"Lately, conversations feel empty."
Yuki said at Café Shannon.
"What kind of conversations?" Professor S asked.
"Somehow, even when talking, nothing gets through."
Aoi became interested. "Might be conversations with low mutual information."
"Mutual information?"
"How much information two variables share," Aoi explained. "For conversation, how much information was exchanged between speaker and listener."
Professor S added. "Formally, I(X;Y) = H(X) - H(X|Y)"
"That's difficult..."
"Simply put," Aoi simplified. "How much your uncertainty decreased by hearing the other's statement."
Yuki began to understand. "If I learned nothing, mutual information is zero?"
"Yes. Being told things you already know or unrelated things gives no information gain."
"That's why it feels empty."
"Probably," Aoi nodded.
Professor S asked. "What kind of conversation do you think has high mutual information?"
Yuki thought. "Conversations where both learn something new."
"Good answer," the professor acknowledged. "But that's not all."
"What else?"
"Knowing the other's state changes your behavior," Aoi supplemented. "This is also mutual information."
"For example?"
"If you learn a friend is sad, you encourage them. This behavior change is evidence of receiving information."
Yuki nodded deeply. "Information influences action."
"Exactly," Professor S smiled. "The essence of information is resolving uncertainty and changing behavior."
Aoi continued. "So high mutual information conversations change each other."
"Change?"
"Thinking, feeling, behavior. Something changes."
Yuki said quietly. "Conversely, conversations that change nothing."
"Have mutual information close to zero."
"But," Professor S said carefully. "Change isn't everything."
"What do you mean?"
"There are confirming conversations. Re-confirming what you already know."
Aoi gave an example. "'Are you well today?' 'Yes, I'm well.' Low information content but important."
"Why?"
"Maintaining relationships. Even if mutual information is zero, there's social meaning."
Yuki understood. "There are things information theory alone can't measure."
"Right," the professor nodded. "But being conscious of it is important."
"Conscious?"
"Whether your conversation has mutual information," Aoi explained. "Whether you're conveying something to the other, receiving something from them."
Yuki pondered. "Am I conveying properly?"
"This conversation has high mutual information," Professor S said.
"Why?"
"Yuki had questions, we answered. Our mutual understanding deepened."
Aoi added. "And Yuki's future conversations might change."
"I want to change," Yuki said seriously. "I want to have more conversations with mutual information."
"Good goal," the professor smiled.
Aoi said quietly. "Conversations with mutual information. They emerge from an attitude of respecting and trying to understand each other."
"Not technique?"
"Technique is important. But mindset is more important."
Yuki nodded. "Being interested in the other."
"Yes. What they think, what they feel. Trying to know that."
Professor S concluded. "Mutual information can be measured. But the essence is beyond measurement."
The rain stopped outside. Yuki took today's conversation to heart. Conversations with mutual information. They are conversations that exchange hearts.