#triangle obs

[cri-cri-de-boa]

A friendly chatting between hosts! I hope nothing ba-

Oh... Hey...

[isdalinarhot]

ok whatever dalinar and navani trapped in the spiritual realm scary bodes poorly awful I DONT WANT TO THINK ABOUT THAT. i want to think about radiant implying that sadeas ALSO murdered his way up a couple dahns WHILE BEING 15. and im guessing this was a joint effort with ialai? again, when they were Fifteen Years Old. like holy shit

[sillydum]

what are these scenes from?????? (I desperately need it because i literally cannot find it, also i got these images off of google lmao)

UPDATE: i found out it's from last episode of obs :))))

[umboloae]

Art therapy notes: all he draws are red and blue triangles

Obs: pls read the warnings! Also heads up for flashlights (it's mostly glitching effects but better be safe)

So, I've posted this animatic before but seeing it again I didn't like the result, so I redrew some frames and re-edited it (I suck at video making stuff. It's a curse), mostly bc i wanted to post it on TikTok, but hey, copyright did not let me JEYCJDJFDKJ so u guys here will be the only ones seeing it. Hope u like it!!

[sweetfwr]

𝄃𝄃𝄂𝄂𝄀𝄁𝄃𝄂𝄂𝄃 SWEETFWR’s upcoming works

masterlist here!

SUNKISSED & STAKED

⤿ you were supposed to be his next meal. you, the pretty new girl who moved to this dreaded town to give her mother an easier life. of course the werewolf had to get in his way.

vampire!sunghoon x reader x werewolf!jake, twilight au, love triangle

TO WRECK A HOME

⤿ when nishimura riki finds out his long-time girlfriend is arranged to marry yang jungwon right from under his nose, he's determined to keep a firm hold on her.

"...i'm a home wrecker? you took my home away from me first."

ni-ki x f!reader, ANGST

COURTSIDE GIRLFRIEND ENEMY

⤿ kim sunoo, resident campus sweetheart who's famous for his killer jump serves and his warm and smiley nature has no enemies!! except... for you, apparently. why does his gaze seem to go icy and his smile turn downwards whenever you’re nearby!? some would call it pure hatred, others would consider it special treatment.

volleyball player!sunoo x f!reader

MISSION: MATRIMONY

⤿ your handler was very clear what your mission entailed: get in, get information, then get out, no matter the cost. when you find yourself in a sham marriage to avoid suspicion from the enemy country’s government, you begin to realize the cracks in your ever-so-sweet husband’s facade. turns out, the enemy might be even closer than you thought.

spy!jungwon x spy!reader

FAMOUS & FURIOUS

⤿ unwarranted, two-way glares during award shows and a viral clip of the kind, sensible oldest member of enhypen rolling his eyes at your MAMA speech were enough material your fans needed to become invested in a years-long industry mystery: what the hell is going on between you and lee heeseung? a racy coachella sighting might just crack the case.

idol!heeseung x idol!reader

LAST MAN STANDING

⤿ running away from your problems and into your best friend’s vacation home in paris for the summer has never felt better for him. how couldn’t it, when it’s always him you run to at the end of the day?

best friend!jay x f!reader

HEALING HEARTS

⤿ life on the job as a medical professional in training has never been easy, so much so that you think it might be driving you a little insane. so insane, that yang jungwon, your supervising resident has begun to look a little too handsome lately.

ob-gyn!jungwon x f!reader

IF IT’S NOT YOU…

⤿ after years of cleaning up after your conglomerate family’s shady activities and adhering to your every whim and demand as his wife and boss, (boss-wife?) jungwon decides he’s finally done with your marriage. that is, until he realizes he might not ever be able to let you go.

lawyer!jungwon x ceo!reader, queen of tears au

LOST AND FOUND

⤿ you did it, you've finally done it for yourself. you have a home, a successful career, and a fiancé that would turn the world upside down for you. the question is, how much of your new life would you be willing to give away to have your greatest love back in your arms?

heeseung x f!reader

ROSES & RETRIBUTION

⤿ when you are accepted into solstice academy on a scholarship, you seek revenge on the illustrious park family, the very people that took away the life of your best friend. park sunghoon, an attendee of solstice, is sloppy, unaware of his surroundings, and completely out of touch- the perfect target for a clean assassination. the only problem? his irritatingly loyal best friend jake, who happens to be student council president, the son of one of the 7 families pulling strings in the academy, and the man you would later refer to as your greatest love.

jake x f!reader, academy au

IN THE HEAT OF THE SUMMER

⤿ the hot, humid summers of your youth usually meant practicing at the ice rink ‘till you dropped or manning your parent’s video shop. park sunghoon, who lived next door’s summers usually meant delivering newspapers and taking every odd job possible. in the heat of the summer of 1998, your paths finally crossed for the first time.

news anchor!sunghoon x figure skater!reader, inspired by 2521

READY PLAYER 02

⤿ how do you tell your best friend sunoo you’ve been harboring secret feelings for him for years? simple, you don’t. when a love letter ends up in the wrong hands, faking a relationship with the help of the hot new transferee proves to be a lot easier.

ni-ki x f!reader x sunoo, love triangle

[RELEASED] WILD UNCHARTED WATER

⤿ as the son of the nefarious pirate king, jungwon's sole duty is to capture you, the only daughter of the very royal family that threatens his livelihood and his home. however a few ship raids, late night ventures, and exchanges of hate (love?) letters later, it seems that you have captured him instead. body, mind, and soul.

pirate!jungwon x princess!reader

[raven-at-the-writing-desk]

To add onto that Malleus popularity speculation, I think another major reason why that you never mentioned is the simple fact that characters of Malleus' archetype are just more popular in general in the west amongst working age women.

