Mira smiled. Just that changed the atmosphere in the club room.
"That just now seemed really meaningful."
Yuki said with wonder.
"Just a smile?"
Aoi observed with interest. "Mira's smile has high information content."
"Information content? In a smile?"
"Yes. Facial expressions are the epitome of nonverbal communication. And information density changes with context."
Yuki opened her notebook. "Information density?"
"Information content per unit. When you can convey much with little expression, information density is high."
"How is Mira's smile high information content?"
Aoi explained. "Mira usually hardly changes expression."
"True."
"So when she smiles, it's an extremely low-probability event."
Yuki began to understand. "Low probability means high information content?"
"Correct. I(x) = -log₂ P(x). The lower the probability, the greater the information content."
Mira quietly showed her notebook.
"Context amplifies meaning"
"Context amplifies meaning," Aoi translated. "The same smile has different meanings depending on the situation."
"What do you mean?"
"For example, a smile from someone who always smiles has low information content. It's predictable."
"But when a usually expressionless person smiles, you think 'something happened.'"
"Right. That surprise itself is information."
Yuki thought. "So words are the same?"
"Same. A word from a usually quiet person carries weight."
"High information density."
Aoi continued. "Conversely, talking too much decreases the value per word."
"Riku?" Yuki laughed.
"Well, as an example. But that's also a strategy."
"Strategy?"
"Mix important things into lots of talk. Overall noise level is high, so the other lets their guard down."
"Steganography," Mira wrote.
"Concealment technique," Aoi explained. "Technology to hide information in seemingly meaningless data."
"I don't think Riku-senpai thinks that sophisticatedly."
The three laughed.
"But," Aoi became serious. "Adjusting information density is an important communication skill."
"How do you adjust it?"
"First, be conscious of your transmission frequency. Constantly transmitting lowers individual value."
"Use silence strategically too."
"Right. A word after silence carries weight."
Yuki remembered. "Professor's occasional words really stick with me."
"He's a master of information density. Talks only the bare minimum."
Mira nodded.
"Same with writing," Aoi continued. "Packing much meaning into short sentences. Like haiku."
"The extreme of compression."
"Yes. In some cultures, brevity is a virtue. Because they value high information density."
Yuki summarized. "Conveying much with little expression. This is the technique to increase information density."
"Perfect. But there's a prerequisite."
"Prerequisite?"
"Shared context. Without context, compressed information can't be understood."
Mira wrote an example. "'That'"
"'That' alone sometimes gets through, sometimes doesn't," Yuki said.
"Right. With shared knowledge, one word suffices. Without it, lengthy explanation is needed."
"Information density and context are a set."
Aoi summarized. "Mira's smile has high information content because there's context of her personality."
"And the timing of that smile was exquisite."
Yuki understood. "Expression frequency, context, timing. Everything affects information content."
"Correct."
Mira smiled again. This time, she felt she understood the meaning a bit.
"Information-rich smile," Yuki wrote in her notebook. "Wonderful concept."
"Information theory teaches us beauty without waste."
The three quietly nodded. Packing much into little expression. That was refined communication.