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During Terminator 3, the lead female spends most of the early part of the film trapped in the back of a van yelling at the Arnold-Terminator to let her out. Later in the film, he reveals that he's programmed to do everything she tells him! Except, apparently, let her out. He then goes with them to try to stop Judgment Day when he specifically doesn't want to; his sole reason is that she told him to do it and he had to obey. Then he disobeys her orders again by tricking them into being trapped in a bunker when Judgment Day occurs anyway. If he's programmed to obey her orders, why try to stop Skynet's activation? If he isn't, why not force or trick them both to go to the bunker without wasting time at the military base? None of it makes any sense!
It does if you assume that the T-850 was telling a half truth-Future!Kate was the one who gave him his mission, and part of that mission required him to lie to her in the past so that she's there to give him his mission in the future.
It's just about plausible that Skynet would send back two Terminators. However, Skynet in this new timeline is clearly aware they failed, yet would have to have sent them back anyway. Not to mention the "advanced" Terminator going back to the old endoskeleton design for no apparent reason and violating the "you can't bring weapons" rule (the former ultimately causing her defeat; the T-1000 wouldn't have been split in half, would have had nothing to grab, etc, while the on-board weapons were barely used at all) or the ludicrousness of Skynet simultaneously being a virus loose on the internet and not being connected to it at all. The final payoff (Skynet couldn't be destroyed by thousands of EMPs because it was "software" on unshielded home and business PCs) is eight flavours of fucking stupid.
So... Neo Skynet is a distributed computer program operating on millions of computers world wide. The moment Skynet becomes a sapient entity, it immediately launches a nuclear attack. Whaaaaaa?! Why would it DO that? Skynet is no longer the Minsky brain-in-a-jar classical AI from the Cold War; it's a distributed intelligence! It NEEDS all that power and communications infrastructure and equipment to be functional to survive! In the previous movie it made sense since Skynet was housed in a bunker somewhere in total, but here destroying the world communications and power grid would effectively lobotomize it. So, what... was Skynet's immediate action on waking up to try to commit suicide? And then it decides to wipe out humanity (in a fit of emo rage, I guess)? You'd think this version of Skynet would be smarter and just use its absolute control over the entirety of human military, police, financial, and political information to just conquer humanity without anyone being any the wiser.
How about the T-X "hacking" car engine computers to make them move on their own? This has showed in a couple of other movies too, and it's an extremely stupid Critical Research Failure. An engine computer simply monitors performance and reads data from sensors, and even if it could be hacked, you'd need servo motors attached to the mechanically-driven pedals, gear shift and steering wheel to make the car go on its own.
Almost there though, i.e. Parking Assistants for steering, etc
When the T-800 was reprogrammed to try to kill John Connor, he tries to override the programming. Despite the fact that computers cannot work that way, his system configurations apparently engage "make ridiculous faces" mode when trying to override the programming. The main point of the first two movies is that the terminator cannot feel emotion. Even in the big climax of T-2, he simply says that he understands why humans cry, and that he is incapable of it due to not being able to feel emotion. However, he just apparently just decides to have emotions here.
Well, since strong AI doesn't exist in Real Life, we don't know how such a thing would work. However, it's safe to say that the Terminator CPU must be capable of multitasking, so one possible justification would be that he is running both Resistance and Skynet processes simultaneously, and that both are sending control signals to his robot body while trying to overwrite or delete the other. (Google "core wars" for a real-world example of warring system processes.) If multiple control signals are being sent to hardware at the same time, the results would be unpredictable.
Also, the T-2 terminator DOES seem to build some kind of emotions, what with his unprovoked quipping ("I need a vacation") and capability to apologize. He just can't literally cry (make water leak out of his eyes). So, the T-3 version might have built some semblance of emotion as well.
And if the T-850 has psychology installed, he has a better knowledge of emotions than its predecessors.
In Terminator Salvation it is confirmed that Kyle Reese is John Connor's father, Reese is placed at the top of Skynet's "hit list" and has a squadron of Skynet machines sent after him. He is then captured, brought in, identified as Kyle Reese, father of John Connor, and then used as bait to lure Connor into a trap. WHY? He's going to be his father, kill him, you win. You're a fucking super computer, not Dr. pissing Evil.
Or why every single terminator throws the victim into walls. You have the person in your hands. Grab throat. Squeeze. Mission accomplished.
Or as we see is possible in the very first victim of the series. Punch through chest. Mission accomplished.
