The Most Controversial Problem in Philosophy

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Many thanks to Dr. Mike Titelbaum and Dr. Adam Elga for their insights into the problem.

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References:

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Written by Emily Zhang, Derek Muller, Tamar Lichter Blanks
Edited by Fabio Albertelli
Animation by Ivy Tello, Fabio Albertelli, Jakub Misiek
Additional video/photos supplied by Getty Images & Pond5
Music from Epidemic Sound
Thumbnail by Ignat Berbeci
Produced by Derek Muller, Petr Lebedev, Emily Zhang

[veritasium]

If you want to vote by liking/disliking the video: “Agree with me” means 1/3 and “Disagree” means 1/2.

Latest update (Nov 23, 2023): 217, 332 agree with me, and 97, 502 disagree with me.

[sinistril]

"What coin? What are you talking about? Where am I? Who are you?"

[mohdansar]

I'm a simple man. The probability of everything is always 50-50. It either happens, or it doesn't.

[kirtirattan]

My reactions when I see a Veritasium video. Amazed by the title-> Understands the concept-> Trying to understand deeply-> Gets lost-> Forgets what was the video about-> Perplexed about the reality-->Video ends->Hits the like button.

[laurineder]

Derik: vote with like and dislike button
Youtube: makes dislikes invisible

[lexxynubbers]

As a Canadian, I would be quite happy for a 20% chance of winning against Brazil

[relatively_random]

Whenever there's no consensus in probability puzzles like this one, it usually does boil down to subtle disagreements about what is actually being asked, not the answers themselves.

[anneshleah]

For me it becomes less paradoxical when I think of the question as rephrased as "How likely is it that Heads is responsible for you waking up this particular time?"

[zodiakgames]

Its not that theres a 1 in 3 of heads, its a 1 in 3 that she was awoken for it being heads

[jo_devs]

If sleeping beauty was asked "What's the probability the coin came up heads?", I think she should say 1/2. If she was asked "What's the probability that you've been woken up as part of the outcome of a heads result?", I think she should say 1/3. I think the key thing with this question and the reason there isn't (and probably can't be) consensus comes down to how it's communicated and how we as individuals interpret what's being asked of us with the answer. If your goal is to reinforce your understanding about how the coin works, you are probably a halfer. If your goal is to be correct in answering the question from the perspective of sleeping beauty, you are probably a thirder.

[Asterism_Desmos]

“Do not hit the like button” 87 people instantly ignored him

[topherhenny]

I'm changing my answer to 1/2 - it doesn't matter how many times she is woken up the probability the coin came up heads in the initial toss remains the same. The experiment where you count your coin toss and then mark the outcome as either Monday heads, Monday tails, Tuesday tails - is seeing the chance of being woken up by a heads flip. This is different to the probability of the initial flip.

[hpmyizd]

In my opinion the question you seem to ask is: What is the probability that today isn’t Monday? The probability of a coin flip is always a coin flip as we say(50-50).. but the question refers to the coins state only in regard to what day it might be.. meaning that if it was H she’ll be asked once, while if it was T she’ll be asked twice, so it’s not really a philosophical problem, just that the question appears to be misleading

[dukemagus]

Lessons learned: never let a researcher put you to sleep and never pay them in cash

[HoustonLucas]

There's a hidden lesson here about imbalanced classes in a dataset. Halfers are trying to model the distribution of the data generating function, while thirders are trying to minimize some loss function for the estimator.

[lethaldose]

Possibility of getting heads is always half, because we cannot determine what day it is when the question was asked, if it is Monday then probability is just half but if it is Tuesday than probability is 0(in case of heads). One thing which we can determine is the fact that coin was only tossed only for once on the Sunday and awakening on either day is completely dependent on toss conducted on Sunday. On the Sunday probability of getting either of the outcome was equal, thus in this case the day is not important as it cannot be determined.

[hockeyholic]

It's 1/2, think of it like this. You randomly get assigned a red or blue magnet, which you cannot see. They only attract coins of the same color.
You are given a bag with 1 million blue coins and 1 single red coin. You will then stick in and pull out a coin with your unknown color magnet.
What is probability that reaching in with the unknown color magnet that it will pull out a red coin?
If the random 50% chance assigned you a red one you will therefore will pull out the 1 red coin.
If the 50% chance assigned you a blue magnet, therefore you will pull out a blue coin, which will be one of those 1 million blue coins. The 1 red coin will always be pulled every time yours is red, but any specific blue coin (outcome) will only be pulled one / one millionth of the time yours is blue, the 50% blue probability is split amongst the one million blue coins you have a random chance at pulling, so those specific outcomes has far less weighted probability than the red coin. The red magnet's 50% will never split its probability because there's only 1 coin. More blue coins added just further dilutes the probablity of any specific coin being pulled from the blue magnets probability, but the sum will always still just be 50%.

[a_mouse]

When I reached your poll, I didn't understand the controversy. If the question is "What is the probability that the coin WILL be heads?" the answer is 1/2. If the question is "What is the probability that the coin WAS heads?" is 1/3. These are two completely different questions. The first has to do with flipping a coin. The second is about what day it is.

[jasont]

The experimenters look on in horror as the coin rests upon its edge. They somberly pull the sheet over Sleeping Beauty's face. After an appropriate period of silence, Erwin asks, "You guys wanna put my cat in a box with an unstable nucleus, a hammer, and a vial of nerve gas?"

"Not again, Erwin..."

[PhilbertDeZwart]

I think the question asked is really: "is this a heads day or a tails day?" and the chance of it being a tails day is twice as high as it being a heads day.