← All Posts /

The Potato Paradox

One less potato from the potatoes we have is half the amount of potato we had originally. Already confused? Well, don’t be. The potato paradox will help you understand how doubling one portion of the whole affects the whole in drastic ways. It requires the other one’s size to be reduced by half of the whole, whether it’s doubling from 1% or .00001%. Or 10%.

Potato, one of the most commonly used vegetables in cooking, which we’ve long connected with for making us fat or being our favourite carbohydrate, actually has a perplexing paradox built into it. But potatoes have never been contradictory, have they? Wrong! THE POTATO PARADOX IS HERE.

Assume you have 100 pounds of potatoes, and 99 % of their weight is water. The remaining 1% of their weight is made up of carbohydrates, proteins, pectins, and minerals. They dry out a little after being left out overnight. They’re only 98 % water when you wake up, thus just 2% of it is solid. So, how much does your sack of potatoes now weigh? Your sack of potatoes would now weigh 50 pounds after this minor adjustment. So, what causes this? Is it true that the potato went on a complete carb-free diet in one night? Maybe not, because they’d been killed doing it. Clearly not. Let’s delve into the math now to better grasp this.

The 1% change in composition reduces the weight by HALF. How? Considering the case of Potatoes is the simplest method to visualise the solution. There are a hundred of them. Let’s use one painted potato to represent the 1% solid potato substance we started with. The water is represented by the remaining 99. The amount of solid stuff in the potatoes does not alter as they dry out. The water is the only thing that disappears. So, if we take away ONE unit of water, we’re left with 99 pounds of material, one of which is dry and the other 98 being water. So, let’s just perform some quick math here; 98.989899 % is 98.989899 %. Okay, that’s a lot of water.

Let’s just take out another pound of water, and we’ll have 97 of the 98 pounds here that are water. So we’ll go with 97 out of 98, which is 98.979591836 %. There’s simply too much water. There has to be a better way to do things.

The issue is that this is decreasing extremely slowly since for every unit of water that evaporates, the total amount remaining decreases as well. Let’s take a look at the final result to see how many we need to remove. So, instead of 98 or 97, we need to cut our water supply to 49. What’s more, here’s why: So we’ve got 98 % water and 2% solids, but only one solid unit. Let’s change that 2 to a 1.

So, we’ll divide 2 by 2 and get 1, and we’ll do the same thing with our 98, so we’ll divide that by 2 and get 49.

So 49 plus 1 equals 50, and the solution is 50 pounds. So we have to get rid of a LOT of water potatoes. I’m not sure how many are left, but I believe there are 49 waters and one solid. And 98 % is equal to 49 divided by 50. It was a success! That is the solution. The potato paradox comes into play every time there are two items and the concentration of one doubles. That requires the other one’s size to be reduced by half of the whole, whether it’s doubling from 1% or .00001%. Or 10%. Ask your friends to solve this problem and see what they say.

Most of the time, our first response is to assume that not much has changed since 1% is so small. This isn’t something to be ashamed of – our brains evolved to compare quantities like this: there’s one wooly mammoth and there’s five of us or how much food do we need to keep the family surviving through the winter? Evaluating concentrations is more abstract and not usually a life-or-death issue that natural selection would play a role in shaping.

Unlike other well-known paradoxes, such as time travel ones, the POTATO conundrum is a VERIDICAL paradox, meaning it has a TRUE solution that we can all agree on and verify, but it is nonetheless startling. So, the potato paradox is a type of paradox that isn’t based on misunderstandings, impossibilities, or speculation, but rather on a deep understanding of how the mind works.

Recommended » Benford's Law