Dear Miru,

We were playing with a ball today, but you said it wasn’t a ball. Or, as you put it, that the ball was “kapot”. You meant that the ball lacked significantly in “ballness”; that its “ballness” was broken. I understand your intuition: The ball we were playing with didn’t look like any other ball you know. It was round, okay, but there were so many holes in it. In fact, it was more hole than ball. It was more like the skeleton of a ball.

This is a sphere, according to the dictionary:

“A three-dimensional closed surface such that every point on the surface is equidistant from the center”

Clearly, the ball doesn’t have a closed surface, so it’s not a sphere. Here’s what the dictionary says about a ball:

An object with a spherical shape

I think they call our toy a “buckyball”, after Buckminster Fuller, who discovered large molecules (fullerenes) with a large empty cage and at least 60 carbon atoms. A buckyball is just a spheroidal fullerene.

But how can we know? This definition seems pretty useless. We can do better than the dictionary and come up with a definition of the ball ourselves, ok? See, what makes the ball a ball? Not the fact that it is perfectly spherical (what about a ball with a small dent in it or a football that is a bit deflated?).

Let’s look at some properties of the ball. What do you think about rolling? Isn’t a ball something that rolls?

But wheels also roll.

Yes. So let’s correct it. What do you think about something that rolls in every direction?

Ok. But there are some weird shapes that can also roll in every direction. For example, a giant rubber dice with rounded edges. This is clearly not a ball.

Ok. What do you think about something that rolls in every direction at a constant speed? That means it must be round, and we can test its roundness by rolling the ball in every direction and measuring the speed.

But what about the ellipsoid ball they use in rugby? They call that a ball too. Should we make an exception or say it is not a “real” ball?

Maybe we can say it should roll at at most three different, constant speeds in every direction? That will rule out the really weird shapes with humps and dents and shapes that don’t have any apparent symmetry.

So we came up with a definition of a “ball”. It’s probably not perfect, but its enough for today.

An object that rolls at at most three different, constant speeds in every direction.

You seem to accept our definition. The ball is not “kapot” anymore – you repaired it, just with your mind.

*This is an example of what my daughter and I are developing as a series about “philosophy for children”. Any suggestions are welcome*