Cianain* has 100 lbs of potatoes, which consist of 99% water**. He then leaves them outside overnight so that they consist of 98% water. So what is their new weight? Hint: The answer isn't 98 lbs.
Surprisingly, the answer is 50 lbs. The easiest way to think about this is to look at the non-water weight, which stays constant. The non-water weight is 1 lb, which is 1% of 100 lbs. The next day, water accounts for 98% of the total weight, so 1 lb of non-water is 2% of the total weight. 1 lb is 2% of what? The total weight has to be half as large for the non-water weight to double.
The answer would still require the total weight to double even if we used concentrations of 99.999% and 99.998% instead of 99% and 98%, as long as the non-water weight concentration doubles.
Paradoxes challenge our heuristics. They require us to take an alternative perspective to a problem. Sometimes paradoxes put us in Strange Loops.
The philosopher Kierkegaard wrote,
But one must not think ill of the paradox, for the paradox is the passion of thought, and the thinker without the paradox is like the lover without passion: a mediocre fellow. But the ultimate potentiation of every passion is always to will its own downfall, and so it is also the ultimate passion of the understanding to will the collision, although in one way or another the collision must become its downfall. This, then, is the ultimate paradox of thought: to want to discover something that thought itself cannot think.
*My Irish grandfather's name. His version is What weighs more, a pound of bricks or a pound of feathers?
** Potatoes are closer to 80% water.