"I'm surprised!"
Yuki rushed into the classroom.
"About what?" Aoi asked.
"I found a rare book in the library."
Mira said quietly. "Surprise... information."
"Yes. Surprise and information are the same," Aoi nodded.
Yuki asked curiously. "What do you mean?"
"Information amount can be measured by the magnitude of surprise. Shannon's definition."
Aoi wrote an equation on the whiteboard.
"I(x) = -log₂ P(x)"
"Lower probability events have higher information."
Yuki understood. "Because it's rare, I was surprised."
"Exactly. We're not surprised by the obvious. Information amount is also low."
Mira joined in. "But... why we want surprise?"
"Good question," Aoi thought. "Surprise is evidence of gaining new information. A moment of learning."
Yuki wrote in the notebook. "But too much surprise is scary."
"That's right. Moderate surprise is pleasant."
Aoi drew a diagram.
"Too predictable → Boring → Low entropy Moderately unpredictable → Interesting → Medium entropy Completely unpredictable → Confusion → High entropy"
"Balance is important," Yuki said.
"Yes. Music too—completely regular is boring. Completely random is unpleasant."
Mira said quietly. "Shared surprise... special."
"Shared surprise?" Yuki asked.
"When two people are surprised simultaneously. That's evidence of high mutual information."
Aoi explained. "To be surprised by the same thing requires having the same expectations."
"Because expectations are similar, surprise can be shared."
Yuki understood. "That's why sharing surprises with friends makes us happy."
"Exactly. The essence of empathy is information sharing."
Mira pondered. "I... different background. Surprise different."
"That's cultural difference," Aoi acknowledged. "What surprises us depends on prior knowledge."
Yuki asked. "Then to share surprises?"
"Create common context. Understand each other's backgrounds."
Aoi wrote another equation.
"H(X|Y) = H(X) - I(X;Y)"
"Uncertainty of X after knowing Y. What remains after subtracting mutual information."
"The more shared knowledge, the less remaining uncertainty."
Yuki looked outside. "If we understand each other completely, won't there be no surprises?"
"Theoretically yes. But the world constantly changes."
"New experiences, new knowledge. They generate new surprises."
Mira smiled. "So, we can always have new surprises."
"Yes. As long as we keep learning, surprises never end."
Riku entered the club room. "What's the topic?"
"The relationship between surprise and information," Yuki answered.
"Were you surprised by my entrance?"
"Low entropy, so not surprised," Aoi answered immediately.
"Cold!"
Yuki laughed. "But sometimes you do unpredictable things, so we're surprised."
"Is that a compliment?"
"You're a high-information person," Aoi acknowledged.
Mira said quietly. "I want... share more surprises with you all."
"To increase shared surprises, we should experience new things together," Yuki proposed.
"Good idea," Aoi nodded. "Common experiences generate common surprises."
Riku got excited. "Then let's all do something new!"
"Like information theory experiments?"
"I want something more fun."
Yuki closed the notebook. "Let's go look for shared surprises."
"Exploring surprises. That itself is information gathering," Aoi smiled.
The four quietly left the classroom. In search of shared surprises.
New information is always there.