A Certain Magical Index/Headscratchers

Accelerator

 * The whole attempt at a Pet the Dog for Accelerator... It just doesn't work the way they portrayed him in the Sisters arc. He's too much of a monster to ever cross back over the Moral Event Horizon. Just think of the numbers. How long has he been butchering 14/15-year-old girls (even when they try to flee or are otherwise disarmed) for the project? Now, divide that into * 10,000* . If the project had been going on three years, he would have had to kill (nay, horrifically murder) 10 Misaka Imoutos a DAY for each of those years. That's just... staggering. I can't see how any amount of Pet the Dog could save him, no matter what Last Order says to make it seem okay.
 * Well, to be fair, they didn't exactly present themselves as human: didn't present emotions, never ran (the only time it seems one is running, they were leading into a trap or otherwise attacked first,) always arrived at the meeting time, fought him and never asked for mercy, they even insisted on following the experiments rules. It is entirely possible Accel didn't see them as human, and only when he did did he begin to regret his actions. Even the Sisters themselves refer to themselves as non-human. With all this, why should Accel see them as people? The only time he spent with them was when they fought him of their own volition. Oh sure, he is still a monster, but he is trying his best to be a better person. There are lots of things to consider with Accelerator; he is not nice for one, but such subtle things lead to a lot of Alternate Character Interpretation
 * When Last Order is talking to Accelerator in the diner, she literally opens up an alternate interpretation for his monstrous behavior as depicted during the experiments. Supposedly, his callous taunts and mockery of the Sisters were meant to invoke a human response (fear, anger, desperation). When the clones displayed none of those emotions, Accelerator could accept that they were little more than lab rats, and could believe (at least on the surface) that he wasn't actually committing murder.
 * My personal theory is that when Last Order said "we determined that the only logical explanation was that you were trying to get us to give up" was completely wrong, but Accelerator later decided that he liked that interpretation of himself, and decided to do his Heel Face Turn. Of course, by accepting redemption he's accepting that he murdered ten thousand girls (not to mention all the people he killed when he was younger), which explains his self-loathing.
 * The funny thing is... that Accelerator himself doesn't accept the idea that he can be suddenly redeemed which is why he's disgusted at himself by the end of the arc, in fact thats why he's annoyed at Last Order bringing up such an idea. My interpretation is that Touma beating him served as some sort of wake-up call. Accelerator DID take out the MISAKAs with malicious sadism, but it's not like he went on a killing spree across the street for no reason. He wanted become stronger cause thats the only thing he was good at. He's beaten by a Level 0, he figures that his killings weren't doing any good and decides to find another path (which he doesn't want to be redemption, but gets dragged into it when he sees last order in trouble).
 * Another possible reason for Accelerator agreeing to go along with the experiment is that he knew full well that nothing he could do would change the fact that the experiment would still go on, with or without him, as long as the General Superintendant of Academy City ordered it. The scientists could continue the experiment even with the Tree Diagram destroyed and with all of their research facilities trashed by Mikoto. Even if he refused, how much would the second ranked Level 5 need to kill? 40,000? 50,000? As the number one ranked Level 5, the deaths would be kept to the minimum required for a supposed Level 6 Shift, and if you consider Last Order's theory, then the only thing he could do was to put up a front and attempt to scare the Sisters into running away from him, which didn't even work because they're devoid of emotions. Just throwing another theory out there.
 * Just reading the concept of Accelerator bugs me. The tropes make him into a No Limits fallacy that stinks to high heaven of lazy writing. It helps that he's Brought Down to Normal in part, but the mere concept of his abilities being limitless just bugs the hell out of me: where the HELL does he get the energy for it?
 * Even if his abilities hasn't shown an upper limit to them, it doesn't mean there isn't one. As for the energy part, his ability is explicitly "alter the Vectors of anything that he touches" and he keeps it in an automatic state of "reflect". In essence, he completly screws with Newtons Third Law of Motion, there is no "action" to him, only a "reaction". To give an example, say some thug strikes him with a pipe. The thug applies 50 pounds of pressure in his strike, hits Accelerator, and the thug recieves the natural 50 pounds "reaction", plus the reflected 50 pounds "action". Again, due to Newtons Third Law, the thug will then give 100 pounds of pressure in "reaction" back to Accelerator, who reflects back to the thug. It keeps happening until something gives, inevitably the thugs limbs. Due to the above, all the energy comes from an outside source with Accelerator just redirecting it. Bad writing? I don't think so, it's probably one of the best explanations for a character's ridiculously broken capabilies. Besides all that, espers are essentially low-grade Reality Warpers, so just chalk it up to that.
