What is a hole?

November 11, 2020 2:51 PM

Generally, people don't know what a hole is.

Bonus: How many holes does a human have? (warning: probably best not to watch the intro at mealtimes, or possibly at all)

posted by Stark (162 comments total)

After reading the full article, all I really know is...

There's a hole in the bucket, dear Liza, dear Liza
There's a hole in the bucket, dear Liza, a hole.
posted by hippybear at 2:56 PM on November 11, 2020 [20 favorites]

So so many holes, everywhere you walk. Mostly filled in so you don't notice them, or fall into, but holes just the same.
posted by sammyo at 2:58 PM on November 11, 2020 [1 favorite]

Oh, wait, they're talking about a discontinuity in a multi-dimensional manifold. Well anyway, previous comment holds.
posted by sammyo at 3:00 PM on November 11, 2020 [1 favorite]

It does bring up a sort of philosophical question about holes. Like, is a pore in your skin a hole? Is a pore in your skin filled in with a blackhead also a hole?

I'm going to be thinking about the implications of this for a long time. Thanks MetaFilter, I think.
posted by hippybear at 3:04 PM on November 11, 2020 [4 favorites]

Ok but are these discontinuous multi-dimensional manifolds safe for work or not.
posted by mhoye at 3:07 PM on November 11, 2020 [1 favorite]

They're mostly represented by pie charts in the article. Which are not holes.
posted by hippybear at 3:09 PM on November 11, 2020 [1 favorite]

In other news: Are fish 'wet' when they're underwater?
posted by bartleby at 3:12 PM on November 11, 2020 [6 favorites]

How many does it take to fill the Albert Hall?
posted by zompist at 3:16 PM on November 11, 2020 [26 favorites]

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.

I actually find this ostensibly helpful quote rather confusing.

• I can put a donut on a necklace, so it and all other torii (though not the gates, ha) have one-dimensional holes.
• I can fill a bowl with toothpaste, so it has a two dimensional hole.

Is that right? My brain doesn’t like it because it seems like a bowl has no holes whatsoever in a topological sense.
posted by Going To Maine at 3:18 PM on November 11, 2020 [2 favorites]

I think psychologically and linguistically people are differing on "hole in the surface of an object, which I kind of think of as otherwise hollow" and "passageway through a solid object". These are both salient characteristics but for different things in different circumstances. Could be talking through a hole in my head of course.
posted by Wrinkled Stumpskin at 3:20 PM on November 11, 2020 [3 favorites]

According to the pie charts, most don't think of a spoon as having a hole. Which is... interesting.
posted by hippybear at 3:22 PM on November 11, 2020

Is there a word for the kind of word that approaches close enough to suffice in most circumstances, yet does not fully engage with, every possible usage in the realms of physics, theoretical mathematics, and lived experience via human perception?
posted by niicholas at 3:25 PM on November 11, 2020 [2 favorites]

According to the pie charts, most don't think of a spoon as having a hole. Which is... interesting.

A spoon is a pretty simple convex shape that can be continuously shrunk to a point, per the article. Where does a stereotypical spoon have a hole??
posted by GuyZero at 3:26 PM on November 11, 2020

Well, so does a bowl have a hole? Or more saliently, is a fire pit dug into the ground a hole? A spoon is really just a tiny portable fire pit sort of hole, isn't it?
posted by hippybear at 3:28 PM on November 11, 2020 [4 favorites]

I've heard there is one in the bottom of the sea
posted by jazon at 3:30 PM on November 11, 2020 [8 favorites]

All of this just belies that humans are bags of flesh wrapped around a tube.
posted by Your Childhood Pet Rock at 3:30 PM on November 11, 2020 [12 favorites]

As for straws — reason tells me they only have one hole but I know in my heart they have two.

They have an infinite number stacked on top of each other.

Or: How many beans can fall through this hole in my plate?
posted by Abehammerb Lincoln at 3:31 PM on November 11, 2020 [6 favorites]

I've got a hole in me pocket
posted by BungaDunga at 3:35 PM on November 11, 2020 [9 favorites]

Note to self: Ignore all surveys from floam. Could end up in a hole. Or full of same.
posted by Splunge at 3:35 PM on November 11, 2020 [3 favorites]

In terms of dataviz, I can't help but think adding a few holes to make them donut charts would have helped.

My favourite use of holes has to be in semiconductor physics where they're little bubbles of "no electron" which can pass through materials and you can count them and measure their speed.

Also, saying a spoon has a hole is as counterintuitive to me as saying I have two holes in my sock - one for my foot to go in and one for my toe to stick out of. Were people considering serving spoons that could be hung up or some other spoon that might typically have a topological hole?
posted by Wrinkled Stumpskin at 3:36 PM on November 11, 2020 [1 favorite]

Anyone who doesn't subscribe to the topological definition of a hole is immediately suspect.
- If you have to come out the same way you went in, it ain't a hole.
- If you go in a hole and there's only one way to leave, that's one hole.
- If you go in and there's multiple ways to leave, shit I don't know either but it's definitely at least one hole.
posted by Mr.Encyclopedia at 3:49 PM on November 11, 2020 [10 favorites]

The question is phrased passively, which is confusing, i.e., how many holes does a given object have. For some of the objects, like straw or rubber band, the answer is none; unless the question allows for how many holes does a given object create. Like, an unbroken, perfect rubber band doesn't have any holes in the thing itself, but it does create a hole within its shape.
posted by LooseFilter at 3:52 PM on November 11, 2020 [5 favorites]

So wait -- a hole is a thing that a head is not like?
posted by mandolin conspiracy at 3:52 PM on November 11, 2020 [4 favorites]

My first philosophical question, circa fourth grade, was Can you dig half a hole?

I argued that half a hole is still a hole, so no.
posted by njohnson23 at 3:53 PM on November 11, 2020 [7 favorites]

They're mostly represented by pie charts in the article. Which are not holes.

Thanks for mentioning this, it bothered me maybe more than it should.

Papyrus...
posted by LooseFilter at 3:55 PM on November 11, 2020

The question is phrased passively, which is confusing, i.e., how many holes does a given object have. For some of the objects, like straw or rubber band, the answer is none; unless the question allows for how many holes does a given object create. Like, an unbroken, perfect rubber band doesn't have any holes in the thing itself, but it does create a hole within its shape.

This makes no sense. If a straw doesn't have a hole in it, what the hell DOES?

