Veritasium - 2023-02-11
For decades, the Sleeping Beauty Problem has divided people between two answers. Head to https://brilliant.org/veritasium to start your free 30-day trial, and the first 200 of you will get 20% off an annual premium subscription. ▀▀▀ Many thanks to Dr. Mike Titelbaum and Dr. Adam Elga for their insights into the problem. ▀▀▀ References: Elga, A. (2000). Self-locating belief and the Sleeping Beauty problem. Analysis, 60(2), 143-147. - https://ve42.co/Elga2000 Lewis, D. (2001). Sleeping beauty: reply to Elga. Analysis, 61(3), 171-176. - https://ve42.co/Lewis2001 Winkler, P. (2017). The sleeping beauty controversy. The American Mathematical Monthly, 124(7), 579-587. - https://ve42.co/Winkler2017 Titelbaum, M. G. (2013). Ten reasons to care about the Sleeping Beauty problem. Philosophy Compass, 8(11), 1003-1017. - https://ve42.co/Titelbaum2013 Mutalik, P. (2016). Solution: ‘Sleeping Beauty’s Dilemma’, Quanta Magazine - https://ve42.co/MutalikQ2016 Rec.Puzzles - Some “Sleeping Beauty” Postings - https://ve42.co/SBRecPuzzles The Sleeping Beauty Paradox, Statistics SE - https://ve42.co/SBPSSE The Sleeping Beauty Problem, Reddit - https://ve42.co/SBPReddit Sleeping Beauty paradox explained, GameFAQs - https://ve42.co/SBPGameFAQ The Sleeping Beauty Problem, Physics Forums - https://ve42.co/SBPPhysicsForums ▀▀▀ Special thanks to our Patreon supporters: Tj Steyn, Meg Noah, Bernard McGee, KeyWestr, Elliot Miller, Brian Busbee, Jerome Barakos, M.D., Amadeo Bee, TTST, Balkrishna Heroor, Chris LaClair, John H. Austin, Jr., Eric Sexton, john kiehl, Anton Ragin, Benedikt Heinen, Diffbot, Gnare, Dave Kircher, Burt Humburg, Blake Byers, Evgeny Skvortsov, Meekay, Bill Linder, Paul Peijzel, Josh Hibschman, Mac Malkawi, Mike Schneider, jim buckmaster, Juan Benet, Ubiquity Ventures, Richard Sundvall, Lee Redden, Stephen Wilcox, Marinus Kuivenhoven, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi. ▀▀▀ 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
"What coin? What are you talking about? Where am I? Who are you?"
I thought something similar at first too, but actually it is all carefully crafted to prevent this from being a valid answer. It is only when she is put "back to sleep" that she forgets, and what she forgets, is being woken up. So every time she is asked the question, she remembers the original explanation, the original time being put to sleep, and being woken up that time.
That would logically mean X, but I don't like X, so it doesn't mean X.
Great science right there, chief 👍
Wait, why am I naked?
you are either a mechanical engineer or a philosopher 👍
@@stilldreamy5181This comment still makes sense, since the paradox itself stands because it introduces "knowledge about the system", which leads to the "simulation theory" aspect of the question. If you are exclusively a part of the system, meaning you can't imagine a system containing the system you are in, then the question will have only one valid answer; it's when you assume the possibility of a "hyper-system", a system that contains the system you are in, that the question becomes a paradox.
Therefore, questioning the reality of a "system within a system", like the original comment does, is the key to "solve" the paradox. In other words, the hundreds of papers discussing this paradox, are really people debating their belief in the multiverse or simulation theory (which is actually unprovable, therefore a theological debate).
As a Canadian, I would be quite happy for a 20% chance of winning against Brazil
fax
Amen
In the particular universe that produces Canadian dominance of Brazil in soccer...pigs can fly. Pig guano everywhere.
As a Brazilian, I’m happy there’s at least one scenario where we are more likely to win against Canada
@@diegototti we are also more likely to win against canada in a war. they would apologize for being involved in a fight and raise the white flag
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.
Thank you
Exactly. Seems fairly obvious
But what if it was a 1% chance ( a 1 on a 100-sided die) to wake up 1 million times? Even if you were asked what the probability of the die being 1 WAS, it was still only 1%. Its unlikely that you were put to sleep a million times in the first place.
@@alexs1277 Not clear what variation you are describing here. But If 99% to wake once, and 1% to wake 10^6 times, chance die WAS 1/100 is 99.990%. No?
Changing the tense of the question has no impact. Again just consult the soccer game analogy. It’s obvious
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.
I changed due to this
I agree.
Exactly my thoughts! "Tuesday tails" simply doesn't exist, if we're talking about coin flipping.
