The evening sun streamed into the club room.
"Information is made of particles."
Yuki murmured while looking at the monitor.
"Particles?" Riku asked back.
"Digital images. When you zoom in, you see little squares called pixels."
Aoi supplemented. "The minimum unit of information. Bits."
"Bits?"
"Binary digit. Binary values of 0 or 1. The foundation of digital information."
Riku thought. "Why just 0 and 1?"
"Because it's easy to implement in electronic circuits. Voltage high or low, magnetic direction, light on or off."
"Physical two-states express information."
Yuki asked. "But the world is more complex, right? Colors, sounds..."
"We discretize it. Quantization."
Aoi drew on the whiteboard. A smooth curve became stair-stepped.
"Converting analog signals to digital signals."
"Rounding continuous values to discrete values."
Riku gave an example. "Like a thermometer displaying 20, 21, 22 degrees?"
"Right. It might really be 20.5 degrees, but rounds to 21."
"Sacrificing precision to make it manageable."
Yuki worried. "Isn't information lost?"
"It is. But if you divide finely enough, humans can't distinguish."
"CD sound quality. Sampling frequency 44.1kHz, 16-bit quantization."
Riku was surprised. "Measuring 44,100 times per second?"
"Right. By the Nyquist theorem, it covers the human audible range."
Aoi continued. "With 16 bits, you divide sound intensity into 2^16 = 65,536 levels."
"With that many, it sounds smooth."
Yuki wrote in her notes. "More bits means higher precision?"
"Correct. Called bit depth."
"16-bit images have finer color gradations than 8-bit images."
Riku laughed. "Then why not infinite bits?"
"Storage and computation costs become enormous."
"So we compromise at moderate precision."
Aoi presented a new perspective. "Bits are also units of information content."
"1 bit = information answering one binary choice."
Yuki thought. "Like the 20 Questions game?"
"Exactly. 'Is it an animal?' 'Yes/No.' You gain 1 bit of information."
"Asking 20 times lets you identify from 2^20 = about 1 million possibilities."
Riku was impressed. "Bits are amazing."
"The foundation of the digital revolution."
Aoi continued. "Entropy units are also bits. H(X) = -Σ p(x) log₂ p(x)."
"Using log₂ makes the unit bits."
Yuki understood. "Information content and bits are connected."
"Shannon designed it that way."
Mira entered the club room. Silently wrote on the whiteboard.
"Qubit - quantum bit."
"Quantum computers?" Riku showed interest.
"Classical bits are 0 or 1. Quantum bits are superpositions of 0 and 1."
Aoi explained. "Until observed, they hold both states."
"Sounds strange."
"It's the quantum mechanics world."
Yuki asked. "What's different with quantum bits?"
"Parallel computation is possible. With n qubits, 2^n calculations simultaneously."
"Exponentially faster than classical computers for some problems."
Riku imagined. "Future computers will all be quantum bits?"
"Many technical challenges remain. But the potential is large."
Aoi summarized. "Bits are particles of information. Atoms making the digital world."
"And their combinations create infinite possibilities."
Yuki looked out the window. The evening sun shone like particles.
"Light is also particles. Photons."
"Right. The world is made of particles."
Riku laughed. "Information, light, particles. All connected."
"In quantum information theory, they merge."
Mira wrote finally. "Information is physical."
"Information and physics can't be separated."
Aoi nodded. "That's why information theory is beautiful."
In the after-school club room, particles of information quietly shone.