My wife and I had to untangle a large skein of wool. The strands had intertwingled every which way, and it was a long task. As we worked (she did a lot more o the dirty job than I, I confess), I thought about how Alexander's solution would not work here; cut through the skein and it would be worthless.
It gradually became evident that we were working in very different ways. We each rolled up the wool from our end as we freed more material. But my wife would methodically uncross one strand at a time, over, under or through. Meanwhile I would stare at the tangle for awhile and pick up a thread I thought was the continuation of my end. A tug would reveal if I was right, and when I was, I passed my ball through perhaps twenty strands at once to reach where the continuation was. My method did not seem to be faster; it was just the way I liked to work on the tangle, and I wondered why.
A few days later I was trying to figure out which computer an internet cable was attached to. We had about eight computers in a refrigerator-size rack, each with two internet cables, and similar cables passing right through as well. Many of them hid behind a CRT. I picked up each possible canidate and gave a tug to see if I was holding this very cable in both hands. And then I had my "aha" moment. Of course, this is how I'm used to untangling threads.