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No, topologically there would be no holes until the moment of contact. This is the same as there being no hole when drilling through from only one side until the surface on the opposing side is broken.
Yes, but topologists can't tell a doughnut from a coffee cup so they're clearly insane.
So how does one “dig a hole?” Straight to China? Or whatever is opposite of you?
Topologically, yes. Buy you could also go down a bit, make a lateral tunnel, then pop back up.
So what you are saying is, if I dig a hole that doesn't go anywhere, then that's not really a hole?
In topology, yes. It must go through to count.
That's fascinating. So most of what I would call "holes" are what, in topographical terms, hollows? Depressions?
I don't even know if they have a name for that since it can simply be undone by stretching the object, which is allowed under topological rules.
Topologically, yes. Coincidentally, "Hole to Nowhere" is the best Talking Heads parody album.
Heh I will have to check that out!