The Potato Paradox

The Potato Paradox


Vsauce! Kevin here. The Colorado potato beetle, first observed
innocently eating native plants in the Rocky Mountains in 1811, went crazy when potatoes,
native to South America, were introduced to the U.S. These beetles were like, “Wow potatoes are
delicious” The beetles were right. But their potato-hunger is so devastating
to crops, entire propaganda campaigns were launched in World War II and again during
The Cold War claiming that the CIA was dropping the “American Bug” in places like Germany
and Eastern Europe as a form of insect warfare. The Colorado potato beetle has been a major
potato problem. But potatoes have never been paradoxical,
right? Wrong. ENTER: THE POTATO PARADOX. It goes like this: say you’ve got 100 pounds
of potatoes and 99% of their weight is water. The other 1% of their weight is solid potato
stuff — starches, proteins, pectins, minerals, that kind of stuff. You leave them out overnight and they dry
out a little bit. When you wake up, they’re only 98% water,
that would make 2% of it solid. So, how much does your sack of spuds weigh
now? While you think about it, let’s get real for
a second with real potatoes, not paradoxical ones. So, real potatoes are 79% water by weight. So I cut this to exactly 100 grams, which
means this 79 grams of water. Looks thirst quenching. 79% is a lot, but we can go higher. Per 100 grams, Watermelon is 91% water. But what’s more water than watermelon? Lettuce. Lettuce is almost 95% water. Meaning, salad is 5% away from being soup. Back to our paradox… probably a good idea
to get back to that. Probably broke the scale. Anyway, we have 100 pounds of paradox potatoes,
and the percentage of water weight goes down by 1% overnight so their weight today would
be 99 pounds. A common answer. And a good one. If by “good” you mean… After this tiny change, your sack of spuds
would actually weigh 50 pounds. The 1% shift in composition cuts its weight
in HALF. How? Well, the easiest way to visualize the solution
is with potatoes. 100 of them. OHHHH NO NO… So here are 100 potatoes. You must hug your potatoes so that they know
that you care. This one painted potato, a lovely space age
silver, is the 1% of solid potato matter that we start with. The other 99 represent the water. When the potatoes dry out, the amount of solid
matter doesn’t change. Only the water goes away. So, if we remove ONE unit of water we now
have 99 pounds of stuff, 1 of which is dry, 98 of which are water. So, let’s just do a little calculation here. 98 out of 99 is 98%… but .989899. We don’t want all those point 9 things,
we just want 98 percent. Okay, so that’s too much water. Let’s just remove another water, alright,
so now we have 97 out of the 98 pounds here are water. So, we’ll do 97 out of 98 and… 98.979591836%. That’s too much. It’s just too much water. There’s got to be a better way. Here’s the problem: This is lowering really
slowly because for every unit of water that dries away, the total amount that’s left ALSO
goes down. To see how many we need to take away, let’s
look at the final result. Excuse me, potatoes. Okay, here’s what we’ve got going on here. Okay, so. We need to reduce how much water we have not
to 98 or 97… but to 49. And here’s why: So we have 98%, 2% solid, but we only have
1 solid unit. So let’s turn that 2 into a 1. So, we’ll divide 2 by 2 and we get 1. So we’ve got to do the same thing now to
our 98, so we’ll divide 98 by 2 and that equals 49. So 49 plus 1 equals 50, and 50 pounds is the
answer. So, we’ve got to get rid of SO MANY water
potatoes. I don’t know how many are left, but it should
be 49 waters and 1 solid. And 49 divided by 50 is exactly 98%. We did it! That’s the answer. The potato paradox comes into play every time
there are two items and the concentration of one doubles. That requires the other one’s size to be
reduced by half of the whole, whether it’s doubling from 1% or .00001%. Or 10%. Ask your friends to solve this problem and
see what they say. Most of the time, our first response is to
assume that not much has changed since 1% is so small. This isn’t something to be ashamed of — our
brains evolved to compare quantities like this: there’s one wooly mammoth and there’s
five of us. Or, how much food do we need to keep the family
surviving through the winter? Evaluating concentrations is more abstract
and not usually a life-or-death issue that natural selection would play a role in shaping. Unlike other famous paradoxes, time travel
ones for example, the POTATO paradox is a VERIDICAL paradox, which means it has a TRUE
solution we can all agree on and prove, but is nonetheless surprising. So, the potato paradox is a kind of paradox
not built on misunderstandings or impossibilities or speculation but instead, is one that really
teases out how the mind works. Now if you’ll excuse me, I have a vintage
potato toy to turn into a potato man before he loses 1% of his water composition and half
his weight. And as always – thanks for watching. The awesome potato paradox animation at the
beginning of this video was created by VFX wizard Eric Langlay using After Effects. If you want to learn how to do cool visual
effects, there are dozens of courses just on After Effects over at Skillshare. And they’re taught by experts who really
know what they’re doing, so you’ll really learn what you’re doing, whether you need
to know the basics — OH, LOOK OUT — or you just want to learn some new techniques. Which, I think we all can always use some
new techniques. An annual Skillshare subscription is less
than ten bucks a month and the first one thousand people to use the promo link at the top of
this video’s description will get their first two months for just 99 cents, which
is less than this potato cost me. And I would give this guy an arm… or a hand… I guess he has an arm, but the hand, it’s
broken. Listen, this thing is 60 years old. It’s amazing that it… ok, let’s see
if it… doesn’t. What if it stood… will this hold it? WILL THIS HOLD IT? IT HOLDS IT! The Potato Man lives and breathes in a potato
stand. I didn’t mean for that to rhyme, but it
did. Let’s look at this thing for a second. Mr. Potato Head Funny Face kit, this was the
original thing. And it really wasn’t just for potatoes,
you can see you can make peppers, beets, oranges, apples… OHHH NOOOOO! Really, it was all about turning vegetables
into people, which I think is something we can all get behind. *sigh* I have so much to clean up.