Topologically speaking, a rubber band and a straw and a donut are identical - they are objects with a single hole.
posted by showbiz_liz at 3:57 PM on November 11, 2020 [3 favorites]

Where does a stereotypical spoon have a hole??

Specific use case, but absinthe, maybe?
posted by mandolin conspiracy at 4:00 PM on November 11, 2020 [3 favorites]

A straw is a hole wrapped in a cylinder of some material that makes it portable
posted by treepour at 4:06 PM on November 11, 2020 [20 favorites]

I think these guys have the best explanation.
posted by Lanark at 4:06 PM on November 11, 2020 [3 favorites]

A spoon is basically just a very small, and usually very shallow, bowl on a handle. So, if you think that a bowl has a hole, it's not unreasonable to think that a spoon has a hole, especially if the bowl of the spoon is deep, like a ladle or a measuring spoon.

I think that "holes" are defined by their function; no matter what their shape or construction, what they have in common is that they are openings that you can put stuff into, take stuff out of, or pass stuff through. You can put a neck through a necklace, so a necklace has a hole. You can put soup in a bowl, so a bowl has a hole. Does a spoon have a hole? That depends on whether you think of putting stuff in the spoon or on the spoon, and that in turn will likely depend on how shallow or deep the bowl of the spoon is.
posted by J.K. Seazer at 4:11 PM on November 11, 2020 [2 favorites]

The spectrum of IMO doughnut yes; washer yes; rubber band no has really got me thinking.
posted by Mitheral at 4:13 PM on November 11, 2020 [1 favorite]

Well to take the straw thing another step further, how many holes does a sweater have? Armholes, a headhole, and a torsohole, or do some of them don't count because they're just the other end(s) of one or more of the other holes?
posted by aubilenon at 4:14 PM on November 11, 2020

A hole is an absence, defined by the presence of a surrounding context. So a spoon has a hole, right where the rim of the bowl is - it doesn't matter what's beyond/below (in other words, it doesn't matter how deep or shallow the spoon is, as the hole is right there at the cusp of the rim)
posted by niicholas at 4:14 PM on November 11, 2020 [1 favorite]

How many holes in a sandwich?
posted by It's Raining Florence Henderson at 4:15 PM on November 11, 2020 [8 favorites]

I wonder how much overlap there is between those who think a spoon has a hole and those who think a hotdog is a sandwich
posted by treepour at 4:16 PM on November 11, 2020 [2 favorites]

Is there Swiss cheese in the sandwich?
posted by aubilenon at 4:16 PM on November 11, 2020 [10 favorites]

When my kid complains that his straw has a hole in it, it's usually fork-related and means he wants another one.

But some of the holes you guys are describing are just divots without their toupees.
posted by Mchelly at 4:17 PM on November 11, 2020 [1 favorite]

More seriously: common words are defined not by verbal formulas but by prototypes, and we think in terms of how close something is to the prototype. The prototypical hole is something like a big circle smashed through a wall. There's another usage cluster for big hollows, like a hole in a golf course.

People don't think like topologists. In topology, a donut, a straw, and a rubber band are identical. That's fine for topologists, but it's not how the rest of us think. (To a topologist, golf courses don't have holes at all, so their scores are terrible.)

Prototype theory can be tested. E.g. ideally you'd ask these questions on a timer. People will answer questions about prototypes faster. It takes time to decide about less typical cases, like rubber bands and spoons.
posted by zompist at 4:19 PM on November 11, 2020 [14 favorites]

The word 'hole' is a just word that groups together a few experientially related things. Lots of words do that. There's no requirement for two or more ideas expressed using a common word to have a relationship in a mathematical sense. In this case, you can make a case that there's some logical correspondence, but it's imprecise at best.

If I take a hollow sphere and drill a single hole from the outside in, is there a hole? In the common sense, yes. Topologically, no.
posted by pipeski at 4:20 PM on November 11, 2020 [4 favorites]

As a language person, I don't think the real problem is with understanding what a "hole" is. The problem is in stating the question such that you are clear whether there is a hole "in" something (contained by) or whether there is a hole "through" something.
posted by It's Raining Florence Henderson at 4:21 PM on November 11, 2020 [6 favorites]

Is there a word for the kind of word that approaches close enough to suffice in most circumstances, yet does not fully engage with, every possible usage in the realms of physics, theoretical mathematics, and lived experience via human perception?

I think that's just, like, all words ever
posted by one for the books at 4:25 PM on November 11, 2020 [11 favorites]

Is a hole a sandwich?
posted by Going To Maine at 4:28 PM on November 11, 2020 [3 favorites]

I always knew people couldn't tell their ass from a hole in the ground.

It's great to finally get some empirical research into this pressing matter.
posted by sydnius at 4:29 PM on November 11, 2020 [9 favorites]

This makes no sense. If a straw doesn't have a hole in it, what the hell DOES?

Sure it does, a straw has a hole through it, not in it.

The problem is in stating the question such that you are clear whether there is a hole "in" something (contained by) or whether there is a hole "through" something.

This.
posted by LooseFilter at 4:30 PM on November 11, 2020 [1 favorite]

TIL that I might have been using a nonexistent word for years?
Can someone back me up?
A sphondyloid shape is um, a long torus. Or a tall donut.
An earthworm is a sphondyloid. The magnetic field induced around a straight piece of electrified wire. Or one of those liquid-filled things from the 90's that you squeeze at one end and it wriggles out of your grip by rolling inside-out.
posted by bartleby at 4:31 PM on November 11, 2020

In the Tao te Ching, Lao Tsu said that what makes a window, a cup, and a wheel useful, is the hole. To look out, to hold tea, to put an axel. Absence makes the brain to ponder.
posted by njohnson23 at 4:33 PM on November 11, 2020 [7 favorites]

A hole in the ground is not a hole. Unless it's a very, very deep hole. In which case it's a volcano.
posted by ook at 4:36 PM on November 11, 2020 [2 favorites]

the whole hole in the ground situation is giving me a lot more sympathy for the bowl holers.
posted by macrael at 4:39 PM on November 11, 2020 [2 favorites]

What is a hole?

I don't know either and it's about time someone looked into it.
posted by Joe in Australia at 4:49 PM on November 11, 2020 [13 favorites]

Lots of assumptions going on here about what the absolute frame of references can be. A hole in the ground is not a hole? Are there no substrates to consider? A hole through the groundcover, a hole through the soil, a hole through the sand, a hole through the clay, a hole through the first rock layer...
posted by It's Raining Florence Henderson at 4:51 PM on November 11, 2020 [3 favorites]

"Ground" does not necessarily imply the entire planet.
posted by It's Raining Florence Henderson at 4:53 PM on November 11, 2020 [2 favorites]

After reading the full article, all I really know is...