There are plenty of adult novel containing male supernatural love interests. Fae and vampire romance novels are still extremely popular amongst adult readers. A Court of Thorns and Roses is technically an ADULT novel, NOT YA. Even m|m supernatural stories even fall into this category with Stolas/Blitz from Helluva Boss being an extremely popular over here. That pairing is from an adult animated show. Stolas shares a lot of similarities with Malleus.

Hell, even if you step into western contemporary romance novels, the male love interest tends to be more brooding and angsty with flawed leads. Everything from classic literature like Jane Eyre to modern shit like anything Colleen Hoover writes. (Don't get it twisted. I'm NOT saying that Malleus is anything like those leads. Just using those very popular example of brooding bad boy love interests in adult contemporary fiction in the west.)

Meanwhile in East Asia, those sorts of leads tend to be geared towards teenagers. Working age women want a more stable, realistic love interest that would take care of them like Trey.

Westerners seem to prefer more complex, intense romantic relationships, where the stakes feel higher and the emotional payoff is more significant. They will naturally write Trey off as a "big brother" character instead of seeing him as a romantic lead material thanks to being more used to seeing characters like Malleus as the love interest in stories.

I could be way off base, since I'm not Asian and far from being an expert on Japanese culture, but that's my two cents based on my observations. This is also based on broad generalizations. Neither culture is a monolith.

[Referencing this post and (more specifically!) my speculation here!]

Oh, for sure 💀 I made a post a while ago talking about how Malleus (especially from the yumejoshi/self-shipping perspective) reminds me a lot of the new "Shadow Daddy" archetype that has emerged in the romantasy genre. I mean, just look at how many of the Shadow Daddy traits Malleus ticks off:

is a nonhuman being (usually fae)

500 yrs old (or at least several hundred years old or a significant age gap between the Shadow Daddy love interest and typically female main character)

looks young and hot/conventionally attractive despite the age

is OP (usually with shadow/night/darkness related magic)

is royalty or in some kind of position of power

dark hair and/or skin (sometimes both)

“morally grey” and/or has issues (you can fix him)

brooding

looks or is rumored to be intimidating but is actually lonely and misunderstood, with a heart of gold

animalistic in some manner (usually with bat/raven/dragon-like wings)

has a tattoo or some kind of bodily markings (Malleus has the scales under his hair; you could also count the OB facial markings I guess)

Outside of romantasy novels geared towards older teens (18-19) and adults, the west seems to really love brooding bad boys as love interests in a lot of its media. Something else I noticed is that the "good guys" or the "boy next door" types like Trey tend to be "the other man" in heterosexual love triangles, which miiight also explain why he gets looked over in the western fandom. (I discussed some of my own observations, which are similar to the points mentioned here, in the posts linked above.)

I wouldn’texactly phrase it like westerners preferring "more complex, intense romantic relationships [... with higher stakes and more significant emotional payoff]", as that unintentionally implies that there has to be brooding or angst in order for the story or character arc to be "good". I feel a lot of it actually depends on the execution rather than the tropes present. For example, I've seen many "Shadow Daddies" that exist purely for wish fulfillment rather than emotional or story/character complexity (which, to be clear, there's nothing wrong with if this is the kind of thing you enjoy!). Wholesome or "normal" romances also have the capacity to be complex, intense, high-stakes, and emotionally significant too! Again, it all depends on the quality of writing and what one's personal preferences are. You'll find outliers regardless of culture as well--as the asker has stated, no culture is a monolith!

[nadvs]

push and pull ୨ৎ playlist

pairing twin!rafe x female reader x twin!zach

summary life felt complicated enough when you started falling for zach. then you meet rafe. he’s the complete opposite of his twin brother, but he captures your attention just the same.

tags college au set in the obx universe. mutual pining. angst. love triangle. miscommunication.

author’s note i thought it’d be fun to introduce my upcoming rafe/zach twin au fic through a playlist!! each song represents the way a character feels at some point in the story and gives a sense of the fic’s vibe. the complete two-shot is posted here!

୨ৎ ࿐ reader

༄ personality . . . sweet, easygoing, confident

[ 01 ] it’s okay / tommy genesis — i hope that you don’t love another, i’m thinking that i might just run away

[ 02 ] boy with the blues / delacey — i know that you’re a little broken, you know i don’t care

[ 03 ] yours / alina baraz — paradise in your eyes, but i’m not yours and you’re not mine

[ 04 ] all to myself / stacey — i want you all to myself, and i don’t at the same time

୨ৎ ࿐ rafe cameron

༄ personality . . . guarded, protective, reckless

[ 01 ] worthless / d4ad — i feel out of body, the way the world keeps wishing death upon me

[ 02 ] therapy / khalid — you were in my head when i thought i lost my mind

[ 04 ] trust / brent faiyaz — i know that i get rough, but i just wanna feel love sometimes

[ 04 ] still no good / amir obe — looking for affection, i been hollow

୨ৎ ࿐ zach cameron

༄ personality . . . friendly, loyal, down-to-earth

[ 01 ] intolewd / matt maltese — you’re the kind of angel, dancing by the table, i was doing fine then i met you

[ 02 ] how things used to be / ali gatie — i wonder how you are, i wonder if you think of me

[ 03 ] fall in love with you / montell fish — better off as friends, but maybe i could be worth your love

[ 04 ] list of people (to try and forget about) / tame impala — they’ll say my love has died but it was waiting in the wings

if you want notifications on when i post my fics, follow @xorafe-library and turn on notifications 💘

[maennertanga]

