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The Unexpected Hanging Paradox
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- เผยแพร่เมื่อ 10 ก.ย. 2017
- In this video we take a look at the unexpected hanging paradox, also known as the surprise exam paradox. Almost 100 papers have been published on the paradox, but there is still no agreement on what the correct solution is. Can you solve the paradox?
Sources and additional reading:
goo.gl/JFtjjy
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goo.gl/mUK7aw
goo.gl/RT3JKZ
Music:
"Constancy Part Three"
Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0
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Website: www.smartbydesi...
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Executioner: **knocks on door**
Prisoner: "HA! I KNEW IT!"
Executioner: "aw man" **sad face and leaves**
Lol 😭😭😭
Underrated comment
Dora The Explorer vs Sweeper
I just changed my name *sweeper*
Executioner: "understandable,have a nice day"
The judge eventually decided to give him the electric chair, leaving him both shocked and surprised.
Literally shocked
@@uchikattana I'm going to guess that that was the joke.
I laughed louder than I shoukd have
You tickled me
This is very good
The prisoner's fatal logical flaw is that he adds a final option, ie that the execution does not take place. Because of this it becomes possible that he can be executed on Friday, and still be surprised (since he was expecting to get off free), so he can no longer eliminate any other days.
I will make it simple to understand it. Imagine the judge said to the prisoner that he will be hanged either on monday or Tuesday at noon on suprise. Tuesday cant be the suprise day coz when Monday noon passes he automatically knows its Tuesday, so he has to be hanged on Monday but then he knows that he will be hanged on Monday.
@@MadMax-xc4lr If he doesn't die on Monday, he'll be confused because Tuesday wouldn't be a surprise. All of Tuesday that contradiction will exist, and he'll be stuck wondering. He'll start to think that he might survive; that maybe the judge screwed up. Because Tuesday wouldn't make sense, right? So even if he dies on Tuesday, he'll be surprised, though probably not by much. Because just a bit of him hoped he might live. The puzzle seems illogical because it kinda is. The crux of it is an emotion (surprise), and they aren't perfectly logical at all.
Or I'm just going way too philosophical on a Wednesday night.
@@tokatstorm9270 if you take the words of judge to be carried out literally then the thief logic cant be denied. Thats the point here. Its like saying grandfather paradox dont exist because time machine doesn't exist. You have to use logic to solve the dilemma here not by simply saying the judge will hang him Tuesday so it would be suprise cause he is thinking he wont be hanged. Its like a math problem. If it was that easy then this wont be in the paradox list it would have been dismissed by great thinkers and philosophers.
Lol
yeah, as soon as he rules out Friday, then Friday becomes a surprising day after all. he can't rule out any day without turning it into a surprising day, so he can't rule out any day. being surprised early (knowing thursday afternoon that it is friday) is just a technical flaw in the judge's setup that can't be avoided but wasn't stated explicitly.
I interpreted the judge's statement as "a day of the week will be chosen at random, and you will not know the result of that random choice". The prisoner is correct that if he isn't hanged on Thursday ,then the hanging is no longer a surprise, but that is based on the knowledge he will have on Thursday, while the judge's statement was based on his knowledge on Sunday.
It also conflates the meaning of surprise. Surprise can convey a statistical and emotional meaning. If he isn’t hanged in Thursday, he’ll think he’s free and won’t be hanged on Friday. When Friday comes and they knock on his cell, he’ll be REALLY surprised that his theory didn’t work out.
this this this this this
"he will not know the day of the hanging until the executioner knocks on his cell door at noon that day"
I also took the judge's sentence to mean that it would be a day chosen at random, and they would not inform him what day had been randomly selected. And I'm no expert but what you said makes me think of the game show host thing? Like, do you pick door 1, 2, or 3? And after one door is revealed, statistically you're better off switching doors when given the option. It's like, your knowledge increases as you go through the week, but that is not the case in the beginning. And so if the prisoner introduces himself the 6th option of not being hung at all, then the odds change in his favor as you go through the week right? Am I making any sense? Is this coherent, at all? 🤔
Also, I just had a thought. I feel like Friday as a surprise option is only taken off the table come Thursday. Like, from Sunday he cannot fathom a guess as to which day a random number generator chose. It could be any of them. So Friday would be viable at the point of only possessing Sundays knowledge. And as he moves through the week, gaining more knowledge of what days aren't hanging days, then the odds of a surprise diminish, right? And as of Wednesday I feel like Friday could still be the day, as from Wednesdays point in time he cannot know which it could be. It's only until he moves into Thursday, and noon rolls around, does he know for sure that it will be Friday - thereby making Friday a non-surprise, and therefore a non-option. Fulfilling his possibility of not being hung, which was not a possibility, and why its a paradox. But my whole point is that he cannot know that at the beginning which of the days were chosen at random. Which, to me, seems like Friday should be theoretically, on the table. Yes? No?
