For decades, the Sleeping Beauty Problem has divided people between two answers. Head to brilliant.org/veritasium to start your free 30-day trial, and the first 200 of you will get 20% off an annual premium subscription.

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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:

Elga, A. (2000). Self-locating belief and the Sleeping Beauty problem. Analysis, 60(2), 143-147. - ve42.co/Elga2000

Lewis, D. (2001). Sleeping beauty: reply to Elga. Analysis, 61(3), 171-176. - ve42.co/Lewis2001

Winkler, P. (2017). The sleeping beauty controversy. The American Mathematical Monthly, 124(7), 579-587. - ve42.co/Winkler2017

Titelbaum, M. G. (2013). Ten reasons to care about the Sleeping Beauty problem. Philosophy Compass, 8(11), 1003-1017. - ve42.co/Titelbaum2013

Mutalik, P. (2016). Solution: ‘Sleeping Beauty’s Dilemma’, Quanta Magazine - ve42.co/MutalikQ2016

Rec.Puzzles - Some “Sleeping Beauty” Postings - ve42.co/SBRecPuzzles

The Sleeping Beauty Paradox, Statistics SE - ve42.co/SBPSSE

The Sleeping Beauty Problem, Reddit - ve42.co/SBPReddit

Sleeping Beauty paradox explained, GameFAQs - ve42.co/SBPGameFAQ

The Sleeping Beauty Problem, Physics Forums - ve42.co/SBPPhysicsForums

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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.

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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

2023/02/10

私のプレイリスト

後で見る

Veritasium 7 ヶ月 前

For the purposes of the title: "agree with me" means 1/3 and "disagree" means 1/2

unnamed53 7 ヶ月 前

ok

🗿rock 7 ヶ月 前

I liked

Aftab Ahmed 7 ヶ月 前

👍

Anas Khan 7 ヶ月 前

First

«SoundGuy» 7 ヶ月 前

??th

relatively_random 7 ヶ月 前

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.

MrTheBigNoze 7 ヶ月 前

Yeah, it just seems like semantics. I depends on whose perspective you are using

Andrias Stefandi 7 ヶ月 前

Semantics, asking the wrong question, wrong definition, etc.

Роман Плетнев 7 ヶ月 前

That's what makes Monty Hall problem so great - it's not about words, it's about the actual concept itself.

Desimere 7 ヶ月 前

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.

CodeguruX 7 ヶ月 前

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.

selsickr 2 ヶ月 前

It all depends on how you define the probability. Both are just 2 different problems. They are describing 2 different things and are useful in 2 different ways. The paradox comes from the fact that we are confusing 2 different cases and saying that they are the same. It is like 1+1=2 and 1+1=10. Both are true. The first is true for arithmetic in base 10 and the second in base 2. In to context of buying apples I will have to pay for 2 of them, in the context of computer calculations it is 10. If we want to know the chance that we will get heads if we flip the coin it is obvious that the rest of the story about sleeping beauty is not relevevant. She was told that it was a faire coin and therefore it is obvious that the chance that one gets a head is a 1/2. The rest of the story is just a decoy and diversion. It is like the children’s riddle where they tell someone that they are the driver of a bus that has 20 people in. After telling them that 5 people get of and 6 get on etc. they are then asked what the name of the driver is. This way would be useful if sleeping beauty was told that she has to pay 1$ for a lottery ticket and would get 2$ back if she could correctly tells us what the probability is of the coin falling on H is. By saying 1/2 she would win 1$. The second way, which is a different problem is that when she wakes up she has to pay 1$ for a lottery ticket and will get 2$ back if she can tell what was the result of the coin flip before she woke up. Here, if she says tails she will win on average (if this is done many times ) 2/3*2-1=1/3$ If she would have said H 1/3*2-1=-1/3$ ie she would lose 1/3$ every week.

Alexander Polasek 9 日 前

Agreed, these are two different questions with different answers.

High Cookie 3 日 前

Yep, "whats the probability it was heads or tails" vs "What is the chance that today is tuesday" - or something along those lines.

Alex Walker Smith 19 日 前

A lot of the other scenarios were not equivalent to the Sleeping Beauty scenario. They were more like asking Sleeping Beauty "Do you think it's Monday?" That's an entirely different question from "What are the chances the coin landed on heads?"

Brad Banks 11 日 前

This is a brilliant comment. Contrasts very well the difference that is muddled in the "what was the probability" question. The answer to, "what is the probability the coin was heads?" is objectively 50%. The answer to the question, "what is the probability that the coin was heads AND that your answer is correct?" is 1/3.

Iuri Frazão 10 日 前

@Brad Banks What? So for the first question your answer doesnt need to be correct for it be... correct? The answer for "what is the probability of the coin to flip heads" is indeed 50%. But thats not the question, the question is "what is the probability the coin FLIPPED heads" with the given that if you are being asked that question you woke up. Similarly if someone flips a coin and it results in a Tail, it would be correct to say the probability of flipping tails in the past is still 50%, but wouldnt be correct to say the probability the coin that was flipped was tails was 50%, because you are clearly already seeing the result, and its 100%. Imagine if the SB only woke up if the coin was Tails and was asked "what is the probability the coin FLIPPED heads?" , it would be ridiculous for her to say the chance is 50% after being asked that question, because she knows she wouldnt be asked that question if it was Heads.

daniel son 5 ヶ月 前

My guy just asked a sleeping beauty problem and just left me on a thought about multiverses. I love this channel.

Raymond' Remarkable Agenda 4 ヶ月 前

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)

roD Draft 3 ヶ月 前

@Raymond' Remarkable Agenda stop dude you're talking to an anime pfp

💧Xavion💧 3 ヶ月 前

@Raymond' Remarkable Agenda Honestly, that isn't just as justifying seeing that she could have done any other operation

EarKittyCat 🇺🇦 3 ヶ月 前

@roD Draft the general consensus is that your pfp doesn't affect your comment

Marko Mikulicic 3 ヶ月 前

After mulling over the sleeping beauty problem you and a friend of yours play a game: There is a number between 1 and 5000 in a sealed envelope. You also pick a number in that range. If your number matches with the one in the envelope you lose and your friend gets to punch in the face every day for a the rest of your life. After several years of concussions you suffer a loss of memory and you wake up one morning without recollection of the experiment nor the fact that you've been getting punched in the face on a daily basis for years. Your friend approaches you that day and asks you what is the likelihood of guessing a number from between 1 and 5000. You answer 1/5000. And then it hits you.

Theeraphat Sunthornwit 2 ヶ月 前

Lol awesome analogy

fleisch19843 5 ヶ月 前

A fun problem where the two answers are actually answering two different questions! The skill is not figuring out which is right, but understanding how the two questions are subtly different. Good thinking exercise and excellent video as usual.

nekekaminger 4 ヶ月 前

There is no question to which the correct answer is 1/3. The whole thirder perspective is flawed because it treats the possible "states" as equally likely and independent, but they are not independent.

Reuben Savage 4 ヶ月 前

@nekekaminger The question would be, ‘What is the probability you were woken up by a flip of heads?’ I think the answer to the sleeping beauty question is 1/2 though because like the original comment said they are answering two different questions.

nekekaminger 4 ヶ月 前

@Reuben Savage She's always woken up, otherwise you couldn't ask her. Prepending the question with the pseudo-condition of her being woken up doesn't actually change anything because it always happens. The question is fully equivalent for "What's the chance heads came up?" which is clearly 50%. I see what you are trying to do. You view each waking up event as an independent event and try to assign a probability to that event (just like Derek proposes in the video), but that approach is flawed since they are not independent. Monday Tails and Tuesday Tails cannot happen without the their also happening. Imagine you have a somewhat unusual coin that instead of heads has one dot on one side and instead of tails it has two dots on the other side. Each dot represents a waking up "event". After the toss pick one of the dots you see (which is either just one, in which case the choice is simple, or two, in which case you just randomly pick one, since SB can't remember being woken up before, the order does not matter) and ask yourself "What is the chance I see this particular dot because the coin came up with the single dotted side?". If two dots were up you answer the same question for the other dot. The experiment is exactly equivalent (if you don't agree, please explain). Do you still think the answer is 1/3?

