"How about naming the club room 'Gentle Information Theory Salon'?"
Riku suddenly proposed.
"Why?" Yuki asked.
"Sounds stylish."
Aoi smiled wryly. "Well, not bad. We actually are exchanging information."
"Information exchange?"
"All conversation is a communication channel. Using sound waves as medium, transmitting information."
Yuki showed interest. "Do channels have limits?"
"They do. That's channel capacity. One of the most important concepts Shannon formalized."
Aoi wrote an equation on the whiteboard.
"C = B log₂(1 + S/N)"
"C is channel capacity. B is bandwidth. S/N is signal-to-noise ratio."
Riku looked confused. "I don't understand any of it."
"I'll explain one by one. First, bandwidth. This is how much frequency range the channel can use."
"Frequency?"
"Pitch of sound, wavelength of radio waves. Communication needs frequency bands. The wider, the more information can be sent."
Mira drew a diagram. Narrow road and wide road.
"A road metaphor," Aoi explained. "A wider road allows more cars. Bandwidth is the same."
Yuki understood. "So what about signal-to-noise ratio?"
"The ratio of signal strength to noise strength. Higher means information can be transmitted more accurately."
"Noise distorts information?"
"Yes. But noise can never be completely zero. So we think about how to send maximum information within noise."
Riku shared his experience. "When there's a lot of noise on the phone, I can't hear."
"That's low S/N ratio. Signal buried in noise."
"Then should we just speak louder?" Yuki suggested.
"That's strengthening the signal. Certainly effective, but there are limits."
Aoi pointed to the equation. "Shannon's discovery is that even with constant S/N ratio, smart encoding can approach channel capacity."
"Smart encoding?"
"Error correction codes, adaptive modulation. Basically, optimally representing information according to channel characteristics."
Mira showed a new note. "Shannon limit - theoretical maximum"
"Yes. Shannon's limit is the theoretical maximum. Cannot be exceeded."
Riku asked. "So what's this club room's channel capacity?"
Aoi laughed. "Interesting question. Voice bandwidth is roughly 300 to 3000 hertz. S/N ratio depends on room quietness."
"It's quiet now, so high?" Yuki said.
"Yes. But if Riku makes noise, noise increases and capacity drops."
"I'm a noise source?" Riku protested.
"Sometimes," Aoi admitted. "But that's also part of information."
Yuki pondered. "Is the internet also limited by channel capacity?"
"Of course. Fiber optic capacity, wireless bandwidth, all follow Shannon's limit."
"Is 5G, 6G increasing capacity?"
"Exactly. Expanding frequency bands, using multiple antennas, various innovations to increase capacity."
Mira drew a new diagram. Multiple parallel channels.
"MIMO technology," Aoi explained. "Multiple inputs, multiple outputs. Effectively increases bandwidth."
Riku looked at his smartphone. "This is also using its limit."
"Theoretically. But codes that completely reach Shannon's limit haven't been found yet."
"So there's still room for improvement?" Yuki held hope.
"There is. Turbo codes and LDPC codes are very close to the limit. But not perfect."
"Does perfect exist?" Riku asked philosophically.
"Mathematically, yes. But implementation is another matter," Aoi answered.
Mira said quietly. "Theory and practice - always gap"
"Yes. There's always a gap between theory and practice. But bridging that gap is engineering's job."
Yuki laughed. "This 'Gentle Information Theory Salon' is also a place for theory and practice."
"Exactly," Aoi nodded. "We're exchanging maximum information in the communication channel of limited time and space."
Riku said. "Should we converse more efficiently then?"
"No," Aoi smiled. "Redundancy is also important. Chat, silence, laughter. They also enrich the channel."
The four enjoyed their time in the salon today, feeling the invisible flow of information.