June 7, 2023

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

How many holes are there in a straw? This was the question recently posed to 4,116 British adults by polling company YouGov. It turns out that’s a pretty divisive question.

The options given to survey participants were ‘one’, ‘two’ or ‘don’t know’. Only 4 percent of people said they did not know, while the remaining 96 percent were relatively evenly distributed. 54 percent went for one hole, while 42 percent plumped for two.

The two-holers may claim that there is one hole at the bottom of the straw and another hole at the top, while the one-holers may insist that this was actually just one long hole. When I repeated the poll on Twitter for myself i also gave people the option to choose zero holes. Of the approximately 2,000 respondents to my poll, around 14 percent went for this option, while 59 percent went for one hole and 22 percent for two holes.

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

In topology, the actual shapes of the objects are not important; instead, objects are grouped together by the number of holes they have. 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 squeezed, stretched, or otherwise manipulated to look like each other without creating or closing any holes in the dough or gluing different parts of it together.

But to a topologist, these objects are fundamentally different from a bagel, a donut, or a basketball hoop, each of which has a hole through its center. A figure eight with two holes and a pretzel with three are again different topological objects.

A useful way to get into the mathematician’s way of thinking about the straw problem is to think of a washing machine. How many holes would you say it has? It is difficult to argue that a disc has more than one hole. How about a Polo mint? Again, you’d probably agree with the Polo’s marketers when they advertised them as “the coin with the hole” (not holes). We would not normally look at a doughnut, for example, and claim that 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, is perhaps what gives rise to the suggestion of two holes. But to a topologist, disks, polos, and donuts are all topologically equivalent to a straw with a single hole.

So that is in the sense that topologists might choose to answer the question, but what about the way non-mathematicians would understand the word “hole”? Well, if my kids and I decide to dig a hole on the beach, our goal is not to dig straight to Australia. Many people will understand holes as a depression in a solid body. This idea characterizes a quite different object than the “hole” of topology, but the definition is equally valid. Try telling a golfer that the hole they’re aiming to sink their ball into isn’t a hole.

The two-holers may argue that the word “hole” is synonymous with the noun “opening”. There are certainly few who would argue against straws having two openings. The Channel Tunnel began life as two holes (one in England and one in France) which eventually merged. From the perspective of a French person and an English person standing at either end of the tunnel unaware of the project to tunnel under the sea, it would be hard to criticize either of them for calling the opening they were standing next to a hole.

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Similarly, I can understand the answer “zero” from an everyday point of view. If someone says to you “my straw has a hole in it”, what you understand by that sentence is that the straw is broken and no longer working as intended. Undoubtedly, you will be satisfied with having a straw in its original “hole-free” condition.

I think this is the key to understanding the different answers to the question – semantics. The mathematicians’ definition of a hole is actually more similar to the everyday definition of a tunnel. If you asked people “how many tunnels does a straw have?” (despite it’s somewhat strange terminology) I expect most people will give the topologists expected answer to one. The key to agreeing on the answer is to define exactly what we mean by the words in the question.

When YouGov posted the results of the survey on Twitter, there were many responses from people who fell firmly into the ‘one’, ‘two’ or ‘nil’ camp and wanted no argument. The respondents I most admire are those who have the courage to suggest I “don’t know” and express an understanding that there are multiple ways to answer the question, depending on the context.

Of course, the poll was never designed to survey the nation’s knowledge of topology or the straw production process, but rather to spark debate. Judging by the responses on twitter, it was successful in its aim.

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

#### Jeff

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