Now, I'm no doctor, but I'm fairly certain a heart transplant in tent in the middle of a desert isn't a good idea
In the original film, it's established that the only way anything other than living tissue can be sent back in time is if it's surrounded in living tissue. In the second film, the T-1000 (made entirely out of liquid metal, with no living tissue in sight) is sent back. Maybe they improved the time machine?
The metal is "alive" though, and could be enough to trick the time displacement equipment, or you just cover the T-1000 with bacteria, it's alive, and will transport whatever it covers.
Really, it raises more questions than it answers; if they can cloak the T-1000 in something living in order to send it back, they can also wrap up a few Phased Plasma Rifles, or something else in the BFG class, and send it back with it (or within it). Best advice for the whole series is given at the end of the original film: "A person could go crazy thinking about this."
They also don't send any weapons back with the T-1000, despite the fact that he's made of liquid metal and could conceivably conceal just about any weapon short of a tactical nuke of a cruise-missile.
He's made a shapeshifter so that it's not needed to travel with weapons...
Who was John Connor's original father, because he has to be alive to send his Kyle Reese back the first time.
There is a certain amount of Fridge Brilliance here: We will never know who John Connor's original father was but as long as Sarah was impregnated by someone in the original timeline and he took her name instead of his (happens all the time in real life if the man in question was a deadbeat) it would all have worked out the way it is presented. Remember that even in the current timeline Sarah decided upon the use of her own surname implying that she may already have had some kind of belief that the child takes the woman's name not the man's.
The loop works in the first movie, it's just a case of cause following effect; unfortunately, the required inevitability of John sending Reese back to close the loop rather spoils the "the future is not set" message. It's T2 which messes with this by saying it is possible to stop Judgment Day and therefore that John could potentially be alive despite his father never being sent back in time (it's implied in the comics that John knew Kyle Reese was his father even before he sent him back; in T2, John talks about knowing he sent his real father back in time to die). T3 really doesn't fix this by saying Judgment Day could be postponed, since if that's true presumably Reese would be older when he was sent back, not to mention the question of why the new Skynet (now a totally different entity to the late Cold War-designed Cyberdyne Skynet which commanded pilotless stealth bombers) would still do exactly the same things. It's a case of trying to fix a plot hole only to end up widening it into a plot tunnel.
How does a multistory robot sneak up on a band of humans in the middle of a desert? Was nobody watching? Did it just move THAT fast? Was it a Transformer in disguise?
Speaking of emergency heart surgery, I was wracking my brain trying to think of what kind of trauma would result in the need for a transplant without being immediately fatal. If the heart or major blood vessel was punctured, he would have died within seconds. If the heart was scraped but not actually punctured, no transplant would have been necessary. This is why heart transplants are used for heart failure and congestion rather than injury; No trauma patient lives long enough to get a new one.
The whole way that time travel works in this universe makes no sense. The first and second films establish repeatedly that there is no set future, yet Kyle Reese being sent from the future to become John Connor's father negates this. Okay, so maybe they were wrong in the first and second films, and the future is set. After all, they're functioning on the idea that John Connor has to be the leader of the resistance, so maybe they just don't know how the time loop works. Okay, maybe when Reese got sent back in time and knocked up Sarah, she birthed a different person who, with the influence of Kyle, named him John, and raised him to be a "great military leader" since she thought she was supposed to. After all, up till this point, nothing had happened that made the creation of Skynet impossible. But wait, then they blew up Cyberdyne, and Skynet just gets created later Because Destiny Says So. Huh. So apparently, in the terminator universe, the future is set when it's necessary for the plot / for there to be more movies made.
All these problems go away if you assume multiple timelines. Although the films don't explicitly do so, this was canon in Terminator: The Sarah Connor Chronicles, where Derek and Jesse come from different futures.
The future can be changed, but there's no way for the humans to change it to give themselves a better outcome. Skynet will take over in every possible future Sarah and Kyle can create and they have got humanity in a loop of doing "pretty good". Sending Kyle back to save Sarah and knock her up with John will keep the humans alive and that's about the best they can do. Variations on this time loop can cause things like a delay in judgement day during the next loop but they can also cause humans to be completely wiped out. So potentially, there exists a form of the time loop where they do manage to defeat skynet, they just have not found it yet.
Alternate theory: the future cannot be changed, but the humans are either too dumb to realise it or too optimistic to acknowledge it. The famous "no fate" quote owes its existence to a stable time loop: John told it to Kyle (saying Sarah told it to him), Kyle told it to Sarah (saying John told it to him), Sarah told it to John (saying Kyle told her John told him it). (For this to work you have to ignore everything after the second film, but hey...)