Every file on your phone — a photo, a song, a video — is just a long string of numbers. The question of data storage is really a question of how many numbers you need, and whether you can get away with fewer. Compression is the art of finding shortcuts in that string: patterns you can describe in fewer numbers than it takes to write them out in full. The two ideas that make it possible are redundancy and entropy — and once you see them, you'll notice them everywhere.

Redundancy is repetition. Think about a video of someone sitting at a desk talking. The background — the wall, the bookshelf, the lamp — doesn't move. Frame after frame, those pixels are identical. A naive video file would write out every single pixel for every single frame: 30 frames per second, 2 million pixels per frame, 7,200 seconds of movie. That's the 100-gigabyte number. A smarter file says: here's frame one in full. For frame two, I'll only describe what changed. If 95% of the frame is a static background, you only need to store the 5% that moved. The rest is just 'same as before.'

Entropy, in information theory, is a measure of surprise. A signal where the next value is totally unpredictable has high entropy — there are no shortcuts, no patterns, nothing to summarize. A signal where the next value is almost always the same as the last has low entropy — you can describe it in very few numbers. The desk video has low entropy (boring background, predictable pixels). The snowstorm has high entropy (chaotic, unpredictable). Compression works by finding and eliminating low-entropy regions. High-entropy content — a snowstorm, a jazz improvisation, a static-filled radio signal — resists compression almost completely. That's not a bug in the algorithm. It's a mathematical ceiling: Claude Shannon (1916–2001, United States), the mathematician who invented information theory, proved in 1948 that you cannot compress a signal below its entropy. You can approach the limit, but you can't beat it.

Modern video compression — the format your streaming app uses — layers multiple tricks on top of this principle. It throws away information your eyes won't notice anyway: fine color detail in dark regions, high-frequency textures in your peripheral vision, subtle differences between nearly identical shades. This is lossy compression, meaning the file you play back isn't a perfect reconstruction of the original — it's a reconstruction good enough that you can't tell the difference. The 2-gigabyte movie on your phone is the result of a codec (a compression algorithm) making thousands of these judgment calls per second, betting that your visual system won't catch what it left out. Most of the time, it wins that bet. The 98 gigabytes didn't disappear — they were judged unnecessary and discarded. Your brain fills in the rest.