There's a hole in the bucket, dear Liza, dear Liza
There's a hole in the bucket, dear Liza, a hole.

There's nothing in my pocket but a great big hole!
...
Now I know the reason why I had to buy the thread.
posted by wierdo at 4:55 PM on November 11, 2020 [1 favorite]

Can you point at a piece of ground that is not a part of the entire planet? ;)
posted by hippybear at 4:55 PM on November 11, 2020

A hole through the groundcover, a hole through the soil, a hole through the sand, a hole through the clay, a hole through the first rock layer...

It's gonna depend on how much room there is for Darlin' Corey.
posted by mandolin conspiracy at 4:55 PM on November 11, 2020

I saw a remodeling show where they were turning a small movie theater into a house. They wanted to keep the distinctive windows from the projection booth (three little rectangles), but found out that the wall wasn't sound and had to be replaced. So they tore down the wall, but kept the holes. The new wall has the same holes in the same spot.

So, after they tore down the old wall, but before they put up the new one, were the holes still there?
posted by echo target at 5:01 PM on November 11, 2020 [4 favorites]

Now I've got that I'm Like a Bird Song in my head, except now it goes "I don't know just what a hole is..."
posted by emjaybee at 5:03 PM on November 11, 2020 [2 favorites]

Did people not read the article? A bowl does not have a hole!

The only exception to the strict topological definition of a hole that I will make is that comb jellies have a butthole, although it's strictly speaking not a real hole.

you are clear whether there is a hole "in" something (contained by) or whether there is a hole "through" something.

Apparently people are still confused whether you stand "in line" or "on line" so I doubt we're going to get hole nomenclature consensus.
posted by GuyZero at 5:03 PM on November 11, 2020

Spoons and Bowls have 0 holes but 1 hollow, you're welcome
posted by Jon Mitchell at 5:05 PM on November 11, 2020 [7 favorites]

A support engineer for an antiquated database (pre-sql) discussed an internals problem with some developers as one of the 'buckets' having a hole (guess where the bits were leaking out) -- thus a young very smart female dev wandering the halls singing "a hole in the bucket" is one of my oldest fondest tech memories.
posted by sammyo at 5:07 PM on November 11, 2020 [1 favorite]

Christ, what is a hole
posted by Foosnark at 5:14 PM on November 11, 2020 [22 favorites]

pie charts in the article. Which are not holes.

Shut your piehole!
posted by Greg_Ace at 5:18 PM on November 11, 2020 [2 favorites]

Can you point at a piece of ground that is not a part of the entire planet? ;)

*points at moon* ;-)
posted by It's Raining Florence Henderson at 5:37 PM on November 11, 2020 [10 favorites]

My first philosophical question, circa fourth grade, was Can you dig half a hole?

I argued that half a hole is still a hole, so no.

In that case, I suppose all holes are whole holes
posted by treepour at 5:39 PM on November 11, 2020 [2 favorites]

Is an inner tube floating on water a hole? What about a voltage-gated ion channel?
posted by dephlogisticated at 5:40 PM on November 11, 2020

In common parlance, hole can mean pore, tunnel or pit. In math, the first two are the same and the last doesn't count. Doesn't make the math version the only definition, though.
posted by tavella at 5:40 PM on November 11, 2020

The most common usage of "hole" in my house is the little cylinder with a circle cut out in the front at the bottom of my cat's cat tree. We call it "the hole."

For the longest time, my cat never went into the hole, but then I got COVID-bored enough to try to train him to go in it. Nudge cat into hole, present treat, etc.

Now he goes inside voluntarily (sometimes when we humans are becoming too much) and it's very sweet seeing him inside :3 We agree that it's one of the best things to come out of 2020.
posted by batter_my_heart at 5:42 PM on November 11, 2020 [5 favorites]

Seriously all you topological a-holes, if you had to dig a hole in the ground would you dig it all the way through the earth?

I swear to god the fact the topological has the word logical in it makes normally sensible people lose their minds.
posted by medusa at 5:45 PM on November 11, 2020 [3 favorites]

Did you know that the only natural enemy of the hole is the pile?
posted by saturday_morning at 5:47 PM on November 11, 2020 [5 favorites]

In honor of veterans day: there are no atheiststopologists in foxholes
posted by medusa at 5:47 PM on November 11, 2020 [13 favorites]

All I know is a grave is a rut with both ends knocked out.
posted by Catblack at 5:49 PM on November 11, 2020

Nothing, what's a hole with you?
posted by rodlymight at 5:49 PM on November 11, 2020 [1 favorite]

This topic has bothered me, more deeply than I should admit, for most of my adult life...

there is a hole in the hole called a bridge...
posted by albion moonlight at 5:50 PM on November 11, 2020

What are holes? We just don't know.
posted by saturday_morning at 6:02 PM on November 11, 2020 [2 favorites]

This is really interesting. I'm not surprised there's ambiguity. I've dug holes in the ground and made holes in my skin. Neither were holes in the topological sense. Thankfully. (Well, I guess some topological holes in skin are fine. I don't happen to have any aside from ones I was born with.)

But, there's a deeper point that using common words in a technical sense requires care. "Hole" probably doesn't matter much for most things that don't involve math outreach. But, "significant" sure does. "Theory" also changes votes.

That the results of donut and washer are so different is truly baffling. Are there that many people who don't know what a washer is and are also happy to guess at random? Is washer a regional term? Surely the letter "O" is common to all English speakers. I don't get how those results can be true. (I'm not doubting that they are.)
posted by eotvos at 6:04 PM on November 11, 2020 [1 favorite]

people don't know what a-hole is

It certainly feels that way
posted by snuffleupagus at 6:09 PM on November 11, 2020

I can't blame anyone for a loop on a knot, though. That really does require several assumptions that aren't entirely obvious even to someone who's taken related classes. I think I know what they meant, but one could argue for other answers. (How many holes are in a knot tied with string dipped in glue? A knot made from a bundle of twisted thread?)
posted by eotvos at 6:11 PM on November 11, 2020

So it turns out there is an important topological difference between one's ass and a hole in the ground.
posted by Foosnark at 6:20 PM on November 11, 2020 [11 favorites]

Does a slinky have a hole in it though?
posted by joeyh at 6:22 PM on November 11, 2020 [4 favorites]

If you cut a hole in a chain-link fence, has the number of holes in it increased or decreased?
posted by dephlogisticated at 6:23 PM on November 11, 2020 [4 favorites]

All that I knew was the hole in my shoe, which was letting in water.
posted by TedW at 6:23 PM on November 11, 2020

Also, a black hole is undoubtably a hole, but it's also a concentration of matter in the middle of nothing.
posted by joeyh at 6:25 PM on November 11, 2020 [1 favorite]

Does a slinky have a hole in it though?

