The Big O/WMG

Angel is Haruhi
Haruhi created this world in a dream after watching too much mech anime one night. Roger Smith is Kyon and Dorothy is Yuki. The reason everything is such a Mind Screw is because Haruhi is dreaming, and the reset is when she finally wakes up from the dream, but not before dreaming of herself as Big Venus. However, Roger does persuade her to not erase the world, which results in her creating a separate timeline to house the reset world of the Big O.

Big O is a (heavily modified) retelling of The Wonderful Wizard of Oz
At least the second season probably is.

Dorothy is the Tin Man, Roger is the Scarecrow, Dastun is the Cowardly Lion, Gordon is the Wizard of Oz, Alex is the Wicked Witch of the West, Beck is the King of the Winged Monkeys, Angel is Dorothy (much like in Serial Experiments Lain, Alice is not Alice), and Angel's "mother" (the leader of the Union) is the Good Witch of the North. Memories are the Silver or Ruby Slippers. So in the end, Angel is able to use her power to become remembered again ("I just want to go home"), setting the world back as it should be.

Please note that the world would probably not be the exact same, but changed subtly to a better world. (Think Serial Experiments Lain, which the author wrote just before The Big O).

Big O is a TV series.
Duh.

Big O is a Show Within a Show.
Angel is one of the producers of a metafictional Big O TV series. She fell in love with the character of Roger Smith (or else the actor was her real-life boyfriend), and so she had herself inserted into the show. The world-famous filmmaker they hired to be the director (who plays Gordon Rosewater -- the role was originally intended to just be a Cameo) gets frustrated with her meddling and starts to make the show more of a Mind Screw in hopes of getting it canceled.

Angel eventually starts to write the scripts to the show; by the end, she is the director, too. The Union woman torturing Gordon is Angel the Director punishing Gordon the Director for messing with her fantasies.

In the end, she realizes that Dorothy is a better match for Roger than she could be, no matter how idealized her character; after writing herself out of the show, she uses Big Venus (herself) to erase the whole mess of a show. Roger the Actor negotiates to stop her idiocy, and his character does the same for Big Venus; she agrees. The next-to-last scene is Angel the writer metaphorically meeting the character (this is why Dorothy says "Roger the Negotiator", to make sure she knows it's not the actors but the characters); then she decides to Remake it, but this time she won't mess around.

The last scene is the remade episode 1, with Angel as a character; but she won't be a Mary Sue this time, which is indicated by how she's slightly off-model and thus imperfect.

We Have Come To Terms.
 * Big O is the play being produced in the film "Synecdoche, New York"

Big O is a computer simulation of a world where Japan has committed world-wide genocide
Alex Rosewater, government agent, was commissioned and paid to operate a simulation of a world where all foreigners were killed and memories of them erased to create an ideal homogenized world. Angel is his research assistant who wasn't told the exact nature of the assignment. However, once she realizes the subtle horror of what she's doing, she introduces stranger and stranger random elements into the program to make it less valid. She eventually tries to shut the entire system down, but only manages to force a reboot.
 * But if that's the case, then why is Paradigm City decidedly not Japanese in style or attitude? What's with everyone having Caucasian names and mannerisms? (With anime, it's always a bit hard to tell nationality and ethnicity.) If Alex is the government agent in charge, then how does Gordon Rosewater fit in?
 * Alex Rosewater secretly loves America and its media Tropes (the American Way of Life), and so he based his simulation on them. He adopts an Americanized name for his in-sim avatar. "Gordon" could be artifacts of the simulation itself, an outside agent getting into the game, or some element of Alex's subconscious that crept in unwanted.

The Big O is a simulation drawn from Alex's subconscious
This would explain a lot. Roger is like Batman because he's based on Batman. The city has Ridiculously Human Robots and Humongous Mecha because Anime does. Paradigm City is half Noir and half Super Robot because Alex enjoys those genres. Et cetera. Hmmm, this could lead to a sub-WMG:

Roger Smith is the Eternal Champion
Roger Smith is a seeker of Order in a world of Chaos; he has friends who are followers; he has a doomed romance; he has a magical black superweapon. And everything is doomed no matter how many times or how much the hero wins. It's pure Michael Moorcock.