That was what I thought too. His first statement is based on the supposition that he isn't hanged of Thursday. Well, what if he is ? He has to see Thursday evening to confirm that.
Or look at it this way: prisoner deduces that no day is possible, so the judge picking any day would be a surprise to the prisoner.
that was my thought process. his smugness fails him
yeah that’s what i was thinking too lol. reverse psychology
i thought the same thing but that cant be THE answer theres no way all these philosophers are all split over this and the answer is as obvious as that..
@@TheTruthWholeTruthNothingButTh sure it can, why not. Lol
I was thinking the same thing
The fact the prisoner is analysing it so much and doesn't know means any day would be a surprise.
Agree, the fact that he did not believe that he would be hanged means that anytime after that is a surprise because he doesn’t believe it will happen.
Exactly what I was thinking
100% agree
I don't know but wouldn't that assumption be based on the fact that the judge knew that the prisoner would react by eliminating all the possible days and therefore expect not to get hanged only to be surprised when the executioner knocks
Except the judge is psychic, or seriously trusts the deducting skills of the prisoner for some strange reason.
But the prisoner isn't a real person.
Executioner: “aight you boutta die”
Prisoner: “knew it”
Executioner: “nvm you’re free to go”
AKA contrarian's paradox
😂
Seems pretty simple. Friday is the only day he could not be surprised. The problem is his logic counts backwards from the end of the week to the beginning, but the week actually goes forward, not backwards. So when his hanging comes on a Tuesday, he would be surprised because it could have been on a Wednesday, Thursday, or Friday. I noticed other people mentioned a self-fulfilling prophecy in which he deceives himself into thinking he won't be hanged, and is therefore surprised when he is. I think this fits very well with what I think.
Well if he thinks he’s not gonna be hanged on any day, then any day would’ve been a surprise.
Yeah that’s how I’m thinking about it. Any day other than Friday is still a surprise
Mind blow.
Exactly, it’s not a paradox anymore. The judge said he would be surprised and he was.
Yup people in the past were dumb for this 1 lol they took a trick question and called it a paradox lol
When one guy on youtube is smarter than 100 graduates writing full papers on some dumb ass theory xD
Sounds like too many people with doctorates are debating the meaning of “Surprise.”
I mean what else are they supposed to do
That doesn't surprise me.
Didn't know Dustin had a brother :O
Lol that was my conclusion
Its a debate of Logic, not really on the definition of the word "Surprise".
These sorts of thought processes sound stupid but they can give incredible insight in to Mathematics and Science. Kind of like the paradox of Achille's race.
For this particular thought experiment, if you can find a solution to it, that sort of solution could potentially be applied to a predictive program or algorithm that could be used in a field of, say, Finance or Actuarial science.
It could also just lead to nothing but a lot of wasted time.
You won't know until well after some sort of solution has been found.
I think the flaw is actually already present when the prisoner deduces he cannot be hung on the Friday. Because if he reaches Friday and thus is correct in his deduction he would still be surprised because he had deduced it was impossible. Just like what happened on the Wednesday. "Basically, if A happens and I think A is impossible because I would not be surprised, I would be surprised".
There is one big hidden variable not being mentioned here: Time. The objective "surprise" assumes time is linear, the future is always unknown, and tomorrow is always a surprise no matter what. The prisoner treats all days like equals. Today is as (un)predictable as tomorrow or the day after.
That, and what can legally be defined as a "surprise" is unclear. The judge keeping the date from him at all would make any day besides Friday inherently surprising. Regardless of whether he guesses, he does not know. Regardless of whether he guesses correctly, I doubt he could convince himself 100%. Logistically speaking, a surprise can mean anything from the unexpected to simply having information withheld from you.
Judge: "i wont tell you when we gonna execute you"
Prisoner: "Oh cmon dont leave me hangin'"
Oh my gaaaaaaaaaaawd
Pls stop!!
ಥ_ಥ
Boogie boogie your a legend
this comment doesn't have the recognition it deserves
Underated comment.
I kinda started to like this prisoner. He was a good prisoner. May his logic rest in peace.
That's because you don't know what he used his logic for when he was alive. I can still hear the mother crying in her testimony... So sad.
That man was a dirty criminal
I love how everyone’s assuming he went to jail for like robbery or murder. We all know that in reality he got arrested for pulling a Yoshi and committing tax evasion
That man commited 4 war crimes in Vietnam, over 6 attempted murder and assassination, a conspirator back in 1960s, money laundring, pedophilia, attempted rape, arson, and several other petty crimes. Yet you still symphatise with him? Shameful.