Does a piece of string? A slinky is just a coiled up length of metal string.
posted by Mitheral at 6:25 PM on November 11, 2020 [1 favorite]

No, you can't dig half a hole, though you can dig a hole that's half as big as the one I just dug. And that's why I didn't rtfa. If you don't mention the challenges of half holes, I am uninterested in your hole ontology.

As a mathematician, I have a soft spot for the narrow topological treatments. But as a scientist and a human I know what a hole in my skin is, and a hole in the ground. And a hole in an argument.

A worthwhile treatise has to address all of these cases and preferably more; please advise if you know of one.
posted by SaltySalticid at 6:30 PM on November 11, 2020 [2 favorites]

The "hole as divot" is a reasonable linguistic convention, as in the spoon or the bowl, but the "hole as absence of object" issue is the whole reason mathematicians are more specific with their definition. The donut does not contain its own hole, so if all you have defined (mathematically) is the donut, how can you tell if it has a hole in it or not?

The answer, as alluded to in the article, is to take a pen and draw a circle somewhere on the donut. Now, can you imagine shrinking that circle to a single point, or did you somehow draw the circle "around" the hole of the donut (unknowingly, since we can't observe the hole directly), such that the circle can't be shrunk any smaller than the hole itself?

If you can't shrink all of your circles to points, a mathematician would say your object "has" a hole (at least one, maybe more). More carefully, you might say that your abstract "donut space" has a topological property that makes circle shrinking non-trivial.
posted by grog at 6:31 PM on November 11, 2020 [1 favorite]

A slinky has two holes, one at each end. It's a coiled piece of string all right but there are loops on both ends so it doesn't have pointy ends to poke kids eyes out with.
posted by zengargoyle at 6:34 PM on November 11, 2020 [2 favorites]

It's a matter of the gestalt principle. A hole is an interruption in continuity of form. A straw or a spoon or a bowl does not establish a continuity of form that is interrupted by the alleged hole. A slotted spoon has holes in it because it establishes a continuity of form that is interrupted by the slots.
posted by RobotHero at 6:36 PM on November 11, 2020 [5 favorites]

What about other languages? Do they have distinct words for a hole in something vs. a hole through something?

We need a bigger vocabulary to make this work. What language can we "borrow" the new terms from?

A blackhole is not an actual hole but something described with a poetic term, like heartbroken or moonlight.
posted by Jane the Brown at 6:37 PM on November 11, 2020 [1 favorite]

A slinky has two holes, one at each end

So all bottoms have holes, but not all holes have bottoms.

I'll show myself out.
posted by snuffleupagus at 6:39 PM on November 11, 2020 [2 favorites]

I'mma hang out here until we get to 'how long does the Slinky of Theseus have to be'.
Or a rant about how Timbits/Munchkins treats are NOT to be referred to as donut HOLES! They're donut ANTI-HOLES!
posted by bartleby at 6:48 PM on November 11, 2020 [1 favorite]

Luke, what's yer dirt doing in Boss Paul's hole?
posted by Rash at 6:57 PM on November 11, 2020

I must have just had knock off slinkies, mine weren't joined into a circle.
posted by Mitheral at 6:57 PM on November 11, 2020

We tested the 3 leading hemorrhoid treatments and took aggregate scores. After compiling the data, we found brand X to be the most effective, on the hole.
posted by bartleby at 7:04 PM on November 11, 2020 [2 favorites]

I mean I'm much too tired to have this argument so I guess I don't know what exactly a hole is, but I know a hole when I see it.
posted by bondcliff at 7:05 PM on November 11, 2020 [2 favorites]

My first philosophical question, circa fourth grade, was Can you dig half a hole?


You can’t, but if you and a friend work together, you can each do so.
posted by ricochet biscuit at 7:13 PM on November 11, 2020 [11 favorites]

My working definition of the word “hole” includes two senses of the word:

a. A passageway through an object.
(Thus, a straw has one hole, as does a bucket, a donut, or a sweater, because the hole is the entire passage.)

...and...

b. A depression in a surface whose depth exceeds some percentage of its diameter.
(The percentage is context-sensitive. So the depth of a pothole may only need to be be a few percent of the diameter to be considered a hole. But the depth of a depression in some other surface might need to be over 50% of its diameter before it could be considered a hole.)
posted by darkstar at 7:25 PM on November 11, 2020 [2 favorites]

Seems to me that the "hole as divot" (hole dug in the ground) is a discontinuity that interrupts a 2-dimensional surface, while the "hole as tunnel" (hole in a donut) is a discontinuity that interrupts a 3-dimensional object. The two concepts of "hole" are actually the same concept, applied in different dimensional spaces.

So then the question is, what is a 4-dimensional hole?
posted by saturday_morning at 7:26 PM on November 11, 2020 [6 favorites]

>What is a hole?

I don't know either and it's about time someone looked into it.
posted by Joe in Australia

What if it looks back at you?
posted by Pouteria at 7:41 PM on November 11, 2020 [1 favorite]

Metafilter: a soft spot for the narrow topological treatments
posted by Greg_Ace at 7:55 PM on November 11, 2020 [1 favorite]

Stanford Encyclopedia of Philosophy entry on "Holes" has some interesting musings on why holes really don't make any sense when you think about them.

After reading this I've started to have real sympathy to the views of Pyrrho of Elis, who believed that there are conclusive proofs both for and against any proposition, and that therefore the true philosopher ought to cultivate a state of sublime confusion.
posted by vogon_poet at 8:00 PM on November 11, 2020 [6 favorites]

holes are like Santa Claus: the true meaning is in your heart

So, like, the holes are the topologies we made along the way?
posted by Reasonably Everything Happens at 8:06 PM on November 11, 2020 [1 favorite]

A sweater has 3 holes. If you cut off the sleeves to make it easier and stretch out the bottom into a circle of fabric, that circle will have three holes in it.
posted by zengargoyle at 8:07 PM on November 11, 2020 [2 favorites]

I know a hole when I see it— a tempting approach. But even in the relatively simple case of a hole in the ground, this is akin to the sorites paradox, the paradox of the heaps. Which also is not mentioned in the article, to my dismay.

