The Most Controversial Problem in Philosophy

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

Only veritasium video i disliked🫡

What if she thinks every time u wake her up it’s Monday or is she told what day of the week it is.

Both answers are correct. In this case, the unconditional probability P(H) = 1/2 is different from the conditional probability P(H|Awake) = 1/3. In the Sleeping Beauty's world, there are two states awoken once if heads or awoken twice if tails. From Beauty's perspective, it is more likely to be living in the tails multiverse, if awoken, even though the underlying process generating this tails branch is 1/2. If the Beauty is asked the same question while still sleeping in every state, then the response would be the unconditional probability 1/2.

A good way to think about the problem is through the Baye's Rule. In this case, the prior probability is 1/2. When the Sleeping Beauty is awoken, she receives additional information and should update the prior of 1/2 to 1/3.

The fact that she is awoken suggests that she is more likely in the tails multiverse; alternatively, in the heads multiverse, her more likely state is asleep.

She has a 66% chance that it’s a Monday (Monday heads/Monday tails/Tuesday tails)and on Monday she has a 50/50 chance of heads v. tails. So by choosing heads she would have a 66/2 or a 33% chance so it would be a 67% chance that it’s tails. However the coin flip itself is 50%, the additional information changes the probability of tails over heads.

Jesus just let the girl sleep already, she probably hasn’t been able to get into a good REM sleep for an oddly long time because of all the metalogical horrors, defying all comprehension, that have been forced upon her

my dumbass misunderstood the question and my answer was 2/3, so you could say I actually just made a scientific breakthrough in the sleeping beauty problem.

Me who hit the like button before the video starts playing😅

1. disagree, 2. it's not 25monday 25tuesday, it's 50monday heads, 50monday&tuesday tails

i was a thirder until the million wakes pro-thirder example... she forgets that she's ever awoken before, so to her, every time she wakes, it is equally likely that it was the first time or some random number from 1 to 1 million................. i think... AGH im so confused

Which side of the coin is facing up when it’s tossed??

33% ough, I think

Your analogy about the marbles is wrong. It's reversed. The probability of picking out the 1 white marble is 1/1000001, because there are 1000001 marbles in the bag. The coin however, only has 2 sides. You could fully recreate the experiment if you want. Just flip a coin. If it lands on heads you have to wake up early on just one day, but if it lands on tails you have to wake up early the next one million days. That doesn't change the probability of the coin flip. The probability of a coin coming up heads doesn't change based on how many times you sleep and wake up, or on if you remember waking up before.

The question about the football games is a completely different question. In the first experiment the researcher asks for the probability the coin landed on heads, in the football one he asks what team won.

The question:
"What is the probability the coin landed heads?" 1/2
would be a similar question to:
"What is the probability Brazil won the game?" 80%

In contrast, the question:
"What side did the coin land on?"
would be similar to:
"Who won the game?"

In these last two questions you would look at how many times they'd get woken up after each option. Since they'd get woken up twice if the coin landed tails, but once if it landed heads, the probability of them waking up to tails is 2/3. However the probability of the coin having landed on tails is still 1/3. Same goes for the football question. Although Brazil has an 80% chance of winning, they would only get woken up once. Canada has a 20% chance of winning, but they get woken up 30 times. Therefore the probability of them waking up to Canada winning is around 88%.

The question isn't what side of the coin she was woken up by, the question is what the probability is that the coin landed on heads.

1/3 no question.

Like experimentally thats the correct answer, probability is always about maximizing odds, not getting it right the first time.

Idk, for me its clear as glass. I did doubted it, but after thinking it yes 1/3 is the answer.

Like just keep in mind the

"Given that youre awake, what are the odds the coin landed tails" like your best bet is to say each has 1/3.

