"What the hell is going on with that hair? Everything else about him is fine, but that single strand of his hair is defying all laws of gravity. You could tie him to the end of a rope and use him to catch fish."
Ahogenote Not to be confused with Eroge. Or Ahegao, a similarly risque concept. (literally idiot hair) refers to the noticeable slim forelock of hair that sticks straight up from a character's head. Originally a hairdresser term for the "stupid hairs" or cowlicks that will not comb down, it later mutated into a literal reflection of a person's intelligence. Thus Idiot Hair suggests that a character is stupid, naive, or strange. (This suggestion is usually accurate, but not always - sometimes a serious character just has funny hair.)
Even if a character is not specifically stupid, naive, or particularly odd, the ahoge also usually represents a general mischievous quality about them in general. Goes hand in hand with the Cat Smile. It can also be used to show that Something Else Also Rises.
Idiot Hair is not to be confused with the two-stranded antennae-style hair, popularized by Love Hina or Ah! My Goddess.
Can be Truth in Television, as people with cowlicks can attest to.
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Anime and Manga
The top image comes from Bakemonogatari. The depicted Koyomi as well as his sisters Karen and Tsukihi have ahoge, but Koyomi's is the tallest.
While Koyomi has the "idiot hair" and does occasionally act the fool, let it be said that he's less an idiot than a Deadpan Snarker hero type with Expressive Hair. His ahoge manages to add amusing sequences to some episodes (like the page picture's source) that are less image-based and more talky.
It manages to forms question marks when he's confused and he even blushes through it in episode 13.
In episode 1 of Nisemonogatari, it formed the kanji for love.
In episode 3, Becky briefly gets one, and she gets so frustrated with hers that she rips Himeko's cowlick right out of her head.
Haré and Weda in Haré+ Guu. Weda isn't really an idiot but acts irresponsible and care-free because it's a more fun way to live life and to avoid facing her issues. Haré is pretty smart and the show's Only Sane Man, but this frequently causes him to run around like an idiot out of stress since he's the only one who can't go with the flow.
Interesting to note: Weda's mom has no ahoge. Weda has one. Haré has two. Weda's second child Ame has three. We can only imagine what Haré's own kids might look like.
Fuyuki in Keroro Gunsou, who's something of a genius in geography and the paranormal. Not Keroro, Fuyuki.
In the closing credits for episode 231 it's hinted that NPG bodyguard Yoshiokadaira Masayoshi has been hiding one under his helmet.
And Yui Narumi, Konata's cousin, has a tiny ahoge.
Several characters in Fullmetal Alchemist have this, although it's almost never indicative of their intelligence.
Ed is the most obvious example. He can be seen invoking this trope in one scene after he gets out of the shower, in which he sticks up his hair before putting on any clothes. He probably does this because of how short he is.
It also seems to be one of many traits PASSED DOWN THE ARMSTRONG LINE FOR GENERATIONS!, as every single Armstrong has this (even Olivier, but she grew it out to make it not stick up).
Mai-HiME's Mai is a borderline case — her ahoge runs across her forehead instead of sticking up. On the other hand, Arika in Mai-Otome has one serious ahoge (among other hair oddities).
For Arika, it's more Hair Antennae. She even earns the nickname Arinko-chan, i.e. Anty.
Yue Ayase from Mahou Sensei Negima! has one running across her head, and is a member of Class 3-A's "Baka Rangers" clique for the students who consistently get the lowest grades.
Nodoka also had an Idiot Hair, but she's ranked something like 23rd in her grade of over 700 students.
Chisame Hasegawa also has one, and she's the only class member without a Weirdness Censor.
A more straight example is Nagi "Five, Maybe Six Spells Tops Thousand Master" Springfield, Negi's missing father. Not to mention Negi himself, who is "an idiot in reverse" due to overthinking, and his obliviousness about girls.
Austria, normally The Stoic, will sometimes express emotion through his ahoge.
Taiwan has the longest of any known country, which seems to fit with her being the only girl with one.
America and Canada both have them.
It's no surprise that they both have one, being brothers. What is interesting is how different they are. America's is short, thick, and curves back over his hair. Canada's is long, thin, has a loop, and falls forward in front of his face.
Australia has two. AND England's eyebrows.
He also a strange dot◊ that floats alongside his idiot hair.
Turkey's splits into two at the nape of his neck.
Not only that, but in the few times Italian and Austrian citizens are represented, they have the very same ahoge style of their respective countries.
Ayano Kannagi from Kaze no Stigma. In episode 13 you can see her putting a great deal of work into making sure she has an Idiot Hair, including combing her hair a certain way and liberal amounts of hairspray. Why? Who knows. It fits, though.
Tadase from Shugo Chara! has one of these, though he's not an idiot; just oblivious.
Rip van Winkle from Hellsing subverts this: she has a very long ahoge, but is far from a fool. She's a Nazi vampire with a single-shot flintlock musket that can shoot down multiple targets (including missiles) with a single shot.
In Crimson Grave the two heroes go dungeon-exploring with a treasure hunter whose expressive ahoge is apparently smarter than she is. It always points in the direction she should go, and she follows it without realizing.
In the manga Inukami! Youko's idiot hair pops up from time to time, usually when she's acting like a ditz.