 * Part of my problem is that it is a perfect conversion of energy with no spill over. Explaining why that is does not help. It works as well with Newton's Third Law as Neon Genesis Evangelion does with Christinaity. In my head there must be a tipping point or upper limit where he can no longer force the conversion. Otherwise, in a Vs. Scenario, he's reflecting the Death Star planet-buster or the Ideon Gun. Another problem is that if he keeps it on "reflect" then why does he not suffocate if he reflects everything coming in contact with him with their own force re-directed? No matter how minimal, the gas around us is in a constant state of motion. If he reflects things headed towards him by default, he'd reflect the very air around him as well. Unless he's warped reality to the point where he does not need to breath, we've got a problem. Subconsciously or unconsciously, he has to make a distinction between what is dangerous and what is not--but given it's reaction time via the sniper survival is just become a more blatant sign of Art Major Physics. I HATE Art Major Physics that tries to pass itself off as anything else.
 * Watching the episodes now and I notice a bit of deflection in each instance of a reflection around the object. An artistic "ripple" that unknowingly indicates that the conversion is not perfect as some of the energy goes into the creation of said "ripple". Which confirms for me it's just fans not knowing how to do proper observations and make wild assumptions based on the boasts rather than what actually happens.
 * You're right, there's not a complete reflection of energy, just none of it hits Accelerator. As for breathing, he lets things like air, sound, light and such through because otherwise, he would die. He can reflect those things (as shown with sound in the episode with Last Order), but without a reason to he just lets them work normally.
 * Your explanation leaves open the question of conscious or unconscious use of the power (as the sniper incident could possibly demonstrate). It can obviously be consciously controlled or perhaps set to default for certain thing... Having watched his first combat in full, there's a rather interesting thing I noticed. He says it affects whatever touches his skin, but he repeatedly uses the power through his boots. And earlier he obliterates a gun without touching it at all--just hanging in mid air when it comes withing a "field of effect" (which caused the aforementioned ripple). Though this is probably just an example of Accelerator being an idiot (of the two options: lack of internal consistency or "the character saying it is mistaken", I prefer to go with the later). I find it amusing when the exposition falls flat on its face. Of course, this is in the Anime, so there may be some Adaptation Decay. This power is problematic (which is funny given its name).
 * His power is set by default to "Auto-Reflect", however he can consciously use his power to change vectors in whichever direction he wishes. After rewatching the scenes in question, the animators did make a error with the gun breaking in mid-air, his power is only effective on whatever is touching him. As for his boots, well, I could say he alter the vectors in the boots to do what is seen, but I just think it's for the sake of not having to write/animate "Accelerator takes of his shoes" everytime he's onscreen.
 * Or they could have had him walk around barefoot.
 * Accelerator's power is to control the vector of everything he touches. So, let's make a list of the non-vector quantities in physics: mass, volume, density, electric charge, gravitational and electric potential, speed, kinetic energy, potential energy, pressure and temperature. I'll accept that he's not changing speed or kinetic energy directly, but as a byproduct of manipulating velocity or momentum, and that goes for most of this list. However, he shouldn't be able to control temperature. There are, in general, three ways to transfer heat; conduction, convection and radiation. Radiation is electromagnetic radiation, which is a vector quantity, so that's okay. However, light is also electromagnetic radiation, yet he can still see, so you could use EM radiation in the visible spectrum to transfer heat. Conduction doesn't use vectors at all. If there is a temperature difference, then simply being in contact with an object, i.e., to fulfill the requirements to use his ability, there will be a heat transfer, no matter how small. Even convection basically boils down to millions of particles conducting heat for a short time and then moving away. Even if we assume the particles are in contact with Accelerator for a much shorter period of time than normal people because of his reflection, there should still be a heat transfer. Also, consider the argument that heat is caused by the vibration of atoms; however, the individual vibrations are determined by quantum physics, thus, they are not predictable. Even though esper powers are caused by people selectively breaking quantum physics, I think this should fall outside the realm of Accelerator's powers.
