A Little to Do with Nothing

There’s an interesting claim made in this Vox article, not so much about nothing as about zero.  Namely that young humans have a delay in processing a specific claim about a zero set, a set with nothing in it.

For example, using their image:

A child is asked (according to the Vox article) “to pick the card with the fewest number of objects”.  That’s a strange thing to ask, “fewest number”, but I guess it works, working from the top left and working clockwise, the answers would be 2, 4, 8 and 1.  By this I mean that there are two numbers of objects in the top right card, 1 and 2 (because there are two, there is also one, making two numbers).  Looking at the bottom left, there is only one number of objects, namely zero, but this would mean that a set of zero objects and a set of one object would both have one number of objects (0 and 1, respectively).

But let’s look past that and assume that the authors meant, but perhaps didn’t quite want to say “fewest objects”.  Looking at the second test, which card has the fewest objects?  The card with no objects on it, or the card with 8 objects on it?

My gut feeling is that it’s the one with 8 objects.  In a sense, the other one doesn’t have zero specific objects on it, it has no objects on it at all.  The logic here is to think, question 1: which of the cards has objects on it, and question 2: which of those cards has fewest objects?

Think of instructing people to go into a room, find the table with the “fewest number of cats on it”, and report back with that number.  If there are seven cats and eight tables, would you really expect them to come back every time with the number zero, or would you expect them to eliminate the empty tables from consideration and to count only the tables with cats on them?

If we are forced to consider such empty tables in terms of what are not on them, then the list of what is there (in lots of zero) is indefinitely long – there are no cats, no dogs, no chickens, no horses, no parrots, no rats, no cacti, etc, etc, etc.  That’s not a rational way to go about categorising things.  (Which table is it on, dear? – The one in the hallway, with the vase on it, and no cats, no dogs, no chickens, no horses, no parrots, no rats, no cacti …)

I don’t find it strange that large numbers of children don’t count a card with no objects on it as being the card with fewest objects on it, because it doesn’t qualify as being a card with objects on it.  I don’t find it strange to think that it takes a tiny bit more cognitive effort to consider whether you are being asked for the lowest non-zero value or the lowest value including zero, or to recognise O. (What is that, noting that it's in another font, is it the letter "o" or the number zero?)

That all said, I do have to say that I nevertheless appreciate the value of nothing, the use of which makes so much possible.