We are not contradicting the fact that a coin has 1/2 odds. Because these are two different scenarios

I have given much thought to this, and changed my mind a number of times. My final answer, however is 50%. Here's why: On Monday when she awakens, the probability of heads or tails is 50%. On Tuesday, she is only awoken if the coin was Tails. However, that doesn't matter, nor does it matter if she is awoken 3, 4, or an infinite number of times. The probability of the coin having been Tails remains 50%. Why? Simply, because nothing changes on Tuesday (or Wednesday, or...). The apparent results of the coin flip test is also irrelevant.

Why, well, quite simple because there is no new event that changes the probability. If the coin was tails, then the conditional probability of her being awoken on Tuesday (and Wednesday, Thursday, etc.) is 100%.

It's a bit easier to visualise if you think in fractional terms, because:

Monday:
Heads 0.5,
Tails 0.5

Tuesday (and Wednesday, Thursday, etc.):
Heads 0.5 (This never changes, because the consequence chain ended on Monday)
Tails 0.5 * 1.0 = 0.5 (This also actually never changes, because the probability of her being awoken on the Tuesday is 1.0 IF the result was Tails, and therefore she was awoken on Monday).

At least, that's my take on it - ie when counting coin answers, you can't add Tuesday's number of coins that were tails to Monday's number of coins, because they ARE Monday's coins, not new coins, so there's no new event and no new information so nothing changes.

saying that if the probability was 50% she should wake up 50% monday heads 25% monday tales and 25% thursday tales doesnt make any sense, because in this case the probability of the coin coming up as heads is bigger

see, if u do this experiment 100 times, 50% of the times the coin will come up as heads and 50% as tales, and she will wake up 50 times monday heads 50 times monday tales and 50 thursday tales

(Before I've watched the full video in case I'm saying stuff that is talked about in it.) It's like how relative speed changes based on frame of reference! Yes the fair coin HAS a 50/50 chance of being either, however because the frame of reference has changed, the chance of it has changed. From the experimenters perspective the chance would always be 50/50, since the coin is fair. But what's happening is that we are basically marking down two lines on tails and one line on heads for every coin flip. And then only looking at the data we received from doing this. Thusly it will always look like 1/3rd is the experimental chance. While that isn't actually the case for a fair coin. This is a great example of experimental versus mathematical chance!

It's a good thing to keep in mind when doing an experiment, are you doing anything that might lead to accidentally inflating or deflating a chance of something happening by how the notation of it is taken.

And further its a neat way to relate to how frame of reference always matters in every place of science. Context and additional information affect the conclusion of an experiment. There is rarely a definite un-influenced answer to a question, and so we must thusly take into account the situation around us.


And I know it can be annoying that so much comes down to the specific wording of things, and frustrating to have to think your way through a problem and factor in all the things that could affect it, but see, that's why we can think like this. We wouldn't have language in the first place if we could just intuitively know everything. Our brains wouldn't collect, sort, and consider out information if it wasn't important for us to do so.

Even way back before we would have had anything resembling modern soceity, it would have been important for our ancestors to factor in context. There's a lion over there! But it's on the other side of a cliff and thusly not dangerous. This fruit is brightly colored! But it's hanging off an extremely flimsy branch. And learning to do those things has been extremely important for both anceint and modern humans.

So remember that before you get terribly upset about the fact that it matters that Sleeping Beauty was asked, "What is the chance that the coin we flipped came up heads?" After she was woken up as opposed to before. Or if she instead was asked "What is the chance of a fair coin landing on heads?" It matters.

She's a woman, so her answer would be "did you remember to take out the trash?".

the question is about the coin not her waking up so the 50/50 stays the same no matter what if she was asked if she was woken because the coin landed on heads then there is a 1/3.

