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Sokka realizes that the best method to defeat the giant drill was to "get inside and attack it's weak points." The Gaang get inside easily enough (too easily, really), and they even gets some blueprints. What does Sokka decide are the drill's weak points? The engine? No. Hydrolic lines? No. Various pistons and drive shafts? No. He attacks the superstructure. The LEAST "weak" part of the entire thing.
1: The term was attacking pressure points, not weak points. The superstructure is what held up the entire drill, and couldn't be replaced as easily as a piston could. 2: Taking out the engine, hydraulic lines, or pistons is a short-term solution. The drill would stop, sure, until they send for/manufacture more parts, which would take, what, a month or two? Taking out the superstructure stops the drill until they build another giant friggin' drill from scratch.
The Drill was right at the wall of Ba Sing Se, taking it out for even a day would be more than enough time to get guys in and deal with it. By the time they get the parts needed to fix it the Earth Kingdom military will have secured the drill. And it will take longer than you think to get the parts anyway, since every part would be custom so that's probably the only drill they're gonna make in the next decade or so. With Sozin's comet coming my question would be why bother with a drill at all?
Realistically? Less time than a month. The Fire Nation is an industrial-age army that uses mechanized warfare. They've got to understand logistics and how important it is. I wouldn't be surprised if there was a supply depot within an hour or day's time away with enough parts to replace anything that goes haywire on the Drill as quickly as possible - and that's discounting the notion that they'd carry spare parts inside the Drill itself for quick maintenance. That thing's also got to have some redundant systems that they can switch over to if one breaks down; a device that big will practically require them if they want to get any maintenance done.
The Fire Nation appears to only have World War I era level industrialization and even in modern times building anything that big takes a very long time it probably took them about a year to build that thing and the Gaang destroyed the main body, forced the crew other than Azula and Co into surrendering (I think) and ended up letting the earth kingdom keep it according to later episodes. Yeah that will take a long time to replace.
The crew probably retreated. Ching at least makes it back to the capital and is in the bunkers during Black Sun Day. The Fire Nation's technology is very much an Anachronism Stew when viewed from Real Life's perspective and I'd rather place its average around the 1870s or so.
Also Sokka was just looking at the blueprints and he's not a mechanical genius when it comes to things as advanced as the fire nation.
In the second season episode "The Serpent's Pass," why did Toph go out onto the ice? She can't see! She was standing on a plot of earth before moving onto the ice, so why didn't she just bend the earth to make a path for herself?
They brought that up. She's initially hesitant to go out onto the ice. Also, bending a path for herself would have been difficult, given the Serpent fight in the water at the time. There's no garuntee the Serpent wouldn't just destroy it.
Aang agonizes over the possibility that he may have to kill Firelord Ozai, which goes against his basic moral principles. So, wait, we're to take this to mean that the crews of all those Fire Nation boats and airships he destroyed throughout the series were all unharmed? Particularly hard to believe in the case of the airships, which of course plummet hundreds of feet after Aang disables them.
Also it probably occurred to someone to invent parachutes in between getting the airship technology and the Grand Finale
He has nightmares about killing people in the Avatar State, including the time where he destroys the Fire Nation fleet at the North Pole, so it is not as though he forgot about it entirely.
Aang destroys only one airship, and that one he disables and causes to descend in a moderately-controlled and slow impact that resulted in almost zero deformation of the airship itself. Throughout the rest of the series, it looks like others have killed Fire Nation troops, but they are not Aang, and he doesn't particularly seem to agonize over this.
There is a very big difference between fighting in a large battle and going out to hunt down and kill a specific person. I can imagine Aang didn't have issues with killing in defence of self or friends, but killing a specific person is probably too much. Note that during the day of black sun, he could probably have bound the firelord in chains during the eclipse, so maybe he wasn't planning to kill him.
There is also a very big difference between the impersonal killing via ranged weaponry, and the very personal killing through melee. The distance helps keeps emotions in check. Aang, even through accident never killed anyone in melee, and the time he came the closest to doing so (the Koizilla incident was the closest he got physically to his victims) briefly gave him nightmares about it. Aang would have to be that same distance and look Ozai in the eye as he died.
Why didn't Aang ask Bumi to teach him Earthbending the first time they were in Omashu?
Because it's assumed that you have to learn the elements in order. Aang was focused on learning waterbending first, and only decided to learn Firebending from Jeong Jeong after he realized that he'd probably never get the chance. Plus, Aang had trouble with Earthbending, but he would have had even more trouble with it if he hadn't first gone through the defensive nature of Waterbending. Remember when he tried to use airbending philosophy with firebending? Burned Katara within 10 seconds.
Why do Aang, Sokka, and Toph take Azula's ridiculous statement as proof Toph can't detect she's lying? Lie detectors, Toph included via her vibration sensing, work by monitoring things like change in heart rate, breathing, blood pressure, and other physical changes that occur when you lie, because you're unconsciously stressed when keeping something you don't want known hidden. Azula just said something completely stupid about being a purple platypus, something so obviously untrue there'd be no way she'd really worry about being found out.
Because its a joke.
The Myth Busters went did something like this. Whenever you tell the truth, the lie detector says it's the truth. If you're telling the truth, lie detector cannot be convinced that you're lying. I can only assume that it works in reverse.
Which, by the way, is a myth in itself. Lie detectors have not been proven to be infallible regardless of what Myth Busters seems to think.
You mean the fact that Azula was wearing shoes didn't do anything for you?
She was pressed up against a definitely stone wall. Toph could detect her heartrate and stuff anyway. Who needs the soles of one's feet when the rest of her body will do?
"I can only assume it works in reverse" No! Universal declarations do not go both ways. Think of Monty Python as an example; characters in Holy Grail humorously conclude that, since all wood burns, all that burns is wood. Untrue for the same basic reason.
