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Jam doughnuts don't even have holes, technically.
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Oct 28, 2020 20:48
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Tenebrais posted:Well, are they? After all, how many holes are there on a human? Because topologically a human is homeomorphic to a donut. Humans aren't homeomorphic to donuts, a straw with a hole in the side is a pair of pants, and straws and rubber bands are homeomorphic.
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Oct 28, 2020 20:53
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How many holes does a Klein bottle have?
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Oct 28, 2020 20:59
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Tenebrais posted:Well, are they? After all, how many holes are there on a human? Because topologically a human is homeomorphic to a donut. Language is weird and imprecise.
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Oct 28, 2020 21:02
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dwarf74 posted:I had a philosophy professor whose entire career was based on defining what a "heap" is. Same concept as "hole" it turns out. Your professor must be old as hell! https://en.wikipedia.org/wiki/Eubulides
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Oct 28, 2020 21:13
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Elviscat posted:There's been a disarmament protest permanently occupying ground outside the Faslane Scotland submarine base since 1982 drat, don't they have squatters rights at this point?
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Oct 28, 2020 21:15
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mobby_6kl posted:How many holes does a Klein bottle have?
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Oct 28, 2020 21:18
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Dr. Arbitrary posted:Your professor must be old as hell! Haha like he settled it. 
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Oct 28, 2020 21:20
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Tenebrais posted:Well, are they? After all, how many holes are there on a human? Because topologically a human is homeomorphic to a donut. https://www.youtube.com/watch?v=egEraZP9yXQ
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Oct 28, 2020 21:26
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https://m.youtube.com/watch?v=SoSx4nxgvgY (From https://rintintin.colorado.edu/~vancecd/phil375/Lewis1.pdf)
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Oct 28, 2020 21:28
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I feel like some of them must be troll answers because I could see arguments for 0 or 1 hole on a donut (comes down to a philosophical argument about whether the gap is "part" of the donut or not), but there is no argument that makes sense for 2.
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Oct 28, 2020 22:42
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It's zero because they take the hole out to sell separately.
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Oct 28, 2020 22:46
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I think the "cup" entry presents some ambiguity, since it doesn't specify if the cup has a handle or not. As for the bowl and spoon examples, it looks like some people understand "hole" to mean "indentation" not "passage through." (The proportion of people saying these things have holes seems to roughly correlate with the depth of the indentation relative to object size.) But if the ends of the passage-through are far enough apart, as in a straw, then it becomes two holes. Conversely, in a rubber band, the ends of the hole/passage are very close so it's less... holey. And you could argue that the letter O doesn't have a hole because it's not a 3d physical object. I guess. Alternatively, everything has infinity holes because matter is mostly empty space, just ask a neutrino. You could say that the definition of a hole is full of holes!
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Oct 28, 2020 22:56
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The Cheshire Cat posted:I feel like some of them must be troll answers because I could see arguments for 0 or 1 hole on a donut (comes down to a philosophical argument about whether the gap is "part" of the donut or not), but there is no argument that makes sense for 2. I don't have an opinion on this, but the argument seems pretty clear to me. There is a tunnel going through the doughnut. On one side of the doughnut is a hole leading to the tunnel, and on the other side of the doughnut is another hole leading to the same tunnel. Boom, two holes. SerialKilldeer posted:I think the "cup" entry presents some ambiguity, since it doesn't specify if the cup has a handle or not. As for the bowl and spoon examples, it looks like some people understand "hole" to mean "indentation" not "passage through." (The proportion of people saying these things have holes seems to roughly correlate with the depth of the indentation relative to object size.) But if the ends of the passage-through are far enough apart, as in a straw, then it becomes two holes. Conversely, in a rubber band, the ends of the hole/passage are very close so it's less... holey. And you could argue that the letter O doesn't have a hole because it's not a 3d physical object. I guess. But if a hole needs to be a passage through then a hole you dig in the ground isn't a hole. 
