What We Talk about When We Talk about Holes (2014) | Hacker News Reader

What We Talk about When We Talk about Holes (2014)

blogs.scientificamerican.com

28 pointsColinWright9 comments

In the spirit of (and referenced by) the Stanford Encyclopedia of Philosophy entry mentioned in the article, here's a lovely little philosophical (and not substantially mathematical) dialogue about holes: http://www.philosophy.org.vt.edu/files/9013/4455/4412/Lewis_... .

(I think the philosophers should be listening to the mathematicians, though. Part of the answer to the question "what is a hole", and part of the explanation for, e.g., the fact that counting the number of holes in a thing is problematic, is that what holed-ness really is is nontrivial homology, and the right question for holes is not "how many?" but "what homology groups?", etc.)

For those who prefer to listen (and see puppets making silly faces): https://www.youtube.com/watch?v=SoSx4nxgvgY

Misleading terminology alert: I would have said that a basketball doesn't have a hole, for the same reason that a tire doesn't have a hole: if it did, it would deflate.

But he means that a basketball is in airtight container, so it has a sort of two dimensional hole. By his definition, when you put a cap on a tube of toothpaste, it creates a hole rather than closing a hole.

The point, to some extent, is that when you talk about a "hole" you need to specify what dimension you're referring to. Making that precise is hard, and is one of the things that makes serious topology difficult.

And useful. I've worked with robot arm systems with 9 degrees of freedom, and thinking of the configuration space as a 9 dimensional manifold with "holes" was the key point.

The terminology isn't misleading, it's technical.

> thinking of the configuration space as a 9 dimensional manifold with "holes" was the key point

Fascinating. Can you expand on that? i.e. what is the configuration space, how did manifolds with holes connect with it, and how did you figure out that the problem should be represented that way?

I'll see if I can write that up - It'll take more time than I have right now. In essence, people tend to think of moving through a space like "robot positions" as moving through ordinary space: "I can see where I'm going - I'll go that way." Unfortunately, in higher dimensions that doesn't work, and you have to develop an awareness of where the holes are so you can go round them.

I'll write that up and submit it.

> he means

She means.

Both are holes, they are just different dimensions of holes. The holes in swiss cheese are still holes, even if you haven't exposed them yet.

I am having trouble following this. It kind of breaks my brain, like discussing time and dimensions with my sons. But I cannot help but think of portable holes in old cartoons, like Bugs Bunny.

Edit: Though I will say I am impressed with her example of torus. Donut glaze is something everyone should be able to relate to.

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