Dope Tech Episode 2

<<@veritasium says : If you want to vote by liking/disliking the video: “Agree with me” means 1/3 and “Disagree” means 1/2. Latest update (Nov 23, 2023): 217,332 agree with me, and 97,502 disagree with me.>> <<@LeggoScratch54321 says : 6:40 As a Canadian I am highly offended.>> <<@anatolykhina says : You should make a clip about the waiting time paradox, and Cover's variant of the two envelopes problem>> <<@genderwars666 says : It all depends on what you consider the "experiment" to be: 1) the whole procedure is the experiment and you want to check if the Beauty guesses the coin flip correctly (assume she always gives the same answer, so one global answer for all days), or 2) every time she wakes up is an experiment. For 1) she has to say one half, and for 2) she has to say one third.>> <<@donjulio5663 says : 1:32 is she Zhang from Zhang et al? :O>> <<@AugustSeats says : 7:35 you will be right four out of the five games, but you would be wrong 30 out of the 34 times you’re woken up>> <<@ArmandVanlerberghe says : Halvers answer the question: "What is the probability that a fair coin lands on heads?" Thirders answer the question: "What is the probability that I was awakened from the coin landing on heads?">> <<@zulubunsen9067 says : I'm not an expert on these and this is more of a gut feeling, but I think the discrepancy comes from the difference between chance/probability and occurrence. Waking her up two times if it's tails does not increase the chance of it in the coin flip, just the occurrence in the data set. If it's tails, the Sleeping Beauty we wake up on Monday and Tuesday is/are essentially two iterations of the same person/reality. The coin flip results in two realities with 50% chance each, we're just taking more samples from one.>> <<@AcceleratedMango says : It's just two different but similar sounding questions. Probability of coinflip? Always 1/2. Probability of head was flipped given you're awoken? 1/3.>> <<@treymatus5014 says : “Given that you are awake” is crucial. It’s a fair coin, it was 50/50. Given she’s awake, it’s now no longer 50/50.>> <<@DoktorPepper20 says : Some humorous questions: What happens if the coin lands on its side? A quarter is incredibly unlikely to do that because of thickness/ridged sides but a nickel is still considered a "fair" coin and it has a 1/6000 chance of landing on its side (smooth side and slightly thicker than quarter). What if she ended up transported into space and the coin never lands? What if she's living in a simulation? What if she's inside a black hole when she wakes up? What if she were in a box with Schrodinger's Cat? What if the original coin is destroyed accidentally and they only had unfair coins left to continue the experiment? What if the arrow of time reversed during the experiment?>> <<@EugeneGlowmark says : i'm confused... i really liked the video so i should press like. but i'm also a halfer-dude.... so should i press like or dislike? why? should i flip a coin to determine?... 🤣🤣🤣🤣>> <<@KatharineSweet-z6j says : We need a 3 sided coin 😂, that one will give a 1% chance>> <<@Mervin82011 says : It’s 50%. You adding an “if” branch to the scenario changes nothing about the core probability. I can just as easily say “if it lands on heads on Monday she is woken up again.” A branching chain of actions based on an existing probability doesn’t change the base probability. I will assume this video is trolling bc you don’t seem that dense.>> <<@ruddytuesday says : I can't even follow what you're trying to say here. You're confounding something i can't even wrap my mind around. It's obviously 50/50. It doesn't matter how many times you flip the coin. I'm so angry that i can't watch more. No one knows what's wrong with your brain.>> <<@fabiomoraes013 says : BRASIL 🇧🇷🏆>> <<@joshburns1777 says : That last question was actually one of the most clear-cut ones, I thought. The near-infinite multiverses don’t necessarily exist. There is a 50% chance they exist and that you are in one of them. There’s a 50% chance that they don’t exist and you exist in the singular universe. Thus there is a simple 50/50 chance that you are in a multiverse or a singular universe.>> <<@philopharynx7910 says : For the simulation argument, right now we can't be sure if it is possible to have a simulation where the simulated people are sapient.