Even if they make a new series, it won't explain anything
But it went from cliffhanger to worse; a new series could go Up to Eleven in confusing and be worth watching for that reason.

Paradigm City is a computer simulation in an endless loop, and Memories are transcription errors.
Either the Director's computer can literally rewrite reality inside the city, or the entire series takes place inside a computer and the characters are just AIs in a Re Boot-style simulated world. Either way, Angel is the only one the system takes orders from.

God-only-knows-how-long ago, she left her post, started living among the peons as an apparently normal person, and fell in love with Roger. When he died, she reset the world in a fit of grief and inadvertently erased everyone's memories in the process, including her own. The cycle repeated, with Roger dying and Angel regaining her powers and resetting the world at the end of the loop an unknown (but probably immense) number of times.

Occasionally, there's a glitch in the computer, and people's memories of the last cycle aren't completely erased during the reset, leaving them with capital-M Memories - things they learned in previous lives, like Beck's knowledge that Roger pilots Big O or Wayneright's being able to design robots.

The plot for Big O was generated by a computer program
Not the real show, but the show-in-the-show. Okay, imagine this: ...Only far more advanced. The program was made to design plots for television shows. It is likely hooked up to a database of plot elements, like this tropes wiki. However, it had some imperfections and generated a severely warped story. At the end of the series, the computer is taken offline, upgraded, and then rebooted to re-write a better version of the series.

The Big O and its world are the result of Third Impact
Roger Smith is Shinji Ikari redefined as a mature and capable womanizer, gifted Super Robot pilot, and devoid of any serious mental problems. The Big O itself is a restructured Eva Unit-01. Norman is Fuyutski, Dorthy is Rei, Angel is Asuka, and Big Duo is Eva Unit-02. Eva Unit-00 became Big Fau, but the spirit in Unit-00 is still not at peace with the world and wishes to keep people away, explaining its energy barrier. Asuka's mutilation by the Mass-Produced Evas in the movies were prepping her for a possible Fourth Impact, giving her the power to carry it through.

Gordon Rosewater is a fusion of Gendo and Yui Ikari, this is why he's so apathetic to everything going. He has what he wants so he doesn't care anymore. Alex is also Gendo, but only the part of him that wants to destroy the world. This part split off in Insturmentality when Gordon formed. The antagonism between father and son is then a sign of the conflict within Gendo himself about his own father and son. He takes it all out on Roger-Shinji, which subconsciously eases his anxiety. Beck is actually Kensuke, warped by jealousy of Shinji, and driven to using Domanus to destroy Shinji and thereby prove his superiority. His fixation with Dorothy comes from her having red hair like Asuka did, before she became Angel.

Twelve Ounce Mouse is a later season of Big O
Every reset of Paradigm City degrades it a little, making it less realistic. Over dozens of resets, tomatoes became corndogs, Big O became Corndroid, and humans became whatever the heck the Twelve Ounce Mouse characters are. It all ends in another reset, but with hints that this time Roger/Fitz has learned how to break the cycle or at least alter it.

It's literally all about tomatoes.
Angel is the owner of a tomato farm, and all the humans in Paradigm City are actual tomato plants. Resetting the world is the harvest, and the passage of forty years in Paradigm City (Paradigm Farm?) correlates to the planting and fruition of tomato plants on the farm.

You're one of the tomatoes.
Seriously, what do you remember about 40 years ago?
 * "The tomatoes... I'm one of...the tomatoes... !!!"
 * That was the sixties. If you remember them, you obviously weren't there.

