Vsauce!
Kevin here, and this PENNY BRICK contains a strictly monotonically increasing sequence
to DETECT FRAUD that depends in part on an 8-year old genius in the 1700’s and how
loaded with useless knowledge YOUR brain is.
It also contains 50 rolls of 50 American pennies, each of which weighs 2.5 grams and is composed
of 97.5% zinc and 2.5% copper.
HERE’S THE PROBLEM.
One of these 50 rolls is full of FAKES.
Which one of you is lookin’ a little SUS...picious?
The fake could be anywhere.
The only thing I know is that the counterfeit pennies are .5g lighter than real pennies.
That’s too light, though, to feel out by hand.
So I’ve gotta measure them.
HOW?
I could measure all 50 rolls one by one until I found the fakes.
Every roll should be 125g for the pennies plus 3g more for the wrap.
It'll work, but it could take up to 50 measurements.
The weird thing is… there’s actually an elegant way to measure just ONCE -- TAKE ONE
SINGLE MEASUREMENT -- to find out exactly which stack is phoney.
THAT solution is not obvious so let’s start with the obvious.
You know you can speed up measuring by, say, breaking the 50 stacks into 5 groups of 10.
Measure the 5 groups and 1 will be light -- measure the 10 stacks in that group until you find
the fake.
If you’re super lucky?
20% chance you get the right group on the first try, 10% chance it’s the right stack…
there’s a 2% chance you can do this in just two measurements, but it could take 15.
There’s a 100% chance it’ll work, and you know that -- because it’s in your System
1.
You’ve stored so many patterns and processes in the dual process model of your brain -- System
1 thinking is the automatic intuition you build up with knowledge and experience.
It’s what your brain knows before you even know you know.
System 2 is the slower, calculated thought you apply it with.
HERE’S A QUESTION.
Which system do you need to measure 50 stacks of pennies just once and be guaranteed to
find the imposter?
Both.
You need both.
First, I gotta find out what 50 stacks of pennies SHOULD weigh -- 2.5g each x (50)^2
= 6,250g = or 6.25kg.
If fake pennies are half a gram short, a stack of 50 will be 25g too light.
Cool.
Now what?
Now you need to know patterns.
You need to know sequences.
Maybe you got it from studying convergent and divergent series.
Maybe it was Euler, maybe it was calculus, maybe it was projected investment growth or
growing student loan debt.
But somehow the long arrangement of numbers and the implications of those sequences and
series need to be SOMEWHERE in your System 1.
Like 1 + 2 + 3 + 4 + 5 + 6 plus… it’s infinite.
And with the Ramanujan summation, that adds up to -1/12 -- but that’s another video.
NOT THIS ONE.
And we’re not adding infinitely, we’re only going to 50.
And that summation is so simple that even an 8 year old can do it -- because literally
an 8 year old Carl Gauss discovered the method.
Carl Gauss is one of history’s greatest mathematicians -- and as a child he realized
that any series of adding consecutive numbers could be done by taking the whole set of numbers
and dividing it by 2, then multiplying that result by the first plus the last number.
So 1 through 50?
(50/2) * (1+50), or 25 * 51 = 1,275.
Thanks, 8 year old Carl.
When I was 8 years old, I was listening to Nirvana’s Nevermind on cassette and begging
my mom for a Sega Genesis.
Anyway, if we treat the 50 stacks as potential consecutive numbers and take 1 penny from
the first stack, 2 pennies from the second stack, 3 pennies from the third stack, and
so on all the way to the 50th stack.
Our consecutive penny stack series will give us 1,275 total pennies.
At 2.5g each minus the wrappers?
That’s 3,187.5g.
When we take one single weight measurement of our divergent-series-inspired Gaussian
child-genius pennies, it will be short by a certain number of grams.
We’ll know exactly how many pennies of the 1,275 are fakes.
Because..
If it’s short 7 grams?
14 fake pennies.
19 grams?
38 fakes.
And since we took the number of pennies corresponding to the number of stacks -- like taking 13
pennies from stack #13 -- however many fake pennies we have in the group actually tell
us which stack the fakes came out of!
SO LET’S FIND OUT.
WHICH OF MY STACKS IS THE FAKE?
N… none.
None.
None of these pennies are fake.
I got them from the bank.
I just really wanted to visualize this problem because it changed my mind about how thinking
functions.
We just do not do this stuff every day.
To stumble on the right process here, you probably had to have done some real thought
about consecutive numbers and number series in the past -- if that’s not in your System
1, then System 2 doesn’t have a lot to work with.
You could just...
I guess sort of figure it outfit you never worked with a number series before if your
name is CARL GAUSS.
The rest of us need to know things.
A lot of things.
And there's no guarantee that what's in your System 1 will EVER be useful.
Because it just isn't... until it is.
Will you need to know specifically how to reveal a roll of counterfeit coins in a single
measurement?
Probably not.
But what problem will you need to solve using the number patterns, mathematical processes,
and even riddle answers that you've acquired over a lifetime?
Without a System 1 loaded with math and science, Archimedes gets in the bath, sees the displacement
of water correlating with his body, and…
I don’t know, washes his smelly armpits.
There would’ve been nothing for System 2 to activate.
There's NO WAY to know how you’ll put information and patterns and relationships and knowledge
together to solve a very real problem in your future -- but the more information you pack
into your System 1, the more likely it is that your System 2 will get the job done.
And as always…
I have so many pennies to roll.
Thanks for watching.