@@antisuyu6075 damn, that man must've had one hell of a life.
I’m a bit confused about the initial example though. The prisoner’s catch 22 error is based on his observations over time. As the week progresses, and more days pass without hanging, the resulting hanging becomes more predictable because the available days reduce. So far so good. But the prisoner can’t make this assumption up front to eliminate Monday to Thursday in advance. The only day that’s actually predictable is Friday, and only if he wasn’t surprised by an earlier hanging. My brain has now turned to jelly.
Imagine that the prisoner does this logic and figures out that he won’t get hanged, and than on the Friday the prisoner still thinks they are getting away when the executioner knocks on the door and hangs them. This goes for any of the days which means that it will come as a surprise and the prisoner won’t know the day no matter what day the hanging occurs.
*Gets Hanged on all five days*
Ha surprised you on that one huh
Not going to lie they had us in the first half
ButterPlayz_YT
Don’t you just hate it when that happens
This is........Requiem.
_Didn't see that coming?_
They had us in *both* halves
When a prisoner takes the word “surprise” too seriously 😐
It won't be a surprise if it was told to him that it was a surprise right?
If he wouldn't think that hard and worry all the time, judge would be wrong
damnLad I think surprise implies not knowing, but since the judge told him he can anticipate that it WILL eventually happen, therefore it won’t be a surprise. I think what is meant is that he will NOT KNOW when it will take place, not necessarily that it will come as a “surprise” to him, as in shock.
If you remove the word surprise, I think the paraxox will not exist.
U guys are missing the point it's a trick question, because the prisoner actually believes that he won't be hanged based on his logic so the original statement of it will be a surprise is true Because he thinks it won't happen lol
I just read “The unexpected hanging” and thought of Sayori.
Bro you said Sayori and I thought of persona 5 lmao
Why do everyone talks about Sayori every time when hanging is the topic?
It's stupid and annoying by now. Although, it's not like it wasn't stupid and annoying before...
Hanging is the common way of ending someone's life. It's not like Sayori invented it or used this method of death first...
@@monoryba4465 that just actually shows how mentally impactful the game was.
*I gently clicked on this video...*
...and actually got impressed by it!
Actually, there is a third option:
1. Statement - you will be hanged by surprise.
2. Deduction - I cannot be hanged on any day because I cannot be surprised, thus I will not be hanged.
3. Outcome - The prisoner is surprised when he is hanged on Wednesday, thus rendering the judge's statement true.
So the third option is thus "Knowing the prisoner would come to the logical conclusion, the judge made a statement which would result in a self fulfilling prophesy by luring the prisoner into a false sense of safety."
Seems pretty straightforward to me; judge was just trolling him. Paradox solved!
I just came to this conclusion myself. The only reason the prisoner is able to be surprised is because he believes it is impossible to be hanged because of his reasoning.
By eliminating every day as a possibility, he therefore makes every day a possibility - even Friday! Because if he gets to Friday, he will say he cannot possibly be hanged that day because he knew it would happen - so therefore believes himself to be safe - so therefore is able to be hanged by surprise.
If anything therefore, his surprise is as a result of his belief that the Judge would only tell the truth. He would be surprised if the Judge lied and he correctly predicted the day he would be hanged. But because he believed he couldn't be hanged, the Judge ended up telling the truth, rather than lying.
You people are truly idiots you need tell the fault in prisoner's logic what fault he did on his logic that led to the judge's statement coming true. He deduced he cannot be hanged on any day without contradicting judge's statement. What was the fault in his logic? You're not allowed to take prisoner's final deduction to solve this problem you need to tell why the solution is wrong. Everybody already know it's wrong.
Clever, but he expects it thus forth to make assumptions upon whether he will be hanged.
I thought of that during the video
@@ashutoshdwivedi4513 Prisoners logic is wrong because even if he removed Thursday and Friday also Monday he would be hanged by surprised on Tuesday or Wednesday.
Solution: If he rules out every day, then any day will be a surprise. Just because the prisoner thinks that it's true doesn't mean that it is.
That would only get him killed on any day because any day is a surprise. What it takes to get over the sentence (assuming there is a geteway) is to just accept death, thus no day would be a surprise and that would mean youre free. But youre not to be fixed in the outcome because that would make you think you would be free and any day would be a surprise. So to overcome death you have to accept it without expecting it to free you from it
This is a philosophical question, not a practical question. Yeah, sure, if he accepted death then of course he wouldn't be suprised. But the point is not to find a practical, real world solution but rather tackle the philosophical problems this paradox creates. By saying "just accept death" you are literally just ignoring the whole point of the thought experiment like as if it just went over your head.