 * QM doesn't mean unpredictable, it means there are limits - like predicting the diffraction grating from a double slit without knowing which hole, and any scalar is trivially a 0th degree vector.
 * "where the HELL does he get the energy for it?" The same place any of the other espers do.
 * As a point to mention, everything Accelerator does is mathematically intensive in the extreme, and he is (was) intelligent enough that he can create equations for his personal reality on the fly. Plus it seems that once they're created, he can solve them subconsciously, like how normal people can find 2*100 without thinking. With the right equations, he definitely can program himself, e.g. if something hits with enough speed to injure, reflect back it.
 * Given the discussion above, that just makes his entire character even more unbelievable. It means he is constantly doing quantum physics equations as he walks around on a daily basis, wracked with paranoia about where the next blow will come from. If he actually had a character that reflected that sort of mind set, perhaps it would be less onerous. The fact that he doesn't have to spend the mental effort to identify whatever it is that's coming at him, by all appearances . . . well, the more we look at his powers, the more they become Silver Age Superman ridiculous. His Required Secondary Powers are to much in need and to little in execution, implementation and explanation (at least in what I've seen in the early anime and what has been discussed so far).

Storyline Specific

 * Well, can anybody explain the Alchemist arc to me? I'm quite confused about the climactic point of the arc. If Izzard can bring his thoughts into reality, why not just think of a vampire? Or how does distorting reality make vampires? My logic is really bending at the moment...
 * The problem was Izzard has never seen a real vampire before so he couldn't imagine one if he didn't know how they look like in the first place. Furthermore, his power was also his weakness because anything he thinks including a moment of doubt, that doubt will be become real. Hence why he couldn't just This is the reason why he needed Aisa's powers in the first place.
 * What is the timing of To Aru Kagaku no Railgun (anime version)? Is it supposed to be while the Sisters project is going on? Because Misaka sure doesn't seem all that focused on stopping it, which she seemed pretty preoccupied during the events of Index. Railgun is definitely after Index moves in with Touma, since they are together in some scenes, but it can't really be after the completion of the Sisters arc, because the chemistry between Misaka and Touma changed pretty drastically after he helps her save her sisters. And that change isn't really reflected in how the two act towards each other during Railgun. So, I presume it takes place while the Sisters arc is going on, and Misaka is just not yet pissed off by the thousands of murders going on under her nose? Or does she just not know about what they are really doing by the time of the Railgun anime? I presume the light novels explain all, but I haven't gotten a hold of them (much less tried to read them with my 3rd year Japanese "skills").
 * Here's a proper explanation. Warning! Spoilers! Hopefully that helps.
 * This doesn't bug, but rather amuse me. For a supposed Misfortune Magnet, he really gets a lot of girls and takes down Reality Warper and Physical God without fatality. Wow.
 * His bad luck keeps him alive, but makes his life miserable. He's not exactly glad he beaten Accy and his harem caused him a lot of pain, one way or another.
 * Technically speaking, shouldn't Touma's Anti-Magic hand be useless at stopping Misaka's railgun attack? Sure, he can cancel any esper power, but the power is only being used at her hand to accelerate the coin; by the time it reaches the target, it's just running on its own momentum. It'd be one thing if it was telekinetically propelled the whole way, but this is different. It's like saying if someone has an ability that negates the explosive properties of gunpowder that somehow lets them stop a bullet after it's been fired. Even worse is that the principle of momentum imparted by powers is not considered part of the power seems to be applied in other situations -- for instance, when Accelerator uses his vector change to hurl stuff at Touma.
 * I was also bugged by that. It can probably be considered the biggest slip-up in the early stages of the series. Otherwise we can surmise that Misaka's railgun doesn't work as a formal railgun, like the electromagnetism continuously imparts the velocity and Touma's canceling of the esper electricity stops anything from keeping the coin moving. EVEN THEN, it still doesn't work because it requires that Touma be touching the electricity first (not the coin).
