"This chat app has a strict character limit."
Yuki showed the smartphone.
"280 characters?" Aoi confirmed.
"Yes. I want to convey something important, but it doesn't fit."
Mira approached and wrote in her notebook. "Channel capacity"
"Channel capacity," Aoi began explaining. "The maximum amount of information a channel can convey per unit time."
"Is character limit also a type of capacity?"
"Yes. A physical constraint. But in information theory, there's a deeper concept."
Aoi wrote an equation on the whiteboard.
"C = B log₂(1 + S/N). Shannon's channel capacity theorem."
"B, S, N?"
"B is bandwidth. S is signal power. N is noise power. This equation determines the theoretical limit."
Yuki took notes. "More noise means less capacity?"
"Yes. The greater the noise, the less information can be conveyed."
Mira wrote an additional note. "Real communication = noisy channel"
"Real communication is all noisy channels," Aoi nodded. "Perfect channels don't exist."
Yuki pondered. "Then for this chat, what's the noise?"
"Character limit, misunderstanding, lack of context, typos. Everything is noise."
"But we can pack information to the limit, right?"
"Theoretically. But that requires optimal encoding."
Aoi gave an example. "English has average entropy of about 1 bit/character. So 280 characters can carry about 280 bits of information."
"But actually it's less?"
"Because of redundancy. But that redundancy helps error correction."
Mira drew a new diagram. A graph showing tradeoff relationships.
"Increasing compression ratio decreases error tolerance," Aoi explained. "And vice versa."
Yuki suddenly thought of something. "Then to convey important things, what should we do?"
"Use multiple channels. Split the message. Add redundancy."
"For example?"
"Convey the main points in chat, supplement verbally later. Or repeat important parts."
Mira showed a note. "Multiple channels = higher reliability"
"Yes. Humans naturally do this. Words, expressions, gestures. All are parallel channels."
Yuki wrote in the notebook. "What happens to information exceeding channel capacity?"
"It's lost. Or sent over time in multiple parts."
"So trying to convey everything immediately is impossible?"
"There are physical limits. But reaching Shannon's limit allows near perfection."
"Shannon's limit?"
"The theoretical limit of communicating at speeds near channel capacity with almost no errors. Achievable with perfect codes."
Yuki was impressed. "So choosing perfect words lets us convey to the limit?"
"Theoretically. But finding perfect codes is difficult."
Mira smiled and left a note. "Perfect communication is impossible. But we can approach it."
Perfect communication is impossible. But we can approach it.
Yuki looked at the smartphone. The constraint of 280 characters. But what to pack into it is up to her.
"With ingenuity, we can convey even with limited capacity."
"Yes. That's the teaching of information theory," Aoi said.
Yuki began carefully choosing words. Every character is precious channel capacity. To surely reach someone beyond the data.
Mira said quietly, "Every bit counts."
Every bit counts. Yuki nodded deeply.