Ohalos, Chapter 13, Mishnah 3. This chapter measures openings: how large a gap in a wall, a roof or a door must be before tumah is able to travel through it from one side to the other. And the guiding principle of the chapter is that the required size depends on why the opening is there.
Two measurements were established at the start of this chapter. When a homeowner cut an opening on purpose, in order to bring daylight indoors, very little is needed: "melo makdeiach gadol," the bore of the large drill that was in use in the Beis Hamikdash. An opening that a person wants and appreciates is a genuine opening even when it is minute. Where the gap formed by itself, however, worn through by water, chewed by sheratzim, or eaten away by salt, nobody had any interest in it, and it attains the status of an opening only at "melo egrof," a large fist's fill. Whose fist serves as the standard? The Chachamim point to Ben Avatiach, whose fist, they report, matched the size of an ordinary person's head.
A gap the carpenter had no choice about
Our Mishnah turns to a case that lies between these two categories: "hachor shebadelas," the gap that runs through the body of a door. Imagine the carpenter at his bench. He lays out his boards, and then comes the disappointing discovery: the lumber falls short. He is not fitting a slot for letters, and he is not installing a peephole. A gap was never part of his plan at all. He looked over the wood in front of him and saw that this door was going to end up with an empty space across its center.
According to Rebbi Akiva, a gap of this sort belongs with the second group. The man who produced it took no pleasure in it and had no other option, so the halachah treats it precisely like an opening that formed by itself, and its measure is "shiuro melo egrof," a large fist's fill. That is Rebbi Akiva's reasoning: whatever a person did not wish for is classified together with whatever came about without any human hand.
Rebbi Tarfon disagrees. He rules "bifseach tefach," the opening becomes significant at a square tefach. He readily grants the premise: the carpenter did not want the hole, and neither did the homeowner who hired him. Nevertheless, the fact remains that a human being made this hole. The carpenter examined his boards, understood that they were too short, and reached a decision: I will build the door this way and leave a gap. A decision taken by a person is not comparable to water, sheratzim or salt eating away at wood, where the opening was decided for you and not by you.
Three cases where nobody decided anything
Everything until now has dealt with a gap left across the door's center. The Mishnah proceeds to a different arrangement: "shiyer bo hacharash," the carpenter left the shortfall, "milmatan o milmaalan," at the bottom or at the top. Once again his boards came up short, but this time he solved the problem another way. He mounted the door without lowering it to the floor, so that the threshold is visible beneath it from inside the house, or he hung a door too short to reach the top, leaving part of the frame above it uncovered. In both arrangements the panel itself is unbroken; there is nothing to see through at all in the body of the door.
The Mishnah adds two more cases. "Hegifah velo mirkah": someone pushed the door shut but did not press it closed all the way. Everyone knows the experience of being told to close the door properly; you thought you had shut it, and it never quite caught. And "o shepesachato haruach": the door was closed properly, and the wind blew it open.
In all of these situations, "shiuro melo egrof," the gap counts only at the size of the large fist. The reason is plain: the space that is standing open here was not put there on purpose by anyone. A man tried to close his door and did not notice that it had not latched, or the wind pushed it open. A door that ends up open on its own is in the very same category as a hole chewed out by water or by sheratzim.
Would Rebbi Tarfon argue here as well?
A question presents itself. When the carpenter's boards fell short and he left the empty space across the door's center, Rebbi Tarfon held that a fist is far too large a requirement and set the measure at a tefach. Does he maintain that position in these three additional cases as well? The answer is that in all three, the shortfall placed low or high, the door pressed shut but never fully closed, and the door blown open by the wind, Rebbi Tarfon too accepts melo egrof.
The Bartenura draws the line. With the gap that runs through the door's center, the carpenter indeed had no desire for it, yet he did plan it out. He acted purposefully and assigned it a location of his own choosing: my boards are too short, so the door should at least have a solid top and a solid bottom, and the empty space will fall in between. Such an act is deliberate, and that is exactly the point of the machlokes. Rebbi Akiva holds that since it was unwanted it ranks with an opening that formed by itself, so a large fist's fill is required; Rebbi Tarfon holds that since a person ultimately designed it, a tefach by a tefach suffices.
When the carpenter merely leaves the door short below or above, though, nothing was done beyadayim. He never studied the door and asked himself where an opening ought to go. He mounted the panel and it failed to cover the frame: he started at the top and it stopped short of the floor, or he started at the bottom and it stopped short of the lintel. No plan was made and no location was selected. Mimeilah, here even Rebbi Tarfon grants that the case is no different from the fellow who pushed his door and failed to close it, or the door swung open by a gust of wind. Such a gap arose of itself, and for a gap that arises of itself, melo egrof, the fill of a large fist, is the shiur.