"Did you hear that? Just now?"
Riku shouted while opening the club room door. It was raining heavily outside.
"I didn't hear anything," Yuki answered.
"Right! The rain is too loud."
Aoi closed the window. "That's noise in communication. Unwanted sound or disturbance that interferes with the signal."
"Rain is noise too?" Yuki was surprised.
"Acoustically, yes. In information theory, noise is any factor that hinders transmission."
Riku pondered. "But we can still talk in noisy places, right?"
"Yes. That's because the human brain has excellent noise reduction functions. Plus, thanks to natural language redundancy."
Aoi drew a diagram on the whiteboard.
"S/N ratio, or signal-to-noise ratio. The ratio of signal strength to noise strength."
"If the signal is strong, it doesn't lose to noise?"
"Basically, yes. But you can't strengthen the signal infinitely. There are power and cost constraints."
Riku raised his hand. "Then what do we do when noise increases?"
"Good question. Shannon proved an amazing theorem. Even with noise, below a certain rate, you can communicate without error."
"Really?" Yuki looked incredulous.
"Shannon's channel capacity theorem. C = B log₂(1 + S/N). B is bandwidth, S/N is signal-to-noise ratio."
Riku attempted the calculation. "The larger S/N, the larger capacity C..."
"And if you send information at a rate below capacity, with proper encoding you can make the error rate arbitrarily close to zero."
Yuki thought. "But if noise increases, capacity decreases, right?"
"Yes. log(1 + S/N) decreases as N increases. So in noisy environments, you need to send slowly."
Riku suddenly burst out laughing.
"What is it?" Aoi asked curiously.
"Earlier, my voice couldn't be heard over the rain, but thinking about it now, it's funny! When noise increases, you have to reduce transmission rate. So I should've spoken louder and slower!"
Yuki laughed too. "True. Riku, you always talk fast."
"In noisy environments, speak slowly and clearly. It's a principle we understand instinctively," Aoi smiled.
"Hey, but," Riku continued. "Noise isn't all bad, right?"
"What do you mean?"
"Because noise makes things interesting. We laugh at mishearings, unexpected things happen."
Aoi pondered. "Philosophical, but you have a point. Perfect communication is efficient, but might lack interest."
Yuki nodded. "Maybe human relationships deepen because of slight misunderstandings and noise."
"That's an insight beyond information theory," Aoi acknowledged. "But certainly, moderate noise can have the effect of making systems robust."
"Robust?"
"Adding redundancy to handle noise. That makes it stronger against unexpected failures too."
Riku looked outside the window. Rain was still falling.
"So this rain isn't bad?"
"From a communication perspective it's an obstacle, but it's necessary for plants and nature. Depending on viewpoint, noise or signal changes."
Yuki was impressed. "How you view one phenomenon."
The rain sound outside became a bit quieter. The three listened to it silently.
"S/N ratio improved," Aoi said.
"But rather than complete silence, having a bit of noise is calming," Riku laughed.
"More noise, more laughter," Yuki murmured like a title.
The three's laughter mixed with the rain sound. That too was a beautiful signal.