Acre ! - So what is the point? To tackle the philosophical problems? What problems? I just don’t quite see them and would like to get it explained. :)
Also, just because he would accept death doesn’t mean it won’t surprise him. There’s still the matter of not knowing *when* he dies
sup johnny
the fact that every option is expected makes them all a surprise
Maybe you could think of it like this: Before the prisoner has experienced any days of the week, all the days he could be executed on are equally likely to each other. As he experiences more and more days of the week, the odds of it being the following days increase, all being as likely as each other. The most surprising thing is when it's unexpected. The most unlikely day would be Monday and the most likely day would be Friday since as he experiences the days of the week the odds increase. Picking the most unlikely day probably isn't the most surprising since it would be too obvious, and the same goes for picking the most likely day, so the most surprising day would be Wednesday because it's not the least likely day or the most likely day, its the most neutral day in likeliness, making it the most surprising/unexpected.
It's just a catch-22. The more certain the prisoner is that he will be hanged on a certain day, the more certain he becomes that that he cannot be hanged that day, which in turn makes it all the more surprising if he is. The logic of the premise is circular.
Yes, it is. Not sure what you're getting at.
@@SeantommyE th-cam.com/video/wujVMIYzYXg/w-d-xo.html
Wednesday is the most surprising day, because Monday is too obvious. Then you think "It might be tomorrow, i.e. Tuesday" and then when it isn't Tuesday, you start to think "I wonder which day it will be now." And bang, you hit him while he's wondering so he's caught by surprise.
LemonZeppelin but, since you could deduce that logically, the prisoner could also deduce that and subsequently expect Wednesday the most, making it the least surprising and the other days more so.
@@AutomaticDuck300 The most surprising day is Saturday. Right when he thinks he's got off.
The prisoner’s reasoning is faulty, and this isn’t a paradox at all. The reality is that no matter what day the prisoner “rules out”, the hanging will still come as a surprise.
Except if he's still alive Thursday evening. Then he knows he'll hang on Friday x
maarten doclo Precisely, but the fact that he already deemed Friday impossible will make it all the more surprising when the reaper still comes to collect his due.
@@Smfsableye Ah - the video states that the prisoner will "not know the day of the hanging _until_ the executioner knocks"
However, if the executioner does not come on Thursday, then he will be surprised in advance, and expect the executioner on Friday. The knock itself will not be a surprise.
What if he always expected the knock, so itd never be a surprise? Would that void his sentence?
WINNER except friday if hes still alive thursday evening, its 100% going to be friday then so it wont be a surprise
I think the deduction itself is what would make a hanging on friday surprising.
I think the answer to the paradox is that they told him "your death will be on a random day" on purpose so the prisoner overthinks it and thinks it would never happen when in reality they already choosen the day
it doesnt matter when they chose the day, the paradox is that he cant rule out any day since then it would be a surprise on that day.
@@nicifrey5989 but what happens if he knows this and believes it will happen on the day he is on right now. The only way then that he could be surprised is if he is not executed.
@@nabilahmed442 how can he know ?
"the prisoner was then surprised when the executioner knocked on his cell"
Congratulations, you solved it on accident by using a poor choice of words. Because the prisoner believed it couldn't happen, he was surprised when it did happen
lol exactly?? the logic is weird in this "logic video" on thursday he wouldnt know either cuz it could still be friday
LMAO true!
@Adam Battersby But if the prisoner rules out the option of being hanged on friday, it would be a surprise if it actually did. I guess that's why it's a paradox in the first place.
So on friday, wtf did he think was going to happen?
@@foxhound963 well like they said, he believed it would be impossible for him to be surprised, so no matter when, it would have been a surprise
1. Prisoner told he will be hanged that week and the day will be a surprise
2. Prisoner deduces that he cannot be hanged on Friday
3. Prisoner deduces that he cannot be hanged on any other day either
4. Thursday passes. Prisoner knows he cannot be hanged on Friday, ergo he will not be hanged. Is elated.
5. Prisoner hanged on Friday. It's a complete surprise.
What? I can’t die on Friday! This is outrageous, it’s unfair!!!!!!!!
The deduction is that the prisoner knows that of he is not hung on thursday then he knows he will be hung on friday, but it wont be a surprise. Therefore he can never be surprised from being hung on friday since he can always deduce by thursday whether he will be hung on friday or not.
