"Oh no, I made another mistake!"
Riku shouted while looking at his experiment notebook.
"How many times now?" Yuki smiled wryly.
"I've lost count. But I feel like I keep failing at the same places."
Aoi approached. "That's an interesting observation."
"Interesting? It's just mistakes, isn't it?"
"No," Aoi looked at the notebook. "Mistakes with patterns contain information."
Yuki asked. "What do you mean?"
"If mistakes were completely random, you couldn't predict or counter them. But if there's a pattern, it shows the structure of the noise."
Aoi drew a diagram on the whiteboard.
"In communication, noise has types. White noise is completely random. But burst errors occur in continuous ranges."
"Burst errors?" Riku asked.
"Yes. For example, a scratch on a disk corrupting multiple consecutive bits. This type of noise has dedicated countermeasures."
Yuki took out her notebook. "Are Riku's mistakes that kind of pattern?"
"Let's see," Aoi began analyzing Riku's notebook.
"Most mistakes happen in the final stages of calculations."
"I lose concentration," Riku made excuses.
"So it's time-dependent noise. SNR degradation from fatigue."
"SNR?" Yuki asked.
"Signal-to-Noise Ratio. The ratio of signal strength to noise strength."
Aoi continued explaining.
"In Riku's case, SNR decreases over time. Knowing this, we can take countermeasures."
"Countermeasures?" Riku showed interest.
"For example, do important calculations first. Or take regular breaks to recover SNR."
Yuki gave another example. "I'm bad at math in the morning."
"Time-of-day dependent noise. Circadian rhythm influence."
Aoi drew another diagram.
"In information theory, modeling noise is important. Understanding noise properties enables more efficient communication."
"Human mistakes can be modeled too?" Yuki was surprised.
"Exactly. In machine learning, we learn human error patterns to make predictions and corrections."
Riku suddenly realized. "Smartphone predictive text too?"
"Yes. It learns your typo patterns and offers correction candidates."
"My mistakes were becoming data."
Aoi continued. "What's more interesting are systems that learn from errors. Mistakes are information sources for improvement."
Yuki wrote in her notebook. "Failure is the mother of success—that's information-theoretically correct too."
"You could say that. Error correction codes are also designed with the premise that 'mistakes will happen.'"
Riku's face became serious. "So I should record my error patterns?"
"Good idea. Error logs are treasure troves for system improvement."
Yuki asked. "But what about unpredictable mistakes?"
"That's true noise. Can't handle it, so prepare with redundancy."
Aoi laughed. "That's why review time is important in exams. A kind of redundancy."
Riku started writing something in his notebook. "I'll try making my mistake list."
"That will be good data," Aoi acknowledged.
Yuki was impressed. "Rather than blaming mistakes, analyze them."
"From an information theory perspective, everything is data. Observing without emotion reveals invisible patterns."
Outside the window, rain was getting heavier. A noisy world. But within it, there are patterns.
"Full of mistakes, but that's learning too," Riku murmured.
Aoi nodded. "Perfect systems don't exist. What matters is how you deal with errors."