Hello! I'm Tom. I'm a game designer, writer, and programmer on Gunpoint, Heat Signature, and Tactical Breach Wizards. Here's some more info on all the games I've worked on, here are the videos I make on YouTube, and here are two short stories I wrote for the Machine of Death collections.
By me. Uses Adaptive Images by Matt Wilcox.
I just learned about ‘The Potato Paradox‘, which refers to this surprising maths result:
Q: You have 100kg of potatoes, which are 99 percent water by weight. You let them dehydrate until they’re 98 percent water by weight. How much do they weigh now?
A: 50kg
It’s not a riddle or a trick, it’s literally true and the terms mean what they seem to mean. The Wikipedia page has some good explanations and diagrams of why the answer is right, which persuaded me that it was, but that didn’t solve the problem for me. To me the problem is: why am I so wrong about this?
I see that it’s true, but it still doesn’t sound like it should be. What’s my brain doing wrong?
I think it’s because we intuitively read the question something like this:
Q. You have 99kg of water and 1kg of dried potato. You remove 1kg of water. How much does all the remaining stuff weigh?
A. 99kg
That’s what the question sounds like – a casual reading of it seems like it’s saying something along those lines, so we expect the result to be along those lines. We’re not 100% we’ve considered all the details – if we were told the real answer was 99.1kg or 98kg, we wouldn’t be massively surprised or interested enough to find out why it’s not what we guessed. But the answer’s 50. We’re nowhere close, we’ve fundamentally misunderstood the concepts.
So what’s wrong with our reading, and what’s the right one?
“You have 99kg of water and 1kg of dried potato.”
This much is true. Whether you think of it as two separate substances or all mixed up in individual potatoes isn’t relevant.
“You remove 1kg of water.”
This is where we fuck up. The original says “you let them dehydrate until they’re 98 percent water”. Removing 1kg of water leaves it as 98.99% water – barely changed at all. Each time you remove 1kg of water, you’re also removing 1kg of the total weight.
The 1kg of dried potato stays the same, so it’s really asking:
How much water do you have to remove until that 1kg of dried potato is twice as much of the total?
Then, I think, it clicks. That 1kg stays, but it makes up twice as much of the total at the end. So how much of the rest must have been removed? About half of it.
I don’t think ‘Maths problems most of us get wrong if we don’t do the maths’ rises to the level of ‘paradox’ though, which is why I’ve been putting it in derision quotes.