Also a slightly more physical reason: The length of a pendulum is what controls its frequency. The weight doesn’t matter, only its length. That means that when your arms are long, they swing slower, thereby fitting a lower frequency of steps. When you run (or go tippy tappy with your feet) you’ll naturally raise your arms to match the higher frequency of your steps.
Why do you need to match your arms to your steps? Because moving takes your whole body and we’ve spent thousands of years perfecting it.
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