Bootstrap paradox

An ontological paradox is a paradox of time travel that questions the existence and creation of information that travels in time. It is very closely related to the predestination paradox and usually occurs at the same time.

Because of the possibility of influencing the past while time travelling, one way of explaining why history does not change is by saying that whatever has happened was meant to happen. A time traveller attempting to alter the past in this model, intentionally or not, would only be fulfilling his role in creating history, not changing it. The Novikov self-consistency principle proposes that contradictory causal loops cannot form, but that consistent ones can.

However, a scenario can occur where items or information are passed from the future to the past, which then become the same items or information that are subsequently passed back. This not only creates a loop, but a situation where these items have no discernible origin. Physical items are even more problematic than pieces of information, since they should ordinarily age and increase in entropy according to the Second law of thermodynamics. But if they age by any nonzero amount at each cycle, they cannot be the same item to be sent back in time, creating a contradiction.

The paradox raises the ontological questions of where, when and by whom the items were created or the information derived. Time loop logic operates on similar principles, sending the solutions to computation problems back in time to be checked for correctness without ever being computed "originally."

It is sometimes called the bootstrap paradox, in reference to its appearance in Robert A. Heinlein's story By His Bootstraps (see below).

Examples

On his 30th birthday, a man who wishes to build a time machine is visited by a future version of himself. This future self explains to him that he should not worry about designing the time machine, as he has done it in the future. The man receives the schematics from his future self and starts building the time machine. Time passes until he finally completes the time machine. He then uses it to travel back in time to his 30th birthday, where he gives the schematics to his past self, closing the loop.

Another example, involving more than one person:

A professor travels forward in time, and reads in a physics journal about a new equation that was recently derived. He travels back to his own time, and relates it to one of his students who writes it up, and the article is published in the same journal which the professor reads in the future.

Examples from fiction

Literature

Robert A. Heinlein's stories "By His Bootstraps" and All You Zombies— involve the predestination paradox, but also play with the ontological paradox. In "By His Bootstraps", the protagonist is asked to go through a time portal by a mysterious stranger, a second stranger tries to stop him, and all three get into a fight which results in the protagonist being pushed through anyway. Ultimately, it is revealed that all three are the same person: the first visitor being his future self and the second an even older future self trying to prevent the loop from occurring. The ontological paradox here is in where and how the loop started in the first place. "All You Zombies—" involves an even more convoluted time loop involving kidnapping, seduction, child abandonment and gender reassignment surgery, resulting in the protagonist creating the circumstances where he becomes his own mother, father and kidnapper.

Isaac Asimov's short story The Red Queen's Race used Lewis Carroll's example of the Red Queen's race in Through the Looking-Glass to illustrate the concept of a predestination paradox, even though the short story itself implies a resulting ontological paradox.

Isaac Asimov's novel The End of Eternity has an ontological paradox resulting from the source of the technology of time travel, which is given to its creator by time travelers from the future, who were able to time travel thanks to this.

In a storyline in the daily comic strip Calvin and Hobbes, Calvin attempted to create an ontological paradox by travelling two hours into the future to retrieve a story he had to write for homework and did not want to do. He reasoned that by that time it would be done and he could then bring it back to the past and spend the time goofing off instead of working. Of course, the future Calvin didn't have the homework either, having decided two hours previously to time-travel instead of doing it. Calvin eventually ended up fighting with two of his future selves, while Hobbes and his future self wrote a story based on the whole predicament. The story (which was about Hobbes saving the day) received an A+.

In The Time Traveler's Wife, Henry DeTamble is visited by an older version of himself, who teaches him various skills such as picking pockets and lockpicking. As an adult, he then visits his younger self to teach himself these skills. Additionally, during his journeys through time to visit the young Clare Abshire he provides her with a list of dates when he will be visiting her; a list which the adult Clare subsequently gives to him so that he can pass this information on to her younger self.

