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Potato paradox

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Mathematical calculation with a counter-intuitive result
For the economic effect sometimes called the potato effect or potato
paradox, see Giffen good.

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The potato paradox is a mathematical calculation that has a
counter-intuitive result. The Universal Book of Mathematics states
the problem as such:

    Fred brings home 100 kg of potatoes, which (being purely
    mathematical potatoes) consist of 99% water (being purely
    mathematical water). He then leaves them outside overnight so
    that they consist of 98% water. What is their new weight?

Then reveals the answer:

    The surprising answer is 50 kg.^[1]

In Quine's classification of paradoxes, the potato paradox is a
veridical paradox.

[220px-Potato_paradox]
 
A visualization where blue boxes represent kg of water and the orange
boxes represent kg of solid potato matter. Left, prior to
dehydration: 1 kg matter, 99 kg water (99% water). Middle: 1 kg
matter, 49 kg water (98% water).

If the potatoes are 99% water, the dry mass is 1%. This means that
the 100kg of potatoes contains 1kg of dry mass. This mass will not
change, as only the water evaporates.

In order to make the potatoes be 98% water, the dry mass must become
2% of the total weight - double what it was before. The amount of dry
mass - 1kg - cannot be changed, so this can only be achieved by
reducing the total mass of the potatoes. Since the proportion that is
dry mass must be doubled, the total mass of the potatoes must be
halved, giving the answer 50kg.

References[edit]

 1. ^ "potato paradox". Encyclopedia of Science. Archived from the
    original on 2 February 2014.

External links[edit]

  * Weisstein, Eric W. "Potato Paradox". MathWorld.

*
Retrieved from "https://en.wikipedia.org/w/index.php?title=
Potato_paradox&oldid=1113695651"
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  * Mathematical paradoxes
  * Potatoes

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  * This page was last edited on 2 October 2022, at 20:29 (UTC).
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