You do realize that the entire purpose of a lie detector is not to be convinced that you're telling the truth if you're lying, right?
To me, this is Fridge Brilliance. Lie detectors in our world work by monitoring heartbeat and breathing and blood pressure. Azula had to learn to master one of those - breathing - in order to be a proper firebender at all instead of occasional bursts of flames. Concerning heartbeat and blood pressure, I always thought Azula had gotten control of those by loads and loads of training before the lightningbending. If you make one mistake doing that, you're burnt to a crisp, so before even trying it, it's a great idea to learn how to stay calm in every situation. Thus there's no rise in heartbeat/blood pressure, so Toph would be unable to know for sure if Azula was lying, since everything she usually checks for stays unchanged.
Also if anyone was running/jogging (s)he may remember that by controlling breath he can controll heartbeat (the faster you breath the faster the heartbeat). The heartbeat is directly connected with blood pressure so by controlling breath you controll indirectly a blood pressure. It's logical as those systems determines how much oxygen goes into cells.
It's based on the Hollywood concept of a lie detector, so it doesn't matter what a true one is capable of or how admissible. The first two questions are always a baseline truth and lie. You can look at it as proving that she can provide a false-truth, or she may have actually proved that she can provide a true-lie. Imagine how devious it would be if she had enough control for Toph to detect her as lying with a statement they already know is truth.
In "The painted lady", Katara destroys a factory in an explosive way wich most probably caused multiple innocent fire nation workers as casualties, hopes this will remove the pollution even though she just emptied molten metal into the waterstream, is surprised when the fire nation retaliates against the villagers and then leaves them to have their village destroyed by the very probable retaliation of the higher ups of the fire nation who probably dont care about her painted lady story.
Why doesn't Toph wake up when Katara sneaks out three times in a row? I mean, she's right next to Katara's sleeping bag. And Toph vs. Factory would've been epic.
She probably was in deep sleep, or just assumed Katara needed to go to the restroom. It's none of her buisness.
There was no one inside the factory when it was destroyed; that was why they attacked it at night. It doesn't immediately remove the pollution, as shown by the fact that they have to clean up the river afterwards. Katara was simply destroying the source of the pollution. It actually doesn't make much sense that the Fire Nation would retaliate against the villagers, as they have no way of really damaging the factory, when it could easily be blamed on Earth Kingdom sabotuers. As for later retaliation, they're planning on deposing the Fire nation in the next few weeks; by the time any retaliation happens, according to the plan, they would have already defeated the Fire Lord; plus, the Fire Nation has shown a history of withdrawing for prolonged periods when occupation/assault forces are destroyed.
It actually does make (horrific) sense to go after the villagers. Even if you think that it was done by Earth Kingdom saboteurs (which they clearly don't), the most likely place for those saboteurs to work would be at the village suffering. By wrecking the village you remind the villagers that it isn't a good idea to allow that sort of thing. It's a time honored (if morally dubious) method.
However, if the soldiers say it is an angry spirit they are (unlike in our world) not going to be dismissed out of hand. Stay clear of the place until an exorcist or ten can be summoned.
Also from what I understood it was a mainland fire nation village. Neither earth saboteurs nor villagers supporting them is likely. The villagers might do it on their own as factory ruins their economy (but once the solders are defeated by multiple bending arts in mist out of nowhere with sound effects in a world where existence of spirits is fact...)
Did Aang really need to learn firebending? He didn't have any time to even use it for any fights at all except the one against Ozai, and it didn't really help him much.
You have to remember that, at the time, they were not planning on finishing the fight during the comet. When Zuko joined, they were still planning on having the final attack be several months, possibly years, later than they were eventually forced to.
Hindsight is 20/20. Besides that, he'd have to learn it eventually, why not when he's already traveling the world picking up master benders?
Storywise, it's so that the Gaang can trust Zuko. Character-wise, it's for Aang to realize that firebending is not evil.
Plus, it makes some sense that firebending would be a good way to defend against firebending. Rather than putting up brute force defenses against Ozai's fire attacks (water/earth/air shields), Aang could instead redirect and bend the fire to defend.
Also, understanding the principles behind Firebending also allows Aang to devise ways of neutralizing fire with other elements more easily. The trick he did with the combination of air and water to break up Ozai's fire bolts probably wouldn't have been possible without an understanding of firebending as well.
Lighting redirection, general mastery of the elements, and Iroh style new techniques are all good reasons.
Why doesn't anyone other than Toph and Iroh remember the events of The Chase? When Katara meets Zuko in the prison, her last encounter with him was when he got into a massive firebending fight with Azula and then got depressed and angry when Iroh got burned. It seems like it should have gotten brought up a few times. Even moreso when the rest of the G Aang meets Iroh. Also, you'd think Toph would have said, "You know the old guy who took a bolt of fire to the chest? I talked with him and drank some tea a little while ago."
That may depend on whether Toph actually recognised Iroh. We know he saw her, because it's that distraction that gives Azula her opening to strike her uncle. But IIRC Iroh doesn't speak during that scene where they're ganging up on Azula, and with no voice to go by, and so many people around it's not guaranteed that Toph could have identified him as anyone other than a firebender also fighting Azula. Although she has been able to tell people by how they move, like with 'twinkletoes', she wasn't with Iroh for long.
Toph did recognize Iroh. When Iroh is on the floor, he, Toph's feet and then Toph's sad face are focused, indicating that she knew he was the old man she had talked before.
Arguably, it does come up, but not mentioned verbally. The mere fact that Katara is even willing to listen and consider what Zuko says indicates, to me, that she remembers Zuko's brief moment of non-villainy with Iroh. Without that scene, she would have had no reason to warm up to him once he starts talking about his mother.