The answer is a bit of physics and a bit of psychology.
From a physics/math perspective, there’s a lot of ways for a rope, string, etc. to be tangled and few ways for it to be untangled. So given some agitation (effectively, letting the rope move around arbitrarily), the rope will more often end up in a tangled state than an untangled one. Making matters worse, there’s typically only one *path* back from a tangled state, and many paths that lead to more tangled states. So once the rope has wound up tangled, it’s very unlikely to untangle itself from arbitrary movement.
From a psychological perspective, there’s also the matter of where you’re directing your attention. If you sit there shaking your headphone cords for a minute, they might tangle or they might not, but it feels like you spent a while trying because you were focused on it. When you put your neatly coiled headphones in your pocket and go about your day for the next 6 hours, you’re not thinking about how you’re giving your headphones 6 hours to tangle up. You just notice they’re tangled 6 hours later when you pull them out. It’s similar to confirmation bias. If you sat there tossing your headphones around for 6 hours, they’d surely tangle at some point. But it would feel like a lot more effort than just sticking them in your pocket and coming back later.
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