Throw Away 4 ヶ月 前

@nekekaminger The part that I disagree with is that I'd argue they are independent events. She could be woken up on Monday Heads and be asked the question, or woken up on Monday Tails and be asked the question, or be woken up on Tuesday Tails and be asked a question. As others have stated, it really comes down to which question is asked of her. If she's asked "What do you believe is the probability that the coin came up heads?", then she should answer 1/2. Because the coin either came up heads, or it came up tails. It doesn't matter which day she woke up; the coin was either heads, or tails. If the question is "What do you believe is the probability that you were awoken on heads?", then she should answer 1/3. Because as I mentioned in my first paragraph, if she's asked this question on Monday Heads, she would be right. If she's asked on Monday Tails, she would be wrong. If she's asked on Tuesday Tails, then she would again be wrong. So it's a 1/3 chance of her being right about the 2nd question.

Llewelyn Williams 4 ヶ月 前

@Throw Away you haven’t tackled his point that these events are not independent. Monday tails and Tuesday tails are essentially the same event. For the example where she wakes up “a million times” it’s 1/2 chance that she’ll wake up a million times or 1/2 chance she wakes up once. Either way if she wakes up on the thousandth Tuesday and is asked “what’s the chance that you will wake up another thousand or so days”, its 1/2 as is “what’s the chance you only wake up today on the monday”. There’s not “more chance” of waking up in the millionth day like it’s compared to being in a simulation. It would be like saying the chance of you living in reality is 1/2, and the chance of you living in any of the millions of situations is also 1/2. 1/3 would be the answer to “what’s the probability today Is Tuesday” regarding the original question.

ElectroBOOM 7 ヶ月 前

So I guess I think if she wants to say the actual probability, she would say 1/2, but she wants to be right more often, she would say 1/3. But does being right buy her anything? If no, I would say 1/2.

A Walk Where I'm From 7 ヶ月 前

I've reasoned about this and I think it is correct to say 1/2. In my opinion 1/3 is simply wrong because it is not equally likely to be in any of the three cases. I'll copy here what I already said in other comments that are lost in the haystack. My opinion: When she is asked about the probability, the coin has already been flipped and its state is determined even if unknown to her. So here the word "probability" should be interpreted as her confidence that the coin landed heads. She is aware of the procedure and she knows that the coin is flipped one time at the beginning. Imagine she is asked the question immediately after the toss (of which she doesn't see the result) before being put to sleep. She would obviously answer 1/2. From now on there is no reason she should change her initial guess because the coin is tossed once for all and there is no subsequent event that could influence the output. It doesn't matter if it's the first or the millionth time she's being awakened: because she doesn't know what day it is she never gains new information and there's no reason she should update her initial guess. 1/3 is simply wrong because it assumes that the probability of being in one of the three cases is uniform while it is not. The probability is actually 1/2 of being Monday and it landed heads, 1/4 that is Monday and it landed tails and 1/4 that it is Tuesday and landed tails. The 1/3 argument moves from the wrong assumption that to the question "what day do you think it is today?" she should be 2/3 sure it is Monday. Actually she is instead 3/4 sure it is Monday to balance for the fact that there is no Tuesday/Heads combo. The probability it is Tuesday is in fact P(it landed tails) times P(it is Tuesday | it landed tails). I put video at 0.25x and he made a terrible error in his experiment. Look for yourself what he does. He simply writes a sign two times when the coin lands tails. He should have tossed the coin a second time to decide where to put ONE sign. If you do it right you get the expected 50-25-25 proportions. I wanna add something to make it more intuitive: in the case she is awakened 1 million times if it lands tails the probability that in any awakening that day is the first Monday is about 50% and not about 0%. Think of it this way: if she is asked "what day do you think it is today?" she is better off answering "The first Monday" because is much more likely to guess it landed heads and hence surely it is the first Monday than to guess it landed tails and then identify one of the million possible days.

Satwik 7 ヶ月 前

Shocking take

John 7 ヶ月 前

The probability of the coin flip doesn't change with the way we want to measure it. If Sleeping Beauty was woken up a million times for a tails flip, it wouldn't make the coin flip any less likely to turn up heads. Being woken up two times instead of one doesn't make one outcome twice as likely as the other, as the thirder perspective implies. If we're asking about the probability of the coin flip alone, like the question in the video (1:04) very clearly is, then the answer cannot be anything other than 1/2. Now, if the question was anything like "For N times Sleeping Beauty was woken up, what is the probability of her being woken up because of a heads flip?", then it'd clearly be 1/3.

Ceshawaris 7 ヶ月 前

Let’s do a little thought experiment: I tell you: „I‘m about to flip a coin. If, and only if, the coin flips heads, I‘ll call you.“ The next day, I call you and say: „I flipped the coin now. What do you believe is the probability that the coin came up heads?“ What would be your answer?

Ceshawaris 7 ヶ月 前

I know it sounds counterintuitive,but the only correct answer for sleeping beauty is 1/3. When she wakes up, there are three possibilities: A: heads/monday, B: tails/monday, C: tails/tuesday. Obviously, A and B have the same probability, because it’s a fair coin flip, so if they would repeat the experiment every week, she would wake up every monday and the coin would have flipped each side 50% of the weeks. The probabilities of B and C must also be the same, because every week she wakes up on tails/monday, she also wakes up on tails/tuesday. So the probabilities of all three possible outcomes are the same. And the sum of the three possibilities must be 100%, because A, B and C are the only possible outcomes, and each time she wakes up, only one of them can be true. Thus, the probability of A: heads/monday is 1/3. P(A)+P(B)+P(C)=1 and P(A)=P(B)=P(C)=1/3

Annelise Lim 3 ヶ月 前

6:47 this is actually like the 80/20 probability questions that the rat group and human group did. The rat group always chooses the green button and secured 80%, whereas the human group always believe that they're special and try their luck by pushing red button occasionally and end up getting 68%. Even if human group got lucky and get over 80% this time. If they play against rat group for 10, 20, 30 more times, they're bound to lose in the long term.

kyle 20 日 前

I feel like the question to consider would be: “what is the probability that the reason you’re awake right now because of a heads coming up?” As described, a coin has 50% chance to be heads. It also depends on if you also flip the coin even when it was tails the previous day. The question is kinda confusing, because it’s too vague

Paul Dann 5 ヶ月 前

I think the _really_ clever thing here is that Derek has carefully orchestrated a video to generate a high "like" _and_ "dislike" count. That kind of controversy will be irresistible to the almighty algorithm 😎

Bryan Mahoney 4 ヶ月 前

Stolen from Tom Scott. Doesn't bother me, but it is.

Theeraphat Sunthornwit 3 ヶ月 前

JPvid algo like that? It might get changed soon if it can be abused.

Paul Dann 3 ヶ月 前

@Theeraphat Sunthornwit Pretty much all social media is optimised for controversy or moral outrage, because that's what drives the most interaction. I don't honestly have any idea about the YT algorithm, but we can be pretty sure it'll rank videos with a widely split opinion above a video that has just a high number of likes, especially if there are lots of comments too.

Fresh Rock Papa-E 2 ヶ月 前

@Bryan Mahoney what video did Tom Scott do that abused the like count?

Akash 2 ヶ月 前

@Bryan MahoneyThat would be the like and dislike number update The ideo of ratios was not stolen though

The panda boii 4 ヶ月 前

I got something on my mind, and i know it’s something that doesn’t play into the hypothetical situation. I am thinking sleeping beauty would most likely give the same answer every time. Not knowing anything, and being only asked the same question, would she not answer the same thing over and over?

Duke Magus 2 ヶ月 前

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

Cas 7 ヶ月 前

As a Canadian, I'm really thankful you gave Canada one in five odds of winning against Brazil 😂

Ivan Freire 7 ヶ月 前

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).

BillAnt 7 ヶ月 前

And there's a 100% chance of another balloon flying over Canada will be shot down by an F22. :D :D

lukatore123 7 ヶ月 前

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!

Ivan Freire 7 ヶ月 前

@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

Abhijeet Kumar 7 ヶ月 前

@BillAnt 🤫🤫🤫

VerraNox ヶ月 前

I think the main issue is that we are approaching this problem from the riddle pov. When in reality, the odds of a coin flip being heads is 50%. Because no information is retained, this is like being asked if a lamp is turned on or off in a closed box.

Kaizoku Jimbei ヶ月 前

Correct.

Stewart Holiday ヶ月 前

No one here seems to understand conditional probability.

3lilougps ヶ月 前

True

3lilougps ヶ月 前

@Stewart Holidaythe question has no condition about the day or your state "What do you belive is the probability that the coin came up head?"

