"Sorry, I didn't catch the last part."
Yuki told Riku.
"Huh? I said 'tomorrow's meeting time is 10 o'clock.'"
"I didn't hear '10 o'clock.' There was noise."
Aoi approached. "This is an error correction problem."
"Error correction?"
"Communication always has noise. Perfect channels don't exist. So we add redundancy to information."
Riku asked, "Isn't redundancy wasteful?"
"Far from wasteful, it's essential," Aoi explained. "There's a mechanism called parity bits."
Yuki opened her notebook. "I've heard of it. But not in detail..."
Aoi wrote on the whiteboard.
"Data: 1011 Parity bit: 1 Transmission: 10111"
"The parity bit is an additional bit to make the number of 1s even or odd. If the bit count doesn't match at reception, errors can be detected."
"Errors can be detected, but corrected?"
"Simple parity can't correct. But advanced methods like Hamming codes can correct errors."
Riku became interested. "How?"
"By strategically placing multiple parity bits. Identify error locations and automatically fix them."
Yuki thought. "Do conversations have such mechanisms too?"
"Yes," Aoi nodded. "In the earlier example, if Riku had said 'tomorrow's meeting time is 10 o'clock, 10 AM'?"
"Even if I didn't hear '10 o'clock,' I'd understand from '10 AM.'"
"That's human error correction. Repeating important information or reinforcing with different phrasing."
Riku laughed. "I often repeat the same thing—is that error correction?"
"Yes. Redundant but reasonable."
Yuki thought of another example. "Does context also serve as error correction?"
"Sharp observation," Aoi was impressed. "Context is a powerful error correction code."
"What do you mean?"
"For example, 'tomorrow is □day.' Even if you don't hear □, you can infer it if you know what day today is."
"Shared knowledge is the key to error correction?"
"Exactly. The higher the mutual information, the more can be restored with fewer bits."
Riku wrote in his notebook. "So that's why close people communicate with few words?"
"Because they share a common context as an error correction code."
Yuki smiled. "Kindness is also a kind of error correction."
"What do you mean?"
"Even when someone's words are incomplete, trying to understand their intent. That's an act of correcting errors for them."
Aoi nodded deeply. "Wonderful insight. Human error correction is more flexible than algorithms."
Riku asked, "But isn't over-correcting a problem?"
"It is. Excessive correction can distort the original message."
Yuki gave an example. "Like when someone says 'a bit tired' but you interpret it as 'it must have been really hard.'"
"Exactly. Error correction should respect the original signal while filling gaps. Balance is important."
Aoi drew a new diagram.
"Turbo codes and LDPC codes have performance close to Shannon's limit. But they have high computational cost."
"Is there cost in human relationships too?"
"Yes. Inferring someone's intent requires attention and understanding. That's cognitive cost."
Riku laughed. "So that's why misunderstandings increase when tired?"
"Yes. When processing capacity drops, error correction accuracy also drops."
Yuki asked, "So how can we have good communication?"
"Both sender and receiver need effort," Aoi answered.
"The sender provides clear, redundant messages. The receiver carefully corrects errors."
Riku understood. "Mutual cooperation is important."
"Exactly. Communication isn't one-way. It's a bidirectional collaborative process."
Yuki closed her notebook. "From today, I'll listen more carefully."
"That's good. But," Aoi added, "you don't need to seek perfection. Noise is inevitable. What matters is a relationship where you can fill each other's gaps."
"Like error correction codes?"
"Yes. Kindness that fills information gaps. That's the essence of good communication."
The three listened carefully to each other's words in the sunset club room.
Perfect communication doesn't exist, but relationships where you fill each other's gaps can be built.
That was the wisdom about human relationships that information theory taught them.