Keilim, Chapter 27, Mishnah 4. Throughout this chapter we have been learning that the four materials, cloth (beged), sack (sak), leather (or) and mat (mapatz), each have their own minimum size before a scrap of them can become tamei. Our mishnah now presents the case in which all four are treated alike, with one single measurement.
The mishnah opens: "Hamkatze'a mikulam tefach al tefach, tamei", one who trims a piece from any of these materials to the size of a tefach by a tefach, it is tamei. Such a small square is able to receive tum'at midras, the tumah of something sat or leaned upon, because a piece of that size is useful for patching the saddle of a donkey, upon which a person sits.
Here lies the important distinction. The various larger measurements listed in the earlier mishnayot, each material with its own size, speak of material that its owner uses for sitting or reclining but that he never physically altered for that purpose. Where no change was made to the object itself, the material must be large enough on its own terms. But once the owner did make a physical change, he trimmed it, shaped it, fashioned it into something designated for this use, then the halachah shifts, and this is the exception taught here: even a piece measuring only one tefach by one tefach can become tamei.
An application follows. The mishnah speaks of "Mishulei hakupah", the lower portion of a basket: if its owner cuts away from there a square of "tefach al tefach", that piece is "tamei", open to tum'at midras. The reason is straightforward: the floor of a basket is level, so a square taken from it yields a flat surface on which a person can rest his weight.
A machloket follows: "Misidadei hakupah, Rebbi Shimon metaher". Where the square of a tefach was cut away from the walls of the basket rather than from its floor, Rebbi Shimon rules the piece tahor. Basket walls bend outward, and a rounded surface does not serve a person who wishes to settle himself upon it. True, this owner did perform an act of trimming, and in his own mind the scrap was destined for sitting. Even so, the principle of batlah da'ato etzel kol adam governs the case: when the judgment of one man stands against the judgment of humanity at large, his own is nullified. Since people in general would find no chair in a bent fragment of this sort, his private plan confers no such status upon it.
"Vachachamim omrim: hamkatze'a tefach al tefach", and the Chachamim rule otherwise. Wherever the square was taken from, "mikol makom", the curved walls included, the piece is "tamei" and subject to tum'at midras. Their logic is that a bent fragment has not lost its serviceability: a person in need of a place to sit could still manage on it.
So this mishnah teaches us the one measurement shared by cloth, sack, leather and mat alike, a tefach by a tefach, and it teaches us why: because a deliberate act of trimming and shaping transforms even the smallest scrap into something a person can sit upon.