Stewart Holiday ヶ月 前

@3lilougps The conditioning is on the fact you were woken.

Jaxson Bateman 3 ヶ月 前

I really have to think the Zero Escape series (999 and co) for introducing me to these concepts before JPvid. Science-adjacent VNs like Zero Escape, the Sci;Adv series and those kinds of things are freaking fantastic for telling a good story while having some really interesting, real science concepts included in their material.

kyle784 2 ヶ月 前

VLR is still my favourite game to date even if it mostly hinges on the story and characters. The chills and thrills I got trying to figure out what was going on.

Sam Walczak 10 日 前

I feel like no matter how many times they wake you up, it still was 50/50 whether you're gonna sleep one day or million

Kaizoku Jimbei 9 日 前

Correct.

Josh POLLNITZ 9 日 前

It is a 50/50 chance on sleeping 1 day or a million. However, each time she wakes up its a 1/1000000 chance of being tails

Kaizoku Jimbei 8 日 前

@Josh POLLNITZ Each time she wakes up it's 50/50 chance she either exists in the heads sequence or the tails sequence. The sequence is one complete package. It doesn't matter how long the sequence is, it's still one package. The reason being that the conditional statement is the fair coin which only has two outcomes at 50% chance each.

therainman777 8 日 前

You are confusing the probability of the coin coming up heads _before_ it was flipped with the probability that it _did_ comes up heads, after it was flipped and the observer has some amount of information pertaining to what the outcome was. These are two very different things. The answer to the first is always 50%, but the answer to the second is not necessarily 50%, depending on what information the observer has observed. This is the fundamental principle behind Bayesian probability.

Paul Mattor ヶ月 前

Derek, your method of gathering data on agreement and disagreement with your position is problematic, as some number of people, probably more than not, will hit the like button simply because they like your video. Which I do. Thanks for being awesome!

Mislav Horvat 5 ヶ月 前

I've read somewhere that to help you understand the monty hall problem imagine that instead of 3 doors there are 100 doors only of which one contains the prize. If you choose one the probability is 1 in 100. Then the host opens 98 other doors that do not contain the prize. So it would make sense that the door he did not open and you did not choose is most likely to have the prize

Ultural Teacher_562 ヶ月 前

Wow this actually made sense to me! Thank a lot for your explanation!

Bhaskar ヶ月 前

You can also think like this, there is 2/3 probability of getting the wrong door, and 1/3 probability of getting the right door. When you have chosen your door and host has also opened another wrong door, its always right to switch to the new door because the probability that you have chosen the wrong door is 2/3, so there is a probability of 2/3 of getting the right door if you switch to the only door left.

Nightwolf 7 ヶ月 前

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.

En théo 7 ヶ月 前

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.

Sanity 7 ヶ月 前

@En théo 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

Timon 7 ヶ月 前

Maybe it's a social experiment on how much influence his opinion has

Adam Sawyer 7 ヶ月 前

Exactly

Tong Lu 7 ヶ月 前

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.

alana oconnor 2 ヶ月 前

The coin was not flipped on Tuesday. You're simply asking her the same question twice in one scenario. Every time you flip a coin you have only 2 outcomes.

Kaizoku Jimbei 2 ヶ月 前

Correct.

Daniel 2 ヶ月 前

Thanks to your videos, the last hour of "work" which always drags by so bloody slowly now goes really quickly!

Brian ヶ月 前

(Awesome video & series) ❤️ The question asked (of Sleeping Beauty) at 1:07 is about probability. So it seems to me that this is an (“unsuccessful”) attempt to make an independent event seem dependent by “falsely” linking it to a pseudo-dependency. Waking me up on any pretext and asking me what is the chance a fair coin flipped while I slept, no matter how many days ago, or on which weekday, or whether you asked me the same question yesterday, was heads should make me answer “one-half.” It’s an independent event.

Brian ヶ月 前

There are other false linkages here. For example, (Monday) and (Monday and Tuesday) are two event chains, "misrepresented" (for logic fun reasons) as three events. The number of times Sleeping Beauty wakes up is the wrong way to define the events. Instead, there objectively are two event chains whose content is irrelevant because which chain happens depends only on a binary independent precursor event (the coin toss). Defining subsequent events the wrong way leads to the conclusion that a fair coin has a one-third chance of being heads, which itself should be clear evidence of wrongness, but which maybe some people find intriguing. 🙃🙂 I'm no mathematician but maybe it matters that the two sets (All Mondays) and ((All Mondays Plus All Tuesdays) OR (All Mondays Plus Maybe The Next Bijillion Calendar Days Or Whatever)) are all, or are all tantamount to, countable infinities. If I understand Cantor correctly, all countable infinities are the same size which might suggest that the two event chains indeed are apples to apples.

Brian ヶ月 前

Throwing in the Monty Hall problem is an impressive misdirection 🙂 but it is another false linkage. The Monty Hall problem is a three way choice at its initial stage, and is not a coin toss (a binary choice) as the Sleeping Beauty problem is. The reason it is optimal to switch doors in Monty Hall is that it is only not optimal to switch doors if your initial choice of one door among three was right, which means at the second stage the odds of being wrong at the first stage, two in three, become merged into the remaining closed door which thus becomes preferred.

Kitso 3 ヶ月 前

If the question asked was "What was the face of landed coin?", then the probability of sleeper answering 'heads' would be 0.5, like the Brazil-Canada problem, but the sleeping beauty problem is asking about the 'probability', they are different.

Ian Jordan 5 ヶ月 前

Veritasium, Conventional probability techniques can be used to solve this problem while avoiding the dilemma of constructing counting arguments that confuse many. The steps to solve the Sleeping Beauty Problem are: 0. DO NOT attempt to use counting arguments -- you may fall into a logic or procedural trap. 1. State the conditional probability representing the question: P(Heads|Awake). 2. Use Bayes rule to transform the conditional probability from Step 1 into the product of a different conditional and the ratio of two independent probabilities. 3. Specify the values of the independent probabilities and the new conditional. 4. Substitute and do the math.

Houston Lucas 7 ヶ月 前

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.

Or Ka 7 ヶ月 前

Then take them both to the consideration and calculate the average. That would be the real solution to this dilemma.

John Morrell 7 ヶ月 前

@Or Ka 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.

George Muhlestein 7 ヶ月 前

@John Morrell I think you hit the nail on the head - those who agree with him are answering a different question than those who do not.

Ioannis Christou 7 ヶ月 前

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.

il_vero_sas pacifico 7 ヶ月 前

@Or Ka here we have the engeneer

20INT 20 日 前

Here's my best explanation for the problem in the 1/3 argument -- the explanation provided answers a different question than the one asked. As you said, if you repeat the experiment over and over, "Monday Heads" has a 1/3 probability. But, that's not because there's a 1/3 chance it came up heads -- that's because there's a 2/3 chance that it's Monday. In terms of Sleeping Beauty actually waking up, there are 3 scenarios -- "Monday Heads", "Monday Tails", and "Tuesday Tails". So if you woke sleeping beauty up and said "What do you think the probability that today is Tuesday?", then the answer is 1/3. But, in terms of the coin being flipped, "Monday Tails" and "Tuesday Tails" share the same probability space. When you were running your coin flip experiment and adding tally marks, you would ALWAYS mark one for monday and for tuesday at the same time, because as far as the coin is concerned, they are the same event -- "Monday Tails" can not be incremented without "Tuesday Tails", because they are only different for Sleeping Beauty, not for the coin.

