"I wonder what Mira's thinking lately."
Yuki murmured. In the club room, just Yuki and Aoi.
"About Mira?"
"Yeah. I feel like we're getting closer, but I'm not certain."
Aoi answered quietly. "Uncertainty. Want to measure it?"
"How?"
"Conditional entropy. When inferring Mira's feelings Y from your observations X, remaining uncertainty is H(Y|X)."
Yuki opened her notebook. "So the part I can't figure out even after observing?"
"Yes. H(Y|X) = H(Y) - I(X;Y). Original uncertainty minus mutual information leaves remainder."
"Larger mutual information, deeper understanding."
"Precisely. But H(Y|X) rarely becomes zero."
"Can never completely understand?"
"Especially in human relationships. Others' minds are always partially uncertain."
Yuki pondered. "But that seems lonely somehow."
"Conversely, it's also possibility," Aoi continued. "Completely predictable relationships have zero entropy. Might be boring."
"Appropriate uncertainty makes relationships interesting?"
"Yes. Because there's surprise, hearts flutter."
At that moment, Mira entered the club room. Quietly as always.
"Mira!" Yuki greeted with a smile.
Mira waved slightly. Then took out her notebook and wrote.
"Uncertainty is not absence of connection"
"Uncertainty is not absence of connection..." Aoi read aloud.
Yuki was surprised. "Mira, were you listening?"
Mira shook her head. But smiled.
"Not coincidence, right?" Yuki said.
"Mira has high mutual information with us," Aoi explained. "From Yuki's expression, she can infer what you're thinking."
Mira nodded. Then wrote again.
"H(Yuki|Mira) is small. But H(Mira|Yuki) is...?"
"Even when I observe Mira, uncertainty remains..." Yuki understood.
"An asymmetric relationship," Aoi said. "Mira excels as an observer. But expresses herself little."
"So we find Mira hard to understand."
Mira wrote on a new page.
"I want to reduce H(Mira|You). Slowly."
"Slowly, I want to reduce uncertainty about myself..." Yuki read.
"Maybe Mira's way of building relationships," Aoi said quietly.
Yuki teared up. "Mira, thank you."
Mira looked away bashfully.
"Disclosing information bit by bit. That's also a communication strategy," Aoi supplemented.
"Rather than conveying everything at once, taking time."
"Yes. Adjusting rate. At Mira's pace."
Yuki wrote in her notebook. "Uncertain, but still connected."
"Like a quantum state," Aoi laughed. "Superposition before observation."
"But once observed, it becomes definite?"
"Human relationships are more flexible. Partially observe while leaving the rest uncertain."
Mira wrote last.
"Entropy decreases with time. Trust grows."
"With time, entropy decreases. Trust grows..."
The three smiled quietly.
"No need to rush," Yuki said.
"Relationships are information accumulation. Slowly and surely."
Mira nodded. Outside the window, the sunset slowly set.
Even while uncertain, connection exists. Information transmits over time. That's the human channel.