"Aoi-senpai, isn't your explanation too long?"
Riku said frankly. Aoi had just spent 30 minutes explaining entropy.
"True, I could be more concise. But I prioritized certainty of understanding."
"Certainty of understanding?" Yuki asked.
"In information theory, redundancy plays an important role. Even if it seems wasteful, it prevents errors."
Riku tilted his head. "But redundant means 'wasteful,' right?"
"Usually. But in communication, intentional redundancy protects information."
Aoi wrote an example on the whiteboard.
"The message 'Meeting at 3.' Minimal, but what if you don't hear '3'?"
"That's troublesome," Yuki answered.
"But if you say 'Meeting at 3 PM, starts at 15:00,' there are three pieces of information: 'afternoon,' '3,' '15:00.' Even if you miss one, you know."
"Redundant but safe," Riku understood.
"Exactly. Natural language is originally very redundant. That's why conversation flows smoothly."
Yuki thought. "So Aoi-senpai's long explanation is redundancy for understanding?"
"Right. Explain the same concept from multiple angles. If you can't understand one, another explanation compensates."
Riku laughed. "I didn't get the first explanation, but finally understood at the third example."
"That's the power of redundancy. Multiplexing information prevents misunderstanding."
Aoi continued. "In information theory, there's a tradeoff between compression and redundancy. Compression is efficient but vulnerable to errors. Adding redundancy is inefficient but becomes robust."
"With a perfect channel, compression alone is fine," Yuki said.
"Yes. But in reality, there's noise. So appropriate redundancy is necessary."
Riku suddenly thought of something. "Then to reliably convey 'I love you'?"
"Make it redundant?" Yuki laughed.
"For example, 'I like you. I love you. I love you.' Say it in three languages for certainty," Riku answered seriously.
Aoi was impressed. "Actually makes sense. Sending the same message through multiple channels reduces misunderstanding probability."
"But efficiency is poor, right?" Yuki pointed out.
"That's the difficulty of design. Consider the other's comprehension, channel quality, message importance. Choose optimal redundancy based on these."
Riku pondered. "More important messages, more redundancy?"
"There's that tendency. Airplane pilots repeat important instructions twice. Because they prioritize certainty."
Yuki understood. "So that's why you rephrase important concepts multiple times."
"Because I want to ensure your understanding. Takes time, but better than not progressing due to misunderstanding."
Riku laughed. "At first I thought it was long, but thank you."
"Redundancy might be an expression of affection," Aoi smiled. "The feeling of wishing it certainly gets through to the other person."
Yuki wrote in the notebook. "Balance of efficiency and certainty. Choose according to situation."
"Answer concisely on tests. But write redundantly in letters to important people," Riku summarized.
"Good contrast," Aoi nodded. "Information theory teaches when to be concise and when to be redundant."
Outside was a quiet evening. The three's conversation was moderately redundant and certainly understood each other. That felt comfortable.