Chris Sloan 4 ヶ月 前

"What's the chance that the paradox disappears when we rigorously define all the terms and the exact question we're asking?" "Seems pretty high to me." There's also a pretty substantial chance of confusion or misunderstandings of probability depending on the backgrounds of the people discussing it.

skepticon ヶ月 前

I’ve asked quite a few people who pride themselves on their intellect, the coin toss problem. The premise is that I have 100 separate U.S. pennies of random dates, minted from random mints. I claim, “After tossing 99 all but one penny, it happened that 78 pennies landed on tails, 21 landed on heads. What is the mathematical probability that the final coin will land on heads.” It’s incredible how many questions are asked, e.g., “Is the table both level and smooth?” I suppose this is somehow relevant to the inquisitive thinker who believes the coin might somehow land on its thin edge. Other questions relate to the superficial data, e.g., “Of those pennies that landed on heads, what were the range of dates… or from which mint did the coins come?” Some might ask both. The bottom line seems to be telling. The odds are high that adult humans are predisposed to make the simple seem far more complicated than necessary. Perhaps this is why too many believe believe that the Apollo 11 mission, that being the first successful lunar landing, was a multibillion dollar conspiracy rather than the incredibly hard earned, successful and historical mission that it was. That Apollo 12 landed two more astronauts on the lunar surface within six months is curiously glossed over. Apollo 13 made us aware of the risks of the program. By 1971, 12 highly trained astronauts had successfully landed on the lunar surface. Though it may be difficult for some to comprehend, a dozen highly trained United States citizens, all courtesy of six successful Apollo missions, did indeed walk and drive across the surface of the moon. They accomplished as much before most of the Apollo 11 detractors were conceived. Oh, that hundredth penny? It will obviously always land on heads; unless it doesn’t.

hejlmatthew 4 ヶ月 前

Man, this is a good one. But I think you correctly deduced the subtle differences in the question at the end: what is the chance of a heads/tails result v. the result she BELIEVES happened, which is obviously greatly influenced by tails getting a double day. Tails may be getting twice as many chances to run up the score, but that doesn't change the fact that the chance of a coin coming up tails is 50%.

Rajiv Kumar 3 ヶ月 前

Okay.... Let's say it this way... Imagine I tell you that I will eat an ice-cream if the coin lands tails, and refrain from doing so if it lands heads... Now you see me eating an ice-cream and I ask you- "What is the probability that the coin came up heads?" Although it's a fair coin, you would not answer 50% Right?

m 3 ヶ月 前

@Rajiv Kumar since I already see you eating ice cream I know its tails. But this is not what the sleeping beauty is about. Sleeping beauty has no way of knowing what day it is

Chris Long 5 ヶ月 前

This reminds me of a debate I got into with a friend of mine (way smarter than I) where I was assigned a 4-digit PIN that arbitrarily happened to match the last four of my SSN. At first, it struck me that the odds of that happening to me were astronomical! He countered that it would ALWAYS be a 1:10,000 and that the fact that it happened to ME is irrelevant. Statistically, I had to agree with him but it still seemed to ME that it would be higher. I don't know why that is but I suspect that it is due to the number being so high. I dumbed it down a bit to a 2-digit number and it still seemed like it would be a low probability to match any last two digits. I dumbed it down further to a single digit and his logic started to make more sense... i.e. manageable. Therefore, I still would say that her probability is to say 50%.

Fresh Rock Papa-E 2 ヶ月 前

A random number of 4 digits coinciding with a given number is always 1/10.000, why would the odds decrease just because it happens to you? Makes no sense at all. If anything the odds are higher because you ignored all the other significant numbers it could have been (for example it could have been the year you were born, and that would have been surprising to you but equally likely), making the odds much more like 1/500 or so

jtron84 ヶ月 前

@Fresh Rock Papa-E I think it's because if you have a sort of main character syndrome where you think that you're the only person on Earth, then even 1:10000 probability seems "astronomical". I.e. if you're only randomly assigned a PIN once or a handful of times in your life, you expect it never to match to your SSN. So you come away with the conclusion that this should not happen to you over your lifetime. This conclusion is ignoring the fact that millions of SSNs are issued, and so the thousands of failures (no match to PIN) that you'd expect to occur DID occur: just to other people. By the same logic as this original commenter, no one should win the lottery, right? Rare things do occur, and they can occur frequently if given enough random trials.

Jo C. H. 7 ヶ月 前

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.

peep poop 7 ヶ月 前

Agree.

Matthew Speed 7 ヶ月 前

I like the way you explained this. His statement “Something changed” was important because it matters that an event occurred between observations.

gunsite45 7 ヶ月 前

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

Quinton Oliver 7 ヶ月 前

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.

Eduardo Espinoza 7 ヶ月 前

AKA take the red pill or the blue pill 💊

JeSuis_Roux 3 ヶ月 前

For me the question is not: was the coin flip result heads or tails? But rather: was the coin tossed before I was woken up? This is true 2/3 of the times with the basic rule but changes dramatically if the rule is different. I think that is what will affect most my response.

Somedooby 21 日 前

Let's be real... There's no such thing as a person that you can wake up and ask them a math/statistics question and get an accurate response. You would literally be waking her up from an 8-24 hour coma. She doesn't know. She'll probably just mumble something incoherent, as anyone would in her situation.

Ava Williams 6 日 前

0:00: 🔢 The video discusses a controversial problem in math and philosophy known as the Sleeping Beauty problem. 1:49: 🎲 Sleeping Beauty's probability of heads is one half because she knows the coin is fair and she receives no new information when she wakes up. 4:34: 🔢 The Sleeping Beauty problem explores the probability of a coin flip based on waking up on different days. 6:15: 🤔 The video discusses the possibility of living in a simulation and presents a thought experiment about a soccer game. 8:53: 🎓 Learn about probability and the multiverse through simulations and critical thinking. Recap by Tammy AI

Robert Robertson ヶ月 前

I think that there is a much easier way to think about this problem. Unseen by the subject, I will repeatedly toss a coin, and ask the subject to guess the outcome. However, whenever the coin comes up head, I will ask them twice. They know that 2/3 of the time it will be heads. And this is easy to see if you increase the number of time that you ask without flipping the coin. I described the Monty Hall problem the same way. If there were 100 doors, and after you chose one, I open 98 the idea of not switching seems ridiculous.

Knot Sure 4 ヶ月 前

has anyone considered that if she flipped her own coin when woken up.... it would match the scientists coin half of the time, no matter the day or how many times she had already been woken up?

Jason T 7 ヶ月 前

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..."

Professional Tiresome 7 ヶ月 前

Split the difference!

Jason T 7 ヶ月 前

@Professional Tiresome They divvied up the hadrons amongst themselves and Erwin got a new cat.

bluzter 7 ヶ月 前

Ahh I dont have enough neurons in my brain to understand this, someone please do the honors.

Steve 7 ヶ月 前

@bluzter it is a reference to Shrodinger’s Cat

Craigape 7 ヶ月 前

@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.

Par 4 ヶ月 前

waking up on monday and tuesday is ONE outcome as a whole, it may sound like the chances of waking up in a tales sequence are more likely (since you wake up twice) but you have to realize these outcomes are each one unit and it doesnt affect the coin. if i were sleeping beauty and woke up, the chances of me being in a tales or heads sequence would still be 1/2. or that's what i initially thought. but as the video went on about the multiverse etc. i started to understand the 1/3 thought processs. Such a cool video

Toby van Reenen ヶ月 前

Yes, the question from her perspective is not, "what is the probability of each sequence", but what is the probability that you're in a particular sequence where heads came up.

Scott Sowa ヶ月 前

The problem with comparing this to the Monty Hall setup is that in Monty Hall, when you pick the door in the beginning, there is 1/3 chance you picked the correct door, and 2/3 chance you didn't. that's why when you are asked if you want to switch, you increase the probability by switching. In the coin toss, there is still a 50/50 chance. It doesn't matter the day the she wakes up, the coin is still 50/50. There is no 3rd state of the coin

Kaizoku Jimbei ヶ月 前

Correct.

Zubungo The Best 10 日 前

I don’t care if I being told I’m right 30 times because it’s always the same reality, for all 30 time I’ve always been right about 1 thing

yannickbehrendt 3 ヶ月 前

Here's another fun question, more about this video than about the sleeping beauty problem though: Do you think the result of the like and dislike count is biased because there's a level of appreciation attributed to them? As in: Do people prefer clicking the like button if that corresponds to them actually liking the video, so maybe people on edge about the problem are more likely to click like than dislike? I personally think both answers are correct depending on what exact question you ask, so I'm gonna go ahead and show my appreciation by clicking "like". ;-)

Egwene Al'vere is cool 2 ヶ月 前

Yes and there is also a bias toward agreeing with who is presenting the information, especially if they are a source one presumes to be trustworthy. There additionally might even be people who watched so little of the video that they didn't know about the meaning of the likes and dislikes and just chose to like or dislike, but that is probably negligible.

Riemann's Last Theorem ヶ月 前

Imagine being in a scenario where you're flipping coins in a room. By using the status of the coin to turn on/off the light(0,1), you observe 1 head (H) and 2 tails (T). However, you're deliberately excluding the times when it's heads half of the time. This intriguingly means there is no randomness involved. Here's the kicker: you have the ability to force the outcome to be any desired proportion. It's fully controlled . Consequently, you end up observing heads (H) one-third of the time and tails (T) two-thirds of the time. Nevertheless, this doesn't alter the probability of the coin itself, which remains 1/2 throughout.

