4 = 16/ station 5 = 23/ station 6 = 42. Take into account that The Flame is allegedly "station 4", it could've been a research facility in a science field, for example lets say it studied Meteorology for a while and then the research was moved to a newer facility, before it became a "communication facility" as claimed by Mikhail.
 If we take the Flame, the Looking Glass, and either the Staff or Tempest as "functional" rather than "research" stations, and disregard the Door, Temple and unknown/Lantern stations since we still lack information about them, then there are six research stations, possibly one for each number.
 If the numbers represent field strength references, then entering them together as a sequence may combine the total field strength (ie at 42 minutes, 23 minutes etc) and cancel out it's effects. These could be the reson why the code can only be entered at 4 minutes before the end, as all numbers are required in order to get field strength references.
Mathematical
Fraction
A 24 hour day split into 108 equal minutes results in a periodic 13.3  Can't get any cursed than this, proving Hurley's view on the numbers.
Valenzetti Equation
See also:Valenzetti Island (theory)
 The Numbers are related to the Valenzetti Equation. Since that the Numbers are associated with the Candidates, the result of these Candidates being killed by the Man in Black, will result in his freedom, causing evil to run across the world, possibly ending human life.
 The Numbers could be the solution to the Valenzetti Equation, specifying either the remaining time left before the extinction of the human race or the date/time of humanity's demise. ie: 42 years, 8 months, 23 days, 4 hours, 16 minutes, 15 seconds, or 23 years, 42 days, 8 months, 4 days, 15 hours, and 16 minutes, or many other permutations of the Numbers. This is unlikely, however, for the following reason:
 The Sri Lanka Video has stated that the Numbers are the "core numerical values" of the Valenzetti Equation. This probably ought to be incorporated into the proper article about the Numbers as the Lost Experience establishes this origin as canon.
 The DHARMA Initiative is experimenting with the equation to see if they can use it to change the future and/or extend human life.
 This is strongly suggested by the Sri Lanka video, in which a man claiming to be Alvar Hanso states "That is the work to which you have committed yourselves. Change the core values of the Valenzetti Equation, and you will change the course of destiny."
 The blast door map makes a reference to "Valenzettirelated research activity".
 This could explain a lot of phenomenon on the Island: the polar bears, who ordinarily would perish in such an environment; accelerated healing; the button's ability to prevent electromagnetic buildup seemingly by doing nothing more than entering the Numbers; the Others (assuming they are connected with the DHARMA Initiative) regarding themselves as "good" people; and so on.
 The Others may have successfully changed one of the core values by kidnapping Walt.
 What would happen when the Numbers change, presuming the Swan station had a real effect on the study instead of or in addition to being a psychological experiment?
 Will the Numbers the buttonpusher enters change (ie, spacetime continuum is preserved and so the "new reality" is the changed set of numbers)? Will the recipient computer somehow sense this? Does, then, the recipient device exist "outside" the space/time continuum?
 Will the reaction to the Numbers change? IE, will the same numbers no longer reset the countdown, requiring use of the Failsafe?
 However the Numbers change, will the researchers be able to determine if it is for the better or for the worse?
 In the Sri Lanka Video, Alvar Hanso made it clear that the Valenzetti Equation was developed in 1962. Obviously any prediction would have to be after this date.
 The Numbers represent a value in the Valenzetti Equation corresponding to different ways of human extinction as mentioned in the Sri Lanka video.
e.g.
4 nuclear fire
8 chemical
15 biological warfare
16 conventional warfare
23 pandemic
42 overpopulation
The goal to reach a mortality of 30% in a village also mentioned in the Sri Lanka video is an effort to change the value 23 to 30 for pandemic.
 If the numbers are related to the Valenzetti equation and represent the fate of mankind then manipulating the numbers manipulates the future, including the possible end of mankind. The numbers can be used to manipulate events almost like they are numerial values for every event which occurs, similar to the way numbers make up the Matrix computer programme in the film of the same name. Perhaps this explains the frequncy of the numbers appearing at certain events on the island and in the story of Lost.
 If the Valenzetti Equation was developed around 1962 (following the Cuban Missile Crisis), wich was before Dharma came to the Island, the core values MUST have been changed by the Incident. If th equation really predicts "Dooms Day", a button pushing protocol to save the world every 108 minutes would have to change it. The Numbers may also have changed after the Fail Safe.