>> <<@jeffjo8732 says : Try a variation: There are three gourmet restaurants in town, randomly (and unknown to Beauty) labeled A, B, and C. There is also a Denny's, labeled D. Beauty will be woken both days, taken to a restaurant, asked about the coin, brought back home, and given amnesia. If the coin lands Tails, the restaurants will be A on Monday, and B on Tuesday. If Heads, it will be C on Monday, and D on Tuesday. Before departing for the restaurant, Beauty can assign a 1/4 probability to each restaurant. This is because the amnesia makes each day a random sample of one of the four possible outings. If she arrives at Denny's, she knows the coin landed on Heads (and that it is Tuesday, but she is not asked about that). If she arrives at a gourmet restaurant, she knows that case D has been eliminated, but learns nothing new about whether she is at A, B, or C. So she uses conditional probability to update the probability of each of these three from 1/4 to 1/3. The probability of C, which is bow the same as the probability of Heads, is 1/3. My points are: (1) A, B, C, and D are just labels that identify Beauty's four possible samples. In the video's version, we could use the labels T1, T2, H1, and H2. (2) Yes, H2 is an outcome of the video's experiment. It happens whether or not Beauty sees it. (3) Halfers confuse the fact that Beauty _must_ separate H1 from H2, with her inability to _detect._ The correct solution is that she can detect the difference between the events {A,B,C}={T1,T2,H1} and {D}={H2}. That "new information" does not mean "evidence of something that was not guaranteed to happen," it means "evidence that changes the sample space.">> <<@Mailand_ihst says : disargree but like anyways>> <<@joelklinger729 says : Strikes me the halfer position addresses the statistics of the probabilistic event (coin flip or soccer score) whereas the thirder position addresses the statistics of the observer (given woken up, what even occurred). They're not a contradiction, they're different statistics>> <<@jamesjohnson9748f says : This is the first time I ever disliked a Veritasium video!>> <<@markconnors5714 says : It's a fallacious scenario. Being fully informed on Sunday and remembering nothing about that on subsequent days is extremely rare at best. Anytime you willingly entrust your fate to a situation not in your control, all that's left in your control is your response to the outcome. 😂>> <<@moeen_unfolded says : Million wake ups seriously? I slept and woke up a million times?>> <<@indecisiveladdus says : Is anyone able to explain why my immediate intuition isn't just obviously correct? If you always say tails, then if it's heads with p=0.5, that you are wrong. If it's tails with p=0.5 then you are right twice. So if you say tails, you are right 2/3 times on average. So the probability of being right if you say tails is 2/3rds. Is that not a simple solution to the problem?>> <<@sidkemp4672 says : I don't see a paradox here, merely a poorly stated question. The probability of any past event is 100% whatever happened. Her idea of waht happened in the past based on limited knowledge does not speak to an actual, factual probability. It speaks to a best guess based on different, limited information.>> <<@lifeinquarks says : 00:01 Whoa! How did you do that? Exactly when you said not to hit the like button, the like buttons glowed. Impressive>> <<@joshuahefner says : The confusion comes from trying to answer two different questions: What do you believe is the probability that the last coin flip came up heads? (1/2) What do you believe is the probability that you are being woken up because the last coin flip came up heads? (1/3) Which question do you want answered? Which coin flip are you referring to? The last one that occurred or the one that led to me being woken up? The question is ambiguous.>> <<@ChrisRussell-o5s says : What's the probability that anyone gives a S:;t😂>> <<@butterfliesrainbows2568 says : 50% probability. Every time.>> <<@Delanyo-w3l says : But for the Brazil game if you don't remember the you could say Brazil in one awakening but Canada in another, assuming Canada won.>> <<@draconyxRPG says : 1/3 if I wanna be happy and 1/2 if I wanna be right>> <<@DWinegarden2 says : That’s not Sleeping Beauty in the visual. This is a fake.