The Golden Ratio of Intuition
"So, you're saying you wanted to analyze whether a song is good using objective metrics?"
"Yes!"
Chul-jun answered brightly, and Choi Yeon-mi shook her head slightly.
Of course, it was a highly novel approach, but...
"Song analysis programs already exist. Streaming companies like Spotify and Apple Music are already using hit-song prediction algorithms. They break songs down into hundreds of variables to make predictions, and their accuracy is quite high."
Hyeong-man, who had been listening quietly from the side, cleared his throat once, and Choi Yeon-mi narrowed her eyes slightly.
Should I have just told him he was amazing?
But this was her world, and she couldn't bring herself to lie about it.
Yeon-mi was stubborn when it came to her profession.
It was better to give him accurate information rather than let him waste his efforts.
Besides, she was currently on edge due to the planning of a rookie idol group.
So, she subtly ignored the look Hyeong-man was giving her.
"Our company has been using those programs for quite a while now, too. When producers compose a song, AI analyzes the hit patterns and modifies it accordingly. It increases the chances of it becoming popular."
Chul-jun smiled brightly and nodded.
"I know that too."
"Oh?"
"Hit song patterns are easy to analyze. The tempos are similar, the chord progressions overlap in very simple ways when analyzed, and the structures follow a strict formula. Even the climaxes are mostly concentrated around the 61.7% mark of the total song length. Because of the golden ratio."
"Oh..."
Yeon-mi nodded slowly.
Because Chul-jun's words were entirely accurate.
When composers' music was fed into the AI, most of it was set to a base of 120–130 BPM, the chord progressions largely relied on the I-V-vi-IV progression, and the structure was arranged to cut off around 3 minutes and 30 seconds to fit proven formulas, with the hook designed to appear within the first 7 seconds.
The golden ratio was also the climax interval most preferred by the AI.
"I tried to analyze it that way too. But music couldn't be broken down so cleanly."
Choi Yeon-mi's eyebrow twitched.
Ever since AI emerged and began to be utilized in music, this was what producers said every single time.
"You can only reach that realm through intuition."
Chul-jun realized it clearly this time.
That there were realms that could never be reached by mathematics alone.
Once he completely separated the world from mathematics, it became clear that mathematics was merely a tool.
"That's why I wanted someone with intuition to listen to it."
Yeon-mi blinked.
It was hard to get used to him speaking so seriously with such a cute face.
"To see if my intuition is correct."
Chul-jun smiled brightly and held up his phone.
"The tempo is on the faster side, the chord progression is unusual, and the song structure is far from the known formulas. The climax isn't at the golden ratio, either. But it's incredibly fun and good. Well, to my intuition, it feels like a good song."
Chul-jun's language had changed.
He was now able to state with certainty that something was good, even if he couldn't explain it perfectly.
"Could you listen to it?"
Yeon-mi's gaze drifted to Chul-jun's phone.
Then, she let out a soft sigh.
"I can't sugarcoat things when it comes to this."
"Yes!"
"If it's bad, I'll tell you straight up."
"Yes!"
"Call me Mom once."
"Mom!"
"Good. Play it."
Chul-jun's tiny finger pressed the play button.
After Aunt Yeon-mi left, Chul-jun lay in bed, his heart fluttering for the first time in a long while.
He felt as good as he did when he first got his phone.
First of all, he was thrilled that his world had suddenly expanded.
By accepting the impossibility of mathematics, he realized there was another world beyond it.
He had vaguely known it, but he had been too afraid to look past the boundary. Now that he had peeked over, it wasn't scary at all.
In fact, it made his heart flutter.
He loved that the world, which had once appeared only as patterns, now felt like a complete, living world.
Once he accepted that it wasn't wrong even if things couldn't be clearly explained, his mind felt incredibly at ease.
It was an even greater excitement than what he had felt when he first discovered mathematics.
And most of all, he loved the fact that his intuition—judging something purely by feeling without any analysis for the first time—had been validated.
He had observed Aunt Yeon-mi closely when he played the song, and she really did seem to think it was decent.
Her expression hadn't changed much, but he saw her finger tapping on her knee.
It had moved quite rhythmically.
And at the end, she had said, "It's not bad."
She even told him to keep at it because he had talent.
Arin is going to love this, right?
Thinking about that made him feel good again.
It was a different feeling from when he played Baduk with Si-woo.
What does it feel like to move toward a dream?
For the first time, Chul-jun felt like he should find a dream of his own.
Then, he would be able to feel the same joy that Arin felt.
Right now, everything was a first, so it was all fun and wondrous, but Chul-jun knew very well that a moment would eventually come when all of this would feel ordinary.
Perhaps the world would become boring.
Chul-jun's brow furrowed.
He couldn't remember at all what dream he had had in the teacher's car yesterday.
But he knew it was a very painful memory.