I'm actually changing my answer to 1/3 because while a coinflip is obviously 1/2, the way the problem is constructed is : heads gets only one question, while tails gets 2 questions (questions not flips!) , so by saying tails you are going to be right twice as much just because you get 2 questions instead of 1 . IF the coin would have been flipped again between monday and tuesday, then the answer would obviously be 1/2. This way it's just 1/2 heads and 1/2 tails, but tails gets double points every time.
Change it again :) Imagine that if heads, she's not waken up at all. She's only waken when tails. She's asked the same question. What should she answer 1/2 or 0?
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.
Agree.
I like the way you explained this. His statement “Something changed” was important because it matters that an event occurred between observations.
This is the correct answer. It depends on how the question is interpreted.
But if sleeping beauty doesn't remember any times she's been woken up, every time is her first. So to her it's always 50/50. Any other wake-up (Tuesday) in her existence never actually happened
I think there should be a distinction between asking "What is the probability A coin came up heads?" and "What is the probability THE coin came up heads?" The question is about THE coin, and given she is awake, the answer is the probability of her being awake.
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.
Yeah, it just seems like semantics. I depends on whose perspective you are using
Semantics, asking the wrong question, wrong definition, etc.
That's what makes Monty Hall problem so great - it's not about words, it's about the actual concept itself.
Yeah, "what was the probability that it came up heads?" vs "what is the probability that it came up heads?" can already make a difference to the answer. Only if you define questions properly can you answer them. I suppose that's why they were philosophy papers and not mathematics. In mathematics you need things to be defined unambiguously.
There is clearly a majority consensus on the entire thing with most people leaning towards the real world side instead of the fairytale book side. Why do you think they use a literal fairytale character to point this out? Math is 100% disconnected from reality. A concept. She's literally missing 25% of her ability to know what actually happened. She is at 75% comprehension of her reality since she can't tell the difference between waking up once or waking up twice. But the knowledge shown to her is letting her know, that she has two chances to respond on a tails flip, or once chance to respond on a heads flip. So she can take the chance of being right or wrong about a 50/50 chance twice in a row, or once. Her best chance of answering correctly on monday heads, monday tails, or tuesday tails is to realize that there is no tuesday heads and eliminate 25% of her ability to answer. Thus leaving 3 equal chance scenarios. Her real world probability is skewed by lack of information. Her fairytale probability is 1/2, because 1/2 is 1/2 and everyone knows 1/2 is 1/2.
The correct position in this "paradox" is:
(A) All conjectures about "the odds of" or "the probability of" are meaningless UNLESS they are coupled to the notion of "expected outcome over a long number of trials" in some kind of chain of events. Therefore, absent that coupling to reality (or even imagined reality), no question about these conjectures has meaning, and no answer to such meaningless questions is "Correct", and no answer is "Wrong".
(B) The correct answer to the question "Expressing your answer in terms of the expected outcome of a long series of coin-flips, what are the 'odds' that it lands 'Heads'?" is "50%" i.e. "1 out of 2" or "half". (These are not different possible correct answers. Each of them is the same UNIQUE correct answer, expressed in different words.)
(C) There is one and only one Correct answer to a third question. The question is longer. It is:
QUOTE:
Assume that Sleeping Beauty never makes a mistake in reasoning or calculation.
Assume that Sleeping Beauty's definition of "the odds of something happening" is the rationally anticipated outcome of re-running the same circumstances for many trials, where 'outcome' means 'the proportion of the trials in which the event in question happened vs. the proportion of the trials in which it didn't happen".
Assume that Sleeping Beauty has a net incentive to make a Correct guess.
(1) Then, under the assumptions above, if Sleeping Beauty is woken up and mentally formulates a guess (whether she is asked to speak it aloud or not) as to the result of the coin-flip, and she formulates that guess based on correct reasoning and calculation, what will her guess be? (2) What will be her rational estimation of the odds of that guess being "Wrong" (bearing in mind that she has a particular way of giving meaning to the expression "the odds of", even if she knows there will only be one run of this experiment)?
And (3) if she answers truthfully about her own thoughts, what will she say if asked what she computes to be the probability that guessing that the coin landed "Heads" will turn out be a "Correct" guess?
UNQUOTE
The third question's ONLY correct answers are: (1) "Tails"; (2) "1/3"; and (3) "1/3".
To make this into a Paradox we have to avoid a lot of specifics in the question above, such as nailing down exactly what is meant by the phrase "the odds of something happening". We also have to obfuscate the fact that "What are the odds that the coin landed 'Tails'" and "What are the odds that you're going to be correct if you guess 'Tails' when asked 'how did the coin land'?" are NOT, ABSOLUTELY POSITIVELY NOT, the same question!