 * Unless the coin is fired like a lightning strike, so there has to be an ionised channel first. That would be consistent
 * This troper has a theory on that. It's explained fairly well in the Clap Your Hands If You Believe entry for both series that esper power is based off of the user's perception of reality. Touma's hand just negates whatever's thrown at by cranking the reality setting back down to completly normal. Basically Touma's power says to anything abnormal hitting it "stop, this is stupid, humans can't maniuplate electricity like that" to which the coin Misaka just fired off replies "that's a good point".
 * This is actually canon, sort of; the powers of espers are the projection of their personal reality. Which means they warp reality to work as they think or want it to work. What Touma does (starting from this is my own theory) is telling reality that the world doesn't work that way. Thus earning its name Imagine Breaker.
 * It should be mentioned that the Railgun Manga, Index anime and Index Novel all portray that scene slightly differently. The Railgun manga is the only one which shows Touma blocking the Railgun. In the anime and novel, she intentionally misses with her attack. However, in the novel he states/thinks that he can block it. Weather or not he actually can is a different story.
 * In the novels, there are a few other times when Touma thinks/states he can block it, and even sorta reminises about having to do so. All of these thoughts are in passing, and never once does it actually show him blocking it.
 * No he says that he blocked it on the bridge in volume 1
 * In episode 24 of Railgun, how does Misaka know Kuroko will be close by? Misaka isn't aware of Telestina's mech until Telestina bursts out from under the road and I can't seem to find any planning during the chase.
 * That's just how much they trust each other. Misaka was just confident that Kuroko would have already disposed of the Mooks she was fighting and would be close enough to assist.
 * Less seriously, Why wouldn't Kuroko know where Misaka is? Misaka probably knew that as soon as Kuroko was done at her end, she'd be tele-hopping over to where Misaka is ASAP.
 * It just bugs me that the wind turbines in the animes sometimes turn backwards, (even when not forced to do that by the Sisters), or have the blades' angles reversed. Since they're all CG, shouldn't the turbines all have one script that turns them the correct direction every time?
 * Maybe these turbines are spinning using electricity and not making any! I'm deadly serious! Something's not right here. This city is definitely hiding something! A conspiracy? Government secrets?! Those turbines are a part of the government's secret plan!
 * Onee-sama, please don't be silly.
 * Interestingly, one of the urban legends mentioned in the railgun anime is that when the turbine's propellors start turning the other way, something strange will happen to the city. Lampshade Hanging, or something more sinister? You decide!
 * Here's one thing that bugs me a little.  Am I missing something?
 * Brain damage.
 * So...exactly why would negating luck bring Touma all sorts of misfortune? I don't think no luck=misfortune. I mean, that's like you are commiting suicide just because your instinct for survival is turned off. Well, not sure the analogy works, but you get the idea.
 * The exact wording was "eliminates luck and the blessings of God." I'm going to go out on a limb here and guess that "the blessings of God" in this case means "protection from misfortune," sort of like a guardian angel. In other words, it eliminates his good luck, and removes his protection from bad luck. Of course, it's very possible that I'm misinterpreting this...
 * In that case, shouldn't his right hand erase misfortune as well?
 * Think of it like that, Touma have zero luck, he will never get lucky if it depend on good fortune, but he also is imune to curses, never will get really bad things (like getting a deity angry at him) to happen to him, like being ran over by a car and the like.
 * What I'm saying is that he negates both blessings and misfortunes. Shouldn't that just make him a normal fella?
 * You never heard of the term Common Miracle, did you?
 * Err, no. Please englighten me.
 * We can think of it like this : speaking in RPG terms (the point-build kind), during character creation ,most if not all games won't allow you to set any status as zero, much less negative, thus the 'normal fella' does have luck, if average, but Touma's Imagine Breaker negates whatever luck he has, setting it to zero, thus each and every time he needs to make a luck check, he immediately fails, but otherwise he does not attract misfortune, only he can't escape them
 * It's quite possible that Kamijou isn't more unlucky than every other person, he just hasn't the luck to compensate. So the only thing he experiences is bad luck and he only focuses on that, and since we follow him as the protagonist, we're led to believe that too. Seriously, does he seem all that unlucky to you or just not lucky?