DqsHidden 6 ヶ月 前

"Waking up on Monday with head" gets me every time.

Red I 6 ヶ月 前

Best way to start a Monday

Dans rod 6 ヶ月 前

That's why I pick heads everytime

R C 6 ヶ月 前

Some people prefer waking up with tail.

Armitage Shanks 6 ヶ月 前

By Veritasium? I'd only want it to be from Sleeping Beauty. If not, I'd pass

Aditya Bagaskara 5 ヶ月 前

bruh

Braxuss ヶ月 前

I am a halfer but I thought exactly that same question about the chances of living in a simulation. 😂 We do, but I'm still a halfer. It's not the same problem. In the sleeping beauty if the coin was tails then she is awaken twice FOR THE SAME FLIP. It's a repetition (but her answer can be different) while in the simulation scenario every universe is different, it's not a repetition. There's one real and infinite stimulated universes, you are probably in one that is stimulated.

Zacharias Burres 3 ヶ月 前

To make the answer more clear, picture you flipping a one sided coin with tails on it after she falls asleep the first time. While there is a 50 percent probability that heads will be fliped, there is a 66 percent chace that she is waking up from a tails flip since there is twice the outcomes that result from the first tails flip. If you were to randomly pick a time she woke up 66 percent of the time would be tails.

SilentGamer 2 ヶ月 前

If they asked what day it was, she’d be incentivized to say “Monday,” because she’s either in (1) H-Monday, (2) T-Monday, or (2) T-Tuesday. It’s demonstrable that she has a 2/3 chance of being right in any given moment by going “Monday,” and at worst will have an even win-loss. If she were asked what the coin came up as, she’d want to say Tails for the same reason. But they’re asking her to assess a probability when she has insufficient data to answer. Monty Hall’s player has all the knowledge they need to compute the probabilities, even if it’s unintuitive to the uninitiated. The tester has sufficient knowledge, and if they flip but guess before looking, it will be 1/2, therefore Heads’ probability is 1/2. But SB cannot know if she’s only awoken once or twice; if she did, it would be self-defeating. So, how might she answer? Think about these two scenarios: Scenario 1: You get a $25,000 prize for EVERY correct answer upon awakening. That means if (1) you answer Tails and it ends up being heads, or Heads and it ends up being Tails, you get $0, (2) if you answer Heads and you get it right, you get $25,000, and (3) if you answer Tails and are right, you get $50,000. The incentive is obviously to go with Tails, assuming you’re a person who wants the most money possible. Scenario 2: You get a $25,000 prize for a correct guess, but you only win it once, not every day you’re awoken. In this case, your odds are 2/4 (or 1/2) for $25,000 and 2/4 (1/2) for $0. It doesn’t matter what you pick (Heads or Tails), because the odds are the same. The incentive structure itself affects the answer, not of probability (which is ambiguous from SB’s POV), but of the logical next question: do you guess Heads or Tails? Either way, I go with the ambiguity and say that it depends. There is insufficient knowledge for SB to answer the question definitively, and the problem with us viewers is that we are taking BOTH points of view (of the tester and SB), which only adds to the conundrum for us, if not for them.

Rob Ross 2 ヶ月 前

This feels like the Theory of Mind experiments they do on children. Up to a certain age, they will think a person knows where a hidden object is because the child knows that it is hidden and assumes the person does as well. But after that age, they understand that the person does NOT know the object has been hidden, even though the child does. The researcher waking up Sleeping Beauty on a Tuesday knows it’s Tuesday, so they know the coin came up Tails, and they also know that Sleeping Beauty does not know that it is Tuesday.

Brock Jensen 4 ヶ月 前

It’s always a 50% chance. For example, if you flip and coin and it’s heads that doesn’t make the 2nd coin flip more likely to be tails. Each time you flip a coin there is a 50/50 chance of it being heads or tails even if by some remarkable unlikely event happened where you flipped a coin and it landed heads 60 times in a row the 61st time you flip that coin is just as likely to be heads or tails as the very first time you flipped it

Sabiki Kasukō 7 ヶ月 前

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.

rantingrodent416 7 ヶ月 前

The formulation of the question directly tells you to consider it from sleeping beauty's perspective.

simonr0204 7 ヶ月 前

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* ?

Declan Cunningham 7 ヶ月 前

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.

The Pup 7 ヶ月 前

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?

HeroNekko The Animer 7 ヶ月 前

@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.

Satisfying Whirlpools 3 ヶ月 前

I think I have an equivalent version of this problem that will shed some light :) 1,000,000 people are put into unique cubicles, and one of the cubicles is labeled "special" without any of the people in cubicles knowing. They are told that if a coin lands heads, the person in the "special" cubical will be asked what they think the chances are that the coin landed heads. If they coin lands tails, the people in the other 999,999 cubicles will all be asked what they think the probability is that the coin landed heads. If you are in one of those cubicles, and you get asked what you think the probability is that the coin landed heads, what should you say? Edit: I'm not sure if this problem is equivalent, since all of the people are distinct and separate entities.

Theeraphat Sunthornwit 3 ヶ月 前

Not exactly equivalent, your question is more straightforward and has no mental trap. But the answer is the same 1 in 2.

John DB 3 ヶ月 前

Let's put all this into a graph. So we design: 1. A dot for every time that the beauty is awake and 2. A line every time she is asleep. SO, let's represent the sleeping beauty being awake as a dot(that's the state in which the sleeping beauty is reading the guidelines of the experiment). Then she is put to sleep and the coin flip happens. So we make two lines that represent the beauty sleeping in two different realities, one for heads and one for tails(like one reality branching into two). Now at the end of each line we put a dot that represents the first awakening on Monday. NOW, we extend the second line that represents TAILS and we make another dot at the end of it that represents the second awakening on Tuesday. So the WHOLE graph looks like this 1. A dot that's named "DOT1" that is connected to two other dots that are named "DOT2" and "DOT3" by two different lines that are named H(for Heads) and T(for TAILS). Both DOT2 and DOT3 are happening on Monday. The "T" line extends and is connected to a DOT4 that is happening on Tuesday. AS WE CAN SEE from that graph only ONE BRANCHING IS HAPPENING , BECAUSE ONLY ONE COIN FLIP IS HAPPENING. DOT4 that represents the second awakening of the beauty on Tuesday is only a byproduct and a follow up of the second reality of the coin flip hitting TAILS. So from my point of view , I would say that the propability of the coin coming up HEADS is 50 PERCENT. But I may also be wrong, cause I'm human. That which I explained is just the way I see it after thinking about it for like 10 minutes.

Dragon Sage Summoner 5 ヶ月 前

This is the Monty hall problem in reverse. The odds of any given day being the correct one is 33%. And because you are put back to sleep it’s like showing you what is behind door number 1, it shifts the likelihood of the heads probably to 2/3. This is the correct probability from the sleeper’s standpoint. Monty hall thinks he is offering you a 50/50 choice when in reality he just gave you an extra 33%.

Laukku 3 ヶ月 前

If she were asked to guess which way the coin came up and always answered tails, she would be correct more times overall, but 100% correct on average in the tails scenario and 0% on average in the heads scenario.

Joshua you don't need to know 3 ヶ月 前

An interesting point here is that each sequence, heads and tails, is a set which is contingent upon its respective result. With no way to know how many times she had been woken up, it shouldn't affect the probability. If the 1/3ers position were true, then we could adjust the probability simply by adding more days that she would be awoken. Let's say 99 for tails, and only 1 for heads, as an example. Would she then have only a 1/100 chance to be on the heads coinflip? If so, then merely by adding words or conditionals, we have adjusted the probability, making the coin toss somehow dependent on the result rather than the result dependent on the cause. Let's go more extreme. Let's say that she would be awoken an infinite number of times on tails. Would that make the heads flip essentially 0%? I'd be willing to bet that if we performed the experiment of repeatedly flipping a coin and basing a sequence off the flip, we would have both sequences at the rate of 50%.

NerdyStarProductions 7 ヶ月 前

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.

Alvaro Rodriguez Gomez 7 ヶ月 前

EXACTLY, probability? heads, obviously, what you think the result for this run was? tails, obviously

Bojan Skoric 7 ヶ月 前

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.

garbar99 7 ヶ月 前

What I was about to type.

