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.