 * Really, it's because the Japanese perception of luck is different than it is here in the west. No good luck doesn't necessarily mean bad luck here, but in Japan, a certain amount of good luck is needed in order to protect one's self from misfortune. Take the manga Luck Thief for example: it starred a hit man that did his job by simply touching his target, thus taking their luck away, and his victim would immediately die in some inexplicable accident. The same thing goes for the Doppliner system in Kurokami, where when a person meets a stranger that's identical to them, one orr the pair gets all of the other's luck, and the one that loses the luck immediately dies in a similar manner to the people in Luck Thief. Thankifully for Touma, the author of TAMNI seems to tone down the reprocussions of having no luck.
 * Why didn't Touma's hand made the ship of The Queen of Adriatic Sea float disappeared when they're clearly made with magic?
 * The novels explain the Ice ships were just like Innocentius, Stiyl's fire summon. As long as the ship's magic source still exists, the ship won't be destroyed unless Touma finds it.
 * Saten-san has a Level 5 and a Level 4 as friends, but never asks them for help leveling up. ESPECIALLY considering Misaka started out as a Level 1. This is made worse by the fact that she asks Uiharu, a Level 1
 * If it was that easy to raise a power level, then Skill-Out wouldn't exist. Also, since she's a Level 0, there's practically no chance of her raising her level in the first place, partly because of genetics and mostly because
 * Was it just me, or is there something odd about Sherry Cromwell being in Necessarius in the Sport Festival arc right after she was quite publicly attempting to murder Index? Suddenly attempting to murder an incredibly valuable asset to the Church and attempting to start a full-scale war is such a minor breach of protocol that you can just turn up at work the day after with no consequences?
 * It was stated in the light novels that Sherry was valued for her fighting and decoding skills, so Laura negotiated with Aleister for quite a long time to allow Sherry to stay in Necessarius. As a punishment, Sherry is now holed up inside doing paperwork and such.
 * Alright, I've read this line numerous times and it just refuses to make sense. "Magic was created for and used by those who could not become espers." That means Espers had to come before magic, and magic has been in existence for hundreds of years in story. That would mean espers have existed for hundreds of years, yet why are there no adult espers at all in the Raildex vers? Academy City was made to produce these espers, but it couldn't have been around hundreds of years. Also, as magic was made for those who couldn't become espers, how could they know they wouldn't be able to become espers without going through the Accadamy City schools? I assume none of them even tried, or else they wouldn't be able to use magic at all (And end up like Tsuchimikado whenever he uses magic). The only explanation I could think of would be the naturally occurring gemstone espers like Sogiita Gunha (Attack Crash) and Himegami Aisa, but that still doesn't explain the lack of adult espers around.
 * Gemstones are in fact very rare, with there being only around 50 in the entire world. Academy City has only been around for less than a century, and considering how the esper program is focused on students still in schooling, AC's espers just haven't grown up yet. There could be adult espers and Gemstones, but they haven't been introduced yet.
 * Exactly, because they are so rare, I don't think the gemstones alone would have been enough of a reason for magic to be created hundreds of years ago. and if academy city is only 100 years old... Well, I guess my real question is "How did espers come before magic?" or was the want of powers like the extraordinarily rare gemstone espers, way back hundreds and hundreds of years ago, enough of a reason for magic to be created?
 * Original Trooper here. I just read up to SS 2, and yes, the gemstones are that special / important that magic was made because others wanted the gemstone's powers.

Miscellaneous

 * Is it just me or is Uiharu a distant referential cameo, Expy or Shout Out to A Certain Legendary Species in another non-relevant universe? I mean, they are both kind, shy, cute, and have the same hair ornaments, so I can't help but wonder what would happen if you gave Uiharu a ..
 * Lol, she might just transform into and Take a Level In Badass.
 * The Angel Fall Spell. It was confusing, first of all. Then, after gaining an understanding, it all made sense: it doesn't make sense! Souls, minds or personalities are supposed to be switched, which is all fine, except that that isn't the case. The Minds are all in the same constellation, just the bodies got switched and noone notices, because the spells puts a filter or visual additives over your eyes.
