"Nothing is absolutely correct."
Professor S said while brewing coffee at Cafe Shannon's counter.
Yuki and Aoi had visited the shop as usual.
"But mathematics is absolute, right?" Yuki asked.
"Within an axiomatic system. But applying to reality always involves uncertainty."
Aoi supplemented, "That's probability theory's role. Speaking in probabilities, not assertions."
Professor S nodded. "In communication theory too, soft decisions outperform hard decisions."
"Soft decisions?"
"Looking at received signals and deciding 'this is definitely 0' is hard decision. 'Probability of 0 is 0.9' while retaining probability is soft decision."
Yuki thought. "Retaining probability has more information?"
"Yes. Later processing can utilize that probability information. Makes a big difference in error correction code decoding."
Aoi wrote in the notebook. "Turbo codes and LDPC codes assume soft decision decoding. That's why they're high-performance."
Professor S served the coffee. "Human relationships are the same."
"Human relationships?" Yuki was surprised.
"Rather than deciding 'that person is definitely bad,' thinking 'high probability of bad behavior' is more flexible."
Aoi continued, "Bayesian thinking. You can update beliefs with new information."
"Yes. Hard decisions can't be updated. Once decided, it's over. But soft decisions allow constant revision."
Yuki looked out the window. "But doesn't that become indecisive?"
"Good question," Professor S smiled. "Probabilistic reasoning differs from indecisiveness. Making the most rational judgment from available information."
Aoi gave an example. "Weather forecasts say '60 percent precipitation probability.' Not asserting, but providing information."
"And given that probability, you decide whether to bring an umbrella."
"Decision theory," Professor S said. "Combining probability and utility function to choose optimal action."
Yuki wrote in the notebook. "Speaking through probability is also humility."
"Yes. Acknowledging limits of your knowledge. That's scientific attitude."
Aoi asked, "Professor, did studying information theory change your life philosophy?"
Professor S thought briefly. "It changed. I use fewer assertive expressions."
"You speak through probability?"
"Yes. Not 'this is correct' but 'high probability this is correct.' Small difference, but big difference."
Yuki said, "That's a gentle way of speaking."
"You feel that way?"
"Yes. It leaves room for the other person to think."
Professor S nodded. "Information theory quantifies uncertainty. But it doesn't try to eliminate uncertainty. Rather, it acknowledges and coexists with it."
Aoi supplemented, "Entropy is the amount of uncertainty. If it can't be zero, we must get along well with it."
"Life is the same," Professor S said quietly. "Perfect certainty is an illusion. But probabilistically correct choices are possible."
Yuki took a sip of warm coffee. "Speaking through probability becomes gentle. I think I understand the meaning."
"Good understanding," Professor S acknowledged.
Aoi said, "Soft decisions retain information. Similarly, probabilistic phrasing retains possibilities."
"Retaining possibilities," Yuki repeated. "Beautiful expression."
Professor S looked around the shop. "Customers here vary too. Students learning information theory, resting office workers, reading elderly. Everyone living uncertain futures."
"But probability of drinking coffee is 100 percent," Aoi laughed.
"Such small certainties support life," Professor S smiled.
Yuki closed the notebook. Today again, she gained a new perspective.
Speaking through probability is humility, gentleness, and scientific attitude.
Peaceful time flowed in Cafe Shannon.