Once someone has gotten rid of a lot of the specifics, it enables them to pretend that the question described in Part (B) above is the same question as described in Part (C)(3) above. Since each of those two questions has an obvious Correct answer, it can then be alleged that the same question has TWO correct (but mutually-exclusive) answers. That's how these char'la'tans COOK UP these phony "paradoxes". Nobody is really in the "HALFER" camp or the "THIRDER" camp. Those who say "I'm a 'halfer' are simply mis-casting their position on Question (B) above as their position on this alleged "paradox". Those who say "I'm a 'thirder" are simply mis-casting their position on Question (C)(3) above as their position on "the paradox" (which doesn't in fact exist). If you ask me Question (B) I say "1/2". If you ask me the Question (C)(3) then I say "1/3". Since those ARE NOT the same questions, I'm not vac'ill'ating or contradicting myself. My two answers are mutually consistent.
I really do enjoy philosophy, but I feel this whole "Paradox" is just for stupid people. It's 50/50. And her waking up twice with no knowledge is both a red herring and irrelevant.
This answer makes more sense to me than the whole video.
Thank you for the frame of this 'paradox', it heavily relies on the presuppositions you have listed. I think this draws eerily close to Schrodinger's Paradox. The outcome of the coin flip is assumed to be both heads and tails, until the individual guess and then sees the outcome. Before that event, the coin flip can essentially be both.
What if I ignore the rules, and I hit the like button? Does this mean I am indicating that I am a halfer or a thirder? Or that I simply "like" the video? OR that I select 'thumbs up' simply because I am crazy?
I enjoyed reading your explaination. Thank you for taking the time to write that.
Me not even understanding the question
Same. It isn't easy to understand it. All we can do is try.
Perfect profile pic. True gigachad
I'm a simple man. The probability of everything is always 50-50. It either happens, or it doesn't.
exactly
Reminds me of the football coach who didn't want his quarterback to throw because two of three possible outcomes were bad. Interception and incomplete.😅
@Glenn Clark ahh the coach is wrong. It's still 50-50. The pass either reaches the teammate or it doesn't. 🤣
Average mulla thought process
No. It’s not. If that was true, you would win any game every second round on average making only random choices, i.e., tossing a coin. Clearly, that’s absurd.
Lessons learned: never let a researcher put you to sleep and never pay them in cash
That would logically mean X, but I don't like X, so it doesn't mean X.
Great science right there, chief 👍
What would I say? I would say “the question ambiguous, please clarify”
I am a halfer. Using the original scenario with 2 vs 1 you could say the odds of Heads are 1/3 but that would be incorrect.
There are two probabilities at work here, not just 1.Te coin flip AND the particular instance of waking up.
For any particular waking moment it could be the 1/3
Either She is being woken up on
1) the only heads up
2) the 1st Tails
3) the 2nd tails.
IF she was asked which one of these it is then, yes, 1/3 would be the odds but she was not asked that
However, She was asked "was the coin flip heads or tails?"
The odds of that, whether you have 2 wakes for tails or a million is still going to be 1/2
So an estimate of probability is only correct if it is what the infinite repetition of a test would converge upon.
Toss a coin and you'll get a head or a tail. Toss it 10, 100, 1000, a million times, and the ratio of heads and tails will converge upon 50/50. That's how you know you got it right.
Here we're asking a princess to judge the likelihood that the coin landed heads.
If we repeat the experiment 1000 times, then we will ask the question ~1500 times. If every answer is "1/2", then they will ALL be wrong, because in reality around 2/3 of the questions will be asked after a tail.
@@peelingOn 1000 experiments, you still ask the question 1000 times, not 1500. Even if you ask 10,000 times the coin flip is still 50/50. If the coin flip was heads, it will be heads on the first ask or the 10,000 ask.
@@claytoncourtney1309 No, over the course of 1000 experiments, you will ask the question approximately 1500 times (once per iteration if it was heads, twice if it was tails).
Think about it this way:
Suppose the experiment is run 1000 times, and each waking of the princess is recorded as a separate video. So there are ~1500 videos.
One video is shown to you at random.
What are the odds that video is from a waking that occurred after heads was tossed?
It is ~1/3rd, right?
You, watching the video, have exactly the same information that she did at the time it was recorded.
So why should her answer be different to yours?
@@peelingI rethought it through, in the shower of course lol, and I agree with you. I DO like your idea of using the video.
I still have problems with the question but am already late for work. I did, once i saw your your response wanted to let you know i now agree with you.
“Do not hit the like button” 87 people instantly ignored him
Now 2,479...
How are you able to see number of dislikes?
@@Varma17 the title is the amount of likes (agree) to dislike (disagree)
@@Varma17 I think the title updates periodically, the number of people disagree
@@Varma17 there are browser plug-ins to show dislikes again. the one I use is "return youtube dislikes". cheers
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..."
Split the difference!