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Things are heating up: Your new favorite read has arrived! Ready to learn the hard facts about the hottest piece of fabric? The men’s thong is more than just a triangle – it’s a statement. Whether you’re already wearing it or just dreaming about it, this book delivers the steamiest stories and the naked truth. Grab it before all you can do is fantasize about it. 🔥📖

https://www.maennertanga.com

#berlin #zürich #london #rio #tokio #sanfrancisco #barcelona #cool #party #kitkat #book #revival #interesting #thong #string #man #male #manstyle #underwear #guy #new #trend #trending #viral #viralpost

[arc-hus]

Triangle House, Epsom - Artefact

[sqvishii]

I just reread book 2 so consider: Silver vs Leona love triangle. I think everybody always pays more attention to Malleus v Leona, but these two have my heart. Maybe Silver is impressed with the Prefect's calm under pressure, charisma, and strategic abilities when they rally Savanaclaw's students against their leader and defeat him long-range with magic from the stands (like having Ace try to blow away the sand with his wind to give other mages clear shots, and using standard fire shots to burn up the oily blot). (Sorry, I just like to play with the Leona OB fight in my head.) And when he wakes up, maybe Leona starts to respect the Prefect's gumption and smarts more, when they still put up a fight in the Spelldrive match and fulfill Azul's contract.

Yuu swears, all they did was defeat a couple of overblotting mages, and suddenly got a loyal, caring friend and a leonine prince hanging around them all the time. And now both are trying to invite them to their home for the winter holidays, glaring at each other all the while? What's a Prefect to do?

there would be three endings:

silver:

you'd be in briar valley, uhh- kind of dangerous place for someone without magical powers, but you can manage. lots of cliffs and mountains, you'd be in a.. cottage (I FORGOT,, BASTA ITS WHERE SILVER WAS RAISED), small and cozy.. or the castle (or something..), but no matter- silver is always there for you if anything happens.

during the winter holidays, you two would sometimes house a bunch of animals that bursted in one day and warm them up with magic.. or make flower crowns-

acorn bracelets.

leona:

wowzers, sunset savannah.

respect, especially if ur one of leona's.. "friends", you'd get along with some of his relatives and if you like kids (NO. NOT THAT WAY 🙏), you can always play with cheka! a ball of sunshine, you like him- leona doesn't.

during winter holidays, he just.. sleeps. what's the point of having you come over to his homeland, then? have you as distraction so that he can sleep and cheka doesn't bother him?

just kidding (kinda),, leona would drag himself to go with you if you ever go somewhere to watch over/protect you, even if it's a woman and he's kind of intimidated (because they are much physically stronger and more strong-willed than the men), he'll try his best to prove his worth.

EITHER.

GO AND HIDE IN RAMSHACKLE !!

you'd want nothing more but to spend the cold winter inside your dorm, raccoon in your arms while you do a certain activity and the ghosts that haunted you since the first day just.. roaming around.

but seriously, stay at the dorm, DO NOT go to the kitchen and get roped into another overblot.

[artzs-c]

At camp, we had an obs ure character day and I decided to dress up as Cube and everytime I mentioned it, they looked at me so confused 💔

I had to use what I had, made the life triangle and ears myself with perler!

[squareallworthy]

Triangle Tuesday 2: The circumcenter, pedal triangles, degeneracy, and what even is a triangle anyway?

The circumcenter is almost as simple an idea as the centroid, which we looked at before. To define it, you start the same way. Take triangle ABC, find the midpoints of the sides Ma, Mb, and Mc. Then instead of drawing lines to the midpoints from the vertices, draw perpendicular lines through the midpoints. These lines all coincide at a point O, which is the center of a circle that you can draw through the vertices. The circle is called the circumcircle, and that's why the point is called the circumcenter.

I say almost as simple, but in a sense the circumcenter is simpler than the centroid, because you could easily discover it by accident in the process of simply finding the midpoints. Drawing that perpendicular line, the perpendicular bisector, is the standard way of finding the midpoint of a line segment. It's covered all the way back in Book 1, Proposition 10 of Euclid's Elements, and it's simply this:

So if you find the midpoint of all three sides of a triangle with this method, you've already identified the circumcenter. But that doesn't prove that the perpendicular bisectors always coincide, nor that their point of crossing is the center of the circumcircle. For that, let's return to Euclid (Elements, book 4, proposition 5). Euclid's proof is very straightforward, and leads nicely into something interesting, so we'll follow that, but I will state the theorem differently.

Theorem: the perpendicular bisectors of a triangle coincide and their point of intersection is the center of a circle that meets all three vertices.

Let ABC be a triangle with midpoints of the sides Ma opposite A, similarly for Mb and Mc. Draw perpendiculars to sides AC and BC from their midpoints to meet at point O. Connect three segments from O to A, B, and C.

Consider the two blue triangles. Their sies AMb and CMb are equal, since Mb is the midpoint of AC. They also have OMb in common. Their angles at Mb are right angles, and therefore equal. So they have two sides and one angle the same, making them congruent, and therefore OA = OC.

The same argument applied to the green triangles shows that OB and OC are equal. By transitivity, OA = OB and O is equidistant from the three vertices. The radii of a circle are all equal, so a circle centered at O passing through A also passes through B and C.

Finally, draw a line from O perpendicular to AB. This creates two white triangles with sides OA and OB equal, side OZ in common, and equal right angles at Z. The two triangles are then congruent and the two sides AZ and BZ are equal. So Z is the midpoint Mc, showing that the perpendicular bisectors all meet.

And the same argument works when ABC is obtuse. The circumcenter lands outside the triangle, and in this coloring the white triangles are no longer white, but all the relationships between the segments are the same.