Nocare 7 ヶ月 前

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.

Pooh Happy 7 ヶ月 前

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.

Laurentiu Motos 2 ヶ月 前

The probability is 1/3 when measured because tails is counted twice, once for every waking of the sleeping beauty but you're not actually flipping a coin twice to account for the second tails in the probability. You're just forcing an outcome without actually flipping. It's 50/50, down to the core. 1/3 isn't wrong however, it's just the answer for a different question. What should I say when I wake up to have a better chance at being right? Not what the chances of the coin landing on tails is. It may seem the same but it's fundamentally different. You're answering in a context with one extra rule, it's not about the coin flip odds anymore.

Sandpiper B F 3 ヶ月 前

I feel like the paradox here comes from the "forgetting" aspect of it. The probability is 50/50, except every instance on the tails side occurs with 50% probability, bc they are not independent of eachother. Treating the cases as 1/3 each means you're assuming that every wake up is independent. Yes, you can tally them and say they each show up with 1/3 probability, but that is bc you're kind of "double tallying" on the tails side. I'm entirely in the 1/2 camp, I don't think it makes sense any other way.

NorthernDruid 4 ヶ月 前

My Spicy solution to this, is to try to consider both angles at the same time. I give a belief at 40% for heads. It's monday twice as often as tuesday, but each monday is equally likely. So counting monday (Heads) as 2:1 with tuesday and monday (Tails) as 2:1 with tuesday. and counting the mondays as 1:1(2:2) with each other I call the final odds as 2/5 monday (heads) 2/5 monday (tails) 1/5 tuesday (tails) Admitedly this is looking at the answer to the question less as a matter of mathematical probability and more a matter of logical/intuitive chance. Sure it's brushing backs with the gambler's fallacy, but I think it's still pretty applicable to an evaluation you have to make in a singular instance rather than in a broader scope. In a sense, giving lower value to it being tuesday because it has more prerquisite events.

Old Blind Darby 4 ヶ月 前

My response (50/50) was completely based on phrasing of the question in that it only references a single toss, therefore the probability of a single toss is 50/50 regardless of any other consideration.

Peter Súkeník 4 ヶ月 前

The probability (not the abstract definition, but the "correct" one which, in simpler scenarios, is somewhat equivalent to the abstract one by the strong law of large numbers) is defined as a frequency of the event occuring in many (tending to infinity) independent experiments. The trouble here is, that the experiments from the point of view of the sleeping beauty are not independent, since "tails" at tuesday deterministically and dependently follows the "tails" at monday. If instead of presenting the beauty with the procedure, the only thing she would know were relative counts of tails/heads occuring in already done 1000000 experiments, she would be forced to conclude "1/3", because she would not know she is experiencing dependent experiments. This happens often in real world statistical experiments, where we rightfully assume that our experiments are independent, even though they are not (such as subsequent dice throws), because we cannot predict the future experiments based on past experiments. However (!), the beauty IS presented with the experiment details, meaning she knows the experiments from her perspective are not independent. Therefore, she must now decide what she wants to answer. Either she can consider the "experiment" to be the whole procedure (either one or two day) in which case she can compute that the probability is 1/2 theoretically, but she doesn't have means of objectively measuring it, even if she would be allowed to record the outcomes of the experiments in "TTHHTTHTTTT..." string, because she cannot say what the instances of the experiment are (they can have length 1 or 2). If she decides that an experiment is just a single day and single waking up, then she either answers that the probability is not measurable, because she is not able to have independent observations, or she can drop the usual definition of the probability and rather go to something more belief-oriented, in which case she can answer 1/3.

Momo 7 ヶ月 前

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.

superkeefo 7 ヶ月 前

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.

Jonathan Mikkelsen 7 ヶ月 前

Danm

0Ne 7 ヶ月 前

@superkeefo 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

superkeefo 7 ヶ月 前

@0Ne 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

Eric Schuller 7 ヶ月 前

This! 100% this! The problem is that the language being used isn't precise enough.

Surely Woo 4 ヶ月 前

I read a paper that interpreted probabilty in one of two ways, based either on frequency of outcome or on belief (perhaps there are other interpretations?). Most of us learn the frequency interpretation and are not exposed to a different perspective unless they take a class in Bayesian learning or philosophy. The multiverse scenario mentioned at the end breaks the analysis because a "frequentist" interpretation of probability breaks down when confronted with infinite outcomes.

Lp Gx ヶ月 前

Which paper was ist?

Surely Woo ヶ月 前

@Lp Gx I don't recall, but there is a lot posted now about the frequentist vs. Bayesian perspective of probability.

Florian Jourda ヶ月 前

One way to break down the dilemma is to add Snow White to the mix :) You keep the exact same protocol for Sleeping Beauty (therefore not changing probabilities) but you add an opposite one for Snow White, waking her twice on Heads and only once on Tails. When Sleeping Beauty is woken up she knows for sure than Snow White is woken up as well, either once or a twice. What do you think the probability of Heads now is? As the protocol for Sleeping beauty depends in no way from the one for Snow White, it’s clear that the number of times we wake Snow White up is irrelevant. Respectively the number of times Sleeping beauty is waken up is irrelevant. From this thought experiment I get a strong conviction the answer is 1/2.

Stewart Holiday ヶ月 前

Apparently you believe the perceived probabilities of two different observers must sum to 1.

Florian Jourda ヶ月 前

@Stewart Holiday Indeed; I think so. I would rephrase: the respective probabilities of two opposed rational observers having "their side win" while "the other side loses" should add up to 1. Those probabilities are both opposed (X + Y = 1) and the same (X = Y) as the protocol is completely symmetrical, therefore the probabilities are both 1/2 (X = Y = 1/2)

Stewart Holiday ヶ月 前

@Florian Jourda You're going to have to define what you mean by "win". What is the game, what decides the result of the game, how many games are decided per experiment? And I assume based on your claim that your game won't permit both to "win" simultaneously?

3lilougps ヶ月 前

I agree

Ivan Konermann 14 日 前

This isn’t a math problem solely…it’s about how the question is asked.

Corey Katouli 2 ヶ月 前

I believe ½. For me it boils down to what’s the probability of her being awaken on Tuesday, which equals to the probability of flipping tails on Sunday. Monday does not count as based on game rules, regardless of the coin flip results she would be awaken on Monday.

Salty Slug 7 ヶ月 前

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.

Brandon Francey 7 ヶ月 前

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.

Andrew W 7 ヶ月 前

@Brandon Francey That makes a lot of sense. I'd bet that is the actual purpose of this video.

Wm Reeves 7 ヶ月 前

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!)

Leo Staley 7 ヶ月 前

I have liked your comment because I agree with it.

Menon 7 ヶ月 前

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

Rogue legend 3 ヶ月 前

i think the objective is to get an answer with the most probability to be right, where a solution can be found...

Paradox, Conundrum, Logic, Interesting Math 21 日 前

It seems to me that the number of times Sleeping Beauty is awakened is irrelevant to her. Therefore, the answer must be one half. From our perspective, if the events were replicated, we should expect the result to also be one half. So in either case, the result is one half.

Unleash 4 ヶ月 前

The chance is 50/50. The question she is being asked is what the probability is that the coin landed on tails. It doesn’t matter how many times you wake her up after the coin flip, or on any of these examples for that matter. The probability of a coin flip is ALWAYS 50/50

AleaIactaEst2009 4 ヶ月 前

It feels to me like there is a difference between asking "what is the probability the coin came up heads?" and "Did the coin come up heads?". I would say the answer to the first question is 50%. But if you are asked the second question and say heads you will only be right 1/3 of the time due to repetition of the error.

