"It's sunny today."
No one responded to Riku's words.
"So?" Aoi said coldly.
"No, just..."
Yuki laughed. "That's zero information."
"Zero information?" Riku asked.
"Stating what's obvious doesn't convey new information," Aoi explained. "I(X) = -log₂(p). When p is close to 1, information content approaches zero."
"Everyone already knows it's sunny," Yuki added. "So saying it doesn't transmit information."
Riku deflated. "Failed at starting a conversation."
"But," Aoi said a bit more gently, "zero information doesn't mean meaningless."
"What do you mean?"
"It functions as a social signal. A meta-message of 'I'm initiating conversation.'"
Yuki understood. "Weather talk is a conversation starter."
"Yes. Not information transmission, but relationship building."
Riku thought. "So what's a zero-information conversation?"
Aoi made a list. "'Good morning,' 'Good work,' 'Nice weather.'"
"All known things."
"But socially important. Maintaining communication channels."
Yuki gave another example. "'How are you?' also has low information content."
"Usually answered with 'I'm fine,'" Aoi acknowledged. "But if answered 'I'm not fine?'"
"Information content surges," Riku noticed.
"Yes. Deviation from expectation creates information."
The club room became quiet.
"But," Riku said, "when zero-information conversation continues, it's awkward."
"Why?" Aoi asked.
"Just confirming what we both know. No progress."
Yuki nodded. "Without new information, conversation stagnates."
Aoi pondered. "That's a mutual information problem."
"Mutual information?"
"I(X;Y). New information gained by knowing the other. Only talking about known things makes it zero."
Riku understood. "That's why it's awkward. Not learning anything new from each other."
"Conversely," Aoi said, "high mutual information conversations are stimulating."
"Unpredictable things, surprising things."
"Yes. Surprise enriches conversation."
Yuki asked. "But predictable relationships aren't bad either, right?"
"Of course. It's a tradeoff."
Aoi explained. "In long relationships, mutual information decreases. But that's proof of understanding."
"Stability and freshness," Riku said.
"Both needed. Completely predictable is boring. Completely unpredictable is anxious."
Yuki laughed. "Moderate zero information and moderate surprise."
"Perfect balance."
Riku looked out the window. "Let me try again."
"What?"
"It's sunny today."
Aoi and Yuki laughed.
"Zero information, but," Aoi acknowledged, "not awkward."
"Why?" Riku asked.
"Because there's context. After meta-conversation, the same words change meaning."
Yuki added. "Message of 'I'm saying this aware it's zero information.'"
"Higher-order information," Aoi smiled.
Riku was satisfied. "Even zero-information awkwardness depends on usage."
"Yes. Communication isn't simple information transmission."
"Relationships, context, timing, all intertwined."
Yuki said quietly. "That's why human communication can't be captured by formulas alone."
"But," Aoi said, "formulas help understanding."
"Not perfect models, but useful tools."
The three laughed together. Sunny again today. A zero-information fact. But they were even enjoying that awkwardness.