 * The fact that somebody could accidentally cause something so major like just by unintentional arrangements of totems are just too ridiculous, if you ask me.
 * Tsuchimikado mentioned that the idols and figurines multiplied and amplified each indivdual's power several times over explaining, sort of, how something like Angel Fall could happen. That and the author sometimes like to use Contrived Coincidences.
 * This is something that directly involves God. If a Contrived Coincidence is ever justified, it is here. Who knows why He did it, but mysterious ways and all that.
 * Plus, Tsuchimikado said that Touma's Father had so many occult souvenirs that it would impossible not to form some sort of pattern, and that they were lucky that it was a spell like Angel Fall that didn't instantly annihilate mankind. This is also given as the reason why Touma can't fix it, because removing any single part would either a) simply make a different world destroying spell or b) explode.
 * Why is that the author has no scale of age/physical appearance? I know it's prevalent in other works too but seriously, look at how many characters are Younger Than They Look, and seriously, Styl is 14? What the hell?
 * They look younger in the light novels, if that helps. Here's the first pic of Stiyl; I'd buy that he's 14.
 * Yoko's 14 by the way.
 * The gargantuan amount of fantastic racism in Toaru; for example, kuroko's comment that a bunch of normal humans (level zeros) could never have beaten a level 4 (butt-monkey Kongo Mitsuko, who fires laser beams)... then there's complete monster Meltdowner (Mugino Shizuri), the girl with a god-complex so large it's a surprise she can even fit her head in a room, who flies into a foaming rage when Shiage beats her using her own ego against her and superior tactics, screeching that she should be able to kill 100 normals like him without "even lifting a finger". her yell there is, sadly the attitude of almost all level 5s, most level 4s and many level 3s: a complete disregard for normal human life, to the point where normal humans are often treated like cattle; Shizuri is able to kill Frenda, and the anti-skills never arrest her, much less charge her with anything. Another example of the massive fantastic racism is the Daihesai contest between middle-schools "200 students from some random middle school versus TWENTY TOKIWADAI STUDENTS", at which point the tokiwadai students proceed to curbstomp the 200 regulars, thus winning the game by default, despite the fact that it's supposed to be a BALL THROWING CONTEST! Then, let's not get started on Dark Matter's plans to rule AC like a fiefdom, or Aliester's plans to
 * also the ambiguity with which many of the powers work; Accelerator comments to Kill Point, that he's an idiot for using other people's locations in his teleportation, a set of powers which supposedly requires "11th dimensional theoretical calculus" to even operate! seeing as those kinds of calculations are the basis for the operation of most powers, how come they're all able to use them instantly? it takes several minutes to solve or complete even basic calculus problems, much less stuff that's involved with quantum physics, which would take days if not weeks! if the author had even a hint of respect for equality and rights, much less physics, a level zero could defeat a level 5 simply by the fact that NO ONE can react fast enough to avoid a bullet that's traveling at 900 meters a second!
 * ...and? The arrogance that most Espers have is addressed instory, like with how Skill Out originally being formed to "protect" Level 0's from Espers. People with power on both sides of the Magic/Science war honestly believe they are better than lower level espers/non believers, that includes the likes of the earnest yet haughty Kuroko but with the rare exceptions like Misaka Mikoto. Mugino is just crazy. As for the Daihesai events that was more a handicap than outright racism, Tokiwadai has a mandated Level 3 limit for students. Considering how the whole event allows the use of powers giving a handicap to lower level schools is an honest attempt at being "fair." Aleister and Dark Matter both suffer from A God I Am. As for the instant high level calculations, it's a combination of geniuses, practice, and the Esper program itself. The author knows that characters with power become prideful and uses that as one of the elements for Academy City's less fortunate residents.