In Jasper Fforde's novel The Eyre Affair, a time-travelling character goes to Elizabethan times to discover who wrote Shakespeare's works. After discovering that neither Shakespeare, Marlowe, Bacon or anyone else seems to have written them, the character must give Shakespeare a copy of his own Complete Works and a rough timeline to ensure their existence in the future. (Confusing things further, however, the sequel revealed that the plays given to Shakespeare only included three comedies. The characters speculate that they proved so popular he wrote new ones himself. Fforde rather makes a point of not having his time travel follow any particular set of rules.)

Similarly, in Tim Powers' novel The Anubis Gates a time traveller attempts to visit the enigmatic 19th century poet William Ashbless, of whom he is a fan. The time traveller is unable to locate him and eventually realizes that he himself is destined to become Ashbless, "writing" Ashbless' works from memory.

The ontological paradox is mentioned in the Doctor Who Virgin New Adventures novel Happy Endings, in which, after taking the Isley Brothers to the 21st century, the Doctor warns them not to listen to any of their songs they haven't written yet, explaining that such information is "written by Time herself, and they contain messages".

In Harry Harrison's novel The Technicolor Time Machine, Barney Hendrickson travels back in time to present his earlier self with a note explaining how to resolve a seemingly insurmountable difficulty. The younger Barney carefully folds the note and puts it in his wallet, expressing his intention to leave it there until he reaches the point in his life where he travels back in time to hand it to his younger self. This prompts some discussion of how the note actually got written, and by whom, which the older Hendrickson dismisses by saying that the note was written by "time" because it needed to exist to allow the predestination paradox to play out. At the close of the novel, Hendrickson also discovers that by travelling back in time to film the Viking settling of America, he actually caused it to occur.

In the climax of J.K. Rowling's Harry Potter and the Prisoner of Azkaban, a series of events leading up to the apparent execution of Buckbeak and Sirius Black's imprisonment are revealed to be the doing of Harry and Hermione, who travel back in time to prevent the deaths of both. A true paradox is created when Harry realizes that the mysterious wizard who saved his life (and who Harry mistook to be his father) was actually his future self. He is able to create the life-saving Patronus because he knew he'd "already done it."

In the web-comic Cat and Girl, in the installment entitled "Cat and Girl Settle In," the two main characters travel back in time to the early 1990s and engage in a discussion of various undesirable trends which have taken place since, thus inspiring passersby to start these trends. Sadly, their attempt to make intentional use of this phenomenon is foiled by a falling grand piano. ^[1]

In Stephen Baxter's novel, The Time Ships (which is the official sequel to H. G. Wells "The Time Machine" ) we learn that the narrator and time traveller from H.G. Wells original novel, was given a mysterious element by a strange man, which made the construction of the time machine possible. This strange man turns out to be an older version of the time traveller himself.

Film

In Star Trek II: The Wrath of Khan, Admiral Kirk receives a pair of antique eyeglasses from Doctor McCoy in the 23rd Century. Kirk subsequently leaves them in the 20th Century in Star Trek IV: The Voyage Home, implying that they would be a gift again. Although presumably the screenwriter's intent in Star Trek IV was to suggest a causal loop involving the glasses, the additional problem of the glasses aging by three centuries with each loop is never addressed.

Also in Star Trek IV, Scotty and McCoy also trade the formula for transparent aluminum to an engineer for materials needed to build a whale tank. Scotty eases McCoy's concerns about changing history by asking, "How do we know he didn't invent the thing?"

However, neither movie presents direct evidence of a loop; the characters merely assume it. It is possible that the eyeglasses that Kirk leaves behind do not "go forward" to become the pair that McCoy gives to Kirk, or that the engineer might fail in his attempt to invent transparent aluminum. (However, in the novelization of Star Trek IV, Scotty recognizes the engineer's name as that of the inventor.)

In the film Somewhere in Time, an elderly Elise McKenna gives Richard Collier a pocket watch which he then takes in time to hand it to her younger self, who will then, decades later, return it to him. As in Star Trek IV, in addition to the paradox, the problem of the watch aging with each loop is not addressed.

