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Potato paradox

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Re: Potato paradox

#111

Post by perlgeek »

gjm11 wrote: post #100
chestervonwinch wrote: post #3

Neat. This bumps up my list of food-related maths from 3 to 4. So far: https://en.wikipedia.org/wiki/Ham_sandwich_theorem https://en.wikipedia.org/wiki/Pizza_theorem https://en.wikipedia.org/wiki/Layer_cake_representation

One of the people I went to university with had a little (very short) mental catalogue of "chromatic mathematical fruit jokes". There are exactly two famous ones. "What's purple and commutes?" "An abelian grape." And: "What's yellow and equivalent to the axiom of choice?" "Zorn's lemon." He invented another, which requires more esoteric knowledge: "What's green and determined up to isomorphism by its first Chern clas…

"What's yellow, normed and complete? A Bananach Space"

Re: Potato paradox

#112

Post by ThrustVectoring »

philh wrote: post #75
ThrustVectoring wrote: post #66

The solution is much more intuitive if you use odds ratios instead of percentage probabilities. You go from a 99:1 ratio to a 98:2 (or 49:1) ratio. In other words, it's another way of phrasing that it takes twice as much evidence to be 99% sure as it is to be 98% sure. Or that it's twice as hard to have 99% uptime than 98%.

> it takes twice as much evidence to be 99% sure as it is to be 98% sure. Not twice as much evidence. Evidence needs to be measured logarithmically. (Otherwise you'd say it takes twice as much evidence to be 67% sure as 50% sure (2:1 versus 1:1), but the second takes no evidence at all for a binary proposition.) It takes twice as much evidence to be 99% sure as 91% sure. 98% to 99% is 17 decibels to 20 decibels, whic…

Yeah, I phrased that poorly. It takes as much evidence to go from 50% to 67% as it does to go from 98% to 99%

Re: Potato paradox

#113

Post by o_nate »

guelo wrote: post #65

I don't think a simple algebra problem should be called a paradox.

I agree. This seems to me an abuse of the term "paradox". Lots of math results are surprising to people who've never worked through them. I think "paradox" should ideally be reserved for things that have two logically incompatible logical solutions.

Re: Potato paradox

#114

Post by munificent »

ThrustVectoring wrote: post #66

The solution is much more intuitive if you use odds ratios instead of percentage probabilities. You go from a 99:1 ratio to a 98:2 (or 49:1) ratio. In other words, it's another way of phrasing that it takes twice as much evidence to be 99% sure as it is to be 98% sure. Or that it's twice as hard to have 99% uptime than 98%.

Yes, I would word the paradox like:

You have 100 lbs of Martian potatoes, which are 1/100 water by weight. You let them dehydrate until they're 1/50 water. How much do they weigh now?

Now the answer is staring you right in the face.

Re: Potato paradox

#115

Post by chestervonwinch »

brobdingnagian wrote: post #49
chestervonwinch wrote: post #3

Neat. This bumps up my list of food-related maths from 3 to 4. So far: https://en.wikipedia.org/wiki/Ham_sandwich_theorem https://en.wikipedia.org/wiki/Pizza_theorem https://en.wikipedia.org/wiki/Layer_cake_representation

This is not an implausible basis with which to start a new list on Wikipedia. It is original research, but it will likely be let in.

"research" is a generous term :) I thought about it, but the qualification to be on my list is pretty subjective. I suppose though, it could be generalized to "ideas inspired by food in STEM fields".

Re: Potato paradox

#116

Post by DannoHung »

I think it's interesting that just the percentage stated makes it hard to comprehend intuitively.

That is, restate the question with a different end water percentage and the answer is immediately obvious:

> You have 100 lbs of Martian potatoes, which are 99 percent water by weight. You let them dehydrate until they're 50 percent water. How much do they weigh now?

And, of course, it's pretty easy to get "2 pounds", but your brain is pretty fixed on the numbers all clustered together in the other example.

Re: Potato paradox

#117

Post by gjm11 »

perlgeek wrote: post #111
gjm11 wrote: post #100

Earlier quoted context omitted.

One of the people I went to university with had a little (very short) mental catalogue of "chromatic mathematical fruit jokes". There are exactly two famous ones. "What's purple and commutes?" "An abelian grape." And: "What's yellow and equivalent to the axiom of choice?" "Zorn's lemon." He invented another, which requires more esoteric knowledge: "What's green and determined up to isomorphism by its first Chern clas…

"What's yellow, normed and complete? A Bananach Space"

Nice! Except it doesn't quite work for me because the vowel sounds don't match. (For me the second and third "a"s in "banana" are like the "a" in "arm", whereas the two in "Banach" are like the "a" in "at", and those are quite different sounds. Other people may differ -- and indeed I may be mispronouncing "Banach".)

Re: Potato paradox

#118

Post by knodi123 »

chestervonwinch wrote: post #3

Neat. This bumps up my list of food-related maths from 3 to 4. So far: https://en.wikipedia.org/wiki/Ham_sandwich_theorem https://en.wikipedia.org/wiki/Pizza_theorem https://en.wikipedia.org/wiki/Layer_cake_representation

Just don't discuss this one at the dinner table:

https://en.wikipedia.org/wiki/Hairy_ball_theorem

Re: Potato paradox

#119

Post by knodi123 »

bbcbasic wrote: post #38
kzhahou wrote: post #28

Another angle on this problem: How much water must you add to the potatoes to make them 100% water? Of course, you can add all the water in the universe and they'll still not be 100% water. The water-percent increment just gets smaller and smaller, the more water you add. This "potato paradox" illustrates the same effect, but in the other direction, where a small relative decrease yields a large absolute decrease.

But does the water remember the potato? :-)

It doesn't matter. I remember the potato, and that's enough for me.
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