Keilim, Chapter 20, Mishnah 7. Our Mishnah turns to the reed mat, the machatzelet, and it opens with a distinction that runs through the whole discussion: what was this mat made for? People would spread such a mat out and sleep on it, and people would also use such a mat as a covering overhead, for instance as roofing over a sukkah. A mat designated for lying on serves a person, and it is therefore subject to tumat midras. A mat designated for roofing serves no person's body, it is simply a covering, and it cannot become tamei at all. The Mishnah now examines several ways in which a mat could be constructed, and asks in each case whether it is the sort of mat people lie down on.
How the mat was built
Picture a rectangular mat woven out of reeds that are soft and pliable, laced one to another. A weave made only of soft reeds would collapse and hold no shape, so tougher, rigid reeds were worked in to give it firmness. Those rigid reeds, however, are painful to lie upon. The craftsman's solution was to insert them crosswise at intervals, leaving open bands between them in which a person could stretch out and rest.
Hard reeds set along the length
The Mishnah begins: "Machatzelet she'asah lah kanim le'orkah, tehorah." Suppose the rigid reeds were installed lengthwise, rather than crosswise as is customary. Such a mat is tahor. A person who lies down does so across the mat's shorter dimension, and reeds running the long way leave him no free band in which to settle. Their placement rules out comfortable reclining, so we conclude that this mat was produced to serve as a covering overhead and not as bedding, and a covering has no ability to contract tum'ah.
The Chachamim take a different position, holding that the mat escapes tum'ah only "ad sheya'aseh kemin chi": only once the rigid reeds have been laid out in the shape of a chi, that is, like the letter U. So long as they run in one direction alone, the mat remains capable of becoming tamei, for a person can still lie the long way, resting in an open band between two of the rigid reeds. Only a U formation obstructs him in both directions at the same time, and only then is it evident that lying down was never the purpose for which the mat was made.
Hard reeds set along the width
"Asah lah lerochbah, ve'ein bein kaneh lechavero arba'ah tefachim, tehorah." Here the rigid reeds were fixed crosswise, in the usual manner, but the open bands they leave measure less than four tefachim. This mat too is tahor: so narrow a strip cannot accommodate a reclining person. The measurements themselves reveal that the mat was intended as a covering rather than as a place to sleep, and it therefore lies outside the reach of tum'ah.
When the mat is damaged
These mats needed protection against unraveling, and the ends of the weave were secured with knots, the ma'adanim. The Mishnah now considers cases in which the mat is damaged in a way that leaves the knots unable to do their work.
"Nechleka lerochbah, Rabbi Yehuda metaher." Should a tear run crosswise through the mat, Rabbi Yehuda holds the result tahor. The fresh edges created by the split carry no knots at all, so the weaving there is destined to loosen and fall apart. Something on its way to disintegration is no longer a functioning utensil, and it stands beyond the reach of tum'ah.
"Vechen hamatir shel ma'adanim, tehorah." A mat whose knots have been loosened by hand is judged in precisely the same way and turns tahor, since its weave is now bound to come undone and it has ceased to be a keli that tum'ah can touch.
"Nechleka le'orkah, venishtayeru bah shelosha ma'adanim shel shishah tefachim, temei'ah." Here the tear runs the long way, straight down the middle, and each of the two resulting pieces is left with three knots at its ends, a width of six tefachim. Such pieces are temei'ah. Because the knots remain in place, the weave will hold and nothing will come apart; and because each piece measures six tefachim across, it is broad enough for a person to lie on. Both halves accordingly continue to be subject to tumat midras.
When is the mat finished?
Since no utensil is susceptible to tum'ah before its production has been finished, the Mishnah closes by identifying the stage at which a mat in the making becomes a finished keli. "Machatzelet me'eimatai mekabelet tum'ah? Mishetikanev, vehi gemar melachtah." When does a mat begin to receive tum'ah? Once its reeds have been trimmed. With the jutting ends shorn off, the surface lies flat and a person can rest on it in comfort, without sharp tips digging into him. That trimming is what marks the work as done. Should the craftsman still plan further touches, painting it or adding some ornamentation, this makes no difference: the mat already serves its purpose and counts as complete, and from that moment on tum'ah can take hold of it.