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.
Here is another mathematical "Potato Paradox"