Uktzin, Chapter 2, Mishnah 6. A large part of Maseches Uktzin is devoted to the question of chibbur: when do two pieces of produce or food count as one single unit for the laws of tumah, and when have they already become two separate items? Our Mishnah applies that question to something that happens in every kitchen: food that has been cut, but not cut all the way through.
Picture a person preparing meat or vegetables for the pot. He knows that the cooking itself will soften the food and cause it to come apart further, so he does not bother slicing each piece cleanly through. He cuts perhaps ninety percent of the way, and the pieces are left dangling on each other by a few strands or fibers of meat or vegetable. Had he cut them into fully separate small pieces already now, the cooking would reduce them to shreds, and that is not how he wishes to serve them. So the partial cut is deliberate: the knife finishes the job, and then the fire finishes what the knife left over.
Here is the halachah for such a case: "Hamchatech levashel, af al pi shelo meirek, eino chibbur" - when a person slices food with cooking in mind, the fact that he stopped short of a clean separation and left the parts hanging together makes no difference; halachically they no longer count as one. As far as tumah is concerned, each piece stands on its own. Should a source of tumah come into contact with one of them, its neighbors, still physically clinging to it, stay tahor.
The Mishnah then contrasts three other intentions: "Lichbosh, velishlok, ul'hanicho al hashulchan" - if he is cutting the food in order to pickle it, or in order to boil it thoroughly and softly (shelikah), or he is cutting it in the form in which he intends to bring it to the table, then it is chibbur. In each of these cases the partial cut is not a step toward separation at all; he wants the pieces to stay joined to one another. Since his wish is that they remain a single mass, the halachah treats them as one, and tumah that touches one piece spreads to the rest.
Next: "Hischil lefarek, ochel shehischil bo, eino chibbur." Suppose he has begun taking the pieces apart, one at a time. The portion he has already started working on is no longer considered connected, even if a shred of it still clings, because the process of separating it is underway. But the pieces he has not yet reached are still chibbur, even though he fully intends to separate them as well. Intention alone does not undo the connection; the beginning of the act does.
From cut food the Mishnah turns to food that has been bound: "Ha'egozim she'amnan, vehabetzalim shecheranan, harei eilu chibbur." Nuts fastened to each other by their stalks, or onions threaded onto a string, form one halachic unit, since the owner arranged them that way with a lasting arrangement in mind, not a temporary one.
Here as well, the moment he starts dismantling the arrangement, everything changes: "Hischil lefarek ba'egozim, ul'falel bavetzalim" - if he has begun to crack a few nuts out of the cluster, or has begun peeling the onions' outer layers so that they will come free of the string, then "eino chibbur." The bundle may still be physically intact and the work unfinished, yet halachically the unit has dissolved: tumah reaching one nut or one onion will not travel to its neighbors.
The Mishnah closes with a related point about the shell of a nut: "Ha'egozim vehashkeidim chibbur ad sheyerasseis." Nuts and almonds are joined to their shells, meaning that the shell serves as a shomer, a guard for the fruit inside, so that tumah touching the shell renders the whole nut tamei, and the shell joins the fruit for the laws of tumah. This remains true even after the shell has been cracked open, the way one sees a pistachio split wide while the two halves still cradle the nut: it is still a protective covering. Only sheyerasseis, once the shell has been crushed into many small fragments, does it cease to function as a shomer for the fruit, even though those fragments are still surrounding the nut.
The thread running through the entire Mishnah is a single idea: physical attachment is not the deciding factor. What decides is where the food is headed, according to the intention and the actions of its owner. Food heading toward separation is already separate; food meant to stay together is one.