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
seven
then you'd move five steps
s e v e
n and land on a five if you pick
uh 11 you'd move six steps
e l e v
e n and land on the six
hold your finger over the screen
starting at 12
and count your numbers letters until
you're on
your new number okay go ahead
[Music]
all right now spell your new number
moving
one position clockwise for each letter
in that number
if you're on the three then move five
spaces
t h r e
e if you're on the six then move
three spaces s i
x if you run out of spaces and get back
to the 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 then stop i'll give you a second to
do that
okay now 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 two so
i'm gonna get rid of that and i know
that you're not on the four either
or the eight or
the twelve 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 five you'll move
four spaces f i v
e skipping the empty eight space and
landing
on the ten 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 three
no no no no no no you are not on the
three
that's gone too the nine gone
or the one gone
you're on
the six and you've just witnessed the
magic
of the kruskal count all right hold on
this beard is really getting itchy this
hat is super tight
one second hold on oh
the troubles of having a beard
oh 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 and 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 on here let's let's
dissect what happens
in the clock trick you're starting at 12
and you have four possible moves numbers
that contain
three four five or six
letters you've got 12 numbers to choose
from but we only have
four 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 at no
point in the game can anyone even land
on the 2
7 10 11 or 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 eight you'll move
five spaces to the one if you're on the
nine you'll move four spaces to the one
and that's it it's already game over for
you and
you didn't even know it then the
performance
really starts i could take away numbers
like 2
4 8 and 12 because i know for a fact
that you're on
the one it's one hundred percent
guaranteed
but there's a very subtle element to
choosing which
numbers to erase those four removed
numbers have letter values of three
four five and six so that subconsciously
reinforces that i'm not
eliminating some specific element or
pattern like
just removing all of the possibilities
with three
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 one i
don't have to do anything if we just
kept playing you'd all just go
from the one to the four i could also
add in as many rounds as i wanted
because you're all
in sync 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 six in
the center
of the screen it just looked better on
tv
so great 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
the predictive power of kruskal's count
is seen most easily
with a deck of cards so allow me to show
you my wonderful wiener
dogs playing cards i'll shuffle a full
wonderful
wiener dog's deck of 52 cards and deal
out 10. you need to choose one of these
10 cards obviously i won't know which
one you 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 one
and face cards count as five and every
other card counts as the
numerical value it displays so like
nine equals nine so if you choose to
start with card number
five that's a queen which is worth five
and you'll go
five spaces one two three
four five and land on an ace which is
one
so then you'll go one land on a king
which is five
one two three four five
land on a ten and then you'll go ten
got it and you'll continue this until
you can't make
a full move so if you land on this nine
you obviously can't go nine
spaces so this nine 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 one to ten
let's say i pick four which is a four
the fourth 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 fourth card
which is a four i'll count four spaces
to another card
one two three four which is a five
and continue until the end you'll do the
same thing for your mystery card
and then it's uh it's wiener time
okay go ahead let's start
your last card in the sequence is
that nine 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 one in six of you are
already
typing a rage soaked comment about how
dumb i am for choosing the wrong number
and
joke's on you buddy because i knew that
would happen
the kruskal's count with a 52 card deck
only works about 85 percent 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 two decks of 52 cards the
odds of me predicting the
right final card for you jump to
95 percent 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
ten the fourth and ninth cards linked up
on this
seven and then met up with the others on
this queen
but three of the ten just kinda did
their own thing
and converged on a second mini chain the
fifth
eighth and tenth cards linked up
together on this
jack and ended up on a six there are a
couple of reasons for this
first landing on a couple of nines
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 the way
we know that this
isn't magic magic works one hundred
percent 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 and i'll link
below because
i like you yeah this is a fun little
trick that 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
veritable one and it has real-world
computational applications in 1978
john pollard applied it to code breaking
and developed
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 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