How many holes does a donut have? That’s pretty easy: one. What about a straw? Two (one at each end) or just one? (Isn’t a straw just an elongated donut?) Does a coffee mug have one hole or two? Does a bowl have a hole? If no, then what about a hole in the ground or a hole in a wall that doesn’t pass all the way through? Does a basketball have a hole? A Reddit user asked 1600 people how many holes were in various objects and the results are fantastically all over the place.

This is a trivial question, but it reveals something interesting about people’s perceptions. The dictionary definition of “hole” includes two main meanings for the purposes of this question: “an opening through something” and “a hollowed-out place”. Mathematics offers another possible meaning:

A hole in a mathematical object is a topological structure which prevents the object from being continuously shrunk to a point. When dealing with topological spaces, a disconnectivity is interpreted as a hole in the space. Examples of holes are things like the “donut hole” in the center of the torus, a domain removed from a plane, and the portion missing from Euclidean space after cutting a knot out from it.

But a hole isn’t clearly defined in math or topology. From What We Talk about When We Talk about Holes in Scientific American:

Here’s my short answer that is also the reason I’m not an algebraic topologist. If you can put it on a necklace, it has a one-dimensional hole. If you can fill it with toothpaste, it has a two-dimensional hole. For holes of higher dimensions, you’re on your own.[…]

Continue reading: Q: What Is a Hole? A: We’re Not Sure!