4 ms·

Or take a sphere and poke a hole in it. Topologist says there are no holes, because now it is a disk. But wow else would you describe poking a hole in a sphere?

by Retra 8y ago

lisper 8y ago
Even that is based on the tacit assumption that the sphere you are poking a hole in is a two-dimensional manifold and not a solid. If you "poke a hole" in a solid sphere (which is what you actually do when you dig a hole in the ground) you haven't change anything from a topological point of view.
- ColinWright 8y ago
  Sphere, not ball. A sphere is inherently a two dimensional manifold with no edges, two sides, and no embedded loops that are homotopically not a point. It's an idealised "shell". However ... I'm trying to understand your points here, but it's almost like you're saying that the things mathematicians do have no value as they stand, and they should be doing something else. That might not be what you mean, but reading your comments as a whole, that's the impression I'm getting. Much of what you say is true, but seems to be going off on that tangent. Mathematicians, in these sorts of circumstances, take abstract things that are, in some senses, approximations of something from reality, and then examine those abstract things to see what they can find out about them. They are approximations, and sometimes the results aren't applicable, but often they are. This video is a case in point. We look at how we can model the straw, and see what the word "hole" might mean in that model, then map it back to reality to see what answer that gives us. But your comments all seem to be saying: But that's not relevant to how we use language, and so you're neither getting the "right" answer, nor doing anything fundamentally useful. So based on that reading of your comments, I'm not sure I have anything further to add.
  - lisper 8y ago
    > it's almost like you're saying that the things mathematicians do have no value as they stand I have no idea how I could have left you with that impression. I'm talking about pedagogy and rhetoric, not math. I opened with: "The problem with being topologically pedantic..." I honestly don't know how I could possibly have made it any plainer.
    - henryseg 8y ago
      At 30 seconds into the video I say "from a topologist's perspective, how you might try and answer this question". I tried to be very clear that this was not the one true answer, but just my perspective. And the impression you got was: > Instead it comes across as a geek being smug about knowing the "right answer" to brain teaser because topology." Perhaps the moral of all of this (and discussions on the internet in general), is that communication is hard.
      - lisper 8y ago
        OK, I re-watched your video, as well as the Actionlab one it was responding to, and this: > it comes across as a geek being smug about knowing the "right answer" was unfair. I apologize. I went back and tried to figure out where the impression I got diverged from reality, and I think it was at 0:26 where you say, "people don't really have a good definition of what a hole is" and my brain extrapolated this to expect something like, "and in this video I'm going to give you one." Which is of course not what you say, but it's not an unreasonable expectation. In fact the impression I now come away with on second viewing is that topologists are just as much out to sea on this as everyone else. I suspect that was not the impression you intended to leave either. > communication is hard Indeed. But if I may offer (what I hope is) a constructive suggestion: the first step to clear communication is to know your audience. It's unclear to me who the target audience of your video was intended to be. You start out speaking very informally, e.g. "objects in topology are kind of stretchy and maybe you can chance something that looks like a hole into something that doesn't look like a hole." That indicates that you intended the video to be seen by a lay audience (also the video you're responding to was clearly intended for a lay audience). But mid-way through you casually introduce the terms "homotopy group" and "homology group" without explaining them (just pointers to Wikipedia pages) indicating that you expect a certain level of mathematical sophistication. I think that was one of the things that originally registered in my mind as "smug". In any case, I applaud the fact that you are putting forth the effort to make educational videos about math. I watched a few more in your channel and really enjoyed them. "Geared Cuboctahedral Jitterbug" was particularly cool! [UPDATE] Triple-piano just totally blew me away!
- Retra 8y ago
  I understand the topological point of view (which also generally considers spheres to be 2-dimensional surfaces.) I'm pointing out that common language does not match the topological point of view. Topology also has 'open' and 'closed' sets, which are not very good names for whether some subset of a space 'has a shared classification of nearness', and 'tunnel' is probably better terminology than 'hole' is. But mathematics is done by intelligent people, and it's a rather esoteric subject, so it isn't exactly a problem that the terms don't align intuitively.
SantalBlush 8y ago
You can poke a hole in the sphere if your "pin" enters one side and comes out the other end. The problem with the conventional notion of a hole is that it depends on the curvature on an object, which is imprecise and arbitrary. In your example, suppose you put a "hole" in your sphere and started flattening it into a disk. As you flatten your sphere, at which point does the hole disappear? Can you rigorously define it so that your definition applies to all objects?

