Kind: captions
Language: en
do not hit the like button or the
dislike button at least not yet I want
you to consider a problem that's been
one of the most controversial in math
and philosophy over the past 20 years
there is no consensus answer so I want
you to listen to the problem and then
vote for the answer you prefer using the
like and dislike buttons okay
here is the setup Sleeping Beauty
volunteers to be the subject of an
experiment and before it starts she's
informed of the procedure on Sunday
night she will be put to sleep and then
a Fair coin will be flipped if that coin
comes up heads she'll be awakened on
Monday and then put back to sleep if the
coin comes up Tails she will also be
awakened on Monday and put back to sleep
but then she will be awakened on Tuesday
as well and then put back to sleep
now each time she gets put back to sleep
she will forget that she was ever
awakened in the brief period anytime
she's awake she will be told no
information but she'll be asked one
question what do you believe is the
probability that the coin came up heads
so how should she answer feel free to
pause the video and answer the question
for yourself right now
this was my reaction after hearing the
problem for the first time I mean the
intuitive answer that pops into my head
is clearly one in three it could be the
Monday when it came up heads or it could
be the Monday when it came up Tails or
it could be the Tuesday when it came up
Tails but you know what's really
interesting is you just answered that
the probability of a coin coming up
heads is one-third I think a lot of this
comes down to what specific question is
asked of her what is the probability
that a Fair coin flipped gives heads
that's 50 what is the probability that
the coin came up heads I would say the
answer is a third from her perspective
yeah I it's it's remarkably the same
question the simple reason why Sleeping
Beauty should say the probability of
heads is one half is because she knows
the coin is fair nothing changes between
when the coin is flipped and when she
wakes up and she knew for a fact that
she would be woken up and she receives
no new information when that happens
imagine that instead of flipping the
coin after she's asleep the
experimenters flip the coin first and
ask her immediately
what's the probability that the coin
came up heads well she would certainly
say one half so why should anything
change after she goes to sleep and wakes
up this is known as the halfer position
but there is another way to look at it
others would argue that something does
change when she's awakened I mean it it
seems like she gets no new information
there are no calendars no one tells her
anything and she knew that she would be
woken up but she actually learns
something important she learns that
she's gone from existing in a reality
where there are two possible States the
coin came up either heads or tails to
existing in a reality where there are
three possible States Monday heads
Monday Tales or Tuesday tales and
therefore she should assign equal
probability to each of these three
outcomes Where Heads only occurred in
one so the probability that the coin
came up heads is one-third
this is known as the thirder position
now I know it seems wrong to suggest
that a Fair coin should have a one-third
probability of coming up heads but
that's because the question she's asked
is subtly different the implied question
is given you're awake what's the
probability that the coin came up heads
and that is one-third now halfers would
counter that just because there are
three possible outcomes doesn't mean
they are each equally likely in the
Monty Hall problem for example the
contestant ultimately has to choose
between two doors but it'd be wrong to
assign them 50 50 odds the prize is
actually twice as likely to be behind
one door than the other in the Sleeping
Beauty problem we know a heads outcome
in a Tails outcome are equally likely so
the chance of waking up on Monday with
heads is 50 and the chance of waking up
on Monday or Tuesday with Tails should
be 50 therefore the Tails probability
gets split across two days 25 each
but if you repeat the experiment over
and over which you can try for yourself
by repeatedly flipping a coin you find
she wakes up a third of the time Monday
heads a third of the time Monday tales
and a third of the time Tuesday Tales
not 50 25 25 like the previous analysis
would suggest
so if you were sleeping beauty and you
were awakened and asked what's the
probability the coin came up heads what
would you say
if you would say one-third then hit the
like button if you would say one half
hit the dislike button
the answer may seem obvious to you but
you should know that to other people the
other answer seems equally obvious and
that's why hundreds and hundreds of
philosophy papers have been published on
this problem over the past 22 years
there have been many variations of this
problem like what if instead of being
woken up twice if the coin lands Tales
she's instead woken up a million times
if the coin comes up heads she's still
woken only once doesn't it seem absurd
in this case when Sleeping Beauty wakes
up to say that it was just as likely
that a coin landed heads as Tails when
we know there are a million more wakeups
in the tales case than in the heads case
I mean if you reach into a bag of one
white marble and a million black marbles
what are the chances that you pull out
that one white marble
I was pretty convinced by this and I
considered myself a thirder but this
same argument is used to convince people
that we're living in a simulation the
thinking goes that our Computing
technology has improved so dramatically
even over just the last 40 years that we
can imagine a time in the not too
distant future when we can create a
completely realistic simulation of our
world and once that occurs it should be
trivial to make unlimited copies of that
simulation and then if you were to ask
someone if they're living in a
simulation they would have to admit that
they probably are because there are many
more instances of that existence than
the one true external reality
but how do we know that this hasn't
happened already and that we're living
inside a simulation I mean if it can
happen then it probably has happened and
we are living in a simulation this seems
like the logical conclusion of the third
or world view now I personally don't buy
that I'm living in a simulation and I
think most people don't buy it but maybe
that's just illogical bias but there's
another thought experiment that makes me
seriously reconsider the third or
position let's say there's a soccer game
between a really great team like Brazil
and a less World dominating team like
Canada so the odds are 80 20 in Brazil's
favor now a researcher is going to put
you to sleep before the game starts and
if Brazil wins they'll wake you up one
time but if Canada wins they'll wake you
up 30 times in a row and just like
Sleeping Beauty you won't remember if
you've been woken before okay so the
game is about to start you fall asleep
and now you're woken up
who do you think won the game the
thirder would say Canada but I would
almost certainly say Brazil I mean why
should I give any weight to what the
researcher would have done if Canada had
one when I'm fairly confident that they
won't to extend this let's say Brazil
placed Canada five times and we do this
experiment each time well then if you
say Brazil each time you're woken up
you'll probably be right about four out
of five of the games but if you said
Canada every time you would be wrong
about those four games but write 30
times in a row when you're repeatedly
asked about Canada's one victory if you
stand to win a bet by correctly
answering the question then by all means
you should bet on Canada but if you want
to correctly pick the winner of more of
the games well then you should say
Brazil and this is what's at the heart
of the dispute between halfers and 30s
in the Sleeping Beauty problem
if you want to be right about the
outcome of the coin tosses well you
should say the probability of heads is a
half but if you want to answer more
questionings correctly well then you
should say one-third
I want to leave you with one last
thought experiment imagine that you know
for a fact that before our universe
began there was a coin flip and if it
came up heads only a single Universe
would be created but if it came up Tails
a quasi-infinite Multiverse would be
created and in each of those Multiverse
universes you'd find every possible
variation of Earth and the people on it
in some versions there would be no Earth
now you becoming conscious is just like
Sleeping Beauty waking up there's no way
to tell if you're in that single
universe or in one of the Multiverse
universes but you know there are a lot
more of them
so would you think that you're for sure
in the Multiverse
or are the chances 50 50.
the best way to develop intuition about
probability is by working through
scenarios or running simulations like we
did for Sleeping Beauty this video is
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