Mira didn't come to the club room.
"That's unusual," Yuki said.
"Yeah," Aoi checked the clock. "She'd normally be here by now."
They waited a bit. But Mira didn't appear.
"Did she contact you?"
"No. That itself becomes information."
"Information? Not coming?"
Aoi opened the notebook. "In information theory, what doesn't happen also carries information."
"What do you mean?"
"When an expected event doesn't occur, the absence itself creates surprise. In other words, it has information content."
Yuki pondered. "But nothing happened?"
"Information content is determined by the difference from expectation. The higher the prior probability that Mira always comes, the greater the information content of not coming."
Aoi wrote an equation on the whiteboard.
"I(event) = -log₂ P(event). If P(Mira comes) = 0.95, then the information content of not coming is about 4.3 bits."
"Not coming has more information content than coming?"
"Yes. Rarer events have greater information content."
Yuki suddenly thought of something. "Then silence also carries information?"
"Exactly. When silence occurs in conversation, it's not just empty space. It conveys something."
"For example?"
"Not answering a question. That itself is information saying 'I don't want to answer.'"
Yuki nodded. "Like the dog that didn't bark."
"Sherlock Holmes. Sharp metaphor. The watchdog not barking was evidence that the intruder was an acquaintance."
They fell silent again.
"What about this silence?" Yuki laughed.
"Thinking time. Processing time. This is also part of information."
Then the door opened. Mira entered. A little later than usual, looking a bit flustered.
"Mira!" Yuki was relieved.
Mira nodded slightly and showed a note. "Sorry. Train delay."
"Train delay," Aoi understood. "That was unpredictable."
Mira wrote another note. "You worried?"
"A little," Yuki admitted.
"That's information," Aoi explained. "From observing that you didn't come, we inferred something happened."
Mira smiled and wrote a new note. "Absence = information"
"Absence is information. Accurate."
Yuki asked, "Then if something unexpected doesn't happen, is that also information?"
"The information content is small. But not zero. As long as probability isn't zero, any event carries information."
Mira added, "Bayesian update"
"Right. With each observation, we update prior probability. What happened and what didn't happen are all material for updates."
Yuki wrote in the notebook. "Silence, absence, delay. Everything is information."
"Communication isn't just words. Timing, pauses, absence. Everything has meaning."
Mira sat down quietly. And began observing, as usual.
Yuki whispered, "I feel like Mira's silence has high information content too."
"Her silence is intentional. Higher information density than random silence."
"Why?"
"There's a pattern. She only speaks at important moments. That selectivity concentrates information."
Mira left a note. "Silence is not empty. Silence is full."
Silence is not empty. Silence is full.
Yuki read it and understood deeply. Information exists not only in sound, but also in stillness. Also in absence. In the difference between expectation and observation, information is born.