@@ChrisContin They divvied up the hadrons amongst themselves and Erwin got a new cat.
Ahh I dont have enough neurons in my brain to understand this, someone please do the honors.
@@bluzter it is a reference to Shrodinger’s Cat
@@bluzter The cat referenced above, plus they're saying that they flipped the coin and it landed on neither heads nor tails, landing instead on its edge and therefore she will never awaken. It's the hidden third result.
Given that she forgets when she wakes up, she should be asking "What coin? Who are you? Why are you in my room?"
The fact that she knows the coin is flipped just once means the answer must be 50%, irregardless of when she is awaken. Then again, if we are in The Matrix, then she must realize that there is no coin, and it was she who was flipped.
'What is the probability that you will wake up from this much heroin dosage'
If 'heads' wipe out all life on earth, and 'tails' doesn't. After the coin has been flipped and before you have seen it, someone asks you, "what is the probability of 'heads'?" What would you answer?
@@Poppillon50
@@adampicki that's the answer to the question "what was the probability of the coin toss". Not the answer to the question "what is the probability that a particular event happened". The key to this is the implied impact of the circumstances under which the question was asked.
@@Poppillon but the probability was still 50 it happened, only because it landed it doesnt make it 100%
"Waking up on Monday with head" gets me every time.
Best way to start a Monday
That's why I pick heads everytime
Some people prefer waking up with tail.
By Veritasium? I'd only want it to be from Sleeping Beauty. If not, I'd pass
bruh
Veritasium uploaded: 0 People Agree With Me, 0 Disagree
0.3 is probability of one side of the coin vs 0.707 probability of the other side
Well no sh*t
@@aucklandnewzealand2023huh? Where does that come from?
@@aucklandnewzealand2023more like 0.33 and 0.66
If they ask me on Monday, I will say it was 1/2 because it could be heads or tails. If they ask me on Tuesday I would say it was 0 because it must be tails. If they don’t tell me the day and I can’t tell what day it is, then I would say 1/2. Imagine the question we will put you to sleep and wake you up tomorrow if it’s heads or in a week if it’s tails, or every day for 7 days if it’s tails. If I have no memory of anything, the passage of time doesn’t matter. Also there is only 2 outcomes, Monday and Tuesday or just Tuesday. The answer is 1/2, and just like mentioned, if it’s heads and she’s woken up one day , for a million days, we are not asking what is the probability of her being woken up on a day, we are asking what is the probability that it was heads which is always 50.
That's the thing, if her memory is wiped, there is no way to know what day it is.
The problem as in the Brazil-Canada football match game is that the question mixes up Expected value and Probability
Well said
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.
Then take them both to the consideration and calculate the average. That would be the real solution to this dilemma.
@@orka6848 no, these are not two approaches to the same question, they are two different questions. Averaging them is kind of meaningless.
Estimating the distribution is not the same as minimizing expected error.
@@johnmorrell3187 I think you hit the nail on the head - those who agree with him are answering a different question than those who do not.
funny, but no: the imbalance of the heads and tails here is only due to a deliberate mistake in sampling; because of a sampling error you record "tails" twice when a single "tails" event occurs, but only a single "heads" event is recorded for "heads" events. The dataset is seriously screwed up; when presented with a new "instance", the "thirder's classifier" will have its probability estimates wrong: it will be predicting "tails" with prob. 0.66 but it will only be "tails" with prob. 0.5.
@@orka6848 here we have the engeneer
The secret to this problem is that it is a trick question attempting to ask 2 different questions at the same time. Attaching probability to it just makes people think there is something more profound happening.
Yeah I agree, it's more about semantic than statistic. Derek just found a nice trick to get tons of likes and views with a question that is more intellectual masturbation than anything else.
@@En_theo exactly. And I love Derek and his content but this video just felt like a gotchya. And the worst part is I can't even express this to him by downvoting the video
Maybe it's a social experiment on how much influence his opinion has
Exactly
I agree it's a trick question, but it's not two different questions. It's just one invalid question. The tail scenarios cannot be viewed as two separate outcomes: informationally they are identical to sleeping beauty, and therefore the same outcome. The question just arbitrarily labeled the tail scenarios as two outcomes, not with any kind logic compatible with reality, but with memory erasing magic.
Imagine someone waking you from sleep and asking you the most controversial question...
So based on the wording of the problem, I would say the following: When she wakes up on Monday and is asked "What do you think the probability is that the coin landed on heads?" then it is 50% because whether the coin landed on heads or tails, she was going to be woken up on Monday. Now if she is asked on Tuesday or any other day that isn't Monday, then the probability that the coin landed on heads is now 0% because the conditions she was given was that if the coin lands on heads she'll be woken up on Monday and if Tails then the she is woken up on Monday and Tuesday (and whatever day the iteration of this problem decides). The coin isn't flipped for each concurrent day. It is only flipped on Sunday to determine if she is woken up on just Monday, or if she'll be woken up on the days following Monday.
