When Is a Heap Not a Heap?

Here is a heap of rice. Ten thousand grains, at least. Nobody would argue with that.

Now take one grain away. Is what is left a heap? Of course. One grain cannot be the difference between a heap and not-a-heap — that would be absurd.

Take another. Still a heap — by the same argument. Another. Another. Each time, removing one grain changes nothing, and each time what is left is a heap.

But follow the argument to the end and you are standing in front of a single grain of rice on a table, which you have just agreed is a heap.

Somewhere in there, the heap went away. So: which grain was the guilty one?

This puzzle is more than two thousand years old, and the uncomfortable part is that no step in it looks wrong. It feels like there should be a line — 4,731 grains is a heap, 4,730 is not — but nobody could ever say where it is, and any line you draw looks made up.

Once you see the shape of the puzzle, it turns up everywhere. How many hairs does a person need before they are not bald? How many minutes late is it fair to say the bus is “late”? How many euros make someone rich? How many drops of water make a puddle? Our words feel solid — heap, bald, rich, late — and each of them has one grain of vagueness hiding inside it.

Some philosophers say the lesson is that words are blunter than the world. Others say there really is a line, we just can’t see it. One of them is wrong. Finding out which grain it is has kept philosophers busy since the time of the ancient Greeks — and they have not finished yet.

What it is really asking

If every single step looks harmless, how does a big change ever happen?

How to tell it

This one needs props — rice, sand, or buttons. Actually take one grain away at a time and make everyone say “still a heap”. Stop when someone starts hedging.

Where this story comes from

Eubulides of Miletus, the sorites paradox

A puzzle from ancient Greece, about 2,300 years old. Sorites just means “of a heap”. Philosophers are still arguing about the answer, which is a good sign the puzzle is real.

This is a retelling, not a translation. The words are ours; the story is theirs.