Start with 100 kilograms of potatoes, fresh from the field and, like most potatoes, about 99 per cent water. You leave them in the sun until they have dried out just slightly, from 99 per cent water down to 98 per cent water. How much do they weigh now?
The instinct is to say a hair under 100 kilograms. You only lost one percentage point of water, after all. The correct answer is 50 kilograms. Half the pile, gone, from a one-point change. This is the potato paradox, and the arithmetic behind it is stubbornly simple.
The trick is to stop watching the water and watch the part that is not water. In the fresh potatoes, 99 per cent is water, so the solid potato matter, the starch and fibre, is the other 1 per cent. One per cent of 100 kilograms is 1 kilogram. Drying the potatoes removes water, but it cannot remove that solid kilogram. Whatever happens, you still have exactly 1 kilogram of potato solids.
Now look at the end state. The dried potatoes are 98 per cent water, which means the solids are 2 per cent of the new total weight. But you already know the solids weigh 1 kilogram. If 1 kilogram is 2 per cent of the whole, then the whole is 50 kilograms, because 1 divided by 0.02 is 50. The single unchanging kilogram went from being 1 per cent of the pile to 2 per cent of it, and for that to happen, the pile itself had to shrink by half.
What fools everyone is treating “99 per cent” and “98 per cent” as almost the same thing. In everyday terms they feel identical. But measured against the tiny solid core, doubling from 1 per cent to 2 per cent is an enormous change, and the water has to collapse dramatically to make room for it. The potatoes did not lose a sliver of moisture. They lost half of everything.
