Chullin, Chapter 9, Mishnah 4. This chapter is devoted to the laws of yad and shomer, the handle and the protective covering of a food, and how they function in the transmission of tumah. Our mishnah applies those principles to the hide of a neveila that still carries meat on it, and then presents a dispute between Rabbi Yishmael and Rabbi Akiva about pieces of meat that are each smaller than the required measure.
The mishnah begins: "Or sheyesh alav kezayit basar", a hide that has been removed from a neveila but still has a kezayit of flesh clinging to it. In such a case, "hanogea besiv hayotzei mimenu", one who touches a thin strand of that meat that protrudes outward, and also "uveseara shekenegdo", one who touches a hair on the hide directly opposite the meat, "tamei", becomes tamei.
Why should touching a protruding thread of flesh, or a hair growing on the other side of the hide, convey the tumah of neveila? Because neither one is treated as something separate from the meat itself. The strand of flesh sticking out serves as the yad, the handle by which the kezayit is held and moved. The hair opposite the meat serves as the shomer, the covering that guards and protects it. A yad and a shomer both have the power to carry tumah from the food outward, so a person who touches them is exactly as if he had touched the kezayit of neveila directly.
Two half-kezayit pieces on the hide
Now the mishnah changes the case: "hayu alav kishnei chatza'ei zeitim", the hide had upon it two separate pieces of meat, each one half the size of a kezayit. Rabbi Yishmael rules "metamei bemasa velo bemaga", such a hide conveys tumah through carrying but not through touching.
The logic is in the nature of each act. When a person lifts and carries the hide, one single act of carrying takes up the full kezayit of neveila flesh. It makes no difference that the meat happens to be divided into two portions; the carrying embraces all of it at once, and so the tumah passes. Touching is different. The two pieces lie apart from one another, so he would need two fingers, or even two hands, to reach both of them. That counts as two distinct acts of contact, and each act touches only half a kezayit, a quantity too small to transmit tumah. Therefore, according to Rabbi Yishmael, there is tumah through masa but not through maga.
Rabbi Akiva takes the opposite position: "Rabbi Akiva omer", and his verdict is "lo bemaga", not by touching, "velo bemasa", and not by carrying either. As he sees it, every fragment is evaluated on its own, and on its own it falls short of a kezayit, so it is batel and amounts to nothing, exactly like the hide beneath it, which transmits no neveila tumah whatsoever. The two fragments never fuse into one entity, and once that is so, lifting them together achieves nothing either, since Rabbi Akiva demands that the portions be attached to each other before their measures may be combined.
Rabbi Akiva's own concession
The mishnah now sets a limit to that ruling: "umodeh Rabbi Akiva", Rabbi Akiva himself grants a different result elsewhere. Take "bishnei chatza'ei zeitim", two portions of neveila flesh, each one only half a kezayit, resting on no hide at all, but "shetechavan bekeisam", run through and skewered together on a sliver of wood, "vehisitan", and someone then shifted them from their place. Here his ruling is "shehu tamei": whoever moved them contracts tumah, because what he set in motion adds up to a complete kezayit of neveila flesh.
The splinter joins them. Even though the two pieces of meat are not in direct contact with each other, the wood forms a bridge between them, and that bridge makes them a single unit amounting to a full kezayit.
Why the hide is different
That admission immediately invites a challenge, and the mishnah puts it into words: "umipnei mah", for what reason does "Rabbi Akiva metaher ba'or", ruling that two halves resting on a hide leave a person tahor? Surely the hide ought to do precisely what the wooden sliver did, binding the two portions into one kezayit and making whoever touches or moves them tamei.
The mishnah answers: "mipnei sheha'or mevatlan", because the hide nullifies them. This is the heart of Rabbi Akiva's distinction. A splinter of wood is nothing more than a connector; it has no standing of its own, so the two pieces of meat remain the significant thing and are simply joined. A hide, however, is itself a substantial object, and the scraps of flesh clinging to it are not its main component. When something small becomes part of a larger and more important entity, it is nullified to it. The two half-kezayit portions are therefore not united by the hide but absorbed into it, each one remaining an isolated piece of less than a kezayit, and no tumah is transmitted at all.