

What We Talk about When We Talk about Holes - ColinWright
http://blogs.scientificamerican.com/roots-of-unity/2014/12/25/what-is-a-hole/?HN_20141228

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gjm11
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_...](http://www.philosophy.org.vt.edu/files/9013/4455/4412/Lewis_and_Lewis_-
_Holes.pdf) .

(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.)

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

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skybrian
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.

~~~
ColinWright
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.

~~~
dang
> 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?

~~~
ColinWright
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.

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Mz
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.