To quote the superhero, Surprise Attack: "Because it is no longer a surprise, it has become a surprise again"
What I like about these paradox videos is that I start watching them so sure I am focused so that I can understand the whole thing, but eventually at some point I get lost, somehow restart the video and get lost again. That’s my paradox 😂
Idk man, doesn't matter if you reduce the # of days. They can still hang you on a Friday after deducting that they won't.
That's a pretty big surprise execution when you think you're safe 🤷♂️
Main problem is that we asume that the statements are absolute and true. For what we know, the judge lies and the inmate can be an illiterate person.
Bottom line is, there's no way for him to get saved as the only true part of the statement is that he will be hanged
It makes more sense to view it as if its sunday and the week hasnt begun, and you have to prove the judge wrong
The checkpoint is the morning of each day basically
Friday is the only day you can guarantee you wond.be surprised becaude if you havent been hanged up until then, ya get beaned. From there though its impossible
Yeah having expectations is one of the most naive things.
I think this is the best answer yet. He WILL be surprised on Friday because his logic tells him it won't happen that day. So, there is no paradox.
leafbelly But since it was said that he would be executed a week day, if hasn’t been executed till Friday then it would only be logical for him to assume that he’s going to be executed on that day
Meaning that it can only be a surprise execution if it’s done on a day he was told was not possible for him to be executed on at all
Basically:
The lawyer says “your hanging will happen next week, ON A WEEKDAY”
The prisoner says “well I know if I am not hanged by Thursday evening then I know it must be a Friday so it wouldn’t be a surprise.” He continues with that argument working with each day backwards.
The problem is he works backwards. Let’s say it’s Monday of that week, he doesn’t know whether he will be hanged or not. If he doesn’t get hanged on Monday he knows it will be either Tuesday, Wednesday, Thursday, or Friday but he cannot narrow it down from there.
The only time the prisoner wins is if it’s Thursday.
On Thursday he knows that he will be hanged because if he isn’t hanged on Thursday then the only day of the week left is Friday.
Nah cause then he would know it was happening on thursday. So it wouldnt be a surprise. We just went over this.
You smart.
@@BuTtErFiNgEr4321 that's why it's a win
Tiny Dong I don’t think there’s really an in real life answer, there are only hypothetical answer, the real life answer is the prisoner doesn’t know what day is it so when he thought it’s weekend, it turns out to be weekdays
There is no winning. The days are irrelevant.
By assuming a surprise cannot happen because you would expect it you then no longer expect it thus it becoming a surprise again.
It's that simple.
i think the fact that it can't be any day of the week is what makes it a surprise, you remove the posibility of every day to be the hanging and that's exactly what makes it an even bigger surprise
I first saw this paradox presented as part of a far longer story (I think by Asimov). The conclusion which was come to in that story is really simple: The judge "lied" (or at least, got it wrong). The judge should have excluded the last day from the surprise aspect of the execution. Once you understand that people aren't perfect and even a judge can make a mistake, there is no paradox after all.
Executioner: "looks like all this thinking has made you tired. Why don't you follow me and lie down in this bed and rest your head on this pillow."
(Bed drops out from underneath him and the prisoner is hanged).
Executioner: "SURPRISE!!!"
The sadistic humor of this is top-notch 👌🏻👌🏻
Lmao 😂😂😂
Now imagine that same exchange, but in Skyrim guard voices.
Underrated comment😆
Easy, whenever someone knocks on his door, just immediately say, "I know, I know, it's the execution day," This tells the executioner that the prisoner was expecting him, and therefore should not execute him that day. Boom, easy hax, u mad bro?
u MAd BrO?😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂
This will only work once, because when he does that twice. His first guess was wrong, therefor the whole assumption
You think people knock on prisoners doors? Its a prison...not a hotel...
Hax fuckin money
Dude you cracked it right open, this is actually huge
This is more of a semantics thing. The prisoner thinks that when the judge says "by susprise" it means at a time he won't be able to deduce, when in fact it means at "a pre-determined day that the prisoner doesn't know about, whether he rationalizes the options or not".
So, really, the "surprise" here simply means the prisoner can't guess the day and the judge doens't have to indulge in this thinking of ruling out friday, thursday, wednesday and so on just because the prisoner won't be "surprised". After all, if you wanna make another try at at mental gymnastics you could say the guy wouldn't be surprised at all because he already knows he's being executed ( lol jk)
Another great post. This is it right here
The paradox has nonsensical language. Another example would be if they guessed the current day each time. They would be guaranteed to be correct.
Prisoner : I have deduced that i cant be hanged
Executioner : Comes on wednesday
Prisoner : *suprised pikachu face*
“I haven’t a clue what’s going on here, but I’ll act like I do!”
