Keilim, Chapter 19, Mishnah 3. The subject of this chapter is the bed together with its ropes, and the question of which components count as a single entity with the bed when it comes to the halachot of tumah. A bed in those days was built as a frame: two short boards, one at the head and one at the foot, joined by two long beams along the sides, the whole thing standing on four legs. Cords were then stretched across the frame in both directions, lengthwise and crosswise, forming the woven surface that held the bedding. It happened at times that one cord did not reach far enough to cover the entire surface, so another cord was fastened onto it to lengthen it.
Whenever two cords are joined, nobody ties the knot right at the extreme edges. On purpose, a small amount of cord is left sticking out on the far side of the knot, since otherwise the knot would work itself loose. Those bits that dangle out of the knot carry the name "nimin".
Which part of the strands belongs to the rope?
The case in our Mishnah is such a lengthened rope: two cords were fastened to one another, and the resulting rope was strung across the frame of the bed. The bed then became tamei, and now a person puts his hand on the ends dangling out of that knot. The Mishnah rules: "Nimei hakesher, hanogea betzorko, tamei." Regarding these dangling ends, if what he handles is the amount the knot actually requires, he contracts tumah.
Why so? Because however much cord the knot truly needs in order to hold is treated as belonging to the rope; strip that amount away and the knot would come undone, so it is not a separate thing at all. Consequently, once tumah reaches the bed, that measure of dangling cord is tamei together with it. Whatever hangs down past the ordinary and needed amount, though, is never absorbed into the rope. It stays tahor, and a person who handles it stays tahor as well.
"Vechamah hu tzorko?" So what amount does the knot actually require? To this the Mishnah brings an opinion: "Rebbi Yehudah omer, shalosh etzba'ot", three fingerbreadths. Cord dangling past that length serves no purpose for the knot, and it therefore remains tahor even when the bed itself has become tamei.