In Back to the Future, Marty McFly steps in for the guitarist at his parent's school dance and plays Chuck Berry's "Johnny B. Goode". Marvin Berry, the band's guitarist, calls his cousin Chuck and tells him that he found the "new sound" Chuck was looking for.

Also in Back to the Future, in the stairwell after the dance and the Johnny B. Goode performance, Marty says goodbye to his 1950's parents who have just had their first kiss. After he leaves, his mother absentmindedly says "Marty - what a nice name..." implying that he inspired her to name her future son Marty. (However, in the third movie, Marty discovers that one his ancestors' names was Martin, which could have been the "original" inspiration for his name)

In The Terminator, the Terminator cyborg sent back to kill Sarah Connor is destroyed, but its components are salvaged to form the basis of the artificially intelligent computer network Skynet that will, in the future, send it back in time on its murderous mission.

Also in The Terminator, Kyle Reese, having traveled forty-five years into the past, gives Sarah a message from his commander John Connor, subsequently fathering John with Sarah. In Terminator 2: Judgment Day, John says that his mother made him memorize the message — which, ironically, says that the future can be changed — in order to give it to his father, so that his father might then pass it on to her. At no point do we learn when or how the message was originally composed. Similarly, Kyle shows Sarah how to fight Terminators. Sarah teaches the same methods to John, who trains Kyle in the future.

In Bill and Ted's Excellent Adventure, the future Bill and Ted introduce their past selves to Rufus. He never actually tells them his name.

In A Chinese Odyssey, Stephen Chow's character, Joker, is abducted by demons who have taken him to a place called "Spiderweb Cave". At one point, he discovers a relic called the "Pandora's Box" which allows him to travel through time. He uses it several times in the movie until he accidentally sends himself back further. Joker then spots a woman passing by and he warns her not to go further because it's the Spiderweb Cave. The woman replies "Do you think I'm blind? The sign says Waterfall Cave". Which shocks Joker. The woman continues "Although, Spiderweb Cave does sound fitting". The woman is a demon who uses her magic and changes the sign to read Spiderweb Cave.

The Jacket reverses the paradox by having a character travel to the future to affect his past.

In Meet the Robinsons, Lewis is convinced by Wilbur Robinson that he is a famous inventor. He takes him to the future to prove it. There, Lewis meets himself, plus his family, who has invented the first working time machine that flies. Lewis goes back in time, is adopted by Bud and Lucille, and creates the world's first working time machine that flies. Child Lewis travels to the future to see himself. The loop continues on.

Television

One scene in the Star Trek: Deep Space Nine episode "Trials and Tribble-ations" shows Miles O'Brien and Julian Bashir, having travelled into the past, attempting to blend in with crewmembers on the USS Enterprise (NCC-1701). At one point, an attractive female crewmember, Lieutenant Watley, joins them in the turbolift. She is obviously interested in Bashir and tells him to meet her later. After she leaves, Bashir remembers that Watley was the name of his great-grandmother - and that nobody ever knew his great-grandfather. He thinks he might be destined to fall in love with Watley and become his own great-grandfather. However, he only suspects this is the case - we never find out whether Bashir and Watley followed through on their attraction.

In the Red Dwarf episode "Stasis Leak", Rimmer encounters the future holographic version of himself who tells him that the future crew had traveled back in time through a stasis leak found on one of the lower levels of the ship. He writes this in his diary. In the future, Lister reads Rimmer's diary and looks for the leak, which the crew finds and uses to travel back in time, where future Rimmer tells past Rimmer about the leak. The paradox not only involves the knowledge of the leak, but also the fact that the phenomenon itself is called a "stasis leak".

In the 1973 Doctor Who serial Day of the Daleks, a group of guerillas from the future are caught in a predestination paradox, doomed to create the very future they are trying to prevent. The Third Doctor breaks the loop, averting the future, because his existence is not dependent on the loop itself. However, he creates an ontological paradox in the process, because if the events that alerted him to the loop no longer exist, where did his knowledge of the loop come from?

In the 1977 Doctor Who serial The Invisble Enemy, the Fourth Doctor derives a cure for the alien virus from a antibody in the blood of his companion Leela, the only person who possessed it. However, Leela was from the future relative to this episode, and so the antibody itself is a paradox.