Naruto.?😮
Naruto reference lol
good one
x over o gang, nice. I use the name "Dxwnward" on everything.
@@SasukeUchiha-ss8lb sasuke
Watched this stoned and now my brain is broken... Thanks
same here brother. and im usually good with stoned philosophy
lmao me to , don't understand shit
jonny Beck bro i swear its the dumbass British english references they have in here they're like blanks in my vocabulary when it comes to stupid british slang/english like n then ill be dwelling on wtf that word even means while the deep thinking and focus just absolutely scrambles n then im sooo confused on the whole fucking situation all cuz u just had to feel like a fucking smart ass n use fuckin words like "deduce" and u talk like a fuckin webster
Lil Juda you are just an idiot then.
Robert Rous same lmao
If the judge assumed that the prisoner would deduce the way he did, then it would be a surprise to the prisoner to be hanged on any day of the week.
all i ever learned from that was "assume they're gonna kill you soon at the first opprotunity"
He wanted the prisoner to conclude he wouldn't be hanged. Then, hanging him REALLY is a surprise
Great!👌
This is exactly what I had mentioned in my comment, glad to have found at least one person with the same conclusion and analysis of this so-called paradox.
Why do you assume the Judge would know the prisoner's thought process after he told him?
Daniel Gonzalez he doesn’t really conclude that he won’t be hang, he concluded that he won’t be surprised if he get hang (which make him think it will be impossible then for him to get hang), I think the paradox is just doesn’t make any sense, especially if it’s in real world
@@fos1451 no, the prisoner definitely concludes he wouldn't be hanged. "00:29"
The answer is super simple:
This “paradox” is really a representation of what is called a self-fulfilling prophecy. Because the prisoner was able to think through the problem and find the loophole in the judge’s logic it made the execution even more surprising to him than if he was expecting it to come. If the prisoner was on death row, he would expect his death to be every day after he survived as the odds of his demise increased day by day. Only because he thought he was going to survive did the execution truly come as a surprise. So this “paradox” is probably more accurately labeled as a catch-22, or like I said earlier: a self-fulfilling prophecy.
Hmm.....
I was thinking along the lines of “The prisoner can’t rule out Thursday, because if the executioner doesn’t knock on Wednesday, he can still be executed on one of two days” but your thought makes more sense
Ah yes the self-fulfilling prophecy, the Greeks never could get around that.
im just gonna act like i understood your answer
@@kokirij0167 But it has to be a surprise, if he's 100% sure it can't be Friday due to him not being surprised by Friday then Thursday is the last possible day, you can forget about Friday. If he's still alive by Thursday then he'd 100% know he's going to be excecuted, meaning it's not a surprise. So it can't be Thursday. That means that Wednesday is the last possible day (sound familiar?)... which rules out Wednesday by the same logic. Then tuesday, then monday.
At first I thought the prisoner would expect the hanging to be any minute. Then it could never surprise him.
The only surprise is how naive the prisoner is when thinking he will escape his sentence.
To me this “paradox” is more striking as an example of how even logic won’t help you in the face of cold reality. Man can think up all sorts of intelligent nonsense but in the end things will go on in the same old way and the executioner will still come knocking. His first mistake was assuming he could think his way out of a death sentence.
A great example of the human brain. We wouldn't have come so far as a species if everytime death was approaching, we accepted it, instead of thinking "How do I survive?"
thats absolute nonsence
"Intelligent nonsense" is an oxymoron.
Its easy !
Friday was to be eliminated IF he still had not been hanged on thursday , However as soon as he eliminated Thursday, The condition of friday's elimination becomes false and it isnt eliminated .. Since friday isnt therefore thursday isnt and so on.. thus it will always be a surprise unless he is still alive on thursday
@@AppleOfThineEye smarty
And in the end he was surprised by a firing squad.
Toby flenderson, is that you?
Nah, he just copied my haircut.
😂
It is true that you can deduce from the statement that none of the days he can be hanged, because it would not surprise him. But knowing that and realizing he will not be hanged, and then suddenly being hanged anyway, IS the surprising part. So the judge was right after all from both perspectives.
"If i won't be hanged on evening (insert day of week here) then i cant be hanged!"
*Gets executed noon*
"Bruh."
Judge: You will have a surprise hanging
Prisoner: HA, I've deduced that there's no way for me to be surprised
Judge: **orders a firing squad instead**
Prisoner: **surprised pikachu**
I forgot to laugh
@@user-ii9ig7vq1e i forgot who asked you
Filip No one asked grace to make a shit joke yet she did
T I agree
@@user-ii9ig7vq1e It was one of the few jokes that were funny.
Also, you are rude, toxic and should get out.
