For me, I stop thinking about the thing bothering me, or I work it out in a way that I wouldn’t have, had I not been moving.
Also, if you set a goal, like “do 100 push ups today” you not only have the health benefits of doing the push ups, you feel good about yourself. You kept your word, so are a good person. And you set a goal and achieved it, so you’re successful.
To add on others: IMO we are programmed like animals:
Problem->action.
Our society does not provide an instant action for everything. Sometime we are “problem->hold->hold more” and you get easily to points where you have 10-100 unsolved, on hold problems. Doing something physical does give a false sense of action, that relieves the stress of being on hold.
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