The Two-Trip Theorem
Posted: Fri Jun 19, 2026 4:22 pm
Statement. No project that needs tools or hardware—no matter how small—can be finished with only one trip to the store.
Mechanism. The first trip is undertaken in ignorance of what the first trip will reveal. A project discloses its true requirements only once work has begun, and work cannot begin until the first trip has concluded. The second trip is therefore not a failure of planning but a structural feature of the project itself: it is the trip you could not have known to take until you had already taken the first.
Corollary I — The Insufficiency of Diligence. Thoroughness of preparation does not reduce the trip count; it merely changes which item is forgotten. The better the list, the more exotic the omission.
Corollary II — Conservation of Trips. A trip eliminated through superior planning will reappear elsewhere in the project as a trip of equal or greater inconvenience. Trips are neither created nor destroyed, only deferred to a less convenient hour.
Corollary III — The Proximity Penalty. The likelihood that a second trip is required approaches certainty as the distance to the store increases, and reaches it entirely the moment the store closes for the day.
Corollary IV — The Wrong-Part Lemma. You cannot confirm that a part is the wrong part until you are home, holding it, with the old part already removed and unavailable for comparison.
Corollary V — The "While I'm There" Expansion. Any second trip will result in the acquisition of at least one additional, unplanned item, justified by the phrase "while I'm there." This item will later prove either unnecessary or the direct cause of a third trip.
On the impossibility of the one-trip project. Claims of single-trip completion, on rigorous examination, reduce without exception to one of three cases: (a) the project needed no hardware and thus falls outside the theorem; (b) a required item was already on hand from a previous, uncounted trip—a prior trip, not a single one; or (c) the project remains incomplete, with the second trip merely deferred. The true one-trip project, like the frictionless plane, remains a useful fiction for instruction and nothing more.
Q.E.D. — though the proof, fittingly, requires one more trip to complete.
Mechanism. The first trip is undertaken in ignorance of what the first trip will reveal. A project discloses its true requirements only once work has begun, and work cannot begin until the first trip has concluded. The second trip is therefore not a failure of planning but a structural feature of the project itself: it is the trip you could not have known to take until you had already taken the first.
Corollary I — The Insufficiency of Diligence. Thoroughness of preparation does not reduce the trip count; it merely changes which item is forgotten. The better the list, the more exotic the omission.
Corollary II — Conservation of Trips. A trip eliminated through superior planning will reappear elsewhere in the project as a trip of equal or greater inconvenience. Trips are neither created nor destroyed, only deferred to a less convenient hour.
Corollary III — The Proximity Penalty. The likelihood that a second trip is required approaches certainty as the distance to the store increases, and reaches it entirely the moment the store closes for the day.
Corollary IV — The Wrong-Part Lemma. You cannot confirm that a part is the wrong part until you are home, holding it, with the old part already removed and unavailable for comparison.
Corollary V — The "While I'm There" Expansion. Any second trip will result in the acquisition of at least one additional, unplanned item, justified by the phrase "while I'm there." This item will later prove either unnecessary or the direct cause of a third trip.
On the impossibility of the one-trip project. Claims of single-trip completion, on rigorous examination, reduce without exception to one of three cases: (a) the project needed no hardware and thus falls outside the theorem; (b) a required item was already on hand from a previous, uncounted trip—a prior trip, not a single one; or (c) the project remains incomplete, with the second trip merely deferred. The true one-trip project, like the frictionless plane, remains a useful fiction for instruction and nothing more.
Q.E.D. — though the proof, fittingly, requires one more trip to complete.