"It's quiet today."
Yuki said while opening the club room window.
"Even the state of being 'quiet' contains information," Aoi spread out their notebook.
"Information? When there's nothing?" Riku asked curiously.
"It's the opposite. The certainty of 'nothing' creates zero information content."
Yuki showed interest. "What do you mean?"
"Information content measures uncertainty. If the result is completely predictable, being told about it brings no surprise."
Aoi wrote an example on the whiteboard.
"The message 'Tomorrow, the sun will rise from the east.' How many bits?"
"Zero?" Yuki answered.
"Correct. Since probability is nearly 1, self-information is -log₂(1) = 0"
Riku pondered. "So 'Riku will be late tomorrow too' is also zero information?"
Yuki and Aoi laughed.
"If the probability is high, that might be true," Aoi admitted.
"But wait," Riku countered. "If I declare 'I definitely won't be late tomorrow,' does that become information?"
"Interesting question," Aoi's eyes lit up. "That's a matter of prior and posterior probability."
"Prior probability?" Yuki asked.
"The probability before hearing the declaration. Say Riku's lateness probability was 90 percent."
"Too high!" Riku protested.
"After hearing the declaration, if lateness probability drops to, say, 50 percent, that declaration carries information."
Yuki wrote calculations in their notebook. "Information content corresponds to changes in probability."
"Yes. When probability changes through Bayesian updating, that's evidence information was conveyed."
Riku suddenly realized. "So completely predictable people have zero information content?"
"In a sense, yes. If there's no surprise in their actions, you can't gain new information."
Yuki pondered. "But predictability also brings peace of mind, right?"
"That's what's interesting," Aoi said. "Information theory and psychology don't always align."
Aoi gave another example.
"A couple married for years might perfectly predict each other's behavior. Mutual information is low, but that doesn't degrade the relationship quality."
"Rather, it's stable," Yuki said.
"Yes. High information content isn't always better."
Riku looked out the window. "Peaceful days like today also have zero information, but aren't bad."
"The value of peace can't be measured by information content," Aoi said quietly.
Yuki closed their notebook. "Information theory doesn't explain everything."
"Of course. A tool is a tool. What's important is knowing when to use it and when not to."
Riku stood up. "Then tomorrow, I'll try being 'unpredictable Riku.'"
"High-entropy behavior?" Yuki laughed.
"That's interesting too, but," Aoi said, "moderate predictability and moderate surprise. That balance might be what makes us human."
Outside the window, the same view as always. A dusk with zero information content. But the three were enjoying that tranquility.
"Even with zero information, there's value," Yuki murmured.
"That's today's lesson," Aoi smiled.