Comments

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    Derick La'Trelle Hardeman Davis

    Kevin: Excuse me, but do you know where I could find 100 potato

    Store clerk: WTF

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    michele landolfi

    You are the most logic person i have ever seen but you did all that talking to explain a very simpler thing.
    The potato weights 50 lbs for the simple fact that if before it was 100 and 1% was solid, but when dried the solid was 2% and considering that solid stays the same, the 2% of solid of the dried potato MUST weight as much as the solid of the watered one.
    So if the solid was 1lb before, it will be 1lb after, and if 1lb is 2% well the total weight must be 50lbs

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    Akrobatus

    tbh i already new this, you just gotta calculate with the % thats missing and not the one we're talking about

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    Hi, I exist. Also I am__Turtles__ #1

    m8 this is about potatoes. I got an ad for AdVentere communist… which is about potatoes

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    Math Kinger

    My method is find the ratio between the solid and the water. The ratio of the solid to water at the start is 1:99, and in the end, it is 2:98. Since water remained the same, the ratio of 1:99 can be said as 2:198 since the 2 units are the same. Thus, the total units in the start is 200 and in the end, it is 100. Since 200 units is equal to 100 lbs, 1 unit is 0.5 lbs and 100 units is 50 lbs, which is the answer. It is simple math involving one unchanged value in ratios. (This is the method I had used to find the answer correctly)

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    Jerrin M

    That space age silver potato really made him crack up and the fact that it made him crack up made me crack up

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    Lewis Macleod

    Hang on, hang on – if i get lost in the desert and lose 1% of my water balance, i don't suddenly lose half my weight. I'm so confused… #probablythedehydration

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    Subscribe For No Reason

    Is it a shame if I tell you that I solved the paradox and came up with 50 lb in first couple minutes of the video!

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    DanGer99

    If 1% of the water dries up, wouldn’t you lose 1% of the total potato? When water evaporates, it becomes a gas, not a solid, so wouldn’t you just have 1% solid and 98% water?

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    DeepBlue

    Actually I calculated it in few seconds and in easier way, before I see the answer in the video:
    1% solid of 100 => solid = 1 lb
    2% solid => total weight = 1 lb / 0.02 = 50 lb
    easy

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    Christopher Scheler

    In the video you only remove water, but I think that's not realistic. If the water and the solid stuff were mixed perfectly, the percentage wouldn't change.