Gundam Seed Destiny: Lunamaria Hawke's ahoge is really quite subdued. Some have suggested that it's a Mythology Gag reference to the commander antenna possessed by Zeon mobile suits in the Universal Century timeline; Luna's ZAKU Warrior doesn't have one, so she got it instead.
DieBuster: Nono's ahoge is epic, and it's certainly a good indicator of her personality in this case. It even stays in place (with a slightly more angular shape) after she goes into Buster Machine mode.
Oddly enough, Cain from Trinity Blood in this picture of him in the manga. He's certainly acting like an idiot...
Three characters, including both main characters, have ahoge in A Little Snow Fairy Sugar. It is played straight with Sugar, but is slightly subverted with Saga, who likes to keep to schedules and only appears to be an idiot because no one else can see season fairies.
Kyoko in Heat Guy J to show her innocence. (i.e. she's one of very few characters that don't come from a dysfunctional family and didn't experience loss of a friend or family member).
Kururu and Hororo in Bottle Fairy, but it's more about not knowing human's customs, and the other two aren't better at it either, and when all four combine into one girl, she gets one that goes all around her head
Inverted with Shirai-sensei of Kodomo no Jikan, who's the utterly stern and strict teacher with a thin but prominent hair over her head. It's still there after her Important Haircut during her Defrosting Ice Queen phase.
Acchi Kocchi has the main couple have ahoges. Neither of them are exactly idiots, but Io's known to be a bit...dense.
Kimi ni Todoke: Sawako also displays this trait, though it is uncommon.
Nikaidou from Sangatsu no Lion is the only character that has one. Its lampshaded when his appearance reverting from a slightly more realistic style due to an Art Shift; it swings right back up from his bangs during the one-panel transformation.
It's more curled than sticking straight up, but every incarnation of Superman has a very distinctive hairdo, though it's more indicative of his staunch optimism (that, perhaps, borders on naivete) than idiocy.
There's also something a bit more to that one, though.
Kyoami in Ran; being court jester to Lord Ichimonji, this makes sense. Subverted in that (like most jesters), he's actually very intelligent, using his humorous facade to speak (horrible) truth to power.
Nyarko from Haiyore! Nyarko-san; since she's Nyarlathotep, it's prehensile to act as a stand-in for a tentacle. It's also a Malign Deity Radar, in addition to being able to form complex shapes like kanji and an at-mark (at least in the anime). Rather than outright stupidity though (she graduated top of her class and went to a prestigious university), it reflects the fact that she's The Ditz.
Hasta from the same series has the twin antenna version, but he's neither stupid nor especially ditzy.
Yamagi Noriko's design from Project NRI gives her an ahoge. According to her, she has been teased about it in the past.
"Um... It wasn't. Don't worry. That's the first time anybody's ever said it was cute, though. Usually I get 'why is it up like that?' or 'haha, Noriko, are you a unicorn?'"
Noriko's example could be a mild subversion of the trope, because Noriko is a brilliant mathematician and one of the more level-headed characters in the story.
One of the portraits for the Medic class from Etrian Odyssey has just this strand of idiot hair. And while there's no actual personality given to her (or any playable character) in-game, official comics from the game creators portray her as a bit of a ditz.
The main characters from Harvest Moon: Tree of Tranquility have these as well.
Celia from "A Wonderful Life", "Another Wonderful Life", "A Wonderful Life: Special Edition", "DS" and "Cute".
Milla Maxwell from Tales of Xillia and its sequel has a really long one. It's her crowning glory and she swishes it like a cow's tail.
Johnny Garland from Shadow Hearts: From the New World has this. Definitely the naive one of the group.
A frequent design feature of Golden Sun characters, especially playables, and it means nothing about their intelligence. In fact, it tends to show up more on brainier characters, as the more conventionally dumb ones usually have spikey hair instead. Alex has an ahoge, as does Kraden.
Team Fortress 2's Medic has a prominent curl in his hair, although it kind of looks like he styled his hair that way on purpose (it pulls double duty to cover for an obviously retreating hairline and to evoke that Superman look). It's even jiggleboned in "Meet the Medic". He's intelligent, but that doesn't mean he knows what he's doing.
Yo-Jin-Bo has Bo, whose hair is otherwise sleek and well-behaved, except for one strand that always hangs in his face. However, he's arguably one of the smarter guys.
Hatoful Boyfriend's Sakazaki Yuuya's faux-human appearance comes with two ahoges. He's far from stupid, but rather easygoing and flirtatious, and kind of the Butt Monkey. In the manga, he seems unhappy about getting one to help differentiate him from the other two white fantail doves.
In Danganronpa, protagonist Makoto Naegi has this hair. The protagonist of Super Dangan Ronpa 2, Hajime Hinata, has it as well. In the third Danganronpa, Naegi's younger sister Komaru is the main character, and has also developed this hair. The fandom often refers to the hairstyle as "Protagonist Hair".
Most characters in Knowledge is Power, with the exception of those whose hair is too uniformly short (like Colin) or long (like David) for it to make any sense. This extends to Ironychan's other webcomics as well, although it wasn't as obvious in Get Medieval.
The main character of TwoKinds, Trace Legacy, who also has blue hair! This character fits the exception of the rule in that he's not technically stupid. It's humored at in this picture that it's the source of his magical powers.
Something of an inversion: everyone in Cyber Six has huge, thick forelocks of hair which are perpetually hanging in front of their faces. If you started selling hairpins in Meridiana, you could probably make millions.