Or take a sphere and poke a hole in it. Topologist says there are no holes, because now it is a disk. But wow else would you describe poking a hole in a sphere?

by Retra 8y ago

Or take a sphere and poke a hole in it. Topologist says there are no holes, because now it is a disk. But wow else would you describe poking a hole in a sphere?

lisper 8y ago

Even that is based on the tacit assumption that the sphere you are poking a hole in is a two-dimensional manifold and not a solid. If you "poke a hole" in a solid sphere (which is what you actually do when you dig a hole in the ground) you haven't change anything from a topological point of view.

ColinWright 8y ago
Sphere, not ball. A sphere is inherently a two dimensional manifold with no edges, two sides, and no embedded loops that are homotopically not a point. It's an idealised "shell". However ... I'm trying to understand your points here, but it's almost like you're saying that the things mathematicians do have no value as they stand, and they should be doing something else. That might not be what you mean, but reading your comments as a whole, that's the impression I'm getting. Much of what you say is true, but seems to be going off on that tangent. Mathematicians, in these sorts of circumstances, take abstract things that are, in some senses, approximations of something from reality, and then examine those abstract things to see what they can find out about them. They are approximations, and sometimes the results aren't applicable, but often they are. This video is a case in point. We look at how we can model the straw, and see what the word "hole" might mean in that model, then map it back to reality to see what answer that gives us. But your comments all seem to be saying: But that's not relevant to how we use language, and so you're neither getting the "right" answer, nor doing anything fundamentally useful. So based on that reading of your comments, I'm not sure I have anything further to add.
- lisper 8y ago
  > it's almost like you're saying that the things mathematicians do have no value as they stand I have no idea how I could have left you with that impression. I'm talking about pedagogy and rhetoric, not math. I opened with: "The problem with being topologically pedantic..." I honestly don't know how I could possibly have made it any plainer.
  - henryseg 8y ago
    At 30 seconds into the video I say "from a topologist's perspective, how you might try and answer this question". I tried to be very clear that this was not the one true answer, but just my perspective. And the impression you got was: > Instead it comes across as a geek being smug about knowing the "right answer" to brain teaser because topology." Perhaps the moral of all of this (and discussions on the internet in general), is that communication is hard.
    - lisper 8y ago
      OK, I re-watched your video, as well as the Actionlab one it was responding to, and this: > it comes across as a geek being smug about knowing the "right answer" was unfair. I apologize. I went back and tried to figure out where the impression I got diverged from reality, and I think it was at 0:26 where you say, "people don't really have a good definition of what a hole is" and my brain extrapolated this to expect something like, "and in this video I'm going to give you one." Which is of course not what you say, but it's not an unreasonable expectation. In fact the impression I now come away with on second viewing is that topologists are just as much out to sea on this as everyone else. I suspect that was not the impression you intended to leave either. > communication is hard Indeed. But if I may offer (what I hope is) a constructive suggestion: the first step to clear communication is to know your audience. It's unclear to me who the target audience of your video was intended to be. You start out speaking very informally, e.g. "objects in topology are kind of stretchy and maybe you can chance something that looks like a hole into something that doesn't look like a hole." That indicates that you intended the video to be seen by a lay audience (also the video you're responding to was clearly intended for a lay audience). But mid-way through you casually introduce the terms "homotopy group" and "homology group" without explaining them (just pointers to Wikipedia pages) indicating that you expect a certain level of mathematical sophistication. I think that was one of the things that originally registered in my mind as "smug". In any case, I applaud the fact that you are putting forth the effort to make educational videos about math. I watched a few more in your channel and really enjoyed them. "Geared Cuboctahedral Jitterbug" was particularly cool! [UPDATE] Triple-piano just totally blew me away!
Retra 8y ago
I understand the topological point of view (which also generally considers spheres to be 2-dimensional surfaces.) I'm pointing out that common language does not match the topological point of view. Topology also has 'open' and 'closed' sets, which are not very good names for whether some subset of a space 'has a shared classification of nearness', and 'tunnel' is probably better terminology than 'hole' is. But mathematics is done by intelligent people, and it's a rather esoteric subject, so it isn't exactly a problem that the terms don't align intuitively.

SantalBlush 8y ago

You can poke a hole in the sphere if your "pin" enters one side and comes out the other end. The problem with the conventional notion of a hole is that it depends on the curvature on an object, which is imprecise and arbitrary. In your example, suppose you put a "hole" in your sphere and started flattening it into a disk. As you flatten your sphere, at which point does the hole disappear? Can you rigorously define it so that your definition applies to all objects?