
Potato paradox - ZeljkoS
https://en.wikipedia.org/wiki/Potato_paradox
======
mikeyouse
Not exactly the same, but I stumbled on another seemingly confusing math
reality a little while back. It's probably obvious for places that measure
their mileage in gallons/100 miles or kms or whatnot, but for MPG:

If you could chose to increase the average fuel economy of a car, which of
these would save the most fuel:

1\. 10mpg -> 12mpg

2\. 12mpg -> 15mpg

3\. 15mpg -> 20mpg

4\. 20mpg -> 30mpg

5\. 30mpg -> 60mpg

Of course with a little thought, it turns out that they all save the same
amount of fuel, but it's hard to wrap my brain around the fuel savings being
equal between 10mpg-12mpg and 30mpg-60mpg.

~~~
mikeash
A similar one I enjoy: you're driving two miles. After one mile, you've
averaged 30MPH. How fast do you need to drive the second mile to have a trip
average of 60MPH?

Answer: impossible. You'd have to travel the second mile at infinite speed to
achieve this.

~~~
fehfn37
If you drive the first mile at 30 MPH and the second at 90 MPH you averaged 60
MPH ((30+90)/2). What is the math that gets "infinite speed" as the answer?

~~~
socalnate1
There is a good explanation of this here:
[http://brainden.com/forum/topic/39-speeding-
up/](http://brainden.com/forum/topic/39-speeding-up/)

~~~
selestify
Good Lord, it's frustrating to see so many people incapable of understanding
such a simple thing.

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rplnt
Another somewhat similar (in that the result is unintuitive) problem about
false positives:

Imagine that you have an HIV test that is 95% accurate (false positive rate of
5%). and around 2% of tested population is infected with HIV. What is the
probability that you actually have HIV when your test comes back positive? Is
it 95%? Nope, actually just 29%. You do the test again.

Numbers from wiki about the paradox:
[https://en.wikipedia.org/wiki/False_positive_paradox](https://en.wikipedia.org/wiki/False_positive_paradox)

~~~
nabla9
Same issue comes up when you discuss effectiveness of ethnic profiling of
Muslims/brown skinned people in airports. Sam Harris was unable to wrap his
head around this and was sticking to his common sense intuition.

Strong profiling is not mathematically optimal for discovering rare malfeasors
[http://www.pnas.org/content/106/6/1716.full?sid=3bc684ec-b59...](http://www.pnas.org/content/106/6/1716.full?sid=3bc684ec-b593-41e9-b03e-2e3f32bc42b0)

~~~
LeifCarrotson
The Sam Harris article referenced, for anyone else who was unfamiliar with the
controversy: [https://samharris.org/in-defense-of-
profiling/](https://samharris.org/in-defense-of-profiling/)

~~~
zouhair
Just wow.

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JumpCrisscross
> _You have 100 lb of potatoes, which are 99 percent water by weight_

Would this be less of a paradox if we talked about water balloons? Potatoes,
in real life, are 80% water [1].

[1]
[http://umich.edu/~elements/web_mod/potato/fact.htm](http://umich.edu/~elements/web_mod/potato/fact.htm)

~~~
OskarS
You can't really "dry" water balloons. The water in them don't really
evaporate.

~~~
douglaswlance
The water does really evaporate, just takes a lot longer than potatoes.

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pgroves
Reminds me of how bond yields work. If the interest rate guess from 1% to 2%
on an existing bond, the bond itself has to lose 50% of its value. I think the
potato story is somehow less intuitive.

~~~
jacobkg
That’s true only if the bond has an “infinite” term. Meaning it pays interest
forever but you never get your initial principal back

If a bond has say a one-year term then it won’t lose 50% of its value if
interest rates double from 1 to 2 percent because you still get your original
full investment back after one year. It’s value instead drops by about 1%.

For a longer term example, a bond purchased for $1,000 and 1% interest rate
with 30 years left is worth $776 if interest rates rise to 2%

Source: [https://m.free-online-calculator-use.com/bond-value-
calculat...](https://m.free-online-calculator-use.com/bond-value-
calculator.html)

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preinheimer
The birthday paradox comes up a lot in computing, I wonder if there's more
places the potato paradox would apply.

~~~
tntn
Profiling code. If you have a hotspot that takes 99% of the time and optimize
it until your whole program is twice as fast, now that hotspot takes 98% of
the time.

~~~
TremendousJudge
hmm that actually sounds more intuitive than the potato example

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umvi
I wonder if this is ever used in marketing tactics to disguise the amount of
loss

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elicash
Wikipedia has a list of paradoxes:
[https://en.wikipedia.org/wiki/List_of_paradoxes](https://en.wikipedia.org/wiki/List_of_paradoxes)

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VikingCoder
Simpson's Paradox is my favorite:

[https://en.wikipedia.org/wiki/Simpson%27s_paradox](https://en.wikipedia.org/wiki/Simpson%27s_paradox)

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Pfhreak
This isn't the intuitive result? If one part in 100 of the potatoes is solid,
and you want to increase that to 2 parts in 100 that's equivalent to 1 part in
50...

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mar77i
no, really, it's true, I just tried it:

1 / 100: 0.01

1 / 99: 0.01010101

That's just a bit more than a percent of that percent of change, and not a
100% change, as would be required for a 2:98 ratio.

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TN1ck
Almost everyone I know could not solve it correctly without a lot of hints.
Even when you say: „It is not the answer you first think it is“. I like to use
it when someone feels too smart and won’t acknowledge that he might be wrong
about something. For example, a friend was arguing that the moon landing
didn’t happen because the capsule was too small to hold the needed fuel. I
asked him the paradox, he got it wrong. I followed with: „how can you believe
to be right about rocket science, when you weren’t able to get this simple
question right?“

~~~
evancox100
And how did the conversation go after that?

~~~
SideburnsOfDoom
Does it matter a lot? Do you really need to be friends with a moon-landing
denier?

~~~
mar77i
Shows how easy it is to reject complicated things if you manage to get so much
of the more simple things wrong.