Paradigm City is Vault 122.
Vault 122 was meant for the sustained comfort of important scientists, researchers, and V.I.P.s; a system of interconnected Vaults, it had luxury standards and many reconstruction materials/G.E.C.K.s. Over time, the inhabitants of Vault 122 - more than 1,000 - were able to emerge and begin rebuilding. Domes were erected over each entrance/exit to protect the inhabitants within. Due to pre-War materials/knowledge, the survivors approximated pre-War life, though remained centered around the Vault due to the rest of the world being Wasteland; the main entrance to Vault 122 is under Paradigm Dome, with the underground connectives as the Big O's 'transport tunnels.' The stylized appearance of the City and its inhabitants is due to the Vault's survivors being generations removed from the originals, basing their new society on what they believed to be "Pre-War Life"... entertainment tapes. To pass down their knowledge, adapted Tranquility Loungers passed memories through generations, effectively making them hereditary; the Loungers were lost, and the original memories mixed with tapes viewed by the Vault's original inhabitants to create the bizarre flashbacks seen by the characters of Big O. The memories remain in some, scattered and fragmented, further submerged with each new generation; the memory-loss in which no-one can recall anything beyond forty years ago is simply due to radiation poisoning reacting with drugs present in the food and water that keep the inhabitants healthy. Gordon Rosewater is among those whose hereditary memories are greater than most, and the references to tomatoes are the agriculture that grew crops in polluted soil; Gordon's ancestors moved outside the dome and Gordon's mind is corroded, prompting him to play mind games with the others. The Union are outsiders who achieved similarly high levels of civilization and wish to acquire pre-War technology housed within Paradigm City - Perhaps they're the Commonwealth, or foreigners who made it to what was once North America.
 * Alternately, Paradigm City is Vault 122, an active experiment. The gears viewable as the Big O sinks are part of a massive mechanical platform that controls the 'suns' around the domes, the electricity, everything. That's why a city 'with no memories' can continue to function. The Vault was meant to gauge just how far the human mind could sink from reality; memories are dulled via mind-scrambling white noise broadcast over the P.A. systems at a sub-audio level. The Mega Deus are remnants of the program that built Liberty Prime, scaled down and under the control of the Overseer; hence why they act on their own and don't respond to their driver. The Union is made up of technicians who know about the experiment and exist among the populace to manipulate the outcome; hence, why those we see have bad accents and over-the-top attitudes. They're literally playing a part. Gordon Rosewater is Overseer, in need of a replacement; his son Alex contracted radiation poison, resulting in an addled mind. Alex's actions interfere with the experiment, so the technicians/the Union are sent to stop him, with Angel one of them. However, she starts buying into the illusion propagated in the city (her descent from aloof femme fatale to uncertain self-doubter), and at the end, Angel takes control of the experiment and re-starts it by performing a mass re-conditioning of the Vault's subjects. Angel becomes the new Overseer, but her appearance at the end of the series indicates that she intends to continue playing in her new sandbox.

Schwarzwald knew he was a robot
When Seebach tried to release the Archetype, he lost much of his flesh, revealing his robotic insides. Most other robot-actors would have died; due to an error, Seebach lived. From this, he learned every person in Paradigm was a robot-actor on a grand stage. He changed his name to reflect that he was no longer a character in a story. He wrapped himself in bandages to hide his robotic exterior, save for his left eye (his right eye may also indicate his android nature as it has the same circular pattern as when Dorothy is shut down). Big Duo just helped him confirm his suspicions when he flew to the "top" of the world.

