Vsauce!
Merlin here -- and I know everything about
what you know and think.
Everything.
I’ve built a vacation home in your mind
and I’m lounging by the pool sipping chocolate
milk right now.
And I can prove it with a little magic that
amazed TV audiences worldwide by having them
rub their fingers all over their screens.
It starts with a clock, and each of the 12
numbers are arranged as you’d expect.
You’ll be moving around this clock in a
way that’s random to me -- you’ll know
which numbers you choose along the way, but
I won’t.
How could I?
You’re wherever you are, and I’m in my
mom’s basement.
Right?
Wrong!
Well, I am in my mom's basement.
But with the power of my fake wizard beard,
no matter what number you choose I will know
where you are.
Now clear your mind of its usual thoughts
-- memes, pizza rolls, energy drinks -- and
select a number.
It can be any number from 1 to 12, and only
you will know what it is.
Ready?
Go.
Pick a number.
Got a number?
Good.
Now I need you to spell your number, starting
at 12 and moving clockwise one step for each
letter in the word.
If your secret number is 7, then you’d move
5 steps -- s-e-v-e-n -- and land on the 5.
If you picked 11, you’d move 6 steps -- e-l-e-v-e-n
-- and land on the 6.
Hold your finger over the screen starting
at 12 and count your number’s letters until
you’re on your new number.
Okay?
Go ahead.
Alright.
Now spell your new number, moving one position
clockwise for each letter in that number.
If you’re on the 3, then move 5 spaces -- t-h-r-e-e.
If you’re on the 6, then move 3 spaces -- s-i-x.
If you run out of spaces and get back to 12,
just keep going around the same way a clock’s
hands move.
Okay.
Did you do it?
We're gonna do this one more time -- spell
your new number again and stop.
I’ll give ya a second to do that.
Okay.
I have no idea what number you started with
or the second one you landed on, let alone
the third number that you landed on after
that -- but I do know that you’re not on
the 2, so I’m gonna get rid of that.
And I know that you’re not on the 4, either.
Or the 8.
Or the 12.
As I sip my delicious chocolate milk next
to your mind pool I can see that you weren’t
on any of those numbers so we don’t need
them.
Hey.
Let’s go one more round.
Spell your new number, and skip the empty
spaces.
One letter, one position, and stop when you’re
done.
If you’re on the 5, you’ll move 4 spaces
-- f-i-v-e -- skipping the empty 8 space and
landing on the 10.
Go ahead.
Are you on the 10?
No.
No!
No.
You are not on the 10.
So the 10 is gone.
You're on the 3?
No, no, no.
You are not on the 3.
That's gone too.
The 9.
Gone.
Or the 1.
Gone.
You’re on the 6 -- and you've just witnessed
the magic of The Kruskal Count.
Alright hold on this beard is really getting
itchy.This hat is super tight.
Hang on.
Oh the troubles of having a beard.
That’s better.
So magician David Copperfield has performed
illusions with several different variations
of this trick, from using a clock face to
celebrities to vacation destinations.
He mesmerized audiences in live shows and
TV shows with his predictive power.
But the man who discovered The Kruskal Count
was mathematician and physicist Martin Kruskal
-- who took some delight in knowing that it
often confused actual magicians because it
wasn’t based on any kind of sleight of hand.
It was based on math.
So what is actually going here?
Let’s dissect what happens in the clock
trick.
You’re starting at 12, and you have four
possible moves: numbers that contain 3, 4,
5, or 6 letters.
We’ve got 12 numbers to choose from, but
we only have 4 possible pathways forward,
and therefore I know no matter what number
you choose, you’ll end up on the 3, 4, 5,
or 6 after your first move.
For your second move, you’ll either move
5, 4, 4, or 3 -- which means that every single
player winds up on either the 8 or the 9.
Notice that at no point in the game can anyone
even land on the 2, 7, 10, 11, 12.
I know that before we start, but you probably
won’t notice it as you play.
And along the way, I remind you that these
choices are yours and are totally random to
me, because reinforcing that randomness distracts
you from thinking about any pattern that you
might be encountering.
On the third move, if you’re on the 8, you’ll
move 5 spaces to the 1.
If you’re on the 9, you’ll move 4 spaces
to the 1.
And that’s it -- it’s already game over
for you, and you didn’t even know it.
Then the performance really starts.
I can take away numbers like 2, 4, 8, and
12 because I know for a fact that you’re
on the 1.
It’s 100% guaranteed.
But.
There’s a very subtle element to choosing
which numbers to erase -- those four removed
numbers have letter values of 3, 4, 5, and
6, so that subconsciously reinforces that
I’m not eliminating some specific element
or pattern, like just removing all of the
possibilities with 3 letters.
It’s spread out among the choices, so to
you it seems just that much more random.
Really, I can do anything once you’re all
on the 1.
I don’t have to remove anything -- if we
just kept playing you’d all just go from
the 1 to the 4.
I could also add in as many rounds as I wanted
because you’re all in synch at that point.
Or I could remove different numbers to get
you to the final number that’s best positioned
on camera… which is probably why Copperfield
wanted to land on the 6 in the center of the
screen.
It just looked better on TV.
So...
