"Look at this!"
Yuki excitedly opened a book. A new application of information theory.
Riku tilted his head. "Hmm."
Aoi's eyes lit up. "This is interesting!"
Yuki nodded happily. "Right!"
Riku looked at them curiously. "What's so interesting?"
"This theorem's proof. It's elegant."
"Elegant?"
Aoi tried to explain but stopped seeing Riku's expression.
"Even if I explain, it might not get through."
Yuki said a bit sadly, "Can't share the surprise."
"Surprise?"
"Yes. Aoi-senpai and I were surprised by this proof. But Riku, you're not."
Riku apologized. "Sorry, it's too difficult for me."
"Nothing to apologize for," Aoi said kindly. "But this is a mutual information problem."
"Mutual information?"
"I(X;Y). Amount of information shared between X and Y."
Yuki supplemented. "Being able to share surprise is because we have common knowledge."
"Common knowledge?"
"Knowing information theory basics lets you see how amazing this proof is."
Aoi drew a diagram in the notebook. "Imagine sets of knowledge."
"My and Yuki's knowledge sets overlap in the information theory part."
"So we can be surprised by the same thing."
Riku understood. "I don't overlap, so I can't be surprised?"
"Right. But it's not bad."
Yuki gave another example. "When Riku talks about soccer, I can't be that surprised."
"Ah, true."
"But with soccer-loving friends, you can get excited about the same play."
Aoi explained. "Higher mutual information makes communication more efficient."
"Efficient?"
"More gets across with fewer words. Because there's shared context."
Mira had been quietly listening but wrote in her notebook. "Shared surprise = connection"
"Shared surprise is connection."
Yuki nodded deeply. "So people who can be surprised by the same things are precious."
"Yes. You have high mutual information with them."
Riku said a bit sadly, "So I have low mutual information with you two?"
"No," Aoi denied. "Just different domains."
"For everyday topics, all three of us have high mutual information."
Yuki agreed. "School stuff, friends, we understand each other on those topics."
"Only information theory is special."
Riku felt relieved. "I see."
"But," Aoi continued. "Mutual information can be increased."
"Increased?"
"If we share knowledge, the overlap grows."
Yuki proposed. "If we teach Riku information theory, we can be surprised together."
"But no need to force learning something uninteresting," Aoi added.
"Better to find parts that naturally overlap."
Mira wrote. "Different overlaps with different people"
"Overlap differs per person."
"That's fine," Yuki understood.
"Don't need to share everything with everyone."
Riku laughed. "So I have friends I can share surprises with."
"Right. Like soccer teammates."
"Diversity is important," Aoi said.
"One person has multiple facets. Each facet connects with different people."
Yuki looked out the window. "But few people can share surprises about information theory."
"That's why it's precious."
Aoi said quietly, "Rarity creates value. Same principle as information content."
"Because it's rare, high information content when you meet."
Mira raised her hand. Unusual behavior.
"I understand your surprise"
Yuki was surprised. "Mira too!"
"Yes. Information theory is beautiful"
Aoi said happily, "Another friend to share surprises with."
"Expansion of mutual information."
Riku watched enviously but soon laughed. "Good for you."
"Riku might get interested someday," Yuki said hopefully.
"Then let's be surprised together."
Aoi looked at the three and Mira. "Each has different surprises."
"But sometimes parts overlap."
"That overlap is proof of friendship."
The four quietly nodded. Surprise is subjective. But having someone to share it with. That's a miracle.
"I want to cherish people who can share surprises," Yuki said.
"Yeah," Riku agreed.
"Let's nurture mutual information," Aoi smiled.
Mira wrote. "Together we discover surprises"
Together, discovering surprises. That's learning, growth, and connection.