"Riku's messages are always full of typos."
Yuki said with a wry smile.
"Sorry!" Riku protested. "But the meaning gets through, right?"
Aoi opened their notebook. "Actually, that's the core of information theory."
"What?" Both asked simultaneously.
"You can communicate even with noise. One of Shannon's most important discoveries."
Yuki showed interest. "Noise is like Riku's typos?"
"Precisely. The transmitted message differs from the received message. That's noise."
Riku pondered. "But to transmit perfectly, we need zero noise."
"That's wrong," Aoi shook their head. "Even with noise, you can transmit information accurately with proper encoding."
"How?" Yuki asked.
Aoi drew a diagram on the whiteboard.
"Add redundancy. Send the same information multiple times. Use error correction codes."
"That's why when I type 'oaky' instead of 'okay,' it still gets through," Riku understood.
"Yes. The human brain is an excellent error correction device. It can infer correct meaning from context."
Yuki wrote in the notebook. "But if there's too much noise?"
"It exceeds channel capacity. In that case, perfect communication becomes impossible."
"Channel capacity?"
"The maximum amount of information that can be reliably sent through a noisy channel. Also called the Shannon limit."
Riku's face became serious. "So if I make too many typos, meaning won't get through?"
"Theoretically yes. But in your case, the noise level is still within acceptable range," Aoi laughed.
Yuki suddenly realized. "It's the same with human relationships, right?"
"What do you mean?" Riku asked.
"No one is perfect. Everyone has noise. But we can still understand each other."
Aoi nodded. "Good insight. Redundancy, context, shared knowledge. All help with error correction."
"That's why we can say 'I like you even if you're not perfect,'" Riku said quietly.
"Exactly. Information theory is also a science of accepting imperfection."
Yuki looked outside the window. It was raining. Water droplets on the glass distorted the view. But you could still tell what was there.
"Even with noise, the essence gets through."
"Yes. That's the beauty of communication," Aoi answered.
Riku took out his smartphone. "Then from today, I won't worry about typos."
"No, that won't do," Aoi immediately stopped him. "Effort to reduce noise is also important. To not exceed channel capacity."
"Harsh!"
"But you don't need to aim for perfection. There's an appropriate balance."
Yuki laughed. "That's such a senpai answer."
"Information theory is the science of balance."
The three quietly left the classroom. The sound of rain outside reminded them of a noisy channel. But even in it, conversation continues.
Even with noise, what gets through gets through. That was what they learned today.