Paradigm City is Gotham.
Just try and tell me Roger isn't Bruce Wayne and Norman isn't Alfred. Schwartzwald may be the Joker.
 * Bah! Everyone knows that Alan Gabriel is the Joker-analogue! With maybe a twist of Two-Face thrown in for fun. (No real evidence for this wacky theory, though. It'd be better to suggest... Wait a sec...)
 * Alan Gabriel is a cybernetic Joker, yes; Schwartzwaldt is a cybernetic Thomas Elliot, aka Hush. Let's look at this a second: Covered in bandages, check; completely batshit crazy and wants to watch a city burn, check; has a weird mirror-image thing going with a rich-guy-by-day-vigilante-by-night character, check... yep, that's Hush!
 * If you've watched Batman: The Animated Series, Big O can be seen as a retelling and expansion of the episodes "Heart of Steel" parts one and two and the followup, "His Silicon Soul." In "Heart of Steel," Batman fights and destroys an AI bent on phasing out humanity by replacing critical members of society with androids. In the process, Batman fights, unmasks, and destroys a robotic version of Harvey Bullock, whose character design is similar to Schwartzwald's, and who also serves as a lesser antagonist to Batman. The linkage to the Big O becomes much more convincing in "His Silicon Soul," wherein a surviving android programmed to replace Batman discovers its own artificial nature due to a damaging accident. The android searches for and discovers the AI's creator, now a reclusive, rather misanthropic farmer who has substituted growing tomatoes for his previous attempts at engineering life. Inside a domed greenhouse, it is told that its lifespan is short, and that its memories are simply data fed to it by the deceased AI; as proof, the creator asks it questions about its childhood, which naturally can't be answered. Its meeting is interrupted by the arrival of the real Batman. After a brief fight, the robot brings the roof down, saves the creator, and flees. It searches for, discovers, and incorporates a remnant of the AI; afterwards, it is repaired and modified to work as an agent to re-initiate the AI's human-replacement plan. At the last moment, after striking down Alfred and the real Batman (who get better), the robot rediscovers its human empathy via the implanted memories of Bruce Wayne, and destroys itself and the last traces of the AI in order to end it. In short, this troper holds that Roger was the android, complete with spotty memory, that Gordon Rosewater was indeed the AI researcher, Karl Rossum, that Alex Rosewater was the megalomaniacal AI, and that Paradigm City was the android's conception of reality, shattered by an act of principled will. This troper might more hesitantly speculate that the entire thing could be a retelling in which the AI succeeded in its original aims, but was at length subverted by the tendencies granted to one of its own creations. This might help explain the presence of entities such as Dorothy and Schwartzwaldt; several Big O characters bear at least passing resemblances to some of the AI's original host of android minions, including a bob-haired fem-bot that attempted to seduce Bruce Wayne. Angel, in this theory, would be a pink-suited Selena Kyle/Catwoman. Gabriel AND Beck have striking resemblances to the Joker, and Norman Burg's resemblance to Alfred is almost blatant. The prematurely-deceased Shwartzwaldt is possibly some incarnation of the Harvey Bullock android Batman destroyed, obsessed with revealing its version of the truth. It's a bit of a stretch, but even old Timothy Wainwright bears a moderate resemblance to a value-inverted version of Selena Kyle's treasured cat, Isis (which I suppose would cast Dorothy as Catwoman...no theory is perfect; also, this theory admits to having two Jokers on the cast, a rather frightening thought. Maybe the human Joker was just batty enough to recognize and survive the effective end of the world, in which case my money is on Beck as the human, what with the whole tech-exploitation theme). As for one last speculation, this Troper suggests that Roger's car is the Batmobile, and that the mecha actually represent the costumes regularly donned by the various Batman characters.

The Batman series is a comic/show/radio drama in Paradigm City!
As a young child, traumatized by the mind-altering and implanted-training he had to undergo, a young Roger Smith found solace in the story of a lad like himself, one Bruce Wayne, who adopted a stylish black-wearing persona to do good. Young Roger sought refuge in the story of this hero, and while growing up erased many of the memories he unconsciously began to re-create his childhood stories by patterning himself after Bruce Wayne: The stylin' black outfits, the multi-talented butler, the semi-antagonistic relationship with the local police-chief, the cool-ass car. The appearance of Dorothy begins moving him out of this mental safe-room and towards developing his own persona, as seen in his banter with Dorothy; however the change isn't easy to make, as it would mean sacrificing his childhood comfort. It's further complicated with the appearance of Angel, serving as the Selina Kyle/femme fatale.

