Tuesday, December 3, 2019

Shapes of holes

The ordinary notion of a hole is kind of dubious. Consider the hole in the thin wavy sheet of rubber on the right. What is the shape of that hole? How thick is it? Is it exactly as thick as the rubber sheet? But the rubber sheet varies in thickness, actually. How does it stretch from its wavy edges to the middle? Does it have a sinewave bump in the middle, to correspond to where there are sinewave bumps in the sheet elsewhere? Or does that depend on the history of its formation (e.g., maybe if the sheet used to have a bump there but then a hole was made--that's how my code generating this picture works--then the hole has a bump, but if the sheet was pre-made with a hole, then the hole is flatter)? I think there really are no good answers to these questions, and hence holes don't exist.

9 comments:

Martin Cooke said...

Great question! It sounds like a classic analytic puzzle, but I have never heard of it before. I think that holes obviously exist. Perhaps I could defend my position by posing similar questions of other things that obviously exist.

The thickness of a hole is perhaps not an important property of it. So perhaps it is like the loveliness of your sheet of rubber. Loveliness is an important property of people and pets and views and works of art and many other things. And while it is a matter of opinion, that does not mean that there are not good answers to questions of loveliness. Hitler was clearly not lovely, for example. But, while you probably like your sheet of rubber, even you might doubt its loveliness. It is kind of dubious. Still, the sheet exists (so to speak). And similarly, although I have no idea how thick the hole in it is, still that hole exists.

Philip Rand said...

PROPOSITION: I think there really are no good answers to these questions, and hence holes don't exist.

CONCLUSION: It is impossible to fall down a hole because holes don't exist.

Philip Rand said...

Interesting conclusion regarding Aristotle, i.e. formal causes don't exist.

Alexander R Pruss said...

The shape of a hole does seem to be an important property of it.

Alexander R Pruss said...

It's also odd that for a hole in a thin wavy sheet, there may be no point in space such that it's definitely the case that the point is in the hole. Maybe that's an ok amount of vagueness.

Martin Cooke said...

While the shape of a hole is an important property of it, that is not its three-dimensional shape but its two-dimensional shape. The thickness is not so important, just so long as it goes all the way through, just so long as it is a hole.

If it was very thick, then it would be less of a hole and more of a tunnel. There is probably a grey area between a hole and a tunnel. And I guess you could think of string as a tunnel in space.

A hole in an unusual substance could be very odd indeed, but that is less about the existence of holes in general. And while points in a hole are odd, so are, for example, atoms in our bodies, so I think that such vagueness might just be par for the course.

Martin Cooke said...

A hole through a wall, for a very thick wall, would also be a tunnel.

But if the ends of the hole were filled in, the wall would have no hole in it, only a cavity. Whereas if the ends of the tunnel were filled in, the tunnel would still be there.

That is not too odd though.

Philip Rand said...

Martin Cooke

There is probably a grey area between a hole and a tunnel.

There is probably a grey area between a hole and an arse-hole.

What is the difference?

Philip Rand said...

Martin Cooke

Think of holes and tunnels as porosity. This should remove the grey area between a hole and a tunnel for you.