But what is a hole if not for the heap?
posted by SaltySalticid at 8:11 PM on November 11, 2020

If you cut off the sleeves to make it easier and stretch out the bottom into a circle of fabric

If you do this to your sweater, your mother will yell at you for ruining a perfectly good piece of clothing.
posted by hippybear at 8:12 PM on November 11, 2020 [2 favorites]

Why don’t they sell bagel holes? Asking for a friend.
posted by Mchelly at 8:15 PM on November 11, 2020 [1 favorite]

Bagels are usually formed by turning a dough rope into a circle, while doughnuts are usually made by punching them out. The "holes" are actually leftover dough from the process; the equivalent does not exist for bagels.
posted by hippybear at 8:18 PM on November 11, 2020 [1 favorite]

A hole is not a structure or a shape. A hole is a process. A hole is a relationship between me and some object or environment. Holes are everywhere. Holes are contexts. Any other definition is made of logical holes.
posted by polymodus at 8:36 PM on November 11, 2020 [1 favorite]

Looking forward to the Schoolhouse Rock rendition of A Hole Is A Process.
posted by Greg_Ace at 8:40 PM on November 11, 2020 [3 favorites]

How many holes does a skirt or kilt have? 0, 1, or 2?

How many holes does a pair of trousers have? 0, 1, 2, or 3?

(Presume there are no pockets in any of the above garments, and no buttons)
posted by Garm at 9:37 PM on November 11, 2020 [1 favorite]

CAD answer: a straw has two circular edges and therefore two holes. A bowl has one circular edge, hence one hole. A donut/torus is just one face with no edges, so it does not have a hole. (96.9% of people be damned!)
posted by equalpants at 9:45 PM on November 11, 2020 [2 favorites]

So then the question is, what is a 4-dimensional hole?

See: my neighbor
posted by pee tape at 9:49 PM on November 11, 2020

So then the question is, what is a 4-dimensional hole?

When one of the 5th Dimension died?
posted by Greg_Ace at 9:59 PM on November 11, 2020

I have two pieces of Belgian Lace. One has holes in it, the other does not. Which piece is the one with holes in it? Or, to put it another way, there is no hole in 1 but there is a hole in one. Similarly, I have a sieve which works really well because there are no holes in it. Also, I have a bowl (which is a hole) which is full of holes and is called a colander. If I take some clay from the ground I leave a hole and when I form the clay into a bowl by making a hole in it I am making a bowl which, being a hole, cannot now be used to fill the hole it came from. So, in reality when something has a hole in it then it is considered broken until it is made whole. Whole is in part a hole.

I now have a hole in my brain where these thoughts came from.

Metafilter: a hole of many parts. NOTE: you cannot have part of a hole.

Wanders off muttering to self.... but what color is a hole which is not a black hole. A black hole being something you cannot enter or leave. Feels self falling into the black hole and ceasing to be whole... in part.... aaaaaaaaaaaaaaaaagh!
posted by IndelibleUnderpants at 10:15 PM on November 11, 2020

With complex questions like this, it is essential to go back to primary sources: The Hole Idea
posted by fairmettle at 10:33 PM on November 11, 2020

Why don’t they sell bagel holes? Asking for a friend.
posted by Mchelly

Bagels are usually formed by turning a dough rope into a circle, while doughnuts are usually made by punching them out. The "holes" are actually leftover dough from the process; the equivalent does not exist for bagels.
posted by hippybear

“As you ramble on through life, Brother,
Whatever be your goal,
Keep your eye upon the doughnut,
And not upon the hole.”
posted by Pouteria at 11:21 PM on November 11, 2020

telecommunications network construction perspective: hole - a medium that's unusually cheap to haul cables through.
posted by are-coral-made at 12:12 AM on November 12, 2020

All of this just belies that humans are bags of flesh wrapped around a tube

Make that six to eight tubes roughly in a star configuration: gut plus mouth plus two nostrils plus the two tiny ducts that run from your eye corners into the back of your nose, plus one or two Eustachian tubes depending on how many busted eardrums you have.
posted by flabdablet at 12:43 AM on November 12, 2020

Also, it seems to me that extended contemplation of what the word "hole" means is a pretty good grounding for understanding why there is something rather than nothing.
posted by flabdablet at 12:44 AM on November 12, 2020 [1 favorite]

a straw has one hole, it's just a long one
posted by rifflesby at 12:57 AM on November 12, 2020 [1 favorite]

" So then the question is, what is a 4-dimensional hole?"

I'll note that we often refer to time as a fourth dimension, and that when people have blackouts in their memory, they sometimes refer to that as a hole....
posted by i_am_joe's_spleen at 1:03 AM on November 12, 2020

Heh. After reading the Magna Carta discussion where people are commenting on magical thinking, these kinds of threads over word meaning amuse because they come from the same kind of place, the assumption that communication is just words and/or symbols, strictly defined, rather than discursive events in context where meaning can shift rapidly based on point of reference and need.

A straw can have no holes, one hole, two holes or more depending entirely on how one is referencing the object, or space, as framed by the needs or understanding of the conversing parties. The attempt to drill down to "a" definitive meaning is what common reference refers to as jargon or specialized speech desired by certain groups to clarify reference.

One can, for example, say with minimal confusion that a straw is defective because it has a hole, carrying the implication that a "true" straw is one without holes based on an assumed shared concept of a straw as having an understood utility that can be impaired by a "hole". One can reference "the hole" in a straw placed in a glass of water as the point of reference is the more immediately useful "end" of the straw, rather than the submerged part. Bend a straw into a U shape and one might reference it as having two holes if there is some use in conveying that information, as in cover one of the two holes.

Place a divider part way into one "end" of the straw so it is bifurcated and the straw could be said to have three holes or one depending on what the needed aspect is one wants to emphasize, have the divider go all the way down and it may be four holes or not, place the straw under water or even fill it with concrete and one can still refer to the "hole" by dint of reference to assumed shared knowledge of the construction of straws, even though that hole is filled and lacks usual utility and likely will not have it again.

Similarly one can have a flat sheet of paper and call it a straw if one rolls it up to mimic the use of a "regular" straw, where those that witness the event may still refer to the sheet of paper as a straw even after the paper returns to its flat state, where anyone else would have little reason to understand it as a straw or think it therefore had "holes". Cut a paper straw lengthwise so its utility is gone and one may still refer to that now piece of paper as a straw based on the knowledge of its contextually initial state, and still speak of the ends as holes if desired based on that shared understanding.