(What Euclid didn't prove is that the perpendicular bisectors of AC and BC do in fact meet somewhere, that is, that they aren't parallel. It's not difficult, but I'm not going to prove that either, at least not yet, for reasons.)

Let's develop another idea. We located the circumcenter by drawing the perpendicular bisectors, but now consider doing this construction in reverse. That is, pick a point, and then draw perpendiculars to the three sides. The intersection of the perpendicular and the side is called the foot of that point with respect to that side. If you do that with with the circumcenter, the feet are of course the midpoints, but you can find the feet for any point.

And if we connect those three feet, we get a triangle. In this case, the medial triangle, which we have seen before. For a point in general, the triangle formed by its feet is called the pedal triangle of that point. ("Pedal" meaning "related to feet," and yes, that is why a lever operated with your foot is also called a pedal.)

So let's draw the pedal triangle for an arbitrary point, move it around, and see what happens. The point is going to sometimes be outside the triangle, but that's all right. With extended sides (dashed lines) we will still be able to draw a perpendicular to find a foot, no matter where the point is.

So there's something interesting -- the three feet become colinear and the pedal triangle flattens out into a straight line when the point is on the circumcircle. Does that always happen?

Looks like it does! So let's prove that. Below is a drawing of the flattened-out pedal triangle of a point on the circumcircle, all labeled up. I've also added a couple dashed lines to make following the proof easier. What we would like to show is that ∠JKP + ∠PKL = 180°.

We're going to extract some information from this drawing based on two facts: a) in a cyclic quadrilateral (meaning it has all vertices on the same circle), opposite angles sum to 180° and b) if two right triangles have the same hypotenuse, the triangles have the same circumcircle. I'm not going to prove either of those here because this post is long enough already, but both of these results follow straightforwardly from the inscribed angle theorem.

Theorem: For a point P on the circumcircle of a triangle ABC, the feet J, K, and L with respect to ABC are colinear.

Okay. PCBA is a cyclic quadrilateral, so

1) ∠BAP + ∠PCB = 180°.

And ∠BAP is the same as ∠LAP, so

2) ∠LAP + ∠PCB = 180°.

The two triangles AKP and ALP are right triangles with the same hypotenuse (the dashed segment AP), so all four points are on the same circle and ALKP is a cyclic quadrilateral. Therefore,

3) ∠LAP + ∠PKL = 180°,

4) ∠PKL = ∠PCB.

Quadrilateral PKCJ is also cyclic (again because of right triangles sharing the same hypotenuse), so

5) ∠JKP = ∠JCP

by the inscribed angle theorem. ∠PCB is supplemental to ∠JCP, so

6) ∠JKP = 180° - ∠PCB

and then combining 4) and 6),

7) ∠JKP + ∠PKL = ∠PCB + (180° - ∠PCB) = 180°,

which means that the pedal triangle of a point on the circumference of a circle is flattened to a line segment. Can we consider such a figure to be a triangle?

Now we can return to Euclid's omission in the existence proof of the circumcircle. Proving that the perpendicular bisectors aren't parallel is equivalent to proving that no two sides of a triangle are parallel, or that the three vertices of a triangle aren't colinear. Euclid didn't do that, but it's pretty simple, so he could have. And then he would simply have said that such an arrangement of line segments isn't a triangle. Modern geometers working with projective geometry can answer differently, and might say that this is a degenerate triangle, but we haven't gotten into that yet.

Let's do one more thing. We can extend the flattened line segment into a line, called the Simson line, after Robert Simson, who never wrote anything about it. It was actually discovered by William Wallace, but not named for him, because that's how things work in math.

The set of all Simson lines from all points on the circumcircle form an envelope in the shape of a deltoid, the Steiner deltoid, named for Jakob Steiner, who for all I can tell was its actual discoverer.

The deltoid is tangent to the sides of the triangle at three points where the Simson line coincides with the sides. I'll have more to say about this lovely deltoid later, but for now, please just enjoy this gif. It took me several hours to figure out how to make it, so if people reading this could spend a collective several hours staring at it, that would be great.

If you found this interesting, please try drawing some of this stuff for yourself! You can use a compass and straightedge, or software such as Geogebra, which I used to make all my drawings. You can try it on the web here or download apps to run on your own computer here.

An index of all posts in this series is available here.

[sorchasolas]

More SLA aus that are outlandish and niche

•Restaurant industry AU. Dalinar runs a Michelin Star restaurant, Sadeas owns a gross and cheap restaurant chain. Kaladin’s won best employee for about a year straight because even though his boss(Gaz) fucking hates him, the EOM is a vote but not like a council vote the EMPLOYEES vote and everyone just picks Kaladin

•Cultivations Champion AU. Probably thought up before but like. Cultivation starts feeling left out and steals one of Dalinar’s Radiants (totally kaladins its gna be kaladin) to make her Champion. And since the duel os between honors and odiums champion kal just stands there watching Ft. Kal with REALLY long hair

• A twist on the shakadolin love triangle that went on from wor-ob but its shallan and adolin fighting over kaladin. The Kholin family knows about this and is somehow completely unfased by this (Dalinars only complaint is like “heirs…:(“ but he. He gets over it this isnt the focus of the conflict and Kaladin is COMPLETELY oblivious to the entire situation Ft. An exceptionally better first impression between shallan and kaladin

• Kaladin isnt brought up as a surgeon or even like as a surgeons son and we’re reminded that Alethi actually encourage war and murder (our understanding of Alethi culture has been muddled by Dalinar’s honor and Kaladin’s INNATE “i dont like death” type thing. Adolin killing Sadeas is, illegal, yes. But also no one in Alethi culture would fault him at all??)