The show is a visual of an experimental AI program ala S1m0ne designed to create multiple tv shows and types.
They are doing a dry run after running a Mecha style show and were trying a more noir one. Unfortunately the erasures weren't perfect from the old show, as a result Arthur knows how to pilot a megadeuce without any real technical training. And our villain who screamed about what this world was had been smart enough to realize what they were and it drove him batty. The end episode was an attempt to restart the series again with a more complete erasure, rather than reusing old props they'd just try to rebuild the whole thing from scratch but keep the first few scripts. --Blackjoker

Episode Fourteen was the REAL world.
For those who didn't see the episode (or forgot it): In episode 14, Roger hallucinates a world where he's a homeless man and ex-cop gone over the edge, Paradigm City is a normal 1950s-era world with sunlight and no domes, and everyone from the 'show' are different people. It turns out to be a construct of Roger's mind; when he accepts his place as a Negotiator, it all goes away.

This theory proposes that Roger's hallucination is the reality behind what we know as The Big O. Roger is that ex-cop, who - finally sickened by the horrors of his job - went over the edge and built an elaborate dream-world where he can solve all the problems of his city in the span of a single episode. The Big O really is just a newspaper comic. Dorothy Wainwright is the socialite daughter of the wealthiest man in town. Angel is just a co-worker whom Roger once had a relationship with and since was distanced from -- hence her ambivalent portrayal in the show. When Roger 'hallucinated', he was coming to his senses; the return to the 'real world' of the show was Roger refusing to accept the reality of his reality and sinking back into his delusion.

The Myst theory.
It's not that the show is a literal Crossover with Myst; it's that Paradigm City is analogous to an Age created like those in Myst.

The real world was destroyed in a cataclysmic war. Paradigm City is a facsimile of the real world, physically a different place located in Hammerspace, where as many survivors as could be saved were relocated. This is why the show spends its entire run showing signs that range from vaguely symbolic to blatant about how everything is a play on a stage, and also has every symbol that represents the audience show them as absent (the faceless characters from Roger's delusion in the season two premiere, Schwartzwald saying that waiting for them weren't the gods watching their every move but only abandoned equipment). In the play analogy, if Paradigm City is the play, then the audience watching the play, the manufactured world, must be the people in the real world. But there's no one left in the real world, no audience for the play.

By this theory, we do get some glimpses into the real world during the series. The first glimpses are the seemingly random scenes of the Bigs burning everything to the ground. Then, during the final episode, we see more literal flashbacks, like mass-produced Big Os wrecked on a battlefield (remember Schwartzwald saying a Megadues wasn't anything special before forty years ago?) and Roger dead in Big O's cockpit wearing a military uniform that exists nowhere in Paradigm City. Whoever made Paradigm City was smart and set it up so that the last survivors of humanity had room to make the same mistakes and recover instantly until they, one day, finally learn to not destroy the world. This is why the world isn't perfect and why anomalies like Roger (who clearly died in the real world but is still here) and the mecha exist.

Big O really is inside Myst
And if Myst VI is ever made, there will be a book leading to Paradigm City.

The world of Paradigm City was the prototype for the Eternal Sphere.
The game changed a lot over the course of development. In this earlier version, they hadn't yet worked out how to create AI with pre-existing in-universe memories. The reboot at the end was simply starting the server over from a save while they worked out a better version that wouldn't destroy itself.

Everyone in Paradigm City is a robot.
I'm surprised this theory isn't more well known, but here we go: Everyone in Paradigm City is a robot. Some have been implanted with human memories and think that they are human. Some are obviously not human and have no identity issues. Some, like Roger, Shwarzvald, Angel, and everyone else who think that they are human, are manufactured with the belief that they are human but the memory-copying process is imperfect.

The original purpose of Paradigm City, the Bigs, and the various other robots has been lost in time. Something went wrong in the past, and the original program was corrupted or lost. The whole system breaks down periodically resulting in what appears to be mass amnesia, but is really more of a soft reboot. At the end of the second season, Angel takes over the system and we get to witness a reboot.

If this theory is right:

1) Everything Shwartzvald does makes sense.

2) All of Roger's flashbacks make sense.

3) The ending to both seasons make sense.