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    Stephen Lujan

    So I immediately thought that half the 99 lbs of water (49.5) has to evaporate leaving 50.5 lbs, not 50 even. Unfortunately, I was still "WRONG" as 1 / 50.5 is not 2%. Halving one side does not double the ratio of the other to remainder. Ah well.
    Also. Guys. I'm like 70% soup.

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    Kacper M

    The grandfather paradox
    The laier's paradox
    The birthday paradox
    The potato paradox
    This is getting ridicules next thing will be something like the toothbrush paradox

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    james hallam

    but at no point does the solid become 2% of the whole, it would be 1.010101010101010101010101010101010101……. of the whole after removing 1% of water

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    Order of the True Force

    100lb of potatoes is the 100% where, 99% (99lb) is water, 1%(1lb) solid. Now, 1% (1lb) of water is lost, so, 99lb potatoes is the new 100% where, 99% out of 99lb (98lb) is water and 1% (1lb) solid (which stays the same because only water was lost).  That = 99lbs which checks.  It’s not a “potato paradox” it is a miscalculation. Heat the potatoes in an oven to evaporate the 1% of water and weight them, then will see whos wrong. I dare you.

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    Stefan Peev

    To every genius here that says this is totally easy and not a mindfuck.
    Calculations are wrong, its not that simple , its not so obvious before results that 1 lbs potato equals 2% of the total, since when you remove 1% of water you remove a part from the original composition not just water. So if you have 99lbs of water and 1 lbs of potato and remove one lbs water (which should logically be 1% of the whole), youd have 98 lbs of water and 1 lbs of potato, making it a total of 99 lbs. 1 lbs of 99 lbs doesnt sum up to your "obvious" calculations of 2% , so to reach a 2% composition you have ro remove a lot more lbs of water, the brain is fooled because 1% seems to be equal to 1 lbs, but its not, its equal to 49 in reality.So it is a paradox, and as he said a veridical one.Concentration and ratios work out strange in reality, the mindfuck is not because there are 2 answers as in a traditional paradox as superposition, its because there is an answer, it just plays out so weirdly in reality and when you put traditional logic in it.

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    Isaiah Zhamil Pablo Santi

    https://www.google.com/search?q=retention&rlz=1C1NDCM_enUS859US859&oq=retention&aqs=chrome..69i57j0l5.2663j0j8&sourceid=chrome&ie=UTF-8

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    Isaiah Zhamil Pablo Santi

    Reduce salt intake. Salt promotes fluid retention. There are no official guidelines for avoiding salt for lymphedema, however people who are sensitive to salt might exacerbate their symptoms if they eat high-sodium foods. Current recommendations for salt intake are less than 2,300 mg for healthy individuals and less than 1,500 mg for people who have cardiac disease, diabetes and kidney disease.

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    Motu Thicc

    but isn’t the idea of a veridical paradox paradoxical within itself because paradoxes don’t have an answer yet this kinda of question with no answer has an answer: BOOM paradox

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    NBAKIDD

    can someone help me? he said the percentage of water goes down by 1. i get that. there’s a shift in percentage. but what if FROM THE PERCENTAGE of water 1% is removed. like it’s literally only 1% water less. but 1% out of 99 is 0.99 isn’t it? so it’d still be 1.99% more solid mass and by his method almost the same result. isn’t the mistake that 1% solid potato in 100lbs potato doesn’t has to be 1lb? i mean i refuse to believe that just because 1% of water is removed (no matter if it’s 1% LESS water from the total or 1% OF total water in the potato) the mass of the potato halves. i’ve never felt more off reality… pls help

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    j g

    OK. So it's not a physical paradox (impossible) but a language paradox, sneaking in the 2% solid, which must mathematically mean the potatoes must weigh half to accord with the double percentage of solid. A bit like a car salesman's guarantee…"Up to 100 mpg…" A linguistic, not a math problem.

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    andy sitton

    Very long winded. Far simpler to just point out that that the 1lb of solid now represents one fiftieth of the total so the total is fifty. Why all the extra unnecessary arithmetic?

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    Dean Hentschel

    Wrong. If 50% of the water is 50% of the weight, then 100% of the water is 100% of the weight. That means that the solid contains no mass, and doesn't exist. Therefore, the paradox potatoes are soup.

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