• jobs AU set not in modern times but like… kind of in the future??. Shallan is a Medical Illustrator, Adolin is. He doesnt have a job come on hes riding off of Dad’s money.(but he does attempt fashion stuff) Kaladin is an emergency physician (MY personal dream job, go kal), and Renarin is the Crazy Inventor (tm)

•not even remotely niche but the “this entire thing is just a show theyre actors” au. And they all conveniently have the same exact name as their role. Kaladin IS ACTUALLY Dalinar’s son irl and theyre so bad at acting on that part they had to write in that Dalinar was a father figureish to Kal. Rlly out of the blue but Venli (who has makeup on but the listener/singer appearance is mostly cgi) and Shallan are sisters, not revising my opinion on this. Everything else can be figured out later i just wanted to define those two things (this specific AU is something im kinda actually working on for Red Rising (sobs in half the cast is dead)

[thoughtportal]

One evening in 1951 astronomer William Wilson Morgan was strolling home from Yerkes Observatory in Wisconsin when he looked up at the night sky and had a “flash inspiration ... a creative intuitional burst.” It solved one of the great mysteries of astronomy.

The observable universe contains billions, possibly even trillions, of galaxies. With a modest telescope, their varied forms are discernible—spirals, ellipsoids and others with irregular structures. But what about our own galaxy, the Milky Way?

Morgan had been calculating the distances from Earth of groups of big, hot, bright stars, nowadays called OB associations. He knew that in spiral galaxies these clusters reside in the trailing arms. Gazing at the sky while walking home, he located the familiar dots of the OB associations. But this time the flat image of the night sky merged in his mind with the star distances that he had calculated and committed to memory, and it sprang to three-dimensional life. Morgan’s vision: the stars of the OB association are arranged in a long strand—an arm of our spiral galaxy.

An “aha! moment,” such as Morgan’s marvelous insight that the Milky Way is a spiral, is a new idea or perspective that arrives abruptly, often bursting into an ongoing stream of thought. It may pop up while someone is actively trying to solve a problem, but it can also arrive spontaneously. “When I write songs, it’s never a conscious decision—it’s an idea that floats down in front of me at four in the morning or in the middle of a conversation or on a tour bus or in the mall or in an airport bathroom,” singer-songwriter Taylor Swift related to an interviewer. “I never know when I’m gonna get an idea and I never know what it’s gonna be.”

These revelations feel pleasing, even thrilling, and they can be portals to a scientific breakthrough, an innovative business proposal, a hit song or the plot of a best-selling novel. Or they may provide a life-changing perspective on a personal dilemma. People can overcome many challenges by analyzing them step by arduous step, but leaps of insight are more often associated with out-of-the-box ideas. And though often obvious in hindsight, the revelation can be astounding when it arrives.

Scholars have sought to capture the elusive essence of the aha! moment for more than a century, and it is finally within our grasp. We now know where it happens in the brain and when it’s more likely to happen. And we’re discovering some surprising benefits of insight, including elevated mood, memory and, oddly, the ability to distinguish fake news from real.

Jen Christiansen

Jen Christiansen; Sources: “Intuition in Insight and Noninsight Problem Solving,” by Janet Metcalfe and David Wiebe, in Memory & Cognition, Vol. 15; May 1987 (triangle and polygon reference); “Restructuring Processes and Aha! Experiences in Insight Problem Solving,” by Jennifer Wiley and Amory H. Danek, in Nature Reviews Psychology, Vol. 3; January 2024 (candle problem reference)

The 1990s saw rapid developments in neuroimaging. By the early 2000s cognitive neuroscientist Mark Beeman and one of us (John), both then at the University of Pennsylvania, concluded that imaging technologies were advanced enough for us to try to see what happens in the brain when a person has an insight. We used two complementary methods: electroencephalography (EEG) and functional magnetic resonance imaging (fMRI). EEG measures the electrical activity of the brain with electrodes placed on a person’s scalp. It provides very precise information about when something is happening in the brain. In contrast, fMRI measures slower changes in blood flow (when a region of the brain is working harder, it draws more blood) and provides very detailed maps of where things are happening. By using EEG and fMRI in parallel experiments with different people solving the same puzzles, we were able to isolate the brain’s aha! moments in both space and time.

We couldn’t rely on difficult brainteasers, because to get statistically significant results, we needed each test subject to solve many problems. Instead we used little verbal puzzles such as compound remote associates (CRAs), which people can solve either insightfully or analytically. Each CRA consists of three words, such as “pine,” “crab” and “sauce.” The participant’s job is to think of a fourth word that can be used to form a compound word or familiar phrase with each of the three given words. Immediately after a volunteer solved one of these puzzles, they reported whether the solution had popped into awareness suddenly or been discovered through deliberate, step-by-step thinking. We were thus able to isolate aha! moments and compare the brain activity during them with the brain activity for analytical solutions. (If you’re curious, the answer to the CRA in this paragraph is “apple.”)

Our key result: an aha! solution corresponds to a burst of high-frequency brain waves in the brain’s right temporal lobe, just above the right ear. That part of the brain, the right anterior superior temporal gyrus, connects with many other brain regions. It is associated with our ability to realize connections between concepts that may initially seem unrelated, as occurs when comprehending metaphors, jokes and the gist of conversations. Our findings linking this specific area of the brain to the aha! experience supported previous work by Edward M. Bowden of the University of Wisconsin–Parkside and Beeman suggesting that the solution to such a problem can be unconsciously present in the right hemisphere, ready to emerge into awareness as an insight.

The number of puzzles people solved by insight—but not analysis—predicted how well they could discriminate between real news stories and fake ones.

