Turn and Turn

In the Alpha timeline, there's a woman called Sarah Connor.  Sometime after May 12, 1984, she conceives a child by an unknown father.  When the child is born she names him John for some reason, cheerfully oblivious to how apropos his initials are going to be later.  It's possible she marries the father, and given her personality she probably takes his name, but either way, the next time we hear from the kid he's using his mother's surname.

Meanwhile, somewhere there's a computer geek who has a revelation.  (We have no idea when this happens, nor where; it doesn't have to be in LA or even necessarily in the US.)  It's possible the whole thing is an accident, but there are two important bits: the hacker invents a computer program of heretofore unimagined flexibility, and he or she has never read Asimov.   Anyway, the flexibility of the new system is so useful that it gets tied into all sorts of things, including the systems that control such things as the controls for launching nuclear weapons (because apparently the people of the Alpha timeline are singularly stupid).

Somewhere in here, a bad thing happens.  There's an exchange of nuclear weapons that the survivors remember as a nuclear war.  We don't know whether this was a "natural" event, caused by humans being dumb, or somehow engineered by the system that is, by now, known as Skynet, nor do we know who the combatants were, but the exchange smashes civilization.  That, however, is not the bad thing: the bad thing is that Skynet "wakes up", becomes self-aware, and decides that humans as a species have got to go.  Unlike certain other machine intelligences, Skynet has no use at all for the ugly bags of mostly water and just wants them dead.  It sets about this program with literally mechanical efficiency.

And here we catch up with John Connor again, because he rallies humanity.  People fight back.  They're sufficiently successful that Skynet starts taking its metal soldiers and turning them into infiltration units by covering their skeletons to mimic humans--they aren't very good at it, but it's sometimes enough to get them into a human hideout and kill.  The first series has "rubber skin", but eventually Skynet starts using actual flesh, grown for the purpose.  This will be important later, but isn't enough; the human resistance, against all odds, manages to win. 

Skynet, meanwhile, has been doing a lot of research.  Right before its final defeat, it makes a theoretical and practical breakthrough and produces an actual, working time machine.  Problem is that the field will only send living organisms back in time...but hey!  There are these infiltrators that are covered in living tissue; it doesn't stay living very long, but long enough to get itself and its internal metal skeleton back in time.  So Skynet takes one of its off-the-shelf terminators (to the eye a necessarily tall, bulky man because the flesh has to fit over one of the tall, bulky metal skeletons) and, right before the humans smash its defenses once and for all, sends the cyborg back in time with orders to find and kill the mother of John Connor before she conceives her son.  This is where the nuclear war comes in handy for the humans; Skynet only knows Sarah's name and that she lived somewhere in LA.  The humans break into the time-travel complex, work out what Skynet did, and send a couple of soldiers back as well to stop the terminator.

This is where the Beta timeline starts. 

On May 12, 1984, the terminator and the human soldiers appear in Los Angeles.  One of the humans doesn't survive the trip; he and his companion materialize in midair and fall, probably because the humans aren't as good at controlling the time travel device, and he falls onto something spiky¹.  The surviving human is called Kyle Reese.  He manages to find Sarah Connor before the terminator does; over the next few days they run from the machine and, under the influence of one too many near-death situations, have sex and conceive a child Sarah will call John because Kyle tells her about the future.  One way or another they destroy or nullify the terminator, but Kyle is killed and Sarah, alone, heads for somewhere to wait out the war so that John can become the savior of humanity.  Somewhere in here, someone takes a Polaroid picture of Sarah, which she will later give to John.  Everything goes according to the Alpha timeline with the exception that John has a different father and, upon meeting Kyle, gives him the photo of Sarah--because no one knows this is a Beta timeline, and John thinks that he has to send Kyle back in time in order to be born at all.

The Gamma timeline starts with the first film.  Kyle's already in love with Sarah when he gets to 1984, and they destroy the terminator in a factory owned by a tech company called Cyberdyne Systems.  Some of the bits of the cyborg are recovered and the R&D department goes to work on them; the nameless hacker is no longer needed because Cyberdyne has bits of the machine from another timeline.  In this one, we know how and when the "war" happens: Skynet becomes self-aware on August 29, 1997 and the folks who control it try to turn it off when they realize what's happened; in retaliation, Skynet launches its nuclear missiles at Russia so that Russia will in return launch at the US.  Lather, rinse and repeat the human resistance, with the exception that Skynet, with the boost from the found tech, is farther in its development and creates the shapeshifting T-1000 before its defeat.  Skynet still sends a T-800 to go after the young Sarah, but in case of failure sends the T-1000 (apparently having gotten around the living-tissue problem, since the T-1000 is metallic, or maybe the shapeshifting properties make that metal an exception to the rule) to the next mention of John, the early 90s when he's in foster care and Sarah in an institution for the criminally insane--seems that she decided to try to stop the war and got caught attempting to blow up a computer factory, though whether it was a Cyberdyne facility is unclear; there's evidence both ways.  The human resistance reprograms a T-800 to go deal with the T-1000 and sends it after Kyle and his doomed companion leave.

Therefore, the Epsilon timeline starts in the early 90s with the two terminators arriving in LA.  Sarah and John hook up with the T-800 and manage to both defeat the T-1000 and destroy Cyberdyne's future-tech.  By now the various perturbations have apparently screwed up the unknown hacker's research, so lacking Cyberdyne's help Skynet is never built.  From there, matters proceed apace.  We can leave things there, with a sunny future for humanity, or we can...not.  Having not seen The Sarah Connor Chronicles much--specifically I missed the pilot, which would clearly be important for further timeline fun--I can't comment, and I understand that the TV series itself completely ignores Rise of the Machines.

1: This is from the novelization; it was filmed but cut from the movie as not contributing much. 

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