How many holes are there in a straw? The answer may surprise you

The two-holers might argue that there is one hole at the bottom of the straw and another hole at the top, while the one-holers might insist that this was, in fact, just one long hole

How many holes are there in a straw? This was the question recently asked of 4,116 British adults by polling company YouGov. It turns out that it is quite a divisive question.

The options given to the survey participants were “one”, “two” or “don’t know”. Just 4 per cent of people said they didn’t know, while the remaining 96 per cent were relatively evenly split. 54 per cent went for one hole, while 42 per cent plumped for two.

The two-holers might argue that there is one hole at the bottom of the straw and another hole at the top, while the one-holers might insist that this was, in fact, just one long hole. When I repeated the poll on Twitter for myself, I also gave people the option of choosing zero holes. Of the roughly 2000 respondents to my poll, about 14 per cent went for this option, while 59 per cent went for one hole and 22 per cent for two holes.

So what is the correct answer? Well, that depends on your interpretation of the question. To a mathematician, the problem of classifying how many holes there are in an object falls squarely within the realm of topology. You can think of topology as geometry – the maths of shapes – but where the shapes are made of dough.

In topology, the actual shapes of objects themselves are not important; instead objects are grouped together by the number of holes they possess. For example, a topologist sees no difference between a cricket ball, a baseball, or even a Frisbee. If they were all made of dough, they could theoretically be squashed, stretched or otherwise manipulated to look like each other without making or closing any holes in the dough or sticking different parts of it together.

However, to a topologist, these objects are fundamentally different to a bagel, a doughnut or a basketball hoop which each have a hole through the middle of them. A figure of eight with two holes and a pretzel with three are different topological objects again.

A useful way to get into the mathematicians’ way of thinking about the straw problem is to think of a washer. How many holes would you say that has? It’s hard to argue that a washer has more than one hole. What about a Polo mint? Again you’d probably agree with Polo’s marketers when they advertised them as “the mint with the hole” (not holes). We wouldn’t usually look at a doughnut, for example, and claim it has one hole in the top and one hole in the bottom.

The long, thin aspect ratio of the straw, and the fact that the two openings are relatively far apart, are perhaps what gives rise to the suggestion of two holes. But to a topologist, washers, Polos and doughnuts are all topologically equivalent to a straw with a single hole.

So that’s the sense in which topologists might choose to answer the question, but what about the way in which non-mathematicians would understand the word “hole”? Well, if my kids and I decide to dig a hole at the beach our aim is not to dig right through to Australia. Many people would understand hole as meaning a depression in a solid body. This idea characterises quite a different object to the topologist’s “hole”, but the definition is just as valid. Try telling a golfer that the cavity into which they are aiming to sink their ball isn’t a hole.

The two-holers might argue that the word “hole” is synonymous with the noun “opening”. Certainly, very few people would argue against a straw having two openings. The Channel Tunnel began life as two holes (one in England and one in France) which eventually joined up. From the perspective of a French person and an English person standing at either end of the tunnel unaware of the project to tunnel beneath the sea, it would be hard to criticise either of them for calling the opening they were standing next to a hole.

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In the same way, I can understand the answer “zero” from a colloquial viewpoint. If someone says to you “my straw has a hole in it”, what you understand by that phrase is that the straw is broken and no longer works as intended. Arguably you would be pleased to have a straw in its original “hole-free” state.

I think this is key to understanding the diverse answers to the question – semantics. The mathematicians’ definition of a hole is actually more similar to the colloquial definition of a tunnel. If you asked people “how many tunnels does a straw have?” (despite it being slightly strange terminology) I expect most people would give the topologists’ expected answer of one. The key to getting agreement on the answer is to define precisely what we mean by the words in the question.

When YouGov posted the results of the survey on Twitter, there were plenty of replies from people who fell decidedly into the “one”, “two” or “zero” camps and would brook no argument. The respondents I most admire though, are the people who have the courage to suggest I “don’t know”, expressing an understanding that there are multiple ways to answer the question, depending on the context.

The poll, of course, was never really designed to survey the nation’s knowledge of topology or the straw manufacturing process, but instead to initiate debate. Judging by the replies on twitter, it was successful in its aim.

Kit Yates is a senior lecturer in the Department of Mathematical Sciences and co-director of the Centre for Mathematical Biology at the University of Bath