Our later research revealed, however, that aha! moments may excite other areas of the brain, depending on the type of puzzle. In 2020 John and his co-workers showed that insights that solve pattern-reorganization problems activate the frontal lobe rather than the right temporal lobe. Anagrams—for example, rearranging the letters in BELAT to get the solution TABLE—are among such problems. Thus, the distinctive feature of an insight is the sudden burst of high-frequency brain-wave activity, which can occur in various parts of the brain, depending on the type of problem solved.

Some problems lend themselves to an analytical, as opposed to an insightful, solution. Analytical problem-solving recruits areas of the brain involved in “executive” processes such as “working” memory that rely on the brain’s frontal lobes. Virtually everyone can use either insightful or analytical methods, but many people tend to use one rather than the other. Nobel laureate physicist and mathematician Roger Penrose, for example, can obviously think analytically but seems to be inherently insightful: “I had this strange feeling of elation, and I couldn’t quite work out why I was feeling like that,” he once said in an interview. It turned out he’d had an epiphany about the formation of black holes while crossing a road. “I do most of my thinking in visual terms,” he related, “rather than writing down equations.”

In the 2010s Brian Erickson, then a doctoral student in John’s laboratory at Drexel University, and his colleagues demonstrated that people’s tendency toward insightful or analytical thinking is evident during “resting-state” brain activity—while a person relaxes with no task to perform or expectation about what is to come. Erickson recorded people’s resting-state EEGs and then, weeks later, tasked the same participants with solving a series of anagrams. The astonishing result: a few minutes of EEG predicted, up to seven weeks in advance, whether a person would solve the puzzles mostly insightfully or analytically. Our predominant thinking style is stable over time.

Jen Christiansen; Source: “Resting-State Brain Oscillations Predict Trait-like Cognitive Styles,” by Brian Erickson et al., in Neuropsychologia, Vol. 120; November 2018 (reference)

Although individuals may be inclined toward more analytical or insightful thinking, we aren’t locked into one or the other. Your thinking style can shift or be nudged, at least temporarily, to the other strategy. One factor is mood. In a 2009 study led by Karuna Subramaniam, then a doctoral student in Beeman’s lab at Northwestern University, researchers found that participants who reported feeling more positive solved more puzzles by insight, whereas those who reported greater anxiety solved more puzzles analytically.

Why might that be? Consider the following example, courtesy of Beeman. Imagine you are in Africa 25,000 years ago. You see a lion off in the distance and are gripped with fear. Your thinking immediately becomes very careful and deliberate—analytical—because one mistake and you are finished. Can the lion see me or hear me? Am I upwind or downwind? If I run, is the lion close enough to catch up?

You manage to escape. That evening you are back in the cave with your people. There’s a fire, so it’s warm, and the day’s catch is cooking on a rack. You are enjoying what researchers call psychological safety. In your protected haven, you don’t have to suppress rambling, fanciful thoughts—the stuff of creativity. You are empowered to say or do something imaginative. That may be why, 25,000 years later, we find the innovative, practical flint tools and breathtaking cave paintings that sustained and inspired the lives of the ancients.

Jen Christiansen; Source: “An Insight-Related Neural Reward Signal,” by Youngtaek Oh et al., in NeuroImage, Vol. 214; July 2020 (reference)

To discover whether more complex insights could lift mood over a longer time, Christine Chesebrough, then a doctoral student in John’s lab, developed word pairs that formed ongoing analogies, such as steering wheel/car followed by rudder/boat, both of which suggest an implement that guides a vehicle. The next word pair could be either handlebars/bicycle, which continues this theme, or voting/government, which forces the subject to reinterpret the ongoing analogy in a more abstract way as one entity controlling another. This conceptual expansion sparked strong aha! experiences that elevated participants’ moods for at least the hour-long test session—the more insights, the better their mood. The vibe persists. The joy of insights can thus impel scientists, artists, writers, and others to feel such a strong drive to express their creativity that they forgo a well-paying job to immerse themselves in their vocation, contributing essential ideas to culture and science.

The thrill of an aha! moment can increase risk-taking. As a doctoral student in Beeman’s lab, Yuhua Yu led a study in which she and her colleagues gave people CRA puzzles to solve. Between some of these puzzles, they offered the participants a choice between taking a small payment—a sure thing—and taking a chance to win a larger prize with the risk of no payoff. After finding an analytical solution, the volunteers tended to take the smaller, guaranteed payoff. But after enjoying an insight, participants were more likely to gamble on winning the bigger prize. Experiencing an aha! moment can therefore promote an appetite for risk, which, as Maxi Becker of Humboldt University of Berlin and her colleagues showed in 2023, involves the nucleus accumbens, a dopamine-rich part of the brain’s reward system.

Tolerance for risk can be good or bad depending on the circumstances. But one unequivocal benefit conferred by insightful thinking is reduced “bullshit receptivity,” as Carola Salvi of John Cabot University in Rome and her collaborators have found. People are flooded by biased information and slanted reporting, and their limited capacity to deal with this torrent of information makes them vulnerable to false messages. Fortunately, insightful thinking is largely unconscious and does not tax attention or working memory the way analytical thinking does. Salvi and her co-workers observed that the number of puzzles the participants in their study solved by insight—but not analysis—predicted how well they could discriminate between real news stories and fake ones, as well as between meaningful statements and “pseudo-profound bullshit” statements. Insightfulness is not only for dreamers: it confers real-world skills that help people navigate the overwhelming information landscape.