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Oct 28, 2020 23:48
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mobby_6kl posted:How many holes does a Klein bottle have? Oof.  What we think of as a Klein bottle, the glass bottles you can buy from Cliff Stoll, are just a three-dimensional projection of a four-dimensional structure. To make this work in 3D, you need to add this circled 'intersection'. If we analyze the 3D glass object as-is, including the intersection as intended part of the design, well you have the opening in the 'bottom', you can use to pour water in if you juggle it enough, but that's equivalent to the opening to the top of a vase so it's not a hole. Then there's the part where the 'neck' loops around to get to the intersection, and that looks equivalent to a donut hole to me. I'm not a topologist but I'd say the number of holes for the 3D projection of a Klein bottle is one. To get a more correct answer you'd need to look at the actual 4D structure, in which a Klein bottle can exist without such an intersection. There's no way you can do that in just 3D. And now we run into a problem. I have literally no idea how to even define a hole in 4D. Usually to think about 4D, it's helpful to think about going from 2D to 3D first. I'm not sure what a "hole" would be in 2D. What does it mean to go "through" a 2D object? I'm not sure. A flatlander could try to drill a hole through a square or something but he'd end up in cutting the square in half and that doesn't happen when you make a hole in something in 3D. You could take a circle and and cut out an inner circle or something, but that just feels like a 2D projection of a torus, and won't allow the flatlander to go through the circle and end up on the other side. I don't think it is possible to have a hole in the topological sense in 2D. So, holes cannot exist in 2D. There's a clear, single definition for a through-hole in 3D, in the topological sense. ... And I'm no closer to understanding 4D. If that trend continues there might be multiple valid ways to define topological holes in 4D. And since I don't know how to do that, I don't even know how to start answering the question of how many holes a true, 4D, Klein bottle has. But it was quite interesting to think the problem through up till this point.
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Oct 28, 2020 23:53
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Carbon dioxide posted:What we think of as a Klein bottle, the glass bottles you can buy from Cliff Stoll It was fun to recently find videos of Cliff Stoll (I'm thinking of the one showing-off his miniature remote-controlled robot forklift he built to store things in the crawlspace under his house) and him turning out to be just as nutty-professor as he sounds in The Cuckoo's Egg.
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Oct 29, 2020 00:05
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Captain Hygiene posted:It's zero because they take the hole out to sell separately. This is the only correct answer
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Oct 29, 2020 00:19
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Outrail posted:This is the only correct answer
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Oct 29, 2020 00:29
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This graph is probably a parody of bad political graphs, but it's a perfect example of it.
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Oct 29, 2020 01:49
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E: already posted
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Oct 29, 2020 01:55
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ultrafilter posted:Anyone who thinks that a donut and a straw have a different number of holes is very confused. I actually rather like the results because it suggests different conceptions of the construction of shapes. Is a donut a disc with a hole in it, or is it a continuous loop? Is a straw a cylinder with a hole in it, or is it a very wide, very small loop? If it does have a hole, is it one continuous hole or does it have a hole at either end that meet in the middle? Is it different on a donut because the distance between the two ends of the possible hole is smaller? Does a cup have a hole in it? Does a coffee cup with the lid on? It's a conceptual question about how you parse what "a hole" is. OwlFancier has a new favorite as of 01:58 on Oct 29, 2020 |
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Oct 29, 2020 01:56
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There's a pretty nice video that talks about holes in the last few posts.
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Oct 29, 2020 01:59
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Donuts have holes in them if they were formed as discs of dough and had their centres punched out. They do not have holes in them if they were formed as rolls of dough whose ends were joined, nor if they were made in moulds.