Exactly
So the case (Tuesday + tails) is absolutely useless to the probability of heads occuring.
As it was never defined that heads will result in her waking up in tuesday
I think the problem is she doesn’t know what day it is
@@Nanbread-bw7nq If the problem is dealing with what day it is that she was woken up vs. what is the probability that the coin landed on heads, then those are 2 independent probabilities.
The probability of the coin flip (reminder that it only occurs on Sunday) landing on heads is and always will be 50%
Now if we consider this specific problem and its wording, then there are only 2 days that she will be woken up: Monday and Tuesday. This information is what is always known (she doesn't forget the problem itself, only the outcomes she is told when she is woken up and then goes back to sleep).
Okay, so now we can ask the following question: What is the probability that today is Monday? well we know based on the information provided in the problem as it was worded, that she would only be woken up on Monday or Monday and Tuesday, which means we can eliminate Wednesday through Sunday. This means that the probability of the day she wakes being Monday is 50% and Tuesday is 50%...if she assumes it's Monday then the probability of the coin flip stands to be 50/50...if she assumes it's Tuesday then it's a 100% probability that the coin landed on Tails.
If the problem accounts for more days being woken up, then that changes the probability of what day it is that she is woken up, but that's a different question than "what is the probability that coin landed on [insert heads or tails]".
@@N8ive49er But the question is not asking what the probability of what a coin toss "will be". It's asking about probability of what it "was", given that you were already woken up after the experiment has started.
I think the question is subtly mixing up the probability distribution of the coin toss with the probability distribution that the sleeping beauty was woken up with a certain coin toss. So it really comes down to what you think the question is asking for.
Yeah, one of the confusions is that "what's the probability that the coin came up heads" can mean different things. Halfers think it's a question about the behaviour of coins. Thirders think it's a question about your on-the-spot beliefs about past events.
@@AzrgExplorers I agree. Thirders actually think that the question is, "what are the chances that you were woken up once before?"
yup, like nearly all things, the readers interpretation is what truly matters... and yet the world doesnt care
@@wordsofcheresie936 No, thirders are answering the exact question asked. Sleeping Beauty wasn't asked "did the coin come up heads?" She was asked, "what are the chances that the coin came up heads?" In the soccer analogy @veritasium used, he talked about this difference without actually pointing it out.
About ten billion humans have been born. So the odds of you being born as you is one in 10 billion. So when I ask if you are you, what is your response? If I ask what were the chances that you would be born exactly as you are, what is your answer?
The questions are different and so the answers are as well.
The best way to explain it is the way he already did. Let's Make a Deal gives you 3 doors, with only one valid prize, heads. The other two have tails behind them. Then they take away a confirmed wrong door, giving your probability of choosing heads an increase. That's why you always switch the door you choose after the removal of a tails door.
This method is simply presenting you with two possible doors but then adding a 3rd confirmed possible door. Your safest bet is to be realistic and realize that the original two doors always had a 1/3 chance of having heads no matter what door you chose. Changing doors still results in a 1/3 chance of choosing the heads door.
As a Canadian, I'm really thankful you gave Canada one in five odds of winning against Brazil 😂
As a Brazilian I'm thankful for 4 out of 5... Canadian team is getting better and better (Brazilian team have been a lot better).
And there's a 100% chance of another balloon flying over Canada will be shot down by an F22. :D :D
As a Croatian, we beat you both, even though Brazil was better but unlucky against us. It was that 1/5 win for us 🙂
Good luck to Brazil!
@@lukatore123 - I think it was more like 2/5. Croatia's got a great team (maybe the best one per capita - amongst Uruguay and Portugal). Brazilian team, of course, had better individual quality, but Croatia had a very interesting collective game.
Afterall, i think it was very well deserved
@@BillAnt 🤫🤫🤫
Because some people are commenting about “being right more often” means we have a different understanding of what problem we’re even considering.
After a minute in, it seems so obvious. There are 3 ways to be awakened; only one was due to a heads flip. 1/3. Now, I watch to see how dumb I am.
I think this scenario highlights, more than anything, that it’s odd to phrase a question with multiple answers with a yes or no prompt.
Maybe that was the real point the originator was trying to make but people just totally missed it and now here we are
My first reaction was that the problem is too contrived to be interesting.
actually, the probability of it being monady or tuesday is 33 percent, but the odds of it being tails is 50 percent
@@Sad_cat_studio no the odds of it being Monday is 66%
That would logically mean X, but I don't like X, so it doesn't mean X.