AntiValenzetti
This whole equation story is a bit weak. Please have in mind that the Sri Lanka video may be fake or explaining some cover up. If the Numbers are some factors in an equation they should be an ordered set, in other words each number should correspond to a particular value in the equation. Now what we see is that the Numbers are in sorted order  it is extremely unlikely that an equation of such great complexity to have factor ordering matching the sorted sequence. The second thing is that the Numbers are small integers, which is nearly impossible for a realworld (physical) equation.
There has to be some logical explanation why the Numbers bring bad luck, and why exactly Hurley crashed on the Island. The only possible reason could be that the Numbers trigger some "mental skills" in the people who use them. Once you use the Numbers a certain organization can track you and organize your transportation to the Island. In case the Others are in possession of mindcontrol technologies there are many possible scenarios how they could organize this. They might even be able to make Desmond follow Kelvin outside the Hatch and cause the system failure to bring the plane down or make the pilot to fly the plane to the Island.
 There is a smoke monster on the Island. There does not have to be a logical explanation.
Now thinking about why the Numbers could be in sorted order  may be they show the magnetic peaks of the geological magnet in the Swan. The last number is 42, the number of years between start of the experiment and the crash. There is no next number because the magnet has been destroyed. Possibly this magnet protected the world from something and now it's gone. Walt warned Locke not to open the Hatch, which suggests that something bad will happen if Locke open that hatch (no more magnet).
 If the Initiative was formed with the purpose of changing the values of the numbers, the workers on the Swan site probably would've remembered them, but clearly they needed a paper.
 It seems unlikely that lowerdowns such as construction workers would know the true nature and purpose of the DHARMA experiments.
 I just relized if you add up all the numbers its equals 108.
Coordinates System
8:15 as Lat/Long
8 and 15 appears as the second and third numbers from the Numbers and in Oceanic Flight 815. If you input 8:15 for both Latitude and Longitude degrees (8 deg, 15 min, 00 sec) you wind up in the middle of Nigeria. Check it out here Interesting, as Mr. Eko is from Nigeria. Also from Lostpedia: "The coordinates 9.338 7.731 are located in central Nigeria, 93387731 = 9FFTR731 (on a phone keypad) (DI 9FFTR731  the code on the Food packaging)"
The Island contains at least two things that might have come from Nigeria: the drug smugglers' plane filled with heroine, and the slaves in the Black Rock.
Alternative Coordinates
 Is it possible that the Numbers are indeed coordinates, but not to a location on a map, more to a particular dimension in time and space?, as suggested in Walt's comic, Green Lantern and Flash Faster Friends. To talk about 6 dimensions we need to look at the Many Worlds Interpretation on Wikipedia, which states "This sixdimensional object can also be regarded as a quantum superposition of two "alternative histories" of the original system S, one in which "up" was observed and the other in which "down" was observed.", this would also seem to tie in with the ideas of portals and dimensions that are featured in Faster Friends 2.
 It could also be the coordinates of a linear trajectory encoded by two points in threedimensional space: e.g. (4,8,15), (16,23,42).
Numpad
Numbers revealed 
What if we follow one's hand movements, entering The Numbers using numpad on the keyboard? This combination provides an encoded Swan station logo. The Numbers were also present on the hatch, so it was a conventional sign of what's inside. All other stations have logos outside, on the wall or door, except The Swan. In fact, the Swan did have its logo on the outside of its main door, just not on the outside of the hatch.
 We can decode 108 as well: and we'll see a "V" sign that is the sign of correctness (so the Numbers were entered correctly).
 We know that the programmer of the Looking Glass station was a musician. The man who invented this code was an artist, for sure.
 This theory was suggested by one of the Russian LOST Fan Clubs on the 5th of January, 2009 (1:00 AM). Image is copyright: (c) DHARMA Club.
Other
See also: Constellations and the Numbers.
Significance to time?
 In "The Constant", Faraday tells Desmond to tell Faraday in 1996 to set the device to 2,342. The last pair of digits in the Swan computers numbers is 23 and 42. This means 23 and 42 in the numbers represents some kind of time failure for the world. If one of the pair of digits fails, time will collapse. Based on Desmond's behavior in "The Constant", because he may have lost his constant when leaving the Island. Only he was effected because of his long exposure to the electromagnetism inside The Swan. The Swan was used for research on how to break or disturb the effects that DHARMA was researching about in The Orchid, and thereby finding a way to save humanity from a time collapse.