Neither straw nor hole in common usage will have a set definition because communication is facilitated by ease in shifting referents. We can see this in practice when we shift from saying "hole" to something else, like "end" or "opening" depending on what best communicates what we are trying to get across. Words like "hole" are used in multiple shifting contexts because of assumed sense of association that does not require strict definitional understanding.

We may find it desirable to have a broad and/or more specific vocabulary for some situations, but that makes communicating more uncertain or unwieldly by having to remember a vastly larger group of words, many of which may only be needed rarely, and in conveying intended meaning to others who may or may not share the same vocabulary or points of reference. The simpler the idea the easier it is to convey through association to other common concepts or uses. The would be wag understand this and uses shifts of reference in an attempt to make witty by imposing a known unintended reference on the expected one, while these kinds of questions, "Is a hot dog a sandwich?" or "What is a hole?" are so popular because they ask people to consider words without context and then note the fluidity of the concepts and potential seeming contradictions within.

(Magical thinking arises from believing there is "one true" meaning to words and symbols that only the adept "really" know and can utilize, it finds some association of its own through the need lawyers and other specialists have in trying to define things more precisely to limit unwanted association, but takes on an added life through thinking its the words themselves that have power rather than the shared understanding the words in context might convey. People as controlled by words rather than controlling them in shifting ways.)
posted by gusottertrout at 1:59 AM on November 12, 2020 [16 favorites]

Not to get too serious or Derridean about a light hearted post, but there is some real consequence to treating the shifting nature of language as something more concrete, where the somewhat arbitrary categories we create take hold in the imagination as something more real and defining rather than ideas and values fit to a context.
posted by gusottertrout at 2:24 AM on November 12, 2020 [7 favorites]

For brief discussions of various ontologies like this, I'd recommend the Robot or Not? podcast with John Siracusa and Jason Snell.
posted by jenkinsEar at 4:07 AM on November 12, 2020

Polo Holes can still be had in Japan.

From Shortlist: Polos are normal mints, but they have a hole in the middle, so they are "different". What they did with Polo Holes was bring out another normal mint, but leave it as exactly that: just a normal mint. The marketing campaign was that it was the tiny pieces missing from regular Polos, but the fact remained: they were just normal mints. Still, they tasted quite nice, and a friend at school once brought a load in in a see-through baggy and convinced everyone he was a drug dealer. I miss them if not just for that, really.
posted by Cardinal Fang at 4:56 AM on November 12, 2020

A hole is an absence, defined by the presence
of a surrounding context. So a spoon has a hole, right where the rim of the bowl is - it doesn't matter what's beyond/below (in other words, it doesn't matter how deep or shallow the spoon is, as the hole is right there at the cusp of the rim)

Huh?

I think I need a diagram.
posted by tiny frying pan at 6:55 AM on November 12, 2020

My metaphysics professor in college (Achille Varzi) has spent most of his career trying to answer this question. It's fascinating. The media even consulted him during the hanging chad fiasco of 2000.
posted by Lutoslawski at 6:56 AM on November 12, 2020 [4 favorites]

hi i'm on metafilter and i could overthink a hole of beans.
posted by Klipspringer at 7:27 AM on November 12, 2020 [2 favorites]

How many does it take to fill the Albert Hall?

same as Blackburn, Lancashire apparently ... in 1967 anyway.
posted by philip-random at 8:09 AM on November 12, 2020

The reason people get different answers is because you can't evaluate the truth of a statement without considering its context. The same statement can be both true and false in two different contexts. Rhetoricians employ this to their benefit by getting you to agree to a statement that's true under one context, then silently switching contexts to get you to agree with something that is false.
posted by hypnogogue at 8:11 AM on November 12, 2020 [1 favorite]

A hole is to dig.
posted by lampoil at 8:34 AM on November 12, 2020 [2 favorites]

I have noticed a lot of frustrating political arguments between people who insist words have single objective meanings, and people who insist there is only pragmatics and information conveyed by the words themselves doesn't matter at all. This divide seems to exist within and across political groups. This is one situation where I am convinced it is actually correct to be a moderate.
posted by vogon_poet at 8:41 AM on November 12, 2020

Summary of the first link: self-aggrandizing blog writer does the climate science denial "teach the controversy" thing to random math topic.

Topologists agree on what a hole is, mathematically speaking. Precise, clear definitions so that we all know that we're talking about exactly the same thing are part of what makes math math. Mathematical objects live purely in the realm of imagination - we can't bring an arbitrary set or operation or other mathematical object into a lab and do physical tests on it to study its properties. So we have to have very precise technical definitions that leave no room for ambiguity.^*

The fact that mathematicians often repurpose regular words to have precise technical definitions is definitely an impediment to non-specialists being able to easily understand random math stuff. Lots of mathematicians are bad at trying to explain technical concepts in non-technical language for non-specialists, too, which is another separate and non-helpful thing. Both issues seem to have contributed to this rather unfortunate blog post.

* As new fields of math get developed, there are arguments about "I think this should be how we generalize this definition to other contexts for x reasons", "no, I think the more general definition should be this other thing instead for different reasons". Mathematicians on both sides will still provide clear definitions and understand exactly what each other are talking about. It's more like the debate when a new species is discovered of where it fits in taxonomic classification schemes - a disagreement on whether some new organism should be classified in a pre-existing genus or should have its own new one doesn't mean that biologists don't understand or disagree on what the pre-existing genus is. Mathematically speaking, hole is the pre-existing genus. Some topologists might want to also call another newly discovered thing a higher-dimensional hole or generalized hole, and that naming detail might not be agreed on yet by everyone, but everyone still agrees on the original definition of a manifold has a hole whenever you can draw a circle that can't be topologically collapsed to a single point. Topologically, a straw still has one topological hole.
posted by eviemath at 8:46 AM on November 12, 2020 [5 favorites]

Seems to me that the "hole as divot" (hole dug in the ground) is a discontinuity that interrupts a 2-dimensional surface, while the "hole as tunnel" (hole in a donut) is a discontinuity that interrupts a 3-dimensional object. The two concepts of "hole" are actually the same concept, applied in different dimensional spaces.

So then the question is, what is a 4-dimensional hole?