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Oct 29, 2020 02:07
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OwlFancier posted:I actually rather like the results because it suggests different conceptions of the construction of shapes. Is a donut a disc with a hole in it, or is it a continuous loop? Is a straw a cylinder with a hole in it, or is it a very wide, very small loop? If it does have a hole, is it one continuous hole or does it have a hole at either end that meet in the middle? Is it different on a donut because the distance between the two ends of the possible hole is smaller? Does a cup have a hole in it? Does a coffee cup with the lid on? Yeah the straw vs. donut thing comes up in the video posted above and it sums it up pretty well where people colloquially think less about "holes" than they do about "openings". Straws feel like they have two "holes" because they have two openings that are separated from each other and have distinct functions (one goes in drink, other goes in mouth). Meanwhile a donut also technically has two openings but they are so close to each other that nobody really parses it as such, and there's no functional difference between each side of a donut so there's no reason to logically separate them into distinct features. This is also why people think of stuff like jars having "holes" in them even though topologically they don't, because the one opening they have serves a functional purpose.
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Oct 29, 2020 02:11
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The issue is similar to the tomato fruit debate. High‐falutin’ academics came up with a new definition of word that’s been in use since time immemorial and are gaslighting the public into believing that theirs is the one true definition.
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Oct 29, 2020 02:13
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The cup>bowl>spoon trend I think is a good one too.
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Oct 29, 2020 02:20
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The Cheshire Cat posted:This is also why people think of stuff like jars having "holes" in them even though topologically they don't, because the one opening they have serves a functional purpose. But this would mean a hole in the ground isn't a hole?
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Oct 29, 2020 02:25
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Outrail posted:But this would mean a hole in the ground isn't a hole? topologically, it wouldn't be, unless the other end comes out somewhere else, because in topology those are the only holes that matter. And so we see the dangers of taking a definition that is used in a specific context and trying to apply it universally
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Oct 29, 2020 02:32
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Oct 29, 2020 02:35
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Angepain posted:topologically, it wouldn't be, unless the other end comes out somewhere else, because in topology those are the only holes that matter. And so we see the dangers of taking a definition that is used in a specific context and trying to apply it universally If a hole ain't a hole than it's a holeload of nonsense. If it needs to go somewhere it's a tunnel.
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Oct 29, 2020 02:38
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mobby_6kl posted:How many holes does a Klein bottle have? The math questions thread says that it has two. That's the 4-dimensional Klein bottle, mind you, and not the 3-dimensional representation you're used to seeing.
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Oct 29, 2020 03:07
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"metals" should probably be "who cares"
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Oct 29, 2020 06:01
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ultrafilter posted:The math questions thread says that it has two. That's the 4-dimensional Klein bottle, mind you, and not the 3-dimensional representation you're used to seeing. Did they give an explanation? And if so, do you have a link?
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Oct 29, 2020 08:14
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this is not awful or funny. this is a good and useful periodic table. redleader posted:"metals" should probably be "who cares" No, we care about metals. Metals are trace elements, but they're still important to stellar dynamics.
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Oct 29, 2020 09:23
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Elviscat posted:There's been a disarmament protest permanently occupying ground outside the Faslane Scotland submarine base since 1982 There's been a continuous Aboriginal land rights protest in Canberra since 1972.
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Oct 29, 2020 09:37
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NoNotTheMindProbe posted:There's been a continuous Aboriginal land rights protest in Canberra since 1972. It’s a good effort, but it stretches the definition of “continuous”. “Since 1992” is more like it.
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Oct 29, 2020 09:49
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redleader posted:"metals" should probably be "who cares" "Statistically insignificant"
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Oct 29, 2020 10:42
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Sereri posted:"Statistically insignificant" They are significant though. Metal content affects the life cycle of stars for one thing.
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Oct 29, 2020 13:22
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Carbon dioxide posted:Did they give an explanation? And if so, do you have a link? Amniotic posted:2! (at least in the sense of genus) Not much of an explanation but someone who knows what genus is probably doesn't need one, and someone who doesn't has a lot of background reading to do.
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Oct 29, 2020 13:24
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https://twitter.com/Laurie_Garrett/status/1321627987847139329?s=20
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Oct 29, 2020 16:58
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