# How Many Holes In A Pair of Pants

On this MIT alumni mailing-list I'm on, somebody asked:
"How many holes does a pair of pants have?"

Much discussion ensued. Here is my response.

If we mean "hole" in the topological sense, the answer is clearly TWO. If you have an excess of fabric and no fashion sense, you can make a gigantic pair of uncomfortable harem pants by cutting two holes in a very large circle of fabric and then sewing an enormous drawstring along the circumference. You'll probably also want to gather up the fabric between your legs with some kind of loincloth arrangement or maybe a bunch of creative ruching, and let's be honest, you're going to end up with a kind of diaper-like effect that is both awkward and fugly, but the point is, you only have to make two cuts in the fabric to do it.

If we're talking about holes in the sense of an opening into a separated space, then there are plainly THREE: the waist hole and two ankle holes. If you were to put stretchable rubber pants on someone and inflate them with air to comical effect, or if you wanted to engage in the time-hallowed sport of ferret-legging, those are the three places where air/ferrets may be introduced to the inter-trouseral space, and also the places that you must ensure are snugly fitted so as to prevent their escape.

Finally, if by hole we mean a place where there is something missing, where properly there ought to be something but instead there is nothing, then the answer is undoubtedly ZERO. We're talking about idealized pants here. They consist only and exactly of what they ought, no more and no less, perfect and flawless in their abstraction. By this definition, they CAN'T have holes.

So, how many holes does a pair of pants have? (2 + 3 + 1.78 + 0) / 4 = 1.695, which we can round up to the much funnier value of ONE POINT SEVEN.

Of course, that's for idealized pants. For *actual* pants, the number is more variable.

First, most pants have a buttonhole at the fly. Some slacks have a little tab thing instead, and of course there are elastic- and drawstring-waist pants that have no buttons, but there are also button-fly jeans. For simplicity, I'm going to assume that they cancel out, leaving us with a net +1 hole by definitions 1 and 3.

Then there's beltloops. Those are holes only in the topological sense, but there are a lot of them. For pants that have them, I think the average number is between 5 and 6. Most pants have beltloops, but there's a fair fraction that don't, so that probably brings the expected value back down to, oh, around 4?

And then, of course, actual pants get holes as they wear out. This is a much harder number to estimate. I'd say most pairs of pants only get a couple-few holes in them before they get thrown out. I have no idea what the respective dwell times are for new, worn, and discarded clothing, other than that pants don't stop being pants just because no-one is wearing them, and textiles take a very long time to decay in a landfill. And then of course there are pants that start out with holes in them, sometimes quite a lot of holes, because fashion is ridiculous. Let's just be arbitrary and call it 2.2.

So that's an additional 2/4 + ~4/4 + 2.2 = THREE POINT SEVEN extra holes for actual pants as opposed to notional pants.

(This isn't even getting into the issue of what happens to the question if you ask it in British English instead of American English and end up asking about underwear.)

Point being: I think people tend to invest a lot of unnecessary effort into arguing about questions like this because they falsely assume that there is a single correct answer. Words usually mean more than one thing. They're not point-like and precise, they're fuzzy little clouds of meaning. It's not just denotation; context and connotation exist and matter. So if you actually want to get anywhere in your discussions, it pays to keep the question "so what do you mean by that?" at the ready, and to seek clarification when you perceive a disagreement, rather than operating under the assumption that disagreement necessarily indicates that somebody is wrong.
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