"Have you ever written a letter?"
Yuki was surprised by Mira's unusual question. The normally taciturn Mira had initiated conversation.
"Not much recently... mostly emails."
"Letters and emails, just different channels, but the essence is the same," Aoi added explanation.
Mira drew a diagram in her notebook. A simple communication model.
"Sender → Encoding → Channel → Decoding → Receiver"
"Shannon's communication model," Aoi nodded. "The foundation of information theory."
Yuki stared at the diagram. "Between sender and receiver, there's a channel..."
"Right. The channel is the path information flows through. Could be physical cable, or radio waves. Sound waves through air are also a channel."
Mira added. "Channel has noise. Message may change."
"Channels have noise. So the sent message and received message can differ."
Yuki suddenly thought. "Human conversation is the same, right?"
"Exactly. When you put it in words, that's encoding. When the other person hears and understands, that's decoding. In between, misunderstanding as noise enters."
Mira nodded quietly.
"But," Yuki continued. "Mira-san is taciturn, but things get through."
Mira showed a slightly surprised expression.
Aoi smiled. "That's mutual information. I(X;Y). The amount of information shared between sender X and receiver Y."
"Shared information?"
"Of the information the sender has, the part that actually reaches the receiver. With perfect communication, all information gets through. But with noise, only part reaches."
Mira drew a new diagram. Two overlapping circles. A Venn diagram.
"One circle is sender's information, the other is receiver's information. The overlapping part is mutual information."
"What about the non-overlapping parts?" Yuki asked.
"Information the sender has but didn't convey. Or information the receiver independently inferred."
Yuki understood. "So even with few words, if mutual information is high, it conveys well..."
Mira smiled quietly. A rare expression.
Aoi continued. "Communication efficiency is determined by channel capacity and transmission rate. But in human conversation, speaking fast isn't simply better."
"Encode appropriately at a speed the other can understand," Yuki said.
"Right. Communication doesn't work with just sender or just receiver. It functions only when both and the channel combine."
Mira showed a note. "Communication is mutual. Not one-way."
"Bidirectional?"
"Strictly speaking, feedback is also part of communication. To confirm the receiver understood, send a response. That also goes through the channel."
Yuki thought. "Mira-san nodding is also feedback."
Mira nodded. That itself was feedback.
"On the other end of the channel, there's always someone. Being conscious of that person is the first step to good communication," Aoi said.
Yuki drew a diagram in the notebook. Herself as sender, the other person as receiver. Channel between them.
"The channel has noise, but with proper encoding, mutual information can be maximized."
"And receive feedback from the other person to adjust encoding."
Mira handed Yuki a small paper.
"Thank you for understanding."
Simple English, but it had high mutual information.
Yuki smiled. "Likewise. I'm learning a lot from you too, Mira-san."
On the other end of the channel, there's always someone. Choose the best encoding for that person. That was the essence of communication.