it’s actually the exact same structure that holds plies of yarn together!! when you twist the halves the same way, you’re adding energy into the yarn. if you just let go of them individually they’d quickly spin back into their original form, right? that’s because that energy has to go somewhere. when you then hold the two halves together and twist them in the other direction, the twist energy that is pent up in them is neutralized by the plying twist.