Insight also enhances learning and memory. Amory H. Danek of Heidelberg University in Germany and her colleagues showed participants videos of magic tricks and asked them to explain how the tricks were done. Later the subjects remembered the solutions that were experienced as aha! moments better than explanations that were not. Danek and Jennifer Wiley of the University of Illinois at Chicago followed up this study by showing that the pleasure accompanying insights made them easier to recall. Jasmin Kizilirmark of the University of Hildesheim in Germany and her colleagues have been exploring how this so-called insight memory advantage can be applied to improve memory in older adults.

Aha! moments can have a downside. Insights are more likely to be correct than analytical solutions—but they are not always correct. The dilemma is that people tend to be particularly confident about their insights, even the false ones. Furthermore, work by Ruben Laukkonen of Southern Cross University in Australia and his colleagues suggests that statements presented along with anagrams that people solve by insight also feel more believable than statements presented with anagrams solved by analysis. Aha! moments may create an aura of truth that envelops accompanying information.

The fact that mood can alter one’s thinking style has profound implications for our understanding of creativity. Subramaniam’s fMRI analyses isolated the lone area of the brain that responds to both differences in mood and differences in thinking style. This area, the anterior cingulate cortex, located in the middle of the front of the brain, detects conflicting strategies. When you are relaxed, your anterior cingulate cortex is better able to detect the presence of an alternative to the most obvious, but possibly ineffective, problem-solving strategy and switch to it, sparking an aha! moment. But when you are anxious, it is less able to detect the subtler strategy, and you will continue to grind through the problem in a straightforward, analytical manner.

An obvious way to increase insightfulness is therefore to relax and carve out a span of time when you aren’t anxious or rushed. Another way is expansion in space: When you are in a large room or the great outdoors—under a starry sky, as Morgan was—your attention expands to take in the large space. That broadened awareness shifts the mind toward considering the whole rather than the parts, thereby enhancing insightful thinking. Filtering out the world around you can have a similar effect: aha! moments are often preceded by eye blinks and looking away from a problem to reduce distractions. People solve more thinking problems when they close their eyes. In contrast, objects that grab attention will narrow your focus on details and induce you to think analytically.

Steven Smith of Texas A&M University and his collaborators have also shown that if you take a break from a problem to do something else, preferably a relatively undemanding task such as light gardening or housework, any misleading information or misinterpretation will loosen its grip, and you will be more likely to achieve an insight. Kristin Sanders, now at the University of Notre Dame, and Beeman showed that sleep can enhance this process, supporting the many stories of scientists who have experienced great ideas during or right after sleep. Colleen Seifert and David E. Meyer of the University of Michigan and their colleagues reported another benefit of breaks: you may encounter a trigger—a person, a street sign, anything—that can spark an aha! moment because the trigger bears some resemblance to or association with the needed solution.

How about drugs? The thought of popping a pill that would unlock creative insights may be appealing for some people. Microdosing psychedelic drugs has been proposed to increase innovative thinking. We are not aware of any rigorous scientific evidence that psychedelics can increase the likelihood of insights, although they may cause a person to feel creative and profound. But alcohol, if not taken to extremes, does seem to enhance insightful solving. (That is not an endorsement!)

Perhaps there are other ways to directly intervene in brain function to produce aha! moments. Several researchers, including Beeman, Salvi, Amna Ghani of Charité–Universitätsmedizin Berlin, Caroline Di Bernardi Luft of Brunel University London and Joydeep Bhattacharya of Goldsmiths, University of London, have shown that direct electrical stimulation of test subjects’ right temporal lobes with electrodes placed on their heads—in some cases, synchronized with hints—can increase the likelihood that they will solve CRA puzzles using insight. For various reasons, though—including the fact that different types of insight involve different areas of the brain—it is unlikely that electrical stimulation will become useful as a technique for sparking aha! moments.

Here’s what does not work: expectations of monetary prizes or bonuses. Payments can coax a person to tackle a problem—and people should certainly be compensated for their work—but they can also inhibit insights. A focus on an expected payoff grabs and narrows one’s attention, limiting creative thought. Messages about rewards can enhance insight—but only when they are displayed so briefly that a person cannot consciously perceive them. When innovation is the goal, conspicuous rewards may therefore be counterproductive, as are strict deadlines that switch one’s thinking to an analytical mode by inducing anxiety and narrowing mental focus.

Alternatively, you could just go get groceries. Vishal Rao, an oncologist in India, endured years of frustration before a surprising twist enabled him and his unique team to create an amazing medical device. As a surgeon specializing in neck and throat cancer, Rao knew that most of the tens of thousands of new patients with throat cancer each year in India could not afford the prohibitive cost of surgery to replace their diseased voice box with an artificial one. So, in 2013, Rao formed a team that developed an inexpensive artificial voice box costing less than a dollar.

But there was one roadblock remaining. The artificial voice box had to be replaced yearly in a surgical procedure that costs hundreds of dollars, a regular expense way beyond the means of most of his patients. He needed an inexpensive, nonsurgical tool that a patient could use to remove an old artificial voice box and implant a new one—a challenge that seemed insurmountable.

One day Rao went to the supermarket with his toddler. The boy broke free and started running down the aisles, gleefully knocking things off the shelves. Rao chased and caught him, but only after the boy had knocked down a box of tampons, the contents of which spilled out onto the floor. When Rao saw the tampon applicator, it sparked an aha! moment: here was a safe, inexpensive, nonsurgical implement that could be a model for a voice-box applicator.

When Rao explained this idea to others, they said the device he wanted sounded more like a toy than a surgical instrument. This comment triggered the doctor’s second aha! moment. He recalled that Channapatna, a nearby city, is nicknamed “toy town” because of its centuries-old tradition of master craftsmen who design and make inexpensive wood toys. After interviewing Channapatna toy makers, he found Kouser Pasha, who was intrigued by the idea. It took Pasha just a couple of hours to come up with a design for an inexpensive voice-box applicator.