Great science right there, chief 👍
I've gone through this, and I think I've gotten to the conclusion that I'm a halver, but only on very specific conditions. I feel like two questions are being asked at the same time and each side chooses to focus on only one of them. Halvers are focusing on, sleeping beauty is woken up, she's asked what's the chance that it had come up heads. The answer is 50%, because it:s a fair coin and regardless of the day the answer is 50%.
However, thirders are answering a DIFFERENT question, which is, every time sleeping beauty is woken up, what's the probability of her being right, should she always pick up heads. She's woken up everytime, is asked which one came every time, she picks head everytime, the chance of her being right is 33.3%, but it's not because of the coin, but because they're oversampling the wrong answer.
Halvers are talking about the coin. Thirders are talking about sleeping beauty.
The formulation of the question directly tells you to consider it from sleeping beauty's perspective.
In other words, if we repeat the experiment every week for the rest of eternity, is she trying to be right most on days or right on most weeks ?
I really like how you worded this. And you're 100% percent correct. I personally believe that because of the way that the question was asked that it should be answered from sleeping beauty's perspective just as @rantingrodent416 stated, but the way you acknowledged both points of view without hating on either one I very much respect.
Flip heads, put one green bean in the bowl. Flip tails, put two red beans in the bowl. You pick a bean, what are the odds it is green?
@@rantingrodent416 Well she has no way of telling if she was awaken or not, so her only guiding point would be her understanding of the fact that a coin has only two outcomes, so it would be 50%. If someone flips a coin and ask you what are the pobability of it being heads, with no previous context (as sleeping beauty didnt remember if she had been awaken) you would answer 50%, because there is no way for you to say how many times you have been asked that question.
when you put me to sleep I had the strangest dream that I was watching a reeses ad
A simpler version of this paradox: If it's heads she dies, and if it's tails she wakes up. Given she wakes up, she's asked what's the probability the coin was heads? Would anyone still say 50% ?
My guy just asked a sleeping beauty problem and just left me on a thought about multiverses. I love this channel.
The probability that she guesses the side of the coin is ~1/6. ~1/2*1/3=1/6
But if you ask about the probability objectively, then of course ~0.707
It has no corelation to multiverse unless it exists (probability of Multiverse unknown)
@@aucklandnewzealand2023 stop dude you're talking to an anime pfp
@@aucklandnewzealand2023 Honestly, that isn't just as justifying seeing that she could have done any other operation
@@roddraft3466 the general consensus is that your pfp doesn't affect your comment
I think its the phrasing of the question that made this controversial. What if the question were " What is the chance you've been awakened due to a head coin toss?" Then to me its obvious, its one-third. Because sleeping beauty would be awakened more times due to a tail coin toss, even if she knew it is a fair coin. But if the question were " What is the chance the coin flip is a head " (With prior knowledge that she knew it is a fair one), it then would be 50-50.
Facts I don’t get how the root problem is that complex or controversial lol
@@kuribohoverlord2432 cause you are a genius mate, congratulations
What if the rules dictated that she would only be awakened and asked the question if the coin flip game up tails? Then, there would still be a 50-50 chance that the coin flip was heads. But given the information that she was being asked the question, she would know that the coin flip was not heads.
The fact that she is being asked the question gives her additional information.
What makes this "controversial" is that some people are unwilling to adjust their beliefs when given new information.
It's still just a matter of what's meant by the question. If a flip a coin, and you see that it's heads, and I ask you, what are that chances the coin landed heads, there are two answers depending on how you interpret my question. Either you answer 50% if you take my question as "what was the chance of what you've just seen occuring in general" or 100% if you interpret my question as "what is the chance that what you saw (the coin landed heads) is the actual state of the world (the coin landed heads)"
Thank you. You phrased it beautifully
I have the ambitious position. What we are talking about is actually two questions. Both 1/2 and 1/3 are correct, but they are answers of different questions
"In this instance of waking: how likely is it that this specific instance of waking is associated with the outcome of heads?"
To me it's the phrasing of the question asked that's important. If every time she's woken up, she's asked "do you think the coin came up heads or tails", she should always answer tails, because similar to the Monty hall problem, there will be more scenarios of her waking up and the outcome is tails.
But the question isn't asking her what she thinks *the outcome* is, but instead it's asking her what she thinks *the probability* is. The probability of the coin toss is completely independent of how many times she wakes up, or even if she wakes up at all, and it is always 1/2. So even if she were to wake up and the actual outcome of the toss was tails, she is still correct by saying that *the probability* of the toss is 1/2.
EXACTLY, probability? heads, obviously, what you think the result for this run was? tails, obviously
My thoughts exactly! Was looking for this argument.
What is the probability of coin came heads - 1/2, because that is the fact.
What is the probability that we woke you because coin came heads - 1/3 and is very different question.