Great so we figured out the trick.
Kinda.
Not exactly.
What is happening here?
What Kruskal discovered was that a counting
game like this is really a chain of numbers.
Every new number is a new link in the chain,
and when two chains eventually intersect on
the same link, then they become the same chain
from there on out.
Knowing that, you can appear to predict a
highly-improbable result even when you don’t
know where the chain began.
Let me show you another example.
AThe predictive power of Kruskal’s Count
is seen most easily with a deck of cards.
Allow me to show you my Wonderful Weiner Dogs
playing cards.
I’ll shuffle a full Wonderful Weiner Dogs
deck of 52 cards and deal out 10.
You need to choose one of these 10 cards -- obviously
I won’t know which one your choose, because
I recorded this video in the past and you’re
watching it in your present which is my future.
Then you’ll proceed to count forward from
that card until we get through the whole deck.
Aces count as 1, and face cards count as 5,
and every other card counts as the numerical
value it displays.
So like 9 equals 9.
So if you chose to start with card number
5, that's a Queen which is worth 5.
And you’ll go 5 spaces.
1,2,3,4,5.
And land on an Ace which is 1.
So then you'll go 1, land on a King which
is 5.
1,2,3,4,5.
Land on a 10 and then you'll go 10.
Got it?
And you’ll continue this until you can’t
make a full move.
So if you land on this 9 you obviously can't
go 9 spaces so this 9 would be your final
card.
And even though I don’t know what card you
picked to start, I’ll be able to tell you
which card is the last one in your sequence.
Here’s how.
I’ll also choose a number from 1-10.
Let’s say…
I pick 4.
Which is a 4.
The 4th card will be my first link in the
chain, which Kruskal called a “key card.”
And together, without telling each other,
because I don't know which card you're starting
with, we’re both going to count forward
from our respective cards -- since I’m starting
on the 4th card, which is a 4, I’ll count
4 spaces to another card.
1,2,3,4.
Which is a 5, and continue until the end.
You’ll do the same thing from your mystery
card.
And then uh...
It’s weiner time.
Okay.
Go ahead.
Let's start!.
Your last card in this sequence is that 9
-- because so is mine.
Using the Kruskal Count, I can predict what
your final card will be without knowing where
you started.
Because it doesn’t really matter, at a certain
point our chains intersected on the same key
card and followed the same path to the end.
And this always works, doesn’t it?
No, it doesn’t!
About 1 in 6 of you are already typing a rage-soaked
comment about how dumb I am for choosing the
wrong number.
Joke’s on you, buddy, I knew that would
happen.
The Kruskal Count with a 52-card deck only
works about 85% of the time, and if our final
key cards weren’t the same then you chose
one of the numbers that put you on one of
the 15% of chains that land me in the fail
category.
But the longer our chains go, the more chances
they have to intersect -- so if we played
with two decks of 52 cards, the odds of me
predicting the right final card for you jump
to 95%.
Let's just see exactly how this can play out.
I'll shuffle and deal another 10 cards, color
code them, and mark each chain's key cards.
As you can see, 5 out of the 10 cards linked
up right away on this 9 and then ended up
on this 10.
The 4th and 9th cards linked up on this 7
and then met up with the others on this Queen.
But 3 of the 10 just did their own thing and
converged on a second mini-chain.
The 5th, 8th, and 10th cards linked up together
on this Jack and ended up on a 6.
There are a couple of reasons for this: first,
landing on a couple of 9s caused huge jumps
that reduced chain link opportunities -- the
more key cards in a sequence, the more opportunities
to overlap with the main chain.
If we played with two or three decks, our
big chain and little chain would be almost
certain to converge.
But this game ended up being a weird outlier
where the magician had a much smaller chance
of success than they usually would.
That’s one way we know that this isn’t
magic.
Magic works 100% of the time because it’s
engineered and manufactured to be successful.
Probability isn’t quite as predictable.
There’s actually a great interactive version
by Alex Frieden and Ravi Montenegro from the
University of Massachusetts Lowell that you
can play online that I’ll link below because
I like you.
So yeah this is a fun little trick you can
use to mess with your little brother’s mind,
but what’s the point?
The Kruskal Count feels like magic, but is
considered a probabilistic paradox -- technically
speaking, it’s a veridical one, and it has
real-world computational applications.
In 1978, John Pollard applied it to code-breaking
and developed the A Lambda Method for Catching
Kangaroos also known as the Kangaroo Algorithm.
Which is a great name for an algorithm.
But to me, the trick is an incredible illustration
of how math can be at the heart of coincidence.
What are the chances you run into your old
gym teacher at the supermarket?
What are the odds that you end up going to
the same college as the booger boy who moved
away in first grade?
We’re all living in several different systems
at the same time, some large, some small,
some open, some closed… and every one of
our actions is another link in our own chains.
What we call fate or coincidence may really
be the result of a hidden mathematical master
pulling the probability puppet strings of
our existences together -- at which point
we can decide how closely we want to align
our chains from that point on.
Which is cool, because you probably don’t
want to go home with your old gym teacher.
Especially since he saw you buy cat food and
you don’t even have a cat!
And as always -- thanks for watching.
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Bye.
This is just chili.