4) Roger really did help (re?)build Paradigm City, he just can't remember. Other "fictional"/apparently contradictory events in the past are true.

5) Norman and his team of Big O Maintenance guys makes sense: they're programmed to maintain the Big O. (Furthermore, Norman and others like him probably keep up repairs on the other robots who think they're humans without realizing it because it's part of their programming.)

6) This is why robots can have human memories and vice versa: it's all the same recording format.

7) This is also why, in the manga, people are able to store memories in banks and find them in external objects. They could actually copy memories onto disks, but since they have an incomplete knowledge of what people are, they don't realize that this isn't a normal human ability.

Were there ever any real humans in Paradigm City? I would guess that it was intended for humans but something went wrong and when the humans never arrived the city or whoever was in charge decided to make some with the information available at the time. I would also guess that Roger's memories of the alternate reality are a recorded copy of a real person who lived in the distant past. I would also guess that every "real" human went through the same process Roger did: attempting to recreate real humans using recorded memories.

(Personally, my first guess as to Paradigm's original purpose is that it was supposed to be a giant amusement park with super-advanced animatronic actors. This would explain why characters find concrete physical evidence of events that turn out to be completely fictional. But the whole blurring of fiction and reality could also be accounted for by the system misunderstanding what memories are/were of real events and which memories are/were of fictional stories made up by humans in the past.)

Challenge to this, though: why would Roger need the oxygen tank in the Grand Finale, then? If he were a robot, shouldn't he be like Dorothy and not need to breathe?
 * Roger was waterlogged. The air flushed out his systems.

Better Challenges: How do they bleed when they are shot? How did that dog eat its owner? Why do they eat food? Why would there be andorids that know they are robots when everyone is already a robot?

and if you think those are suspension of dibelief or anything of the like:

How come Roger is never affected by the giant magnets that trap Dorothy, and why have some characters (apparently) aged over the decades while the robots look the same (as evidenced by the Bigs and R.D. On the other hand, we saw that Roger's old-man looking informant was actually a robot, so I guess altered face plates are not completely out of the question.

Paradigm City is on the site of what is now Hollywood.
It's almost self-explanatory! Where else in the world would it actually make sense for an entire city to exist as a backlot, for everyone to be actors who don't remember past 40 years ago because it's in the script, for the entire camera-crew to abandon a shoot and allow it to both fall into obscurity and go on without end? They're probably striking for more scones on the crafts table or something as we speak.

And the close-to-the-ocean thing? Is simply the erosion of the California coast, after decades/more of rising sea-levels. Plus, California's known for its bounteous crops of... Wait for it... TOMATOES.

Everyone in Paradigm City is immortal.
Perhaps one of the previous theories is true and they're all robots or computer simulations, but in any case, nobody ages the way they're supposed to. Just look at Roger. He looks to be in his late twenties or early thirties, but if he's not significantly older than 40, the timeline makes no sense. And even though we only see flashbacks of him with the Tomatoes as a child, which would suggest that he's 48 or so, it's implied that he started working as a negotiator right after losing his memories, which probably means that he's more like 60. Not even Generic Cuteness can explain away that much of a difference between real and apparent age. And it can't be just Roger: if anybody in Paradigm City actually aged, a huge percentage of the adult population would have no memory problems at all, for the simple reason that they're 39 years old or younger.
 * Or perhaps their calendar/planetary orbit is totally different, and a "year" is more like a month.
 * Gordon Rosewater was shown to have significantly aged from before everyone lost their memories -- the fact that Roger appears the same now as he did then was one of the Mind Screws of the show, and in the manga (which was created after season 1 of the manga aired) there was an uprising of younger rich kids who decided that the previous generation should get out of there way since the current one doesn't have any holes in their memories (aborted because they intruded on Norman while he was talking to his favorite statue, while simultaneously putting a machine gun near him at the same time, which probably went a long way towards convincing them that the older generation is not to be screwed with). And then there's the fact that young people/robots were getting memories from before forty years ago, including a little girl who could read the memories of people who couldn't remember them themselves, which just further complicates the situation...

