Mira was organizing photos in the club room.
"Mira, what are you doing?" Yuki asked.
Mira answered quietly. "Selecting important memories"
"Selecting important memories," Aoi translated.
"Because I can't save everything."
Yuki became interested. "Rate-distortion theory?"
Aoi looked surprised. "You know well."
"I saw it in a textbook recently."
Aoi opened the notebook. "R(D) = min I(X;X̂). Minimum information rate under distortion D."
"Distortion?"
"Difference from original information. Error when perfect reconstruction isn't possible."
Mira showed a photo. High-resolution landscape photo.
"Original: 10 megabytes"
Then showed the compressed version.
"Compressed: 1 megabyte"
"Looks almost the same," Yuki said.
"JPEG compression," Aoi explained. "Removes details humans don't notice."
"That's distortion."
"Yes. But if within acceptable range, no problem."
Aoi drew a diagram. Rate-distortion tradeoff curve.
"Lower the rate, distortion increases."
"Conversely, to reduce distortion, must increase rate."
Yuki thought. "Perfect compression is impossible?"
"Entropy is the lower bound. Go below that and information is lost."
Mira said quietly. "Life is also lossy compression"
"Life too?" Yuki asked.
"Can't remember all experiences," Aoi continued. "Brain only remembers important parts."
"That's learning."
"Yes. The brain is rate-distortion optimizing."
Yuki asked seriously. "So what should we keep?"
"That's difficult," Aoi admitted. "Depends on subjective importance."
Mira wrote in her notebook.
"Preserve what gives most meaning with least bits"
"Preserve maximum meaning with minimum bits," Yuki read.
"Beautiful principle," Aoi said.
"But what holds meaning varies by person."
Yuki recalled her own experience. "Last summer, the day I first talked with senpai."
"That's an important memory?"
"Yes. Even forgetting details, I remember the emotion."
Aoi smiled. "Emotions are information preserved even at high compression rates."
"Why?"
"Emotions summarize vast details into one label."
"Joy, sadness, surprise."
"Each is compressed representation of complex neural activity patterns."
Mira nodded. "Emotions are lossy compression of experience"
"Lossy compression of experience," Yuki repeated.
Aoi continued. "So cherishing emotions is rational even from information theory perspective."
"Emotions become memory indices."
"Yes. Function as search keys."
Yuki summarized in her notebook. "Rate-distortion theory is about what to discard and what to keep."
"Applicable to life too," Aoi said.
"Chasing everything leads to breakdown."
"Focus on important parts, let go of others."
Mira selected the final photos. Just ten.
"Ten photos, countless memories"
"Ten photos, countless memories," Yuki translated.
"That's enough," Aoi said. "Meaningful summary over perfect record."
"Distortion is unavoidable."
"But essence can remain."
Yuki looked out the window. Sunset illuminated the club room.
"This moment too will someday be compressed into memory."
"Yes. But important parts will remain."
Mira smiled. "We are all rate-distortion optimizers"
"We are all rate-distortion optimizers."
Aoi nodded. "Preserve maximum meaning with limited capacity."
"That might be what living means."
The three sat quietly. Today's memory too would eventually be compressed.
But this emotion would remain. That was enough.