"Senpai, is it possible to convey feelings perfectly?"
Yuki asked Aoi.
After thinking a bit, Aoi answered. "Do you know Shannon's channel capacity theorem?"
"I've heard of it."
"C = max I(X;Y). The maximum mutual information a channel can carry."
Riku entered the club room. "Difficult discussion?"
"About channel capacity," Yuki explained.
"What's that?"
Aoi drew a diagram on the whiteboard. Sender, channel, receiver.
"Channels always have noise."
"Noise?"
"Yes. Physical noise, cognitive distortion, language limitations."
"So perfect transmission is impossible," Yuki understood.
"But," Aoi continued, "we can send information error-free up to channel capacity."
"C = B log₂(1 + S/N). Shannon-Hartley theorem."
"B is bandwidth, S is signal, N is noise."
Riku asked. "Human conversation also has capacity?"
"Yes," Aoi asserted. "Number of words, time constraints, attention limits."
Just then, Professor S appeared at the club room.
"Interesting discussion."
"Professor," Aoi greeted.
"Channel capacity. Classic but deep topic."
The professor wrote an equation on the blackboard.
"As long as there's noise, capacity is finite. But with clever encoding, we can approach that limit."
"Encoding?" Yuki asked.
"Converting information into a form suitable for the channel."
"For example, error-correcting codes. Adding redundancy makes it resistant to noise."
Riku understood. "Like saying the same thing repeatedly?"
"In principle, yes," the professor admitted. "But there are cleverer methods."
"Turbo codes, LDPC codes," Aoi enumerated.
"Those nearly reach the Shannon limit."
"Shannon limit?"
"Channel capacity. The theoretical upper bound."
Yuki asked seriously. "So in human relationships, encoding is also necessary?"
The professor smiled. "Good question."
"Choosing words, devising expressions. That's encoding."
"But," Yuki said, "no matter how much we devise, sometimes it doesn't get through."
"Maybe because you're trying to exceed capacity," Aoi pointed out.
"Exceed capacity?"
"Too much information trying to transmit at once."
The professor supplemented. "Take time, convey bit by bit. That's realistic."
Riku looked out the window. "So even love confessions are communication theory?"
"In a sense," Aoi laughed. "Sending high-entropy information through limited channels."
"Success rate?"
"Depends on channel state. Too much noise, it fails."
Yuki said softly. "Hearts also have noise."
"Anxiety, doubt, past experiences," the professor enumerated. "They distort reception."
"Then what should we do..."
"Reduce noise or increase redundancy."
"Specifically?"
"Build trust, speak clearly, check the other's state."
Aoi summarized. "Channel capacity is finite. But optimization is possible."
The professor said finally. "Shannon showed perfect communication is impossible."
"But simultaneously showed methods to approach the limit."
"So there's hope," Yuki said.
"Yes. Not giving up, but communicating cleverly."
Riku stood up. "Then I'll try encoding too."
"What?"
"Properly putting feelings into words."
Aoi smiled. "Good encoding."
Before leaving the club room, the professor said. "Communication is also art. Theory and practice, both are important."
The three nodded.
Words have limits. But within those limits, we can convey to the maximum.
Today too, they opened a new channel.