Just as his memory of when his father, Jaegang, died was extremely hazy, that memory was also very faint.
If the world became less interesting than it was now, those memories might become vivid again.
He wasn't sure, but he had a feeling.
Chul-jun quickly pulled the blanket over his head.
Happy thoughts! Happy thoughts!
Smiling brightly, he closed his eyes tight.
Go Chang-ho was looking at Chul-jun with an expectant face.
Chul-jun was looking over the list of competitions Chang-ho had prepared.
"You can take your time. You don't have to do it."
"..."
Go Chang-ho's eyebrow twitched.
Still, mathematics was what Chul-jun was most confident in.
He was a child who had tried to understand everything through math.
"The math competitions there might not match your level, but it's good to build experience. Things like the atmosphere of the testing hall and the format. After that, you can try entering the KJMO in August, and if that goes well, you can challenge the first round of the KMO in November."
Chul-jun's brow furrowed slightly.
"I'm not so sure about math..."
"...Huh?"
"Math is something only I can see."
Honestly, Chul-jun had felt a bit lonely.
"When I think about it all by myself, it's really cool, but when I try to explain it, it doesn't feel cool anymore. If you play music, people get it right away, and if you show them a painting, anyone can see it's cool. But with math, no matter how much you explain it, only those who already know can see it."
Go Chang-ho blinked blankly.
"Even if I go to a competition alone and win an award, I don't think I'll be very happy..."
At this completely unexpected answer, Chang-ho quickly looked over the other competition lists.
What else should he recommend?
Baduk?
Just then, Chul-jun parted his lips.
"If I do it with friends, like playing Rival, I think it might be fun..."
"Huh? Together?"
"Yes! Because math really is fun."
"..."
"The other kids find math fun too, right?"
"Well..."
"Looking at the after-school classes, all the math classes were completely full."
"Ah..."
"Min-jun and Ha-rang take Creative Math after school too."
Go Chang-ho let out a breath and shook his head slightly.
"To, well, to be honest, they probably aren't doing it because it's fun."
"Pardon?"
"Uh, I mean, they're half-forced into it..."
Chul-jun's eyes suddenly sparkled.
Just as Min-jun and Ha-rang had shown him how fun Rival was, he wanted to show them how fun math could be. When his thoughts reached that point, he suddenly became very excited.
Ever since he completely separated the world from mathematics, he had been feeling that math was lonely. But if they did it together, wouldn't it be less lonely?
Since Rival was only fun when played together, too?
"Teacher!"
"Yes?"
"I want to enter a competition with the other kids!"
Go Chang-ho recalled their math assessment scores from the beginning of the semester and swallowed hard.
They were absolutely not at a level to enter a competition...
But looking at Chul-jun's highly expectant face, he couldn't bring himself to just say no.
Chul-jun stared at Chang-ho, then smiled brightly.
"We'll study together!"
"Study?"
"Yes!"
"Well, a level where they can study with you is..."
"I can just teach them! Just like Min-jun taught me Rival!"
Chang-ho's eyebrow twitched.
Teaching a child from a child's perspective?
Perhaps they might experience an unexpected sense of achievement.
This is actually a scene to look forward to.
He immediately got an idea of how to coax those two boys who were completely obsessed with the game.
In his mind, lines to persuade their parents began to float around.
Thanks to the interview Si-woo had given at the Baduk tournament—even though Chang-ho hadn't done much—his popularity in the parents' group chat was currently soaring.
Persuading the guardians would be a piece of cake.
If it's just an hour or two after after-school classes are over...?
Go Chang-ho smirked, curling up one corner of his mouth.
That day, after all the after-school classes had ended.
Min-jun and Ha-rang, who were left behind in the empty classroom after everyone else had gone home, blinked their eyes.
Standing in front of the blackboard, Chul-jun looked at them and spoke.
"Then, do you know decimals?"
"..."
"You know how to do division, right?"
Min-jun, who hesitated for a moment, raised his hand high.
"Yeah!"
"What's 6 divided by 3?"
"2!"
"What's 6 divided by 4?"
Min-jun's eyes shook slightly, and Chul-jun tilted his head.
"...You don't know remainders?"
"..."
Ha-rang, who had been thinking hard with furrowed brows, raised his hand high.
"The quotient is 1, and the remainder is 2!"
"Correct!"
"Booyah!"
Min-jun stared at Ha-rang with wide eyes.
"How did you know that?!"
"I forgot, but I just remembered!"
Min-jun let out a sigh, scowling in frustration.
He had thought he was much better than Ha-rang...
Staring at the two of them, Chul-jun closed the 5th-grade textbook that had been spread open.
It seemed they would have to start over from the 4th-grade level.
Without realizing it, the corners of his mouth curled up slightly.
This was actually quite fun.
Go Chang-ho, who was observing from the very back of the classroom, pinched his thigh hard to hold back a burst of laughter upon seeing Chul-jun's expression.