>> <<@Asmit16 says : To me the answer to any of these questions is 1/2. She knows she will be waken up, she wakes up, she has no new information. So clearly from her perspective there remains a 50% chance the coin landed heads.>> <<@TheRealMichaelHaZe says : Wait, so then are we saying that winning the lottery could potentially be a 50-50 chance?>> <<@Tpstoep says : the question to be asked to her you gave us is, what "is" the probability that the coin came up heads and given that I am awake that is certainly zero so I don't understand why the answer seems to answer what "was">> <<@Zippythewondersquirrel says : 50/50 every time>> <<@DubiusManic says : This one ended like a Vsauce episode.>> <<@ChuckEvanArthur says : I think 1/2 because because 1/2 of 1/2=1/4 so the chances for the outcomes are 1/2 Heads Mon 1/4 Tales Monday and 1/4 Tales Tuesday.>> <<@psilynt1 says : There's no controversy. The coin was only ever flipped once, so if she answered "50%", she'd be correct 100% of the time.>> <<@maximwinter7998 says : There is no controversy>> <<@Brian_Gawl says : Except there aren't three possible outcomes. If it's heads, she's awoken once. If it comes up tails, she's awoken twice. Just because she's awoken twice on a tails flip, doesn't mean that each time she wakes up is a separate outcome.>> <<@Nathalie-j4h says : i like to look at it like this: The probability that you wake up on monday is 100% and the probability that you wake up on tuesday is 50%, on a monday its 50 50 if its heads or tails, so monday heads is 50%, monday tails is 50% and tuesday is also 50%, for sleeping beauty its best to say 1/3 because it's 50 50 50, so they're all the same probability. Idk if i explained it right, and i hope you can understand it.>> <<@MissKnight6 says : U really wanted us to dislike the video 😂😂>> <<@GfarooqRealname says : 50/50>> <<@Sickdudenomnomnom says : But the chance of even grabbing into the bag of a million different marbles is 50%>> <<@mrpicky1868 says : the amount of halfers is another proof of how stupidity is everywhere even in supposedly intellectual fields>> <<@jeffjo8732 says : Perform the experiment this way: Step 1) Beauty is woken on both days. She is asked to assign to, and write down, what she believes is the probability that her current situation is each of the four combinations in {H&Mon,T&Mon, H&Tue, T&Tue}. She obviously writes 1/4 for each. Step 2) If it is H&Tue, she is given the sleep drug. Otherwise, she is given the amnesia drug. Once it has taken full affect, which to her feels just like waking up without memory of step 1 happening, ... Step 3) If she is still awake, Beauty is shown what she wrote. She is asked to make any changes she feels are appropriate given her knowledge of the experiment so far. THIS IS THE SAME QUESTION AS IN THE VIDEO'S VERSION OF THE PROBLEM. The halfer position is that she disregards what she wrote before. She now says H&Tue has probability zero, H&Mon has probability 1/2, and T&Mon and T&Tue each have probability 1/4. The Thirder position is that she applies conditional probability, _changes_ H&Tue to probability zero, and notes that the sum of what remains on her written answer from before is only 3/4. So each of the three other probabilities - all 1/4 - need to be divided by 3/4 so they will again add up to 1. Each changes to 1/3. The error in the halfer answer in the video, is that it assumes that Beauty's knowledge is limited to what she can perceive while she is awake. That she cannot take into account what would have happened in Step 1 because she slept through it. Even though she was explicitly told what happens in Step 1, knows it happened, and knows that Step 3 looks the same to her in either version. This is simple probability theory, folks. It is only when you try to overlay the invalid argument that she is oblivious to what happens while she is asleep, even though she is explicitly told what happens, that you can give any other answer.>> <<@mikesummers9103 says : Probability of A given B is different from probability of A>> <<@Siebel26 says : I think of it like this: if you flip the coin on heads then you get Monday and that's it. (1/2 that the coin came out heads with a 1 probability that you wake up on Monday) if you flip the coin on tails then you get Monday and Tuesday with equal probability for that particular coin flip. (the other 1/2 that the coin came out tails, but with 1/2 chance that you wake up on Monday or Tuesday)>>