Philosophy is the art of complicating semantics.
LotsOLuck777 or diving deeper
That’s not true at all. This is a paradox, not really philosophy.
This isnt philosophy, this is stupidity.
@@sonufmahn2480 lmao
@@fenhen Paradoxes are a common medium for philosophers to use though.
there is essentially no paradox if the prisoner's expecting NOT to be hanged, as he excluded all possible dates for this to happen, hence he's surprised by the date of his hanging.
Sounds like he convinced himself that it wouldn't happen, thus leaving him suprised that it happened at all.
The "paradox" is flawed.
You can effectively eliminate Friday but by eliminating Thursday, you again create the opportunity for surprise.
No, you can't even eliminate Friday. If on the Friday noon the prisoner is convinced that they won't hang him, his hanging would still surprise him.
@@amit_bisht you could also drug the prisioner have him wake up in a truman show like world, and then just hang him while he's having breakfast. If you can change the time at when hangings take place, you could do whatever you want to effectively surprise the prisioner, but thats not the point of the paradox.
Yup, it really is this simple.
Yes, because you can eliminate Friday ONLY if on Thursday you've not been hanged. Therefore you cannot keep discarding the last day of the sequence as the prisoner is doing
@@amit_bisht no the prisoner doesn't have to be convinced he won't be hanged, you know you're going to be hanged next week, the fact that it isn't suprising doesn't change that. So if by Thursday you don't get hanged, it wouldn't be a surprise to die Friday, but you would still die. I don't know why guessing what day you die on means you won't die. The surprise comes from thinking you won't be hanged when if it's the last day logically you will day (and shouldn't be surprised)
We could introduce the fatalistic argument: Once I'm dead, none of this matters.
or, we could say that because the judge said that the hanging will occour between monday and friday, its not a surprise because the prisoner would be expecting it.
This seems like a loop of logic. If the prisoner thinks he can't be hanged on Friday because he won't be surprised, then he can be hanged on Friday because he will be surprised! This paradox seems unsolvable to me because whenever the prisoner suspects he will not be hanged on a day, he can be hanged on that day because he would be then surprised! But it would be interesting to see how it would work if his perspective was focused starting on one of the other days, instead of the beginning of the week.
Philosophy. Great stuff
Friday will only not be a surprise if you are alive on thursday. Thus, from monday to wednesday, friday is a legitimate hanging date.
By assuming “no execution” with the prisoners logic, that would rule in a friday execution as being surprising and any day during the week would come as a surprise to the prisoner who assumes they will escape an execution. Obviously this is a 200 IQ play by the judge by allowing a paradoxical statement to be said
😅Oh duck your right. Nice
This is the stupidest “paradox” I’ve ever heard of
I believe there's a reason for that?
I just don't really get it though, he's always going to be hanged, right? So what does it matter if he's surprised or not?
@@josephpayne113 You are missing the point of a "thought experiment". "What does it matter?" is a non-sequitur because "matter" in this context is not a part of problem. This is why it is called a "logic" problem.
it's a logic problem sure, but it's not a logic paradox (as was in the title). The logical explanation in this video is subject to many flaws.
@@SwiftDustStorm I agree that the use of the term paradox is quite loose in this example. However, there is a paradox in there... it just isn't all that compelling and really just serves to illustrate the limitations of language when trying to articulate state dependent phenomena.
EDIT: Just to clarify, my remark was directed specifically at Juice. It seems as though you are responding to my remark as though it was a response to your initial post. I was only pointing out that to ask "What does it matter" was irrelevant to the thought experiment's intent.
My FBI agent must be concerned af, first I listened to that one Caretaker album. Now a video about hanging
whats next your gonna watch a video about somone getting doughnut-ed (its where they get turned into a doughnut ) speaking of which what do you think of *cherry* doughnuts
The judge's statement is in effect "you will hang on a day from Mon to Fri in which the probability of hanging is less than 1".
Now see this from the executioner's point of view.
He is asked to perform a random number experiment every day to decide whether to hang or not.
On Monday he says to his computer "if rnd < 1/5 then we hang, else we don't hang". On Tuesday he says "if rnd < 1/4" and so on.
He knows that if Friday is reached then he no longer can do it because the 1 is reached.
But why not on Thursday (rnd < 1/2), or Wednesday, or before ?
So it came to pass then the prisoner's unlucky day was Wednesday.
The prisoner having convinced himself that he will not be hanged, means that should he get executed, it will be a surprise to him.
🤯🤯
Yes, but the whole point is to demonstrate how his logic was faulty.
