5 ms·

Potato Paradox

excalibur 4y ago
Why are you assuming that leaving potatoes out overnight would change them from 99% water to 98%? Is your house directly adjacent to an active volcano? Why would you even measure that?
- OJFord 4y ago
  But the existence of the 99% water content potatoes to begin with doesn't trouble you?
vkjlkdjfa3 4y ago
there's no paradox, just a misunderstanding.
- Gunax 4y ago
  I tend to agree, we need another word for 'tricky or misleading problem'.
- tanseydavid 4y ago
  It rolls off the tongue ever so nicely though. Consider: The Potato Conundrum is just not as fun to say or easily memorable (IMHO).
- OJFord 4y ago
  A very prevalent misunderstanding/error though - 'comparing fractions of different things' in general. i.e. here the basic issue is that it's really more like two different potatoes, each with different water content but the same amount of flesh; they're different potatoes so obviously they have different masses, and that's the denominator unit of the (water content ratio) fraction in a sense.
markisus 4y ago
Easier to visualize if you just plot it. Start with total mass is 100 kg, and 99 kg water, and 1 kg dry. Let x be the kg of water removed. Then the ratio of water to total mass is (99 - x)/(100 - x) Plot: https://imgur.com/a/oDaKLVo https://imgur.com/a/oDaKLVo It's intuitive that until x becomes pretty large, there is negligible effect on the ratio.
- karmakaze 4y ago
  It's easy enough to sort out in your head if you consider the non-water component changing from 1% to 2% and staying the same mass.
actually_a_dog 4y ago
This sounds less like a paradox and more like a simple high school algebra problem to me.
- OJFord 4y ago
  I sort of agree, but also, especially under exam conditions, arriving at the (correct) answer I would definitely think 'well obviously I went wrong somewhere'.
  - actually_a_dog 4y ago
    Yeah, but the fact that it's a little tricky to think about, and that the trickiness doesn't come from the algebra part of the problem are exactly why I would say that's a terrible question to ask under exam conditions in the first place. I'd be totally cool with assigning it as homework, both because it could generate some meaningful discussion, and because doing the problem on one's own and with ample time to think gives the student the opportunity to work through the "paradoxical" aspects themselves.
andrewflnr 4y ago
How about "Potato Puzzler", do we like that one better?
xavivives 4y ago
A more relatable example to me is with chocolate bars. A 85% chocolate has 3 times more sugar than a 95% chocolate. I wonder the world-wide impact in people health if they advertised the ratio in terms of sugar instead of cacao.
chrisworden 4y ago
I think it's more interesting that this poorly-worded "riddle" managed to find its way onto wikipedia: A section titled "The Language Paradox" was removed on October 2: > Careful wording must be used to ensure that the "paradox" is correct. With the explanation: "This is 100% original research, which as noted contains errors" So the only thing that makes the "paradox" interesting is that it's badly worded, but any commentary to that effect is original research, so in the end we're just left with a fairly unremarkable riddle on Wikipedia and grumpy people like myself complaining about it.

Why are you assuming that leaving potatoes out overnight would change them from 99% water to 98%? Is your house directly adjacent to an active volcano? Why would you even measure that?

OJFord 4y ago
But the existence of the 99% water content potatoes to begin with doesn't trouble you?

vkjlkdjfa3 4y ago

there's no paradox, just a misunderstanding.

Gunax 4y ago
I tend to agree, we need another word for 'tricky or misleading problem'.
tanseydavid 4y ago
It rolls off the tongue ever so nicely though. Consider: The Potato Conundrum is just not as fun to say or easily memorable (IMHO).
OJFord 4y ago
A very prevalent misunderstanding/error though - 'comparing fractions of different things' in general. i.e. here the basic issue is that it's really more like two different potatoes, each with different water content but the same amount of flesh; they're different potatoes so obviously they have different masses, and that's the denominator unit of the (water content ratio) fraction in a sense.

markisus 4y ago

Easier to visualize if you just plot it. Start with total mass is 100 kg, and 99 kg water, and 1 kg dry. Let x be the kg of water removed. Then the ratio of water to total mass is (99 - x)/(100 - x) Plot: https://imgur.com/a/oDaKLVo https://imgur.com/a/oDaKLVo It's intuitive that until x becomes pretty large, there is negligible effect on the ratio.

karmakaze 4y ago
It's easy enough to sort out in your head if you consider the non-water component changing from 1% to 2% and staying the same mass.

actually_a_dog 4y ago

This sounds less like a paradox and more like a simple high school algebra problem to me.

OJFord 4y ago
I sort of agree, but also, especially under exam conditions, arriving at the (correct) answer I would definitely think 'well obviously I went wrong somewhere'.
- actually_a_dog 4y ago
  Yeah, but the fact that it's a little tricky to think about, and that the trickiness doesn't come from the algebra part of the problem are exactly why I would say that's a terrible question to ask under exam conditions in the first place. I'd be totally cool with assigning it as homework, both because it could generate some meaningful discussion, and because doing the problem on one's own and with ample time to think gives the student the opportunity to work through the "paradoxical" aspects themselves.

andrewflnr 4y ago

How about "Potato Puzzler", do we like that one better?

xavivives 4y ago

A more relatable example to me is with chocolate bars. A 85% chocolate has 3 times more sugar than a 95% chocolate. I wonder the world-wide impact in people health if they advertised the ratio in terms of sugar instead of cacao.

chrisworden 4y ago

I think it's more interesting that this poorly-worded "riddle" managed to find its way onto wikipedia: A section titled "The Language Paradox" was removed on October 2: > Careful wording must be used to ensure that the "paradox" is correct. With the explanation: "This is 100% original research, which as noted contains errors" So the only thing that makes the "paradox" interesting is that it's badly worded, but any commentary to that effect is original research, so in the end we're just left with a fairly unremarkable riddle on Wikipedia and grumpy people like myself complaining about it.