Mishnah 12 is the last in chapter 4 of Maseches Eduyos, even though it is not the end of the group of mishnayos dealing with cases in which Beis Hillel are the ones who rule stringently. The subject of this mishnah belongs to the world of Maseches Ohalos, so we will first present some of the fundamentals of that tractate.
What is an 'ohel' with regard to tumah:
An 'ohel' means literally a tent, but for our purposes (and somewhat simplified, since this is not the topic of the lesson) it refers to a covering through which the tumah of a corpse can travel. The principle is this: when a source of tumah - a corpse or a significant part of one - is under one roof together with something fit to receive tumah, whether a person, a utensil, or food and drink, the tumah passes from the source to all the recipients under that same roof.
Matters become complicated when we are dealing with a sealed room from which the corpse has no outlet; but in a relatively open space - an area with three walls, or even a projecting roof supported on pillars with no walls at all - the question of where the tumah will go is far simpler. In short: under a simple roof, everything beneath it receives the tumah.
Two ohalim adjacent to one another:
When we have two projecting ledges, two ohalim standing side by side, as long as there is no separation between them - meaning a horizontal separation - the tumah passes from one to the other. Viewed from a bird's eye view, straight down from above, the two ohalim will appear to be touching each other, and this is one continuous ohel.
This rule applies even when the vertical height of the two ohalim is not the same: one may be low, even a single handbreadth above the ground, and the other very high, a hundred handbreadths. Viewed from the side they will look completely different, but as long as they overlap on the horizontal plane, they are joined and the tumah spreads from one to the other. This is not self-evident, but such is the case.
A crack that divides the ohel:
An open area with a roof over it - everything is under one ohel. But if a crack runs through the middle of the roof from end to end, we now have two separate ohalim, and the tumah does not spread from one to the other. This is true even of an extremely thin crack: although there is a principle of 'lavud', according to which less than three handbreadths is considered joined, it does not apply to the transfer of tumah in an ohel - this is a separate law, a halachah leMoshe miSinai.
However, if there is beneath the crack (or above it) a small ohel that functions as a bridge, the tumah once again passes from side A to side B.
Let us picture the situation, which is not self-evident: once the crack breaks the middle of the roof, we have, viewed from above, two separate ohalim that are not connected, and the tumah does not pass from one side to the other. But a tiny ohel is enough to bridge between them - and the measure of an ohel is one handbreadth wide by one handbreadth long (the width of a palm), and one handbreadth high above the ground.
Let us assume, then, that inside the large structure a tiny ohel was placed, something like a dollhouse tent, standing exactly beneath the crack. Viewed from above, side A and side B appear separated by the crack, but that small ohel below bridges between them. Its tiny size makes no difference, and it likewise makes no difference that it is low and close to the ground.
It follows that if a corpse lies on side A and a person stands on side B, with a crack separating the two sides, but beneath the crack stands that tiny tent, a handbreadth wide, forming a bridge - the tumah will pass from the corpse to the person on side B.
The stack of towels versus the block of steel:
Picture a stack of folded towels: the bottom towel is folded so that it stands a handbreadth above the floor, and the second towel rests on top of it. The upper towel is a tent in every respect - it is raised a handbreadth off the floor and it measures a handbreadth by a handbreadth in width and length. If it sits directly beneath the crack, it bridges the gap and allows the tumah to pass from side A to side B.
And even though this 'towel tent' is full - after all, the towel beneath it fills its airspace - that makes no difference. The upper towel stands on its own as the surface of the tent, like a sheet spread over it. Therefore, in a stack of two towels or more, as long as the upper towel is raised a full handbreadth off the ground, measures a handbreadth by a handbreadth, and is situated directly beneath the crack - a halachic bridge is created that allows the tumah to pass from side A of the large tent to side B.
A large block of steel lying on the ground in that same structure, directly beneath the crack, by contrast, is not a tent at all. We do not say that the top layer of the block is like the sheet of a tent and that the rest of the steel underneath it is like airspace; it is one solid unit. And since there is no tent here, it does not function as a bridge.
The question of the Mishnah:
What is the law when, in place of a tiny tent, a stack of towels or a block of steel, a person is lying on the ground directly beneath the crack that divides the structure in two? Does the person's body itself function as a tent? Put differently: is its status like that of a stack of towels or like that of a block of steel?
The dispute between Beis Shammai and Beis Hillel:
Beis Hillel - and here they are the stringent ones: The tumah spreads, since a person's body is comparable to a stack of towels.
Beis Shammai: A person's body is comparable to a block of steel, and the tumah does not pass.
An explanation of the position of Beis Hillel: a person has a cavity in his abdomen and chest - that space in which the intestines are set, below the navel. When he lies on his back on the ground, this cavity is a handbreadth wide, a handbreadth long and a handbreadth high. True, the cavity is filled with intestines and the other internal organs, but spread over it is a layer of skin, the skin of the abdomen, and it is like the upper towel in the stack. Just as beneath the upper towel there are additional towels and that makes no difference, so too beneath the skin there are internal organs and that makes no difference. It emerges that a person's body is a cavity with skin over it, and therefore the upper layer of skin of one lying on his back functions as a tent, and his body serves as a bridge that transmits the tumah from side A - which is beneath the crack - to side B.
An explanation of the position of Beis Shammai: a person is entirely one unit, like a large block of steel. And even though his abdomen is raised a handbreadth or more above the ground - what of it? A block of steel too may be raised a handbreadth off the ground, and it is not a tent and not a bridge, but a solid object. So too a person: he is solid, and he does not serve as a bridge to transmit tumah from side A to side B.
The halachah follows Beis Hillel, that a person can serve as a bridge to transmit tumah, and chapter 11 of Maseches Ohalos expands on this subject.
The words of the Mishnah:
Picture a structure with a roofed open area, and in its roof a crack running down the middle lengthwise, dividing it into two halves, side A and side B; and lying perpendicular to the crack, directly beneath it, is a person. Without the introduction we gave, it is hard to grasp what the Mishnah is saying.
"Adam ha-nasun tachas ha-seddek" - a person lying beneath the crack in the ceiling.
"Beis Shammai omrim: eino meivi es ha-tumah" - a person is a single solid entity, like a block of steel, and there is no ohel here; therefore the presence of his body beneath the crack does not enable the tumah to pass from side A to side B.
"U-Beis Hillel omrim: adam chalul hu, ve-ha-tzad ha-elyon meivi es ha-tumah" - a person is hollow inside and resembles a stack of towels: his uppermost layer, namely the skin, is like the sheet of an ohel, and beneath it is a large cavity filled with internal organs. And since that uppermost layer, the skin over the stomach, is raised a full tefach above the ground, it brings the tumah, allowing it to bridge the crack and pass from side A to side B.