 If multiple loops of events do exist, then the numbers could be significant loops, progress as to say. In that way, we could be watching the 42nd time this loop (the show Lost) happens.
 A count down in linear time from some significant event to another significant event. 4 years, 8 months, 15 days, 16 hours, 23 minutes, 42 seconds. For example, the plane crashes 9/22/04 and the story resolves approximately 6/04/09 of the series time line.
The Numbers as a Date
The theory that the Numbers represent a date was debunked in the February 4, 2010 Official Lost Podcast.
Perception of the Numbers
It's possible that if the Island can control people's dreams (ie. Locke's plane dream and Charlie's dreams in "Fire + Water" then could it not be controlling the flashbacks also? ie. adding the Numbers into what they remember, and what we see on the screen? They may still have turned up, but not as often as we have seen, so Hurley still used them to win the lottery and heard them originally from Leonard.
If this is true, perhaps the numbers are the Constants that Daniel mentioned in "The Constant." First, let's theorize that the flashbacks aren't actually flashbacks, but time jumps, such as the ones Desmond was experiencing. In reality, all the characters would be experiencing these, which makes sense, as their plane did fly through that time membrane, if you will, around the island. If they did not have Constants, they would jump back in time over and over until they couldn't ever make it back. But, if the Island, or somebody, wanted them to stay on the island, they would have scattered the numbers through the timeline. The numbers are always present on the Island itself, so if the characters saw them in their "flashbacks," they would have a connection to the future, thereby keeping them there. This explains why it was so hard for Desmond to come back because he had amnesia, and didn't remember the numbers. However, because he found the new Constant Penelope the connection was restored.
It's also possible that the Hanso Foundation or the DHARMA Initiative is controlling the dreams and flashbacks, and used Hurley to try and stop the Hatch from being opened (although they failed), possibly even inventing Leonard. If this is true, then Hurley may have not used the Numbers and may have not even won the lottery. This does not explain why he went to Australia, but again that may just be an implanted memory.
 The coordinates for safe travel used by Daniel, and apparently Michael and Walt, show that the "time membrane" does not fully enclose the Island, hence the plane could have (and I think did) slip through without altering the castaways' conscousnesses, at least not in the same way as Desmond's was altered. His amnesia seemed to be associated with the effects of the radiation, rather than emerging from some other source.
Numerology
In traditional Chaldean numerology "LOST" translates to the number 17 which reduces (1+7) to the number 8. In Chaldean numerology 8 is the number of Saturn, and its meaning vibrates to concept of Karma, Kismet, fate, or destiny.
In addition, each of the numbers has its own secret meaning.
 4  represents Uranus, the father of Saturn. He disrupts and changes the status quo. He breaks down old belief systems and establishes new ones.
 15  represents the Magician. It symbolizes the power to rule, but more importantly, when appearing with the number 4 or 8, is symbolizes dark magic. In that case it represents the misuse of power through black magic, hypnosis, and mental suggestion to victimize others.lis
 16  represents the Shattered Citadel or Falling Tower. The story represented by the number is that of a prince who goes to the top of the tower under false pretenses. There he is struck by lightning and falls to his death.
 23  represents synchronicity. With 23 there are no coincidences. It is an extremely fortunate number in most cases because it represents how the universe uses interconnection to fulfill its purposes.
 42  represents Love, Money, and Creativity. It is another fortunate number that promises prosperous gains in all three areas.
 Taking Under consideration the relationship between the numbers and the survivors, the following relationship between the survivors and the meaning of the numbers in Chaldean Numerology can be assumed:
 4  Locke: Outside the island, was very skeptical concerning the cure of his condition, but as he starts walking once on the island, opens himself up to a newly found faith and tries to disseminate his new belief among his peers.
 8  Reyes: Believes the bad luck brought to him by winning the lottery is Karma chasing him, assuming henceforth that everything that happens on the island is his Karma for receiving such a large amount of money. Once off the island, believes it is their destiny to return and they should never have left.
 15  Ford: Uses manipulation and mental suggestion to manipulate his victims as a con artist.
 16  Jarrah: Sayid is taken back to the island by Ilana under false pretenses and as a result he get shot and killed.
 23  Shephard: He is the one survivor whose life has interconnected the most with others' off the island. He was there when Shannon's father dies, is on flight 815 to pick up his father after he went to Sydney with Ana Lucia, his father was the one responsible for pushing Sawyer into committing murder while in Sydney, he is Claire's brother and so on.