The planet Paradigm City is on is actually in the Warhammer 40,000 Universe
The obligatory 40k WMG for Big O is: Paradigm City is New York during the Age of Strife after Terra's society collapsed, but before the Emperor began his rise to power.

This theory is simple. The place is a wasteland due to a cataclysmic war involving enormous, ornately designed Mechas whose great and terrible power makes people mistake them for gods. No one knows how these machines work, or of their origins, along with other old technology. All knowledge of the past has been lost, and everything seems pretty grimdark.

Angel isn't the reality warper of the Big O universe; Roger is.
Quite simply, the universe revolves around Roger. He lives in a skyscraper with its own power and water, makes lots of money and yet has plenty of free time, has a cool car, has a cool robot with its own subway transportation, has a badass butler, an old friend in the Military Police who's grumpy but loyal, an informant with all the right information, a corrupt omnicorp to rebel against, has a robot maid who's possibly a love interest, has another love interest who likes pink leather and switches between "hurt and needy" and "outgoing and flirty," and usually has some cool adventure to enjoy and weird villain to smash with Big O, who's always repaired and rearmed, no matter what. In short, he's the coolest guy in Paradigm City, because he wants to be the coolest guy in Paradigm.

Season 1 is when Roger is just chilling. While there's a deeper mystery or three in the background, Roger is content to let them be until he needs something to ponder. He takes life as it comes, and is free to smash up the city without any consequences. Villains like Beck and Schwarzwald give Roger adventures (both lighthearted and frightening, respectively) to look forward too; but they don't smother him. He's in danger constantly, but there's always an exit.He has friends who are both loyal and not slavish; he is both a part of the world and not tied down by it. Roger is happy; he can stretch out and relax, until it's ass-kicking time again. He never questions the awesome hand life has dealt him, because it never really occurs to him that he can warp reality. But the evidence is there: when Roger's stumped, he can go to Big Ear, who always has the information. Important people can jump far, like when Roger jumps into Big O's hands or when Schwarzwald jumps sixty stories and Big Duo catches him after flying in from outside the city (seriously, that was hilarious). There are no consequences for smashing up apartment buildings and the domes; the only thing to get hurt is Paradigm's wallet, and they repair the damage anyway. And as always, if something important is happening, Roger's right in the middle with Big O and an enemy robot to fight.

Season 2 is when Roger starts to realize something isn't right.

It's an accident. Roger's once again investigating the mystery behind Paradigm when he talks to Gordon Rosewater and RD and starts to wonder "Why am I here?" There are holes in the story and it makes him angry; he's not enjoying the fight like he normally does. As he starts to realize that his whole life is fake, his subconscious tries to give him what he wants. But it backfires; Roger's now a homeless ex-cop. But note how the new world is shaped; Roger can easily find old landmarks and familiar faces everywhere. Also, he's an ex-cop who was pushed to the breaking point; it has more dignity than say, being a pencil pusher- perfect for Roger's ego. In the end, when Roger decides he doesn't care why Big O fell into his lap (both it and Norman were just waiting for him), he chooses to go back to the fight and his subconscious grants his desire.

But it doesn't work. Roger is still unhappy, which makes him irritable and prone to introspection; before he was sanguine, now he's moody. Roger's concerns about his life affect the world; his fear about his role and destiny create an equal and opposite in Alex Rosewater, who is also rich, has confidence in his role, and has a Big (Alex is also older and less handsome, because Roger doesn't want THAT much competition). Angel also changes: before, she was just a Femme Fatale, now she gets the same emotional baggage Roger has. The first season storylines show up again as Roger questions them, and they are no longer separate episodes but part of a larger narrative.

In the end, as Roger has a mental breakdown, the world he made collapses. Bombs drop from an empty sky. Big Fau was originally broken because Roger still had enough confidence in the world and his place in it to resist any competition; now he's lost all confidence and loses miserably (he can't even hurt Alex). His home is smashed, Dorothy's brain is stolen, and as Roger believes he really is nothing but an actor fulfilling his given role, the world changes to match his belief. In the end, however, Roger decides he hates all this, and wants to go back to his old life in Season 1. Voila: Angel ex Machina!