 * I'm going to call you out on your reply, there, unfortunately; Misaka Mikoto and all other espers are using advanced physics, calculus and differential equations to pull off and chain powers in under a second. for those who do not know what this looks like, a basic differential equation looks like this: this and the answer is this. the best people this troper knows, who are capable of acing such classes--easily with I Qs of 170 of higher--take at least 15 minutes to solve such problems, even with daily practice. there is no way in hell that she should be able to do that; the only way to do so would be to physically increase the processing speed of the brain to something on the order of a supercomputer. the only way to do that is to isolate the human brain in something that moves faster in time and space than the world surrounding it--namely a hyperspace bubble generator moving at the speed of light. there's another fault too; in SS: Liberal Arts City, Uiharu cracks top grade military security in under seven seconds; this shouldn't be possible: firstly, academy city probably uses different code than the outside world, thus making the code foreign and unknown, and secondly, Uiharu is a level 1. Performance at that skill that she is shown to be pulling off would mean that the median IQ of Academy city sits somewhere around 200-240. For reference, the highest IQ score recorded was 228, and 'genius' level I Qs (170+) comprise less than 1 out of every 150 people, roughly 0.75% of global population. IQ scores of 200+, then, comprise less than 1 in 300 people. Considering that Academy City does not allow people to immigrate except espers and japanese citizens who have pre-registered, Academy city should have far fewer espers, far fewer geniuses, and absolutely no reason why it is 30+ years ahead of the rest of the world.
 * An example from intermediate mechanics: setup a simple, ideal game of catch, think about how long it takes to solve, add in various real world effects (friction, arm movement, etc), and marvel at the (intuitive) numerical analysis involved in baseball. Also, IQ is pretty much only useful for differentiating between low, normal, and high I Qs with dubious connections to much else.
 * It is mentioned that the espers of AC all took tests and drugs to increase their calculating speed and therefore there IQ. Plus it's implied that AIM fields help with the calculation of esper abilites. It wouldn't surprise me if the higher your level goes the more smarter you get to. This is supported by the fact that Level 5 Misaka a middle school student can easily help Touma a normal high school student. Also the strongest esper Accelerator needs nearly 10000 clones for him to have half his calculating speed back.
 * Math Is Power, indeed.
 * Can someone explain the bizarre fetish with the "Biribiri" nickname among the English-speaking fandom? It's an arbitrary string of syllables and utterly meaningless to someone who isn't a Japanese-native speaker. Why are people so obsessive about using it to the exclusion of words we English speakers do understand? I'm tempted to dismiss the whole thing as "because weeaboos" but I am hoping for there to be a better reason than that.
 * It's catchy. No really, "Biri-Biri" is simply the Japanese onomatopoeia for electricity and the English equivalents doesn't sound as good. Occasionally you'll find an english speaker who calls her "Sparky," "Shocker," or even "Pikachu," but for the most part people simply Touma's nickname for Mikoto cute and/or catchy. Even so, the above nicknames are still pretty prevalent amongst the english speakers.
 * Also, its literally her In-Series Nickname. Touma spends most of Railgun calling her it, plus even after his memory loss, Touma still calls her it occasionally. Its in bad taste to translate names, nicknames included, even if there is a suitable translation
 * Why does none of the antagonists just shoot him with a mundane gun (correct me if I'm wrong because I haven't read the novels yet, just the anime)? And God help me, don't say things in the line of "They had too much confidence/They are too proud." or I will suffer from aneurysm.
 * I would assume you mean why no-one shoots Touma. The simple answer is: Why should they? Magic and psychic powers tend to be more damaging than firearms. Also the only ones targeting him are on the magic side and it was the Fake Unabara that was first to target Touma specifically, and he ended defecting to Academy City afterwords. On top of the fact that most of the magicians Touma fights were at first from Necesarrius who would prevent crucial information like "Don't use magic" from leaking out. Not to mention magicians shun technology in the first place.
 * And note that Kanzaki, the one who had the most luck against him, did shun direct magic attacks for some spell that involved actually making attacking with a bunch of steel wires practical. But she's a Saint; most magicians couldn't pull that off (and wouldn't see the need to until its too late).
 * Guns aren't as effective on Touma as one would think. Touma improvises against people with guns and gets off without any injury compared to the hard and barely winned battles he has to fight with magicians and power-users as proven by the recently released episodes where he had to fight Skill-Outs.
 * In order for the series to have magic and esper powers be actually useful the author could only include firearms against opponents who wouldn't be troubled by them like Ellis.
