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Potato paradox

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Re: Potato paradox

#41

Post by miciah »

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.

If you add water to the potato infinitely (hypothetically speaking), does the water percentage approach 100%? And also, does the solid percentage approach 0%?

Re: Potato paradox

#43

Post by disillusioned »

mhartl wrote: post #36
cperciva wrote: post #30

Earlier quoted context omitted.

If instead of enriching U235 you think of it as eliminating U238, though, then you've done half of the work. That's the wrong way to think of it though. The right way to measure progress is in terms of Separative Work Units: https://en.wikipedia.org/wiki/Separative_work_units If you start with 10000 kg of natural (0.7%) uranium and you want to separate it into 45 kg of highly-enriched (90% U235) uranium and 9955 kg o…

45 kg … and 9960 kg You mean 40 kg and 9960 kg (so the sum is 10000 kg)?

Annnnd just spent an hour reading that delightful Colin Percival Putnam thread. Thanks for the reminder on that. Man, people really loved to hate on Tarsnap because of his perceived arrogance.

Re: Potato paradox

#45

Post by bbcbasic »

miciah wrote: post #41
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.

If you add water to the potato infinitely (hypothetically speaking), does the water percentage approach 100%? And also, does the solid percentage approach 0%?

Yes. More precisely, given a positive value p > 0, you can choose a "w" such that adding w% of water dilutes it to p% potato.

Or another way - given you pour water in at any constant rate forever, given any p% you want to dilute to, there will be a point in time where that dilution level is exceeded, and will remain so for every point in time after that.

Re: Potato paradox

#46

Post by andrewguenther »

This equation models the amount of weight lost for various percentages of change:

0.99 * 100 - (0.99-x)(100 - y) = y

This assumes that you are starting with 100 pounds of potatoes at 99% water weight. Here's a WolframAlpha link: http://www.wolframalpha.com/input/?i=0.99+*+100+-+%280.99-x%...

Re: Potato paradox

#47

Post by cperciva »

mhartl wrote: post #36
cperciva wrote: post #30

Earlier quoted context omitted.

If instead of enriching U235 you think of it as eliminating U238, though, then you've done half of the work. That's the wrong way to think of it though. The right way to measure progress is in terms of Separative Work Units: https://en.wikipedia.org/wiki/Separative_work_units If you start with 10000 kg of natural (0.7%) uranium and you want to separate it into 45 kg of highly-enriched (90% U235) uranium and 9955 kg o…

45 kg … and 9960 kg You mean 40 kg and 9960 kg (so the sum is 10000 kg)?

blushes

Actually I meant 45 kg and 9955 kg. I adjusted the numbers several times looking for values which would come out with round-ish quantities but %U235 values in the right ranges for HEU and DU.

Re: Potato paradox

#48

Post by [deleted] »

ot wrote: post #37

This is not that uncommon when optimizing code. Your program is slow so you profile it, and find out that f() takes 99% of the time. So you work a lot to optimize f(), and re-profiling shows that now f() takes 98% of the time. Doesn't seem that impressive after all the work you've put into optimizing f(), but your program is actually twice as fast :)

[deleted]

Re: Potato paradox

#49

Post by brobdingnagian »

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.

Re: Potato paradox

#50

Post by thaumasiotes »

tjradcliffe wrote: post #12
pervycreeper wrote: post #4

Why is this a "paradox"? Not sure what this applies to either. It's not even counterintuitive.

There is a certain type of mind that delights in paradoxes, to the extent that even after an explanation has been clearly produced, the person will continue to insist there is a paradox. Naming things paradoxes attracts this sort of individual, so it's a kind of marketing ploy for an idea: it won't just get it talked about, it'll get it talked about forever , because each generation of paradox-mongers will take it up…

related: http://spikedmath.com/334.html

(there's also a followup, at http://spikedmath.com/335.html )

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