tl;dr: Most screens (sRGB and Display-P3) can't reproduce huge swaths of the visible color space, particularly intense cyans, because the gamut is constrained by the phosphors and primaries chosen decades ago. The author shows where to find these "impossible" colors in real life: light filtered through forest canopies, shallow tropical water, iridescent bird feathers and butterfly wings, bioluminescent dinoflagellates, UV-lit scorpions, and—most accessibly—the LED "green" traffic light, which is actually a vivid turquoise outside any screen's gamut.