Maug Seros 4 ヶ月 前

Even in Derek's "Do the experiment for yourself" if you look at the tallies for heads and tails you can see when he cuts off that there are 28 heads and 26 tails... converging upon 50/50. So after 54 flips of the coin in his example, 28 times sleeping beauty would have to say heads to be right and 26 times she needed to say tales to be right. So it's converging on 50/50.. not 1/3, 1/3, 1/3. I'm not convienced that the number of times sleeping beauty is woken up on relevant at all, because weither it's twice or a billion times, it's all contingent on a single flip of a coin turning up tails. Let me explain, Derek goes on to illustrate the 1/3rd position by using an extreme senerio where you wake sleeping beauty up a million times if it's tales, he likens this to reaching into a bag of a million black marbles and one white marble, what would be the chance that you pull the one white marble? Thus there's a millon more likely chance that you pull out a black marble out of a million of them. I don't think that is a valid analagy. The correct analagy would be out of two mables in a bag, one white and one black, what is the odds you are going to pull out a white or black marble (oh.. but if you choose the black marble.. THEN you are going to go ahead and pull a million more black marbles out of this other bag of a million black marbles)? It's 50/50. The millon other black marbles are 100% contengent upon that first marble (out of two) being black. Let's put another twist on that senerio and use something that's not a 50/50 outcome. Let's roll a 1000 sided dice. Let's say if the dice comes up the number 42, sleeping beauty is woken up 10,000 times. But if the number is anything BUT 42, she's only woken up once. Would you then say that once sleeping beauty is woken up that the odds are 9,999 out of 10,000 that the dice came up 42? I don't think so. You've still got a 999 out of a 1000 chance that you were just woken up once and not the 1/1000 chance that she was woken up every day for 27 years. Being woken up every day for 27 years, is entirely contingent upon that one act of rolling a 42 on a thousand sided dice. 1 in a thousand chance. So I don't find the 1/3 argument compelling.

Miha Zupan 7 ヶ月 前

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.

Jonathan Lavoie 7 ヶ月 前

"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.

uRealReals 7 ヶ月 前

that is so perfect an answer. how did you make it so easy,, in that, what is your background?

Miha Zupan 7 ヶ月 前

@Jonathan Lavoie 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.

Jonathan Lavoie 7 ヶ月 前

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.

Jonathan Lavoie 7 ヶ月 前

@uRealReals 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...

Bill Hill 26 日 前

The coin toss is independent of whether sleeping beauty is awakened on monday or tuesday. Therefore the probability is always 1/2. If sleeping beauty understands probability she would know this and choose 1/2.

Kaizoku Jimbei 21 日 前

Correct.

Daniel Hertzman 2 ヶ月 前

The way i see it, a coin was thrown once. It does not matter if "tails" meant shed be awakened a hundred times - the coin was still thrown ONCE = so i vote 50/50 😊 Love your channel 😊

Owen A ヶ月 前

You throw a coin once and see that it landed heads. What is the probability that it landed heads?

Kaizoku Jimbei ヶ月 前

"The way i see it, a coin was thrown once. It does not matter if "tails" meant shed be awakened a hundred times - the coin was still thrown ONCE = so i vote 50/50 😊 Love your channel 😊" Correct.

Redecter 18 日 前

The problem with the simulation point is the amount of computing power it would take for even one person, let alone 8 billion

KG 6 時間 前

Veritasium, I suggest you look into the memoryless property of a Geometric distribution. I think this is a similar concept, since you have no given information about how many times you have woken up, the waking up is totally random to you so the probability has no reliance on past outcomes

Alex D 22 日 前

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

Semmelein 7 ヶ月 前

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.

Meamer 7 ヶ月 前

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.

Words of Cheresie 7 ヶ月 前

@Meamer I agree. Thirders actually think that the question is, "what are the chances that you were woken up once before?"

Bob Edwards 7 ヶ月 前

yup, like nearly all things, the readers interpretation is what truly matters... and yet the world doesnt care

Daniel T. 7 ヶ月 前

@Words of Cheresie 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.

CodeguruX 7 ヶ月 前

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.

colorado841 3 ヶ月 前

The original question can be understood this way: There is a world there is a river that branches out into two rivers. On one river there is only one tree and the river continues out of sight without any trees after that first one. Every time you pass a tree you are guaranteed to wake up because the birds are singing loudly, but will fall asleep before you reach the next tree. On the other river there is one tree after another tree but they are spaced out so you can only see one at a time. You are sleeping in a boat and wake up. You only see one tree. Which river are you on? The one tree cannot be seen as a clue as it not unique to either of the two rivers, and the birds are also not a clue as both rivers have birds. The fact that sleeping beauty woke up once doesn't suggest anything about the odds of the coin being heads or tails. You could devise a strategy of what would be best to do in this case, but you couldn't tell which river you were on. So I am now I am changing my answer to 1/2.

6ros1uc 4 ヶ月 前

That's funny because I used the idea of waking her up many times instead of only two on tails to make my decision, and found it absurd for her to say that the had no chance at all of showing head.

Juddy Ogemdi 2 ヶ月 前

Probability is an uncertainty. This means there is no accurate method of determining the correct answer; the answer could be right or wrong. Therefore, I think it is 1/2 because the question was clear " What is the probability of having a head or a tail"

Hieu Le 4 ヶ月 前

I think the better question is “what are the probability you slept on a tails day?” That would depend on how many tails day you sleep over both. But the question is asking the probability of the coin flip itself. Regardless of how ever many days you slept there was only one flip. And the outcome of the flip is 50/50 but the outcome of the amount of days you sleep on a heads of tails flip is heads or tails / total days of both. This is more or less differences in how we view the questions and which we are answering. The act of the flip itself or the days we sleep based on said flip.

Lucija Šegon 2 ヶ月 前

I can't like this video in usual way, so, I would say thanks for this and many more high quality videos from diverse range of interesting topics.

LemonJoep 7 ヶ月 前

To me, similarly to how in your counting experiment you doubled up the tallies for Tails every time, it's 50% because the tails numbers are being arbitrarily inflated by double-counting. It's similar in my mind to if you said "toss a coin. If it lands on Heads count it as one, but if it lands on Tails, count it as if it happened twice". The coin is still 50% we're just counting it wrong (in my opinion, which isn't worth much).

kev pat guiriot 7 ヶ月 前

👍

Florian Knauer 7 ヶ月 前

+ It's this bloody simple. Counting tails twice doesn't change the chance.

rakino 7 ヶ月 前

Yep. Think about the marble example. Its not pulling one marble out of a bag of 1 million black marbles and one white marble. It should be stated - flip a fair coin then if its heads pull a marble from a bag of 1 white marble and if its tails pull a marble from a bag of 1 million black marbles. Whats the probability of a white marble? 50%

b0nes 7 ヶ月 前

@rakino close. If it's tails, grab all the black marbles. Now you have a lot of black marbles and only one white marble. The chance to end up with that many black marbles is still 50%, but that analogy more closely resembles the mess that is this probability discussion :')

Alcolist Makings 7 ヶ月 前

Exactly, what that test is saying is that 1 heads = 1 heads, while 1 tails = 2 tails. The latter is then saying 1 = 2, which cannot be.

KG 6 時間 前

The sample space given that sleeping beauty is awake is S = {H, T1, T2}. Therefore, the probability that the doin landed on heads GIVEN she is awake, P(H | awake) = 1/3. There are 2 instances of tails in the sample space because the events I defined in the sample space represent her being awake given the coin toss, and there are 2 instances of that when the coin lands on tails. I made the assumption that it is equally likely for all events of her being awake i.e. 1/3 probability. HOLD UP!!! New thought: The probability of her being awake is 1 no matter which path along the probability tree you take, she must wake up. Additionally, I don’t see how you can create a distinction between the events of being awake, they are the same event to her no matter the day because she has no given information, this is why I saw P(awake) = 1, this holds true no matter P(awake | H) or P(awake | T), thus the events are independent b/c she will be AWAKE (day does not matter) no matter what. Therefore P(H | awake) = 1/2 can be found using Baye’s Theorem. (1*(1/2))/1, to get one half, or you can simply realize the fact that statistical independence is symmetrical which means P(H | awake) equals P(H). Therefore, P(H) = 1/2. Note: I am currently in Intro to Probability and Statistics at the university level.

Dark Joker 2 ヶ月 前

One of the best videos I've ever seen by far ❤

Saradomin 2 ヶ月 前

The thirder position confuses probability with time. If she went through this experiment through out infinite time, then yes, the probability of her being in a scenario where the coin was heads, is one third, since a tails scenario takes up 2 times the amount of time. But, the probability of final outcome transcends time, so it is still 1/2.

Robert Brookes 4 ヶ月 前

The best way I've found to argue my point, is by reframing the Heads & Tails scenario: Here I have a bag. In the bag there are TWO sweets. One blue sweet. One red sweet. You pick out one sweet from the bag without looking in it. If you pick out the red sweet, I give you a second red sweet from my pocket. It's clear that since there is only one blue sweet and one red sweet in the bag, the probability is 1/2. You cannot choose the red sweet in my pocket, that is only given if you picked the red sweet from the bag. And since the chance of that first red sweet was 1/2, then the chance you get that second red sweet must be that same 1/2 chance as it's dependant on the initial picking of a sweet from the bag. Thus it is a 1/2 chance you pick a blue sweet. A 1/2 chance you pick a red sweet. And an end result of 1/2 chance of having a blue sweet, and a 1/2 chance of having two red sweets. If this was the Monty Hall problem there would be three sweets in the bag, not two.

