"I don't know how to express this feeling."
Yuki was troubled.
"What kind of feeling?" Aoi asked.
"Happy yet sad, a complex emotion."
Riku laughed. "Can't that be compressed?"
"Compressed?"
Aoi opened the notebook. "There are two types of data compression. Lossless and lossy."
"Lossless?"
"Compression that can be fully restored. For example, zip format. No information is lost."
"Then lossy is?"
"When restored, some information is missing. For example, JPEG images. But compression ratio is high."
Yuki began to understand. "Is expressing feelings in words also like compression?"
"Sharp metaphor," Aoi nodded. "Converting complex internal states into limited words. Inevitably, something is lost."
"So feelings are lossy compression?"
"In many cases. But you can choose how much information to preserve."
Riku gave an example. "Saying 'It was fun' versus 'It was fun, but a bit lonely, yet fulfilling' have different compression ratios?"
"Yes. The former is high compression. Information decreases but transmission is easy. The latter is low compression. More information but also more redundancy."
Yuki took notes. "It's a tradeoff."
"Always. Balance between compression ratio and information preservation."
Aoi drew a diagram on the whiteboard.
"Shannon's source coding theorem. Messages can't be losslessly compressed below entropy H(X). That's the theoretical limit."
"But with lossy, you can compress more?"
"You can. But you must decide what to lose."
Riku asked, "So when expressing feelings, do we choose what to keep and what to discard?"
"Consciously or unconsciously, yes. Prioritize important information and omit minor details."
Yuki pondered. "But don't minor details sometimes actually matter?"
"They do. That's why choosing the right compression ratio is difficult."
Aoi gave another example. "MP3 music compression. Removes frequencies hard for human ears to hear. Most people don't notice the difference, but it's not perfectly the same."
"Maybe we also delete parts the other person won't notice," Yuki said.
"Yes. But those frequencies might be important to someone."
Riku asked with a serious expression, "Then to convey completely, should we talk about everything without compression?"
"Theoretically. But in reality, there are constraints on time and attention. Receiver's processing capacity is also limited."
"So we need to compress appropriately."
"Exactly. Adjust to the other person's context, knowledge, and expectations."
Yuki reviewed the notebook. "Should I also change compression ratio for my complex feelings depending on the person?"
"Yes. Low compression with detailed information for close friends. High compression with just the main points for first meetings."
"That depends on shared knowledge with the other person."
"Exactly. More shared knowledge allows more efficient compression. Context fills in the gaps."
Riku laughed. "Our conversations are pretty compressed."
"Abbreviations among friends, inside jokes. All compression techniques."
Yuki smiled. "Then I can talk about my complex feelings with low compression to you both."
"Of course. We share your context."
"But," Riku added, "remember it's not completely lossless."
"Right. No matter how detailed, 100 percent doesn't get through. That's the limit of language."
Yuki took a deep breath. "But maybe that's okay. If everything got through completely, there'd be no surprise."
"Philosophical," Aoi laughed.
Compression is loss. But loss is part of communication. Perhaps that imperfection is the reason to continue dialogue.