How Many Holes Does a Straw Have?
I recently de-lurked in a forum to write up my thoughts about how many holes a straw has. Answering this question can be relatively straightforward or not, depending on the context of the answer -- and including the context is key to answering the question.
Topologically, my understanding is that a straw shape has one hole, being equivalent to a solid torus. You can, without “tearing” anything or causing self-intersections, stretch a solid torus into a straw. In the context of topology I don’t see there being any serious argument about the number of holes in a straw.
Topology 101: The Hole Truth is a cool article about all of this.
In a less formal context where what, exactly, a hole is the question can be debated in circles. What Alice considers a hole may not be what Bob considers a hole- they both use the word but can actually be talking about subtly different things1. Even if they manage to agree on a definition, a set of words they both understand and in a specific order, that definition could still mean something different to Alice than to Bob. They can't be sure they've both interpreted it the same way. I don’t think there can be a “right” answer in this context because, without resorting to a formalism like topology, it might be impossible to get everyone on the same page about what constitutes a hole.
Personally, I'm with topology even in this context -- there is one hole. It feels right to me and I think it's the most defensible answer.
I was thinking about an example I read arguing for two holes and it seems to me that often the two-hole argument comes down to "I have a thing with one hole, and I change it, so now I must have two holes". I don't think that's true. Instead, you may change the type of hole. Digging a space to stick a post into the ground creates a hole in said ground (colloquially, not topologically). So does drilling through a piece of wood. But while both the dug-out thing and the drilled thing are both called holes, they are qualitatively different. Lets call them type A and type B, respectively. I think that what some (all?) of the two-hole examples do is change a type A hole to a type B hole -- rather than add a new hole.
Theres also a smart-alec reductio-ad-absurdum answer of 0 because atoms are mostly empty space and so no volume is truly surrounded to make a hole. In fact, no shape really exists! Geometric nihilism! I also like this answer because, I think, if someone wishes to continue discussing straw holes it forces a move to straws in the abstract. And from “abstract straws” its just a hop, skip, and jump to topology where you can definitively answer because holes are well defined.