In the 2002 Doctor Who webcast Real Time, Dr. Reese Goddard, a Cyberman from an alternate 1927 where the Earth had been infected by a virus that turned people into Cybermen, came to the planet Chronos to stop the Doctor from giving the Cybermen the virus in the first place. Goddard brought a modified version of the virus deadly to Cybermen, which the Cybercontroller captured and reverse engineered to create the virus which infected Earth. It also transpired that the Cybercontroller infected the Doctor's companion Evelyn Smythe with the virus, so that when she travelled into the past she would begin the infection and eventually become the Cybercontroller herself.

In the 2005 Doctor Who episode "The Parting of the Ways", Rose Tyler, who had absorbed the time vortex from the TARDIS and gained god-like powers, scatters the words "Bad Wolf" throughout time and space. The words would follow her through her travels with the Ninth Doctor, and would eventually motivate her to save the Doctor when they had seemingly been separated forever, and absorb the time vortex, closing the loop.

In the 2006 Doctor Who episode "New Earth", the Doctor sends Lady Cassandra (her consciousness in her dying clone servant Chip's body) back in time to meet her younger self. "Chip" tells the younger Cassandra she is beautiful and dies in her arms. Earlier in the episode, Cassandra had stated that she cloned Chip after her favorite "pattern", implying that she got it from the man who died in her arms so many years before and leaving the origin of Chip's pattern open.

In the 2007 Doctor Who episode "The Shakespeare Code", set in 1599, has a running joke where the Doctor, in the presence of William Shakespeare, quotes lines from plays that Shakespeare has not yet written. In each instance, Shakespeare comments that he "likes that" and might use the line in a future work. The true origin of these lines form an ontological paradox.

In the 2007 Doctor Who episode "Blink", the Doctor records a message on film in 1969 in the form of half a conversation. The other half is filled in when Sally Sparrow views the film on DVD in 2007, which her friend Lawrence Nightingale transcribes. The full transcript, including the Doctor's portion, is eventually handed to the Doctor in 2008, but before he is sent back to 1969 from his subjective viewpoint, so he can use it in creating the message later. The contents of the conversation form an ontological paradox.

The third series of the revived Doctor Who features a subtle ontological paradox. In the episode "Gridlock", a being called the Face of Boe, supposedly billions of years old, gives the Doctor a message he has carried for centuries: "You are not alone". In the episode "Utopia", recurring character Captain Jack Harkness - a human being made immortal - accompanies the Doctor when he discovers the meaning and significance of Boe's message. In the series finale "Last of the Time Lords" it is implied that Captain Jack, able to live forever, will mutate and age very slowly until he becomes the Face of Boe in the distant future.

In the anime series Generator Gawl, the genetic code that led to the creation of the generators is taken from Gawl, a generator who had traveled back in time to change the past.

In another anime series, The Melancholy of Haruhi Suzumiya, a slightly older Mikuru goes back in time to convey a hint to Kyon regarding a future crisis involving Haruhi. During the conversation, in order to prove that she is Mikuru, she shows off a star-shaped mole on her breast, something which she learned of from Kyon. However, Kyon had no idea up to that point of its existence. Afterwards, Kyon confirms this via photographs, and tells the present-day Mikuru of the star-shaped mole, which she exclaims she had never noticed.

In the Stargate SG-1 episode "1969", SG-1 accidentally travels back in time to the year 1969, where they are aided by Lt. Hammond because of a note his future self gave to Carter before they left, spurred by a familiar cut on Carter's hand. Recalling the memory of the future SG-1 visiting him early in his career, Gen. Hammond had ordered research into using the Stargate for time-travel and was subsequently able to provide them with the information they needed to get home—before they left.

In the Stargate SG-1 episode "Moebius", SG-1 travels back in time to Egypt around 3000 BC in an attempt to retrieve a piece of alien technology, and end up inciting the very rebellion that originally drove Ra away and freed Earth, allowing it to progress to the point where Stargate was recovered and the Stargate Program was founded. However, this may not be a true ontological paradox, since there are subtle differences between the world "before" SG-1 went back and time, and "afterward": most notably, after the adventure, Jack's pond now contains fish.