 42  Jin or Sun. Maybe them both together. Perhaps even Ji Yeon. Their love is very strong, Sun comes from a lot of money and Jin does also, once married.
Changed in alternate timeline
 One of the timeline differences is that Jack is sitting in row 24 rather than row 23. Presumably he was put in that row originally because 23 is one of the 'numbers'. The reason he is seated in row 24 now, is because one of the values has been altered, which has changed the way things turn out.
 I.E. The Valenzetti Equation's outcome has been altered by the 1977 explosion? I considered this too. It ties in well with Dharma story. This theory deserves further discussion.
 I agree as well, I was looking for examples of the numbers in the show, but there were plenty of places where they could have put them in, but didn't. Like the "code 341" in the elevator. So I do believe that either the numbers have changed or they are no longer relevant.
 This could also connect to how hurley how says he is “lucky” perhaps he either used different numbers to win the lottery, or he still used 4 8 15 16 23 42 but because of previous events the numbers are no longer a curse.
 I don't think that the numbers specifically have special meaning, but their origin seems to be the island. Since Hurley got it from army men listening to the message from the island, its safe to say the island has to do with his bad luck with the numbers. The alt timeline has no island, hence the numbers and their "evilness" leaking from the island does not affect him.
 Notice that the numbers cited above all have ONE NUMBERIC VALUE difference from the Numbers  Row 23 to 24, code 341 as opposed to 442. This could also be the reason that the flight number isn't identified maybe it's now 714.
 This is interesting. The equation hasn't really been explored in the actual series. Loose ends need to be tied up for viewers at large, not everyone will be familiar with TLE. This might be how it is resolved in the show.
 Also that explains why Hurley is lucky in the alt. timeline, becuase he never used the Numbers, instead used other Numbers that also make him win the lottery and he was in Australia in this alt. timeline, because of business.
 The Numbers have changed before, and this is why the numbers on the wall in Jacob's Cave include numbers other than the ones we are familiar with. Numbers have changed over time.
 The numbers have not changed in the alt. time line because the numbers also represent characters on the show, since they never went to the island they will not fulfill the roles they were ment to. There for the world of the alt. timeline will be distoryed.
 Key references to the numbers, such as the seat numbers and Hurley's lottery numbers have all noticeably been changed. However, after Desmond's moving of consciousness between timelines, as he acts and other losties remember the original timeline, the numbers have noticeably been referenced again. This includes Desmond's order for 42 in meeting with Hurley, floor 15 in the elevator, on various clocks and room 842 in the hotel. This shows the numbers originate from the island in the original timeline and that as the alternative timeline becomes more affected by the original the numbers start to "infect" the timeline.
Changing the Numbers
There are several ways in which the numbers can be conceptualised:
Suppose x = 4, then:
 4 = x
 8 = 2x
 15 = 4x 1
 16 = 4x
 23 = 6x 1
 42 = 6(2x 1)
OR
If y = 2,
 4 = 2y
 8 = 4y
 15 = 8y 1
 16 = 8y
 23 = 12y1
 42 = 6(4y 1)
Using different values for x gives a different set of numbers:
 x = 1 gives: 1, 2, 3, 4, 5, 6
 x = 2 gives: 2, 4, 7, 8, 11, 18
 x = 3 gives: 3, 6, 11, 12, 17, 30
 x = 5 gives: 5, 10, 19, 20, 29, 45
 x = 6 gives: 6, 12, 23, 24, 35, 66
 x = 7 gives: 7, 14, 27, 28, 41, 78
 x = 8 gives: 8, 16, 31, 32, 47, 90
while
 y = 1 gives: 2, 4, 7, 8, 11, 18
 y = 3 gives: 6, 12, 23, 24, 35, 66.... in fact these just repeat part of the sequences for x.
In other words, it would be possible to change the numbers, but still keep the same mathematical relationship between them.
In most cases none of the numbers is the same, in two cases (x=2, x=8), two of the numbers remain from the original 6.
What does this mean (if anything? = no idea!). I just thought it might be an interesting read.
Biblical Numerology
The Bible uses certain numbers to refer to specific things; it's my understanding that the numbers of psalms also tend to correspond to these specific concepts. When the Lost numbers are applied to these meanings, they seem to highlight some key themes in the show.