 * Actually, as of New Testament 3, it's been confirmed that the magicians of GREMLIN are wise enough to see this as the default method of dealing with Touma (aside from also developing spells that are meant to work against him specifically). As such, said magicians are more than happy to use guns against Touma
 * Going way back when, Touma actually got shot multiple times at nigh-point-blank range by Aureolus. It hurt him, yeah, but he still managed to pick himself back up.
 * How did Touma get to Mikoto's dorms in the first place without causing a ruckus? It was clearly established that the district where Tokiwadai is located is restricted access. I though it was for female school students only yet Touma got in no problem. Or is the dorm Mikoto lives in located in a different district?
 * It was at night so most of the student body would be asleep in the first place, and he did need Kuroko to unlock the doors for him.
 * You are missing the original issue. The whole region around Tokiwadai is restricted (as it was shown in Railgun). Touma shouldn't be able to even get near the dorms, if they were located there. Of course, the dorms aren't located there. The dormitory Misaka lives is in the same district, but not inside the restricted Garden of Learning. There are two dorms, but the one Misaka lives is in the non restricted area (the other one is, but it doesn't matter)
 * It was late at night and everyone was supposed to be asleep/indoors due to curfew. Most likely
 * As a follower of the anime mainly, this troper is wondering; does Touma's fighting style get more varied later on? Honestly, he's solved almost every fight with the same kind of attacks. I know they want to emphasize that he's a street fighter, and it's mainly a "magic and science" story, not martial arts one. However, his fights could utilize a bit more ingenuity than simply "run at the opponent, Imagine Breaker, punch".
 * For the most part he follows the same formula later on as well but there are a few instances here and there where he mixes things up a bit and even fights dirty, like his time against the Fake Unabara.
 * Maid Academy. REALLY?
 * There's also Butler school in Real Life so Maid School isn't surprising.
 * Original poster here; I mean, who would specifically build/go to school that teaches kids how to be a butler/maid? It's....just beyond my comprehension...
 * You don't just go off and be a maid; you have to have training first. I'm certain that such schools exist in real life as well.
 * Remember also that whenever the Japanese think maids and/or butlers, they have in mind a (somewhat) romanticised version of aristocratic households in Victorian/Edwardian England, where being a butler/maid (particularly the former, but also the latter, as well as the rest of the serving staff) was, for someone of humble origins, actually fairly prestigious. Certainly, it was the kind of job that tended to be passed along family lines, and as already pointed out, butlers/maids need to learn SOMEWHERE... they'd have learned 'on the job' back in the day, but throw in a dose of modern culture and an academy makes sense.
 * Or, alternatively, just don't think about it too hard. The Japanese like maids, this is a city made almost entirely up of schools/academies. Logical conclusion: maid academy.
 * Orignal poster here. Gurgh...I might as well just accept that.
 * So... why were the Misaka Imouto using guns?
 * They are only level 2 espers, each of them with 1/20000th of the original's power. Hive Mind notwithstanding, they can't read magnetic lines without those visors, while Mikoto can with her naked eye. And even if they can they're just not as powerful as the original individually. Considering that they were not able to train long enough to use their Electromaster abilities to their full potential (they were created to help Accelerator Level Grind after all), they resort to conventional weaponry as they're more practical to use in conjunction with their limited power set.
 * Giving them weapons also enables more options for testing Accelerator's powers.
 * Correct. However, it's when 10032 decided to use her esper powers when conventional weaponry just won't work on Accelerator that she was able to hurt him . But still, because they can't read magnetic lines without their visors, it would be more difficult for them to pull off a Railgun even if they can. Thus, they can only shock opponents to death, which doesn't work if they're immune to electricity, and they can only do so much with their AI, so giving them guns is a more practical option.
 * What made the Russian-Academy City conflict in volumes 20-22 a "World War"? China and India were mentioned (in passing) as supporting Academy City but other than that there wasn't really any involvement from other countries, right? The english-french battle was magical in nature and was probably swept under the rug so not much official military involvement there.
 * Russia was fighting Academy City, and by extension Japan, and China and India while being allied with France who was fighting England. That's almost every international superpower engaged in the war. As for the French/England front even if the magical aspects were downplayed there was still involvement from the royal family, non-magical military involvement goes without saying.