In an hour long special of Dexter's Laboratory Ego Trip, robots appear in Dexters lab to destroy the one who saved the future. After defeating the robots, Dexter decides to travel into the future to see how cool he is. At the end of a huge battle, it is revealed that Dee-Dee is the one who saved the future so Dexter builds an army of robots and sends them into the time portal to destroy the one who saved the future.

In the Sealab 2021 episode "Lost in Time" Stormy and Dr. Quinn accidentally cause a chain of events that destroys Sealab in a nuclear blast which creates a subspace fracture sending them 15 minutes back into the past where they attempt to speak personally with Captain Murphy and Marco in Sealab to abort the mission that would destroy it all over again. Due to the paradoxical and theoretically impossible existence of two Stormys and Quinns, Captain Murphy and Marco ignore their plea and throw them in the brig, thus restarting the same incident over and over until the multiple duplicates manage to make contact with the Stormy and Quinn about to start the chain reaction.

In the Futurama episode "Roswell That Ends Well" the crew travel back in time and Philip J. Fry manages to become his own grandfather. As he is his paternal grandfather, the origin of Fry's Y chromosome is an ontological paradox.

In the Fairly OddParents episode, "The Secret Origin of Denzel Crocker", Timmy travels back in time to stop Crocker from experiencing the horrors of March 15th, but in doing so, he accidentally reveals Crocker's fairy godparents, causing the town to suffer from amnesia, and attack Crocker, which was the horror of March 15th in the first place.

In the Xiaolin Showdown episode Days Past, Omi travels back in time to prevent Wuya from taking over the world. He must open a magic box. Omi freezes himself to pass the many years. In doing this, Wuya takes over the world. Omi eventually opens the box, and defeats Wuya. As he is defeating Wuya another Omi is travelling back in time to try to prevent Wuya from taking over the world.

Video games

In a section of The Legend of Zelda: Ocarina of Time, the player character, Link, enters a windmill where he meets an organ grinder who tells him that seven years ago, a child came to the windmill and played a song, causing the windmill to go out of control (and opening a gameplay area). He teaches Link the Song of Storms, after which Link goes back in time and becomes his younger self, who goes to the windmill and plays the song, causing the effects and planting the melody in the organ grinder's mind.

In The Legend of Zelda: Oracle of Ages, the player befriends a Goron who gives the player a vase, his family heirloom. Then the player travels back a few hundred years, finds the Goron's ancestor, and gives him the vase, to be used as a family heirloom.

In the computer game TimeSplitters: Future Perfect, there are many examples of an Ontological paradox, and they all involve the main character of Cortez. On one occasion, Cortez is walking along and sees another version of himself who gives him a key. Later on, the present version of Cortez finds the same grate where he saw the last version of Cortez, only to see another version who he passes the key to. In addition, the villain, Jacob Crow, gives his younger self a copy version of his time machine after he has completed it, and the younger self in turn gives the older self a copy in the future.

In the computer game Escape from Monkey Island, Guybrush travels through a marsh where time flows differently and encounters his future self on the other side of a gate, who gives him the gate's key and several other items. Unconvinced, the present Guybrush asks what number he's thinking of, and opens the gate when his future self gives the correct answer. Later in the marsh, Guybrush must go through the gate from the other side, and so has to give his past self the key and the miscellaneous items, then pass the number-guessing test by recalling what his future self told him. The question of where the key and items originally came from is thus never resolved. True to the game's humor, failure to repeat everything precisely will cause a "temporal anomaly" that sends Threepwood back to the start.

In the interactive fiction game Sorcerer, the player is given the combination to a safe by his future self. He then has to give the combination to his past self to prevent a temporal paradox.

In the interactive fiction game Spellbreaker, the player finds a spell in a moldy book. Later in the game, the player puts his spell book into the same room, where it becomes moldy.