Why do his reality powers manifest in Angel? Because Roger is a man who enjoys his freedom, and enjoys adventure and challenge. It's why he's never seriously injured. However, if Roger were to realize he's invincible, it'd take away all the fun. That's why Angel suddenly becomes all-powerful, and Roger can talk her into making a new, slightly fixed world- he can't deal with what he really is, so he makes the change through Angel.

France (and maybe the rest of Europe) went to war with America
This occured some after WWII, in an alternate reality where nuclear weapons and mecha were developed during the 50s and were used. The show is a simulation in which the surving inhabitants of New York live, having to be reset every 40 years due to the computer's memory limitations.

Roger is perhaps a programmer that decided to tweek the simulation to make things work out for himself. Also, he is probably a fan of batman.
 * Jossed by a banner that says "Exposition 04" in Schwarzwald's first appearance.

Roger is a clone of Dastun
There.

Paradigm was a military situation programme
Paradigm was originally designed as a military programme to simulate various situations of war and famine and to make minor adjustments and rerun the simulation to see the optimum parameters, i.e., it runs a an iteration, sees how long that iteration lasts and if it lasts longer than the previous one the changes are kept and some new ones are tried. Its last task was examining the best way for the survivors of post-war New York to band together into a new city to survive. Somewhere along the way the people in charge of the simulation died and it was left on auto-repeat. Although the world outside of New York (Paradigm) is not simulated the possibility of foreign powers entering the simulation was left in. The series is one iteration of the programme after it has been run for hundreds and hundreds of time and the changes it has made, while they do make everyone survive for forty years, have become pretty crazy. Angel is all part of the system for determining when to reset and what changes to make. The simulation now contains the only remnant of humanity left on earth and will be lost when the computer's power runs out.

The Big O takes place between the end of the Black History and the Dianna Counter's return to Earth
The Turn A destroyed the world years ago with the Moonlight Butterfly. In northeast Ameria, the humans rebuilt by themselves as best they could, digging out Megadei that were buried under layers of nanomachines, like the Mountain Cycles, along the way. At some point, one of them is activated that wipes the memories of everybody, creating Paradigm. Further Mountain Cycles are discovered and excavated over the next forty years, the Megadei we see in the series, including the Leviathan, a prototype Mechanical Doll that was used as a testbed for the Moonlight Butterfly. Eventually, a Mechanical Doll that uses an exotic branch of technology separate from the Turn A is activated, resonating with the DNA sequence of a descendant of its builder, and "erases" all traces of technology around Paradigm. Everything is forgotten, and rebuilt over time into the Turn A Gundam universe.

The people of Paradigm City are not real.
Remember what Gordon Rosewater said to Roger about the tomatoes? Who's to say that Rosewater hadn't done the same to humans by synthetically reproduce them? That's why the people of Paradigm couldn't remember, it's either because of the process is not yet perfected or the fact that they were just created and artificially aged.

Paradigm City was reset between Seasons One and Two.
It's the little things, mostly. Dastun was a major in Season One and a colonel in Season Two. Roger was referred to as a former lieutenant in Season One, and a former Major in Season Two. Big O has new weapons we've never seen before, but Roger is familiar with. Angel is more competent. Roger's attitude is different, being less snarky and more aggressive- see how he treats Dastun in "Eyewitness"? Compare that to how he acts in "Beck comes Back" or "RD", when Dastun is actually trying to arrest Roger.

It can all be explained away as offscreen promotions and such, but in a place like Paradigm, where memories are uncertain, it seems more suspicious.

Big O and the other Megadeuces are really Eldritch Abominations
They only look like giant robots because that's the only way we can perceive them. Or, like Neon Genesis Evangelion, the metal parts hide something... else.

The Big O took place after the events of Giant Robo: The Day the Earth Stood Still

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