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

From her perspective: let's say she does this 4 times, and the sum of events matches probabilistic outcomes. So, 2 of those times she was woken by heads and 2 by tails. The tails, however, generate 2 additional possibilities: she was awakened on a Monday (by tails) or she was awakened on a Tuesday (by tails) - each one is an equally likely subset of a 50% likely set. So there are 3 possible outcomes, she was awakened on a Monday by heads (50% likely), Monday by tails (25% likely), or Tuesday by tails (25% likely). But whether it's Monday or Tuesday is entirely irrelevant. 50% of awakened states are caused by heads and 50% by tails. The notion that each state M/H, M/T, and T/T are equally likely is nonsensical. And, the "experiment" that shows each of the three is equally likely is just an illusory outcome done by recording each tails twice. The same tails outcome that creates a hit in the first tails column is also generating a hit in the second column. The tails only hits once but it ends up in two columns simultaneously.
Sooo... this begs the question: did you get the setup wrong (is there a detail missing that adds to the complexity of the question?) or are the people involved in the "debate" that blind? There is no mystery here, and the idea that there is any debate at all shows the sorry state of understanding in the world today. It's like the Monty Hall problem in one regard - you might or might not understand the solution, but there is one solution whether you understand it or not.

Regardless of the perception of the subject, or the repetition of the result, the fact is that the coin is not flipped more than once conditionally. There is exactly a 50% chance of the coin coming up heads. Think about it like this, what if we flipped the coin again on Monday if it came up tails, and only put her to sleep to wake up on Tuesday if the new flip also flipped tails? It would shift the total probability of a heads endstate to 75% and a tails one to 25%. By counting the number of times the subject woke up, you're effectively doubling the likelihood of a tails flip by artificially increasing it's probability.

As of 09/14/2023, the video has 211K likes and 86k dislikes (I have a plugin that lets me see likes/dislikes). If anyone wants a ratio update, reply to this comment so I see it and I'll tell ya.

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?"

The way I interpret this problem is that:

I am being asked what the likelihood of heads vs. tails is, not what the likelihood that the given waking moment is due to heads vs. tails

..therefore, my answer would be 50/50

a poorly defined question will always get a less than satisfying answer.

This seems simple to figure out. Just run a simulation. Assume SB places a bet on tails each time she wakes up and run the experiment 1000 times. I claim that obviously about 2/3 of her bets will be placed by while she is the Tails timeline. So she should always bet Tails.

How do I like this episode without committing? :~)

So this seems very simple to me. If the coin is only flipped once and it is a fair coin and she knows nothing else when she is awoken, then the answer is simple, 50% no matter how many times she is awoken because it was only flipped once.

Ultimately, the actually doing it yourself proved what would happen if you flipped it many times. This situation is only one flip, which is two sided. Heads or tails is irrelevant to which day it is, because she doesn’t know what day it is. The amount of days she is woken up is based on the determining factor which is HEADS OR TAILS. That’s my view.

The question that drives both this and the Monty Hall problem is the same: Does Probability determine Reality? I believe that it does not, for similar reasons as why correlation does not equal causation. If one accepts this as the premise of reality, one is free to conclude that the goat in the Monty Hall problem is always behind one and only one door no matter how many deals the Contestant has made (meaning the chance of getting zonked is EITHER 0% OR 100%, but we just don't know which), and that Sleeping Beauty's lack of knowledge doesn't affect the coin in the slightest. It also forces that darned cat to enter reality. It's EITHER dead OR it's alive. Our not knowing doesn't make it both.
Of course, this pragmatic view takes all the fun out of these brain teasers . . . and gambling, so I don't expect many to adopt it.

OTOH, it's really handy for explaining temporal mechanics.

Now that I think about it, this video is one of the best ways to check how well "return yt dislike" is doing

I'm a halfer. If the game is tweaked to earn a reward dollar by guessing heads or tails each time she is awake, then she should say tails to make the most money on average. There is no tweak that changes the probability answer.

