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Potato paradox

en.wikipedia.org

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Re: Potato paradox

#71

Post by allendoerfer »

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…

The Potato Paradox seems to build on a misleading set-up and peoples disability to picture logarithmic scales. The Venus Paradox seems more like something a freshman says, who heard about Boolean algebra for the first time and now applies it human language all the time.

Re: Potato paradox

#72

Post by wobbleblob »

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 :)

Without knowing your code, I can think of a performance hack to get the running time of f() down to less than 10% of the time.

Re: Potato paradox

#73

Post by JupiterMoon »

wobbleblob wrote: post #72
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 :)

Without knowing your code, I can think of a performance hack to get the running time of f() down to less than 10% of the time.

What is this?

Re: Potato paradox

#75

Post by philh »

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, which is less than 20% more evidence.

Re: Potato paradox

#77

Post by amelius »

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 :)

This just shows that the percentage of total time a function takes is really not the thing you should be looking at when optimizing code and you want to know how much faster your code really is.

For example, say your function f() takes 100% of the time. You then make it twice as fast. You look at the percentage, and, surprise, it still is taking 100% of the time!

Re: Potato paradox

#78

Post by vacri »

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.

Simple: 100lbs of water.

At this point, you have 1lb of solids and 199lbs of water, or 99.5%. Then you cough round off, and there you are, 100%!

Re: Potato paradox

#79

Post by vacri »

marvy wrote: post #26
pervycreeper wrote: post #15

Earlier quoted context omitted.

The point is that it doesn't even appear absurd unless you have absolutely no number sense.

If you think that, you have more number sense than many people. Perhaps more than most :)

Part of it is also the ambiguous way the question is phrased. amolgupta above mentions the same thing, but using humans (engineers and managers) and the answer is much more obvious in that context.

Particularly with the second form of the question in the article - anyone who's ever had a potato knows that it doesn't shrink to half it's weight overnight. Poor situation selection and confusing wording do not make a paradox.

Re: Potato paradox

#80

Post by gerhardi »

soup10 wrote: post #16

This is only confusing because of the potatoes. If you said you had a pool that was 99% water, that changed to 98% water, the massive weight drop would be much less surprising.

Hmm how about: You have a 1 liter bottle of 99% alcohol. How much of the alcohol you should evaporate to have 98% alcohol left?
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