Object 4 ヶ月 前

If the sweets could not see the wrapper color but felt movement, what color should they guess they are?

Greg Stunts 2 ヶ月 前

I think a more extreme example can sort of help understand the nuance of the problem. A coin was flipped, and the person is asleep. If it is heads, the person wakes up, if tails, the person is killed. If they were to wake up, there is a 100% chance for it to be heads. However, there is a 50% chance for that to happen. Same with the sleeping beauty case. The chance of a coin being tails is 1/2. However, the chance of the coin being tails given that sleeping beauty wakes up is 1/3. So what really matters is what you mean by the main question.

Peter Moore 7 ヶ月 前

You gotta respect how confident Derek is that 10s of 1000s of dislikes aren't going to hurt his YT stats. :D

Joel Cook 7 ヶ月 前

Dislikes, likes, youtube counts them both as engagement

SixOThree 7 ヶ月 前

@Joel Cook Right. "The algorithm" will often give you things that make you angry on purpose. Thats why republicans are always filled with outrage - because they engage these things. Their feeds are filled with things that make them angry.

文子 7 ヶ月 前

the opposite, the aim of the video is to increase engagement and also shows the counter in the video title. perfect for the algorithm

MinerFinger 7 ヶ月 前

I just think it's his curiosity for the answer of this question that he used likes and dislikes as voting poles. I mean scientists can go as far as to put there life on the line sometimes just to prove or experiment something.

Jake Haugen 3 ヶ月 前

There’s only ever one coin flip. By definition it’s a fair coin, so it’s 50/50. There’s no possible information gained via the problem statement because she forgets she was previously awakened. So there’s no difference in future states of being awakened in the future because from her perspective it’s always the first day. Edit: the question asked is “what was the probability that the coin came up heads” but I agree with everyone else that sleeping beauty should answer tails because she gets woken up more frequently. It’s a good lesson on definitions and details.

Zedro Orko 3 ヶ月 前

The problem with the simulation theory is that we have to "know" that it is possible to have a perfectly convincing simulation before it is reasonable to assume we are already in one. It may well be possible that, for some reason we don't understand, it is impossible to have a perfectly convincing simulation. Until the possibility of such a simulation can be determined we can't use the "thirder" approach to concluding we are in a simulation.

AureliusFeynman 2 ヶ月 前

From our external perspective, the probability that it came up "heads" is 1/3. There's the initial 1/2 chance of head/tails but also the other possibility that she awakened on a Tuesday "tails", being equally probable, hence the 1/3. But we're asked what SHE believes is the probability. So it could make sense that it is a 50/50 probability, distributed as 50% for heads and 50% for both Monday & Tuesday tails (but not quite). The reason for the "not quite" being that the Tuesday tails awakening derives ENTIRELY from the probability of obtaining a Monday tails in the first place (the Tuesday awakening has no probability by itself). So it shouldn't truly be considered when separating the probabilities of each outcome. So that would give a 50% chance of heads and 50% chance of tails from the subjects perspective. Upon awakening, she could reasonably separate it as 50/25+25% chances respectively, but the percentage ascribed to Tuesday tails is for "the sake of mathematical clarity" but somewhat "factitious" in terms of logic? I don't know if this makes sense, I haven't listened to the remainder of the video but it seems to be a question of observer bias or "point of reference", for lack of a better term (this concept surely already has a word for it but I do not know what it is...)

Param Rekhi 2 ヶ月 前

These are clearly two different questions. Estimating probability and recording outcomes are two different things. And they should be dealt with differently. Regarding the multiverse thingy, there is a major divergence from the sleeping beauty problem in that we don't have the prior sleeping beauty had. We are just guessing that such a prior may exist. Which is a whole different thing..

Severice 7 ヶ月 前

This problem is more of a word problem than a math problem. As i worked through it my understanding of the problem grew and as such my answer changed. The question "what is the probability the coin came up heads?" is two questions, depending on how you parse it. I think thirders and halfers are both correct and wrong, because they're answering different questions. One side is answering the probability of the coin turning up heads/tails when it was flipped. The other side is answering the probability of you being in a state where the coin came up heads vs tails. They're different problems with different solutions. What is the probability the coin came up heads? 50/50. What is the probability i will be right if i guess heads? 1/3rd.

Chedta Bogdanski 7 ヶ月 前

Agreed. It is the perspective.

Kragatar 7 ヶ月 前

"Came" is the keyword. It's past tense. When an event has already occurred, any information you can access regarding that event changes the probability that it occurred one way or another. What's the probability that the card I pulled out of the deck is the ace of spades? 1/52. But now you draw a card. It's not the ace of spades. Since you've removed that card from the list of possible cards I might have, the probability that the card I pulled at the beginning was the ace of spades is now 1/51. Since it's a past event, new information about it changes the probability. I draw another card. Now it's a 2/51 probability that I have the ace of spades. You draw another. One less possible card I could have, so now it's a 2/50 probability that I have the ace. And so on and so on until all the cards have been drawn and the probability becomes 1/1 whether I have the ace or not.

penguins forall 7 ヶ月 前

I do think at least for those fully understanding it that it's about how we value information. Thirders are incorporating the fact she lacks information. Halfers are assuming lacking information is irrelevant. For the sake of Halfers it's important we define the problem of her guess in one single instance based on the rules. There is inaruguably three states in the state space. She's awake on a Monday with tails, she's awake on Tuesday with tails and she's awake on Monday with heads. I actually think it's Halfers that have one extra step of justification. (unless you completely missed this is about the shared information that she lacks information.. it's not a matter of perspective). That extra step is say even though she knows there's three states in the state space there's ultimately only two that matter. The third being she doesn't know it's not Tuesday and heads so the question is like saying it's 50-50 on Monday or Tuesday.

mikey forrester 7 ヶ月 前

It's pretty clear that he asked the first question, it's explicitly written on the screen. So thirders are just wrong.

Bruce Patterson 7 ヶ月 前

I agree. And as a halfer I have to point that the question is "What is the probability that the coin was heads"

Kamogelo Maleto ヶ月 前

I'm a halver because the two Tuesday are not separate events but they are interlinked so we perceive those two events as unified event and thus the probability of waking on Monday or Tuesday is l/2 Suppose you have the equation 2x = 5y+3 when you go on to solve for x the two quantities are both covered by the divided 2 and when you separate them both of them still have the two : x = (5y÷2)+(3÷2) they are unified by the addition sign.

Chris Devenport 3 ヶ月 前

I think that this harkens back to the ambiguity of probability. It is all relative. If asked what the chances are that your ring is under a specified cup (when there are 3 cups and your ring was placed under one of them) you could argue either 33.333% or argue the set of {0% or 100%}. The chance of you guessing correctly is 33.333% but the chance of it being under the randomly selected cup is either 0% or 100%. If it is under the cup it is 100% chance it is under the cup. If it is not under the cup it is 0% chance it is under the cup. In this perspective there is no way that there is a 33.33% chance of your ring being under any cup because it is either under the cup or not (in this regard, the chance of it being under the cup is 50%). Therefore depending on your perspective there are 3 correct answers depending on if you are asked 1. The probability of guessing correctly 2. The probability of the coin actually being there 3. The probability of being right about your cup selection.

Off the Record 5 ヶ月 前

It's interesting to see how opinions can be divided on a topic, but it's important to respect and understand different perspectives.

Redshift Drift ヶ月 前

It's more important to read the question.

James Grigg 3 ヶ月 前

Coin toss will always be heads or tails (assuming it does not balance on its edge); so probability is always 50% related to the coin toss. The question to sleeping beauty should be "What is the probability the day is Tuesday ?". Monday features twice, Tuesday once, so one third probability. So you could say that is the probability of the coin toss being tails to sleeping beauty. Having her wake and go to sleep twice on one coin toss confuses the issue of probability. The scenario introduces time which it not present for the result of the coin toss, it is either heads or tails after it lands. This kind of scenario is an example of very annoying stuff people come up with that really makes no sense as the question asked does not consider all possibilities or factors.

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