What I was about to type.
but she wasn't asked what is the probability a toss of a coin comes out heads. She was asked what is the probability the coin did come out heads.
There is a big difference in asking about the probability of an event that has not occured vs the probability that a specific event has happened in the past so long as you gain knowledge when transition from that past point to the present.
One view the point when asked what is the probability of A. Which is 50%
What is the probability of A|B (A given B in statistics).
The probability of A given I have information B modifies the probability of A having occurred.
This is not an independent probability but a dependent one.
i agree with this because fundamentally she can't remember if she been woke up before (according to the experiment) so the fact that she is awake now can't be used to bias the answer dose 50/50 should be the right answer. correlation does not equal causation.
Id say it’s rather a linguistic problem: It’s a 1/3 chance that if she is awake, it was Heads. It’s a 1/2 chance that it rolled Heads when she awakens at all.
Not it’s still 1/3 when she awaken because she awakens twice if it’s tails
It's a fairly complex situation, but I agree completely. If you jump to a conclusion you are ignoring the actual dilemma, which is how semmantics may affect our perceptions of the universe. There's no truly correct answer, only a correct answer given a chosen context.
You wanna know the probability of heads vs tails? 1/2
You wanna know the probability of Sleeping Beauty correctly guessing if today is Tuesday? 1/3
etc
Makes me think how much of actual science is affected by linguistic biases, I would guess most of it.
It’s always the language that is the issue in these kind of paradoxes. Write this problem using only math and suddenly there is no paradoxes
I disagree. It’s a 50 50 chance if when she’s awake it’s heads or not. It’s a 50 25 25 chance if she is waken when MH, MT, TT respectively, because it’s 50/50 whether it’s head or tails and then if tails 50/50 whether it’s Monday or Tuesday.
Wittgenstein is proven right yet again
Why did I click this video while I'm having a headache 😭
I'm a halfer and I answered everything "like a halfer" except the universe question
The dilemma is not "what is the correct answer", but "what is the question being asked?". If Sleeping Beauty is asked what is the probability the coin came up tails, her answer should be 1/2. If the question is "what was the result of the coin toss" and the challenge is to be right (significantly) more than 50% of the time, she should answer differently.
In other words, the disagreement is not about what the answer should be, but about what the challenge was in the first place. The only sensible answer is therefore: Restate the question as to remove the ambiguity.
Or 42. That works too. Same reason.
"what is the question being asked?" is not a dilemma. The question is clearly about "the probability that the coin came up Heads". Answer to that question is 50%. And I agree with you that those who answer 1/3 are answering the wrong question.
that is so perfect an answer. how did you make it so easy,, in that, what is your background?
@@jonathanlavoie3115 what is the challenge being set, then. Is it to answer correctly on what the coin toss was, or something else?
That's the dilemma here - not what is the correct answer, but what is being asked of her in the first place.
If the challenge was « guess the outcome and I give you 1$ » she would answer Tails, not because the probability is 2/3 but because the reward is twice. Just like I give you 1$ if you guess Heads right, and 2$ if you guess Tails right. You would answer Tails not because the probability is higher. It remains 50%. In the SB experiment, the question is the probability it came un Heads.
@@uRealReels Thank you. You're the first person who reply to me so kindly!
A short anecdote about me:
In my programming course there was an exam in probability and statistics. Three of the questions were about the same problem. In a basket containing 9 blue balls and 11 red balls, what are the probabilities of A) draw 2 blue balls. B) 2 red balls. C) 2 balls not the same color.
Questions A and B are very easy. But for question C I knew that the teacher wanted us to use a complicated formula learned by heart. I didn't want to use this formula because 1- The formula is complicated and I'm lazy, 2- I don't like to use a ready-made formula that I don't fully understand and 3- I wasn't sure if the formula really applied to the situation.
So, I solved question C by following this simple reasoning: Probability of 2 blue balls + probability of 2 red + probabilities of 2 different = 100%. Total must be 100% because there is no other possibility. As expected, the teacher's formula answer was not the same as my answer, and I had to argue to get the point, but he had no choice but to acknowledge that his formula didn't apply to the situation, and that my answer was correct.
I argued my point in front of the review board, not because I needed the point (my average was already 98%) but because I like the truth. That's who I am...
Teo things are for sure:
1) The probability that the coin was tails is 1/2
2) The probability that sleeping beauty has a f*cked up sleep cycle at this point is 100%
Underrated comment lol
I like how you state that the chance is a half as one of the two things that are 'sure', despite the dozens of scientific papers with discourse, this video, the other comments, and the whole nature of this debate. Guess you had the answer all along then.
2/3
You are incorrect about #1.
The probability that the coin was tails is either 0% or 100%, depending on its result.