The year 2020
posted by showbiz_liz at 9:00 AM on November 12, 2020 [7 favorites]

A sweater has 3 holes. If you cut off the sleeves to make it easier and stretch out the bottom into a circle of fabric, that circle will have three holes in it.

This is how I think of it as well, at least using the topological definition (IANAT, nor any other kind of mathematician); the confusion is that the outer edge just happens to be shaped in 3-D space to look like a fourth hole, the waist hole - same thing for the straw's second "hole", it's really the outer edge of the washer shape you get if you squash the straw.
posted by solotoro at 9:08 AM on November 12, 2020 [1 favorite]

Actually, having typed that out, and given especially the straw example where either end could be the hole or the edge, maybe it makes more sense to talk about how many edges a shape has than how many holes it has. But probably not worth losing the joy of having a family argument over Thanksgiving dinner on whether the gravy boat has a hole.
posted by solotoro at 9:10 AM on November 12, 2020 [1 favorite]

A sweater has four holes, topologically. The arm holes being on the sides of the tube makes a difference, as opposed to the straw example.
posted by eviemath at 9:11 AM on November 12, 2020 [3 favorites]

Christ, what a hole.
posted by chavenet at 9:12 AM on November 12, 2020 [1 favorite]

There are some nice connections between topology and graph theory in that holes <> edges comparison, though - good intuition!
posted by eviemath at 9:12 AM on November 12, 2020 [1 favorite]

I don't mean to dump on the robust philosophical/English language discussion of holes in this thread. Merely to say that Eve Andersson's Pi Pages predates Kottke's blog by several years, and is probably a better source when it comes to popular mathematics write-ups.
posted by eviemath at 9:16 AM on November 12, 2020

The game Asteroids! is a good place to start for thinking about holes when you don't have any 'outside' space. It's a two-dimensional world, where the map 'scrolls around' both top-bottom and left-right. You can see that it's the same (topologically) as a donut (aka, torus) by connecting the top and bottom edges of the screen (to get a tube), and then connecting the ends of the tube. And we can all agree that donuts have holes. BUT, if you're /living/ in the Asteroids game, you don't get access to the three-dimensional space. And yet the donut hole is still there.

So then a nice way to envision a three-dimensional torus is just three-dimensional asteroids. Think of a VR game in a big cube which 'loops around' in all three dimensions. To 'see' the hole, the torus needs to embed in a four-dimensional space, which is hard to visualize with our puny brains. (usual joke: to visualize thirteen-dimensional torus, look at a donut and say the word 'THIRTEEN' very loudly.)

(but if you want a four-dimensional torus, I suppose you can imagine the three-dimensional torus but with an additional time-loop.)
posted by kaibutsu at 9:33 AM on November 12, 2020 [2 favorites]

The cup I am using has a hole, but cups with no, or broken handles don't have a hole. I would be a torus, but the holes in my head besides my mouth, screw that all up. Wait a minute, maybe not. Never mind....
posted by Oyéah at 9:46 AM on November 12, 2020

A hole in the ground is not a hole. Unless it's a very, very deep hole. In which case it's a volcano.--ook
This comment encapsulates the conflict. You say it isn't a hole, but you use 'a hole in the ground' to describe it. "This hole is not a hole."

Anytime a straw is brought into the discussion, a wiffle ball should be included too. No one would say a wiffle ball has only one hole.

saturday_morning's "hole as divot" interrupting a 2-dimensional surface, vs "hole as tunnel" interrupting a 3-dimensional object could explain the difference between a wiffle ball's many holes and a straw's one hole.
posted by eye of newt at 9:50 AM on November 12, 2020

For more info: Hobby Holes, with K.J. Nutt
posted by Saxon Kane at 10:45 AM on November 12, 2020

(but if you want a four-dimensional torus,

So do the tiny tiny super tiny dimensions that are inside the strings that make up the quarks that are the stuff of electrons and protons and well us, have itsy bitsy donuts or are those very small dimensions just too small for holes?
posted by sammyo at 1:17 PM on November 12, 2020

pipeski:If I take a hollow sphere and drill a single hole from the outside in, is there a hole? In the common sense, yes. Topologically, no.

So, legit question here, absolutely not a callout, and I apologize profusely to pipeski if this is actually your speciality, but if any mathematicians are still reading here, can I get a confirmation on whether the above is accurate? I have just enough higher mathematics training to be dangerous, so I could certainly be wrong, but after reading through a number of references it looks to me that drilling through the surface area of a hollow ball to expose the previously enclosed interior surface would actually create a topological hole. Am I wrong?
posted by It's Raining Florence Henderson at 7:02 PM on November 12, 2020

In a whole doughnut
There’s a nice whole hole.
When you take a big bite,
Hold the whole hole tight.
If a little bit bitten,
Or a great bit bitten,
Any whole hole with a hole bitten in it,
Is a holey whole hole
And it JUST - PLAIN - ISN’T!

[from "Homer Price" by Robert McCloskey]
posted by dougfelt at 8:30 PM on November 12, 2020 [1 favorite]

It's Raining Florence Henderson, nope, not a hole. Imagine the hollow sphere is super elastic. You could take that circular-ish bit that is cut out and stretch it out until you have a flat circular surface. Now take that thin surface and stretch it in the other direction and you could form a solid sphere.

Think of it like making a map of the Earth like peeling down sections of an orange. You make a pin-prick at the north pole and tear down wedges of the skin until they lie flat, then you could keep going and end up with an inside-out skin. Now imagine that you don't have to tear the skin because it's very very very stretcy and from that pinprick you could turn it inside out just like you would a sock. Halfway in-between right side in and inside out is basically a flat circle without any hole.

You need to drill out two parts of the shell to get a hole. Same logic, pick one and flatten and poof there's a hole. Now leave it as a hollow sphere and since everything is super-elastic, make the shell expand on the inside and you'll find yourself with a solid sphere with a hole through it. Squish it into shape and you'll have a torus.
posted by zengargoyle at 8:51 PM on November 12, 2020 [1 favorite]

So, legit question here

On preview, what zengargoyle said.

(And on thinking about it more, I may want to revise my answer about the sweater: if it were made out of clay, you could mold it down to a flat disk with three holes... modulo a detail or two about embeddings.)

