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The Third Policeman is a novel by Flann O'Brien (the pen name of Irish author Brian O'Nolan). It was written in 1940 but published posthumously in 1967, at which point it gained almost instant critical acclaim. The writers of Lost have specifically referenced this book as providing "ammunition" which may aid with interpretation of the show's plot.
About the author
Flann O'Brien was an Irish novelist and political commentator. Born in County Tyrone, and raised in Dublin, he entered the Irish civil service in 1937 and formally retired in 1953. From 1940 until his death, he wrote a political column called "Cruiskeen Lawn" for The Irish Times under the pseudonym of Myles na Gopaleen; his biting, satiric commentaries made him the conscience of the Irish government. As Flann O'Brien, he published three novels, At Swim-Two-Birds (1939, rep. 1960), The Dalkey Archive (1964), and The Third Policeman (1967). He also published a play, Faustus Kelly (1943).
- The unnamed protagonist of the novel is orphaned as a child (though he only his parents have more than "left" later on), and is sent to boarding school where he first becomes acquainted with the work of the bizarre philosopher, De Selby, who is referenced constantly, both via footnotes, and in body of the novel itself.
- Obsessed by the philosopher's somewhat odd theories, the protagonist sets out on a catastrophic quest to publish a definitive commentary on the philosopher. He shares some of his writings on De Selby with John Divney, an unsavory man who has served as reluctant caretaker to the narrator's parents' farm and public house since their death. Divney devises a plan to murder and rob a rich man, which he convinces the narrator into going along with, because Divney explains it is his responsibility to publish the works on De Selby - with fair backing or not.
- De Selby is a natural skeptic of all known laws of physics, who casually dismisses the evidence of human experience. He contends, for example, that "the permanent hallucination known conventionally as 'life' is an effect of constantly walking in a particular direction around a sausage-shaped earth, and that night results from 'accumulations of black air'". (Lost features a monster composed of smoke.)
- The protagonist finally gets hold of his victims' black box only to discover that the box does not contain money, but “omnium” , a substance once described as: “the essential inherent interior essence which is hidden in the root of the kernel of everything”, and which is literally everything one desires. The former holder of the box has been using it to take the muck off his leggings and to boil his eggs just right, but naturally the narrator has more grandiose visions of his future omnipotence.
- In the novel, the first two policemen share an underground structure with the narrator. Without spoiling the ending, the narrator is being punished for his "bad" deeds. One can draw a parallel with this and the new idea that Islanders in danger of being taken by the Others are either "good" or "bad".
Desmond appears to be reading The Third Policeman when the Hatch is finally infiltrated by the mid-section survivors at the start of Season 2. The book is visible on Desmond's bunk in the Swan. ("Man of Science, Man of Faith")
Lost writer Craig Wright claims he is the one who had the idea to insert The Third Policeman into Lost. 
Influence on Lost
According to a BBC report & an article in the Chicago Tribune on September 21, 2005, The Third Policeman was to contain key insights into the show, a fact that led to it selling more copies in the 3 weeks following the episode's airing than in the 6 years that preceded this.
Similarities and shared themes
The third policeman, as seen when Desmond is fleeing the Hatch
While many possible connections can be drawn, most of these are tenuous at best. This section is concerned with elements of the book which have a strong similarity to the events in Lost - and to present the possible "ammunition" referenced by the writers.
- The underground labyrinth described in the book has a strong resonance with the portrayal of the Swan in Lost;
- I saw a long passage lit fitfully at intervals by the crude home-made noise machines….the walls of the passage seemed to be made with bolted sheets of pig-iron…there was a mass of wires and what appeared to be particularly thick wires or possibly pipes….here I saw a dial or an intricate nest of clocks and knobs resembling a control board…
- Policeman MacCruiskeen and his partner are obsessed with taking readings from their underground bunker, and assuring that these readings are within "safe" ranges. They are constantly having to adjust the readings into these safe ranges - and we find out later in the novel that the "third policeman" himself (Policeman Fox) has in fact been constantly modifying these readings into the unsafe range for his own entertainment - This sounds very similar to what happens in the Hatch as far as resetting the clock every 108 minutes - especially when combined with the information concerning the Pearl. ("?")
- The strange, abstract map created by a spreading crack on the roof of the cell in the book is somewhat similar to the blast door map in Lost;
- A map!...When I looked carefully at the ceiling I saw that Mr. Mathers’ house and every road and house I knew were marked there, and nets of lanes and neighbourhoods that I did not know also. It was a map of the parish, complete, reliable, and astonishing…And he lay looking at the map for five years more before he saw that it showed the way to eternity.
- Time stands still inside the bunker in the book; the creators of Lost alluded that time on the island may be altered in some way.
- On one of the occasions when Policeman Fox modifies the readings into the unsafe range he either intentionally or unintentionally saves the narrator from being hanged by Policeman MacCruiskeen as he suddenly has to attend to lowering the readings; there is a similarity to the events of the season 2 finale here;
- In the book, the protagonist finally gets his hands on the coveted black box, only to discover that his money isn't inside it. Instead, the box contains omnium, a substance which creates anything the beholder desires.
- The narrator of the book discovers that items so created (via the interaction of his will with the omnium) cannot be removed from the labyrinth and taken back to the outside world.
- Old Mathers in death seems to be fairly similar to the character of Jacob
- "In the darkest corner of the room near the window a man was sitting in a chair, eyeing me with a mild but unwavering interest. His hand crept out across the small table by his side to turn up very slowly an oil-lamp which was standing on it...His voice had a peculiar jarring weight like the hoarse toll of an ancient rusty bell in in an ivy-smothered tower."
- Leaving the County of the Policeman is difficult, and when the protagonist finally manages to return to his home he finds everything out of sorts. His only hope is to return to the County of the Policeman, which starts an endless loop.
- Essentially the main idea of Season 5.
- When the protagonist returns after three days with the policeman, he discovers that 16 years have past. Likewise, MacCruiskeen and Pluck sleep in the underground hatch. By doing so, they no longer age.