4: Deals with God's creative works or Earth Creation (material completeness). [This is actually the only one I'm not entirely sure about, but I think it does make sense in context with the rest.]
8: The number eight is used in reference to fertility. It has also been used when referring to the Resurrection or new beginnings. [Pretty central to Lost.]
15: Deals with the energy that is found within the acts of divine grace. [Electromagnetism, anyone?]
16: Deals in reference to the things that deals with love. To have passion and hold dear. To cherish and have devotion towards things. [Again, selfexplanatory.]
23: Deals in reference towards things or situations that involves death or extinction.
42: Deals in reference to the Antichrist. ["You disrespect his memory by wearing his face, but you're nothing like him."]
Obviously the show makes references to multiple religions, culminating in an acrosstheboard compromise that presents an interesting take on existence. I think it's likely that, among other reasons, the Numbers represent (through their Biblical significance) the core concepts that the Island itself embodied. And although it's prudent to not read too much into any kind of numerology, I'll add this. There are a total of six numbers in the sequence (as well as six seasons :P).
6: Deals with the number of man. This number is also used when referring to (human labor) or (secular completeness). The number six is also attached when describing the constant battle between spirit and flesh.
One could interpret that all of the Numbers, creating a sequence of six, are a numerical metaphor for the human experience (and the eternal struggle between the physical body and "soul.")
Kabbalistic Meaning
In Hebrew, as far as I know, letters also represent numbers. So replacing the given numbers by letters should therefore lead to either a word or a phrase. We should however keep in mind that Hebrew does not write vowels, so they have to be added. The resulting word could, course be in any language, but I think that either Egyptian, Greek or English should lead to a solution.
4 = D (Daled) 8 = C (Chet) 15 = Y + H (Yud+He) [there are other methods of counting after ten!] 16 = Y + V (Yud+Vav) 23 = K + G (Kaph+Gimel) 42 = M + B (Mem+Bet)
So if I am correct this should lead to: D C Y H Y V K G M B
Maybe someone with deeper knowledge of Hebrew or Gematria could further investigate this lead, especially concerning the correct values of the numbers.
I'm not an expert on the gematria, but I can add this to what you've written: (1) You want to represent chet at CH. (2) Yud Heh and Vav are of the utmost kabbalistic significane because they form the personal name of God. (3) the different ways of counting you refer to aren't really used except to avoid an unprayerful use of the those letters.
Jacob's Wine Analogy
The wine in Jacob's bottle represented the numbers (which were different at that time). When Leonard said to Hurley, "You've opened the box" He was referring to the numbers, and the box referred to the island. When Sam Toomey and Hurley used the numbers in the real world, the numbers suddenly had significance outside of the Island. The numbers could be changed by Jacob crossing out or writing a new candidate's name.
Island=Power of the numbers
The numbers and the island are tied up. In the Flash sideways time line, Hurley said that he was the luckiest man in the world. In the original time line, he was unlucky. Since the island was sunk in the FST, the numbers also lost their power.
The Numbers Are Linked To Their Fate
The numbers may be a sign that our candidates have always been destined for the island. People have difficulty relating Jacob's use of the numbers to Dharma's use of the numbers. On the surface there is no link. Perhaps the numbers appearing everywhere they have; Hurley's lottery ticket, Island radio tower, the Hatch, etc. were subtle hints at the candidates' fate. We know Jacob visited each of them at least once, probably more. He was leading them to their fate on the island, as one would become his successor. Maybe the numbers can be attributed to destiny, that the candidates and the numbers would forever be linked.
Prime Numbers
If you make a chart with prime numbers with a size of 5x10, make all numbers which aren't a prime number black. Then make another chart, which is 3x6 And fill it in like this 5 9 16 17 24 43 4 8 15 16 23 42 3 7 14 15 22 41 Again, make all not prime numbers black. It will look like this.
X 9 16 X 24 X 4 8 15 16 X 42 X X 14 15 22 X
If you look closely, it spells out L X, which might refer to L.A.X airport, where Oceanic 815 left
External links
 wikipedia:Numerology
 wikipedia:Gematria
 wikipedia:Bible Code
 wikipedia:Valenzetti
 thefuselage.com forums  Fancompiled list of numbers and codes as they appear in Lost.