The technical mathematical definition has to do with how many distinct circles (there's a detail here about defining these circles to avoid over-counting circles around two or more holes) can we find that can't be collapsed down to a single point. The space our object is sitting in ("embedded" in) can potentially make a difference here, though - eg. with the sweater example, and whether or not we count the outside as a hole. That gets more into algebraic topology and is outside my area of expertise, so I would not be able to provide more details (at least not accurately).
posted by eviemath at 8:58 PM on November 12, 2020 [1 favorite]

"but if any mathematicians are still reading here"

Oh don't you worry. When the nature of holes is discussed, the mathematicians will be the ones closing down the party...
posted by kaibutsu at 11:10 PM on November 12, 2020 [3 favorites]

If string with loops in it doesn't have any holes in it, then a knitted sweater doesn't have any holes in it?

Of course the knitted fabric is being treated as a material surface, not a string.


Also if I take turns digging a hole with a friend, we each dig half a hole.

I love plating beans....
posted by Wilbefort at 2:05 AM on November 13, 2020

A balloon with a hole can't stay inflated, so balloons cannot have holes. But a balloon without a hole cannot be inflated, so balloons must have holes.
posted by gusottertrout at 2:12 AM on November 13, 2020 [1 favorite]

Thanks so much for responding, all of you - I really appreciate it.

I wrote a lengthy "rebuttal" in which I mentioned that those were the same kinds of analogies I had already considered and discarded, and then described the issues I had with them at length and proposed a couple of other mind experiments to further the argument. I'm glad I took the time to write it all out because in the end I saw where my mistakes were. I was finding issues with analogies instead of letting myself really think about what the math was trying to say.

The math is basically saying oh that's not a hole in a set of coordinates describing a perfect sphere, because now the boundaries of the set no longer contain the coordinates we just removed. It's not a hole in the topology, it's negative space where the topology used to be. Because it's not a hole, it's a new edge.

It was easier for me to picture it using a cube rather than a sphere. Like cutting down cardboard boxes. If I cut a hole in one side of the box, then use that hole to carefully breakdown, unfold and flatten the box, the remaining unfolded carboard will not have a hole through any of the connected panels. But if I punch a hole all the way through two sides of the box, then if I unfold and flatten it using one hole, there will still be a remaining hole in one panel.

So it's dimensional, I guess. If the set of all possible unfoldings of a 3D topology into a 2D space still has a hole in it, then... it has a hole in it. But that will require (at least) 2 holes to begin with.

Which is true because of how we define topologies, not because it's an inherently better (or worse) way to describe the system.

My favorite thing about this is realizing that if I drill one hole through the side of a ping pong ball, topologically speaking, there is no hole in the topology. But if I drill a second hole anywhere else on the surface, I now have exactly one hole in the topology. And it could be either hole, too. Magically transforming the first non-hole into a proper hole without changing anything about the hole itself.

Or maybe I'm just super sleep deprived and I've got it wrong, again. Either way, thanks for playing.
posted by It's Raining Florence Henderson at 2:37 AM on November 13, 2020

A balloon with a hole can't stay inflated, so balloons cannot have holes. But a balloon without a hole cannot be inflated, so balloons must have holes.

You'd might think that'd be terrible, an impossible contradiction, but a balloon knows its knot.
posted by gusottertrout at 4:39 AM on November 13, 2020 [5 favorites]

On the other hand, topological pairs of pants are important for studying surfaces, and it's much more common to call a pair of pants a "three-holed sphere" rather than a "two-holed disk." I think it's the difference between a hole as "something removed from an object" and "something you could loop a piece of string through."
posted by ectabo at 5:30 AM on November 13, 2020 [2 favorites]

take that thin surface and stretch it in the other direction and you could form a solid sphere

Seems to me that this would only work if what you're starting with is a 3D solid that merely approximates a sphere. A mathematical sphere (as opposed to a ball) has no thickness at all - it's a surface by definition - so scaling it in directions locally normal to that surface leaves it unchanged.

What you are doing by poking a hole in a sphere is turning a closed surface into a surface with a boundary.
posted by flabdablet at 6:58 AM on November 13, 2020 [1 favorite]

I've always found that topology could potentially undermine the "you can colour any map with only four colours" argument. That solution depends on the map representing the surface of a plane, e.g. it's a globe showing the boundaries of countries.

But in reality, the world isn't a plane - it has "through holes" for example cave systems with multiple entrances as well as man-made tunnels. If these subterranean spaces can legitimately "belong" to a country that isn't the one sitting "above" it, for example a road tunnel or bridge between two countries that passes a strait belonging to a third, then you might require five (or more!) colours for your map.

I haven't yet found a real example, but the obvious place to look would be cave systems near pseudo-quadripoints, where there might exist caves/tunnels/bridges that connect the two otherwise-disconnected regions but where the tunnel is not considered to belong to any other region (that it passes under/over).

Or maybe there really aren't any. At least, until we put a hole through the Earth like in that stupid movie.
posted by avapoet at 7:27 AM on November 15, 2020

Avapoet, maybe an embassy located over a subway would do what you want?
posted by Joe in Australia at 11:31 AM on November 15, 2020

I've always found that topology could potentially undermine the "you can colour any map with only four colours" argument.

I believe they actually solved the map coloring problem for a toroid before they solved it for a flat plane. A map on a toroid needs seven colors.
posted by showbiz_liz at 11:39 AM on November 15, 2020

The four color theorem is specifically for planar maps, yeah.
posted by eviemath at 12:37 PM on November 15, 2020

One could certainly make a non-planar map with tunnels from each region to every other region, with any number of regions.
posted by aubilenon at 3:04 PM on November 15, 2020

A balloon with a hole can't stay inflated, so balloons cannot have holes. But a balloon without a hole cannot be inflated, so balloons must have holes.

So, if a balloon is tied with a knot, how many holes does it have?
posted by eotvos at 9:16 PM on November 15, 2020

I'm pretty sure that topologically speaking, the kinds of knot you can tie a balloon into don't count as knots.

*(Offer may not be valid in higher dimensions, or Wisconsin)
posted by ook at 10:13 AM on November 16, 2020 [2 favorites]

Hmmm, seems fine to me? Framed knots (basically, knots made with a ribbon, to track orientability) are a thing. The balloon knot (iiuc) would be like making a knot from a torus. Unhelpfully, a "torus knot" refers to a knot which you can draw on the surface of a torus. So I'm not sure if the balloon knots have been studied (maybe just uninteresting from a math perspective, eg easy to describe in terms of the basic knot their built from).

Also the magic word for those who reaaaaaally want to count holes precisely is homology. (As my PhD adviser once told me, those who do not understand homology are doomed to reinvent it.)
posted by kaibutsu at 8:32 PM on November 16, 2020 [2 favorites]