Just as hungry people tend to notice anything related to food, Rao’s initial failure to imagine an inexpensive applicator sensitized his brain to anything around him that looked like it could help him solve the problem. When he took a break from his problem, his old ways of thinking relaxed their grip as he was exposed to a variety of objects in the supermarket. One of those objects, the tampon applicator, was potentially related to the problem, so it grabbed his attention. Once he figured out that a similar device would work, the surgeon still had to figure out how to design and manufacture it. The need for a solution sensitized him to the word “toy,” which triggered his insight about recruiting a toy maker from “toy town.”

The upshot: when you are stuck, take a break and expose yourself to a variety of environments and people to increase the chance you will encounter a triggering stimulus. Perhaps the most important scientific lesson about insight, though, is that it is as fragile as it is beneficial. The aha! moment brings new ideas and perspectives, lifts mood, increases tolerance for risk, and enhances the ability to discern truth from fiction. But anxiety and sleep deprivation can squash these precious gifts.

Jen Christiansen; Sources: “Intuition in Insight and Noninsight Problem Solving,” by Janet Metcalfe and David Wiebe, in Memory & Cognition, Vol. 15; May 1987 (triangle and polygon reference); “Restructuring Processes and Aha! Experiences in Insight Problem Solving,” by Jennifer Wiley and Amory H. Danek, in Nature Reviews Psychology, Vol. 3; January 2024 (candle problem reference)

[liesmyth]

what's your ranking of the stormlight books?

ooooh. thank u for asking

1. Words of Radiance. THEE platonic ideal of a contemporary epic fantasy book. when Kaladin jumps into the arena. when Kaladin shows up at the battle at the end. the Helaran death reveal. Shallan in the chasms. the Adolin & Kal friendship arc. Elohkar. Shallan's backstory. I remember reading this book in March 2014 while backpacking through Ireland and using shitty hostel wifi to connect to discussion boards in the evening. I love it to bits

2. Rhythm of War. epic in every sense of the word. the stakes are huge, the pacing is great, the tension is through the roof. everything is happening at once!! Navani my beloved. Shadesmar is weird and crazy. Kal is Going Through It. it's just so huge in scope in so many different ways and the way everything is tied together is truly beautifully done. my personal experience of reading this book was that it took me months to start in the middle of lockdown depression + OB had lowkey disappointed me, and I liked it SO much that it singlehandedly got me back into reading after a couple of years of a big slump.

3. Way of Kings. I love how it's clearly the first step on a much grander journey, even on first read, but it really strikes the balance of being The Beginning Of A Series and self-contained. the way Kaladin's backstory is introduced still makes my jaw drop. with every reread I love Shallan more. I still remember reading it the first time (summer 2011 on vacation) and being struck by how bizarre and unique the world was. plants that moved! storms that stormed! one of the first books of all time.

4. Oathbringer. I didn't love this one at the time but I think RoW made it better in hindsight. back when I first read it, I remember being disappointed with how quickly certain emotional beats that had been fundamental in the first two books were resolved or glossed over (Amaram first and foremost) even if I understood the series needed to jump to the next level pacing-wise, but it still grated. I still don't love how the book handles Dalinar and Moash both, and I think we should ban Branderson from writing about love triangles for so many reasons, but it has some really really great emotional beats and imagery and I enjoyed it much more on reread

[I'm on chapter 22 of WaT — will report back :D]

[dumb-but-happy-trist]

Pinned post, for real this time

I’m Trist, and there are three “voices” in my head. Trist (Voice of Emotion), Rust (Voice of Wrath) and Ob (Voice of Compassion). It’ll be tagged if it’s one of the other voices talking, if it isn’t tagged, then it’s Trist.

It’s here. The Kirby side blog. @kirbyheritageposts

The profile pic can change at any time, so I’m sorry if you want to recognise me using my pfp, but you’re gonna have to deal with it.

The tags :

#fuck it I don’t care how big the room is i cast fireball : my favourites

#i see four : for later

#baeber #idfwt #screeching in joy : various art tags used for different reasons, you figure out the reasons

#lancer ga shinda : made me laugh or Lancer just died, you figure it out

#fweh : 3d20 of cuteness damage

#gweh : 3d20 of positive mental damage

#nyeh : 3d20 of negative mental damage (don’t expect to see that one much)

#ritsuka is batshit insane : exactly what it says on the can

#cu chulainn my beloved : self explanatory

Fandoms I’m in : Kirby, Pokémon, Mario, Zelda, Ace Attorney, Professor Layton, Fate, and more I’m forgetting.

Fandoms I’ve been in, am not in anymore but am currently writing fan fiction for : MHA

Kirby is my favourite character.

Headcanons : Kirby is aroace, Queen Sectonia is trans, Layton is bi, WW!Link is aroace, Captain Toad isn’t a character but a title to be held.

Do not commit Ad Hominem against me, I will let Rust thrash you.

I also reserve myself the right to block you based on vibes without warning, which means there is no DNI on this blog, since I’ll block you anyways.

Currently holding a notes game.

The Golden Run, which was a live blog of my battles in the Golden Route of Triangle Strategy :

Here’s an important post for this blog :

Here are my favourite sideblogs :

@your-fave-as-a-fate-servant

@ask-the-chaldea-staff

@the-idiot-council

@trists-rp-blog

@foreign-planet-chaldeas

@the-wandering-blade-of-wonder

@mismatched-magical-warriors

@could-they-win-a-holy-grail-war

@trist-with-pokemons for Pokémon irl (same name, different people)

The community :