They are two different questions:
1. What’s the probability of a head in a coin toss? 1/2
2. What’s the probability that you were woken up by a head coin toss given the rule? 1/3

When you phrase them this way, both answers make sense.

i hope the last coin flip about the universe was a tails

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.

are we forgetting she forgets that shes woken up before? in that case she should surley answer 1/2 .

if the question is do you believe that you are in the reality that you are waking up only on Monday all in the reality that you will woken up on Monday and Tuesday then yes it's one-third, but if the question is was the probability of the coin being heads then it's 1/2

the question is not valid, or at the very least, it is improper because probability implies a future event. Since the coin has already been flipped when she is asked the question, the result of the flip is not probabilistic any more. It has already been determined. Now, if you ask sleeping beauty, what is the probability that she would guess the correct result of the last coin flip, that is something that could be answered in terms of probability.

this is such an absurd problem, both answers are correct, they just answer different implied questions

The question is not really what's the probability of a coin coming up heads. The question is what is the most likely coin result now that you're awake.
You go to sleep/awaken once in case of heads, twice in case of tails.
So tails has twice the probability of heads.
Therefore the only correct answer is 1/3.
Math is not a matter of opinions.

Really good explaining as usual, even though YOU ARE WRONG AND I AM RIGHT!!!😡
Nah but seriously dawg, Brazil too good to lose for real tho fam.

Another analogy instead of the multiverse or simulation analogy: "Has mankind, or even the entire life on earth, been seeded, and/or controlled by ny some other superior alien species?" Well, if we assume that any technologically highly developed species will at some point spread out to the stars and seed life on other planets for the sake of technical experiment as well as for maintaining the life in the universe (just like we humans already intervene in nature by creating new species/taces since centuries in animals and plants), it is much more likely that we are one of the many "seeded" species/planets (since there is a vast amount of those) than that we are this one single "naturally evolved" species and planet.
From this logic, I conclude that we are most likely a "seeded" species, from pure probability. Cross-check: The mythologies of ancient gods and religions all around the world seem to confirm this theory.

I don't understand all the philosophical papers written about this. Are these authors all stupid? Seems so! Because it is extremely simple! First we have to be clear what the somewhat ambiguously formulated question means semantically. If this is clarified, the answer is utmost simple! Depending on the meaning of the question, the answer is 1/2 or 1/3 and this is mathematically not debatable!

So after all, are these "philosophers" arguing about the way to interpret an ambiguously formulated question? There is no point in arguing! Anybody arguing about the meaning of an ambiguously formulated question is plain stupid! Again, the only correct reaction is to re-check the exact and precise meaning of the question with the person who asked the question, without speculation, and then to give the one perfectly correct answer.

HERE ARE THE TWO PRECISE QUESTIONS:

If the question is: "What is the probability that the coin used for this experiment shows HEADS after being flipped?", then the answer is clearly 1/2 based on the precondition of the coin being fair.

If the question is: "What is the probability that the coin that was flipped the last time before your current state of awakeness showed HEADS", then the answer is clearly 1/3, as can be proven by just repeating the experiment 1000 times and counting the times of awakeness before which the last coin flip was heads or tails, respectively.

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

Thirder. Let's say I'll flip a coin. Heads, I give you $1. Tails, I give you 2$. How much money am I likely to pay you? A buck fifty, right? That's the economic "expected value". But $1.50 is neither of the two options, so "feels" impossible, but if I flip it 100 times, you'll get near $150. Now, I ask you: "For any one of those 150 dollars you won, what's the probability you won it on a heads flip?" A: 33% The same can be said by Sleeping Beauty any given time she wakes up.

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.

The friends are the 193,340 friends we agreed with along the way

I think the probability is 1/2. And I’d also disagree with your marbles metaphor. In the metaphor, there’s a million black marbles and one white one, so you have a million/million and 1 chance of getting a black marble. But in the sleeping beauty example, you can’t get to the 348th wake-up without having the 347th. So the amount of wake-up’s are linked to the first coin flip. It doesn’t matter how many times she wakes up on tails, since she can’t know if she’s woken up before, it’s a 50/50

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.