@@feha92 thats actually true no joke, since he specified "was tails" and anything that happened in the past either happened or didn't happen
Before He said: "Do not hit the like button" I already did 😂
I just clicked when the commercial still was on the screen
I'm extremely happy you posted this content!
Pure creative thought in action is a beautiful art form! ...and more importantly there's so many perspectives on this idea!
Anyway... just really happy to see someone explain this so well!
Thank you!
He did not explain it well, leading some readers pondering possibilities unreasonably based on a misinterpretation of the Sleeping Beauty scenario. If that was unintentional, then fine. However, this is not a big statistics problem.
I tried to apply philosophy to probability in my Probabilities class in college and almost failed the course. So, you know what my vote is.
That's hilarious. I dominated that class because of multiple degrees in philosophy. And went on to teach deductive, inductive, and probabilistic logic. And intro to inductive and probability logic class is pretty much proving the laws of statistics and much harder than any statistics class I ever took. Stats prof definitely hated me tho.
Philosophy begins where science ends
Or is it the other way round
@@nyeaglesfootballgarbagemen8346
Mathematicians and physicists were philosophers at one time.
@@aglawe1 Science is born of philosophy
The scientific method begins with a question
@@nyeaglesfootballgarbagemen8346
So it is an iterative process, philosophers ask questions and scientists try to answer them.
I think this is more a problem with the question having multiple valid interpretations than it is an issue of the question having multiple valid answers.
Halfers are focusing the question on the origin of the random event that causes a decision to be made at the start(i.e. the flipping of a coin). Thirders are focusing on the end result of the overall experiment (i.e. the number of ways sleeping beauty can be woken up). The tricky part in this whole scenario is that the question is presented as a single event with a single function to model it. However, from my perspective as a programmer, this scenario is better described as a chain or series of two functions. The first one generates a random 50-50 result (flipping the coin). That random result (heads vs tails) is that function's only output. Everyone can agree on the probability of each result for that function on its own. Now we take that outcome, and use it as the input for a separate function. This second function simply makes a decision on the number of times to wake sleeping beauty up. It becomes pretty obvious when looking at this function in isolation that its results are skewed towards the side that wakes her up more times. The second function essentially multiplies the likelihood of the input that would cause multiple wake-ups. Thus we arrive at the two interpretations of the original question and their different answers.
Interpretation 1: How likely is the coin to come up heads? -> obviously 50%. Interpretation 2: How likely are you be woken up by the coin coming up heads vs tails? -> obviously 33%. Both are valid and so my personal stance on it is that the question is ill-formed by being ambiguous.
agree with this, but would say I'm a halfer in this instance because the exact question asked is 'what do you believe the probability of the coin being heads?' not 'what do you believe the probability of being woken up by the coin being heads?' subtle difference, but to one question I'm a halfer, the other a thirder.
Danm
@@superkeefo6951 This. That question sounds to me like question that would be asked in a hospital to check if my brain functions correctly like what's the date, who is current president etc. It made me 1/2er just because of semantics but I understood what he meant and in that context I'm 1/3er, so I don't know whether I should like or dislike
@@0NeeN0 but if you're saying there is context then you are essentially adding it and rephrasing the question given to you to be the second question. That's the point momo was making, the implied context makes you think you need to answer the second question. But really the question should be asked with that context or else it's 50/50
This! 100% this! The problem is that the language being used isn't precise enough.
Waking up is a condition signal for Heads on Monday, Tails on Monday and Tails on Tuesday , we have a total of 6 possible wake up signals thus , 1 signal for HH, 2 signal for HT , 1 signal for TH and 2 signal for TT , P(Signal = H ) = 2/6 ,P(Signal =T)= 4/6 .
This is the paradox of death. How would you know if you are dead or alive without having any memory of being dead or alive previously?
The problem with doing the vote this way instead of a poll is that so many people are going to ignore the beginning and like the video because they like the video and not because they agree.
Knowing Derek, The like/dislike options is a study in of it's self. We'll get another video where the like is the wroner answer and then a later video examining the results.
@@brandonfrancey5592 That makes a lot of sense. I'd bet that is the actual purpose of this video.
I liked this question as a vote to the proposition that people expressing enjoying the video will have a massive distortive effect on any attempt at polling.
(Edit: Wait don't use comments as polls! Dislikes just bury the poll itself!)
I have liked your comment because I agree with it.
I am pretty sure he knows enough scientific methodology to know this liking/disliking thing is complete bs.
It helps increase interaction so I guess it's a smart trick
@veritasium - 2023-02-11
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.
@unnamed5338 - 2023-02-11
ok
@aftabahmed-_- - 2023-02-11
👍
@AnasKhan-fq8yb - 2023-02-11
First
@SoundGuyChannel1 - 2023-02-11
??th
@-nary-zy5jt - 2023-02-11
I disagree with u.