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Potato paradox

en.wikipedia.org

141–142 of 142 posts

Re: Potato paradox

#141
Let p be the percentage of water and m the total mass.

Then m(p) = 1/(1-p) . The "unintuitive" aspect is that we want to think of this function as linear when it isn't.

By taylor's theorem, how bad a linear approximation to this function will be is based on its higher order derivatives. We can get an idea of this by looking at its second derivative:

m''(p) = 2/(1-p)^3. If you plot this graph, you'll see that it really starts to blow up past 0.8, so the nonlinearities start dominating.

Re: Potato paradox

#142

Earlier quoted context omitted.

But does the water remember the potato? :-)

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

No more potato? Now I'm waiting for someone to invent the "Latvian Deprivation Paradox".
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