Exactly,this isn't a paradox he is told he will be surprised thinking he out smarts judge and won't be hanged yet does and as he thought he would not this surprised him
Sharon Murphy it is a paradox. The reason is that his logic seems sound. He reasons that he cannot be hanged and his logic is seemingly correct. At least it’s is extremely difficult if not impossible to formalize an argument to disprove his logic, yet he is still surprised. That is the nature of the paradox.
@@Vgamer311 But the judge said he will be hanged eventually. So the prisoner just took 1 part of the judge's statement (the surprise part) and ignore the rest?
The prisoner can't know that a certain day won't be the execution day based on a day eliminated because another day was eliminated, the friday elimination is logical, as if he does get that far there's no other option, but the rest of the argument becomes invalid the moment he eliminates thursday based on the fact that friday is eliminated. You cannot know that something won't happen based on speculations, the fact that friday can't be the execution day is logically correct, but taking that a step further and saying that thursday won't be the execution day either because he's expecting it is wrong because it's not a factual deduction anymore, it's a speculation that comes from the argument "i'd expect it to be in the last day because i lived long enough" but thursday isn't the last day anymore just because he eliminated friday. The only day deduced to not be the execution day in the story is friday, the rest of the argument is wrong because the prisoner deduced that no day will be the execution day, therefore not expecting the execution to come, making the execution day a surprise
Exactly, at Wednesday night you know that it cant be Wednesday Tuesday or Monday, but you dont know if itll be Thursday or Friday till noon on Thursday if they come get you or not, theres two options and no way of knowing what will be picked
But on Wednesday night you know it can't be Friday, so you deduce it must be Thursday so it's not a surprise. Of course it becomes a surprise by the mere fact you deduced it couldn't be Thursday which means it can be Thursday.
Needed someone comment this
@@brianpadraig Yeah, the real problem here seems to be incorrect evaluation of prisoner's own surprise. If it is not surprising to be hanged on day X=it is impossible to be hanged on day X=it is surprising to be hanged on day X. Contradiction.
Consider the following :
{ here by till x day I mean at a time where that day has arrived and he still hasn't been executed or on the previous day the time till one can be executed has passed (this is for sake of simplicity for me really)}
(1) If he were alive till Friday he can only be executed on Friday. Thus he'd have to be alive before Friday.
(2) If he were alive till Thursday he can executed on Thursday and Friday. Repeat (1). So he'd have to killed on Thursday. But as this is the only option therefore can be predicted with certainty so he'd have to be executed before Thursday.
(3) If he were alive till Wednesday, he can be executed in Wednesday, Thursday and Friday. Repeat (2) so he'd have to killed on Wednesday. Which has also been predicted with certainty so he'd have to be executed before Wednesday.
You get what I'm doing now.
(x) If he were alive till (Friday - x) day he can be killed on (Friday - x), (Friday - x + 1), (Friday - x + 2) ... (Friday - x + x).
Repeat (1+x) {unless x=0. In that case don't repeat anything in that case paste (1)}
so the only option is (Friday - x) but that makes it predictable with certainty so he has to be alive before (Friday - x - 1)
{here x is number. For example (Friday - x) where x is 2 would be Wednesday}
Keep increasing x's value by 1 and there'll be all the days. (now that I think about it I'd probably be better off just putting everything for the days)
The only thing deducible is the hanging on Friday, when he is still alive on Thursday evening. Other than that, theres no other fail safe or certainty to any of the other guesses on any other days. The thought process itself is faulty, as the date is a roll of dice. He can only be sure of Friday, and he cannot build upon that information.
I always thought of this that since he deduced everything, the executioner overheard this, and could do any day and it would be a surprise, even the Friday
The prisoner stopped expecting himself to be hanged, and was then surprised when he was hanged.
The prisoner's flaw is in thinking, before Thursday noon has passed, that he can eliminate Friday on the grounds of "then it wouldn't be a surprise". Yes, *if* the prisoner makes it all the way to Thursday noon, *then* he can conclude that the hanging will be on Friday. But this is not information that's available to him from his perspective at the time of the sentencing. For all he knows, the judge assigns a day randomly, at the time of the sentencing, and simply doesn't tell anybody until it's time to send in the executioner. Every day that passes without the hanging taking place thus further constrains what random choice might have previously been made, but does not (from the perspective of the time of sentencing) affect the level of surprise. The prisoner still faces each day prior to Friday with the dread of "maybe it's today". Without a rigorous definition of what it means to be surprised, I don't think we can say anything more definitive than that.
I agree with you in the short hand.
The prisoner is detracting subsequent days on the basis that other days wouldn't surprise him, in spite of thise further days being available as an option.
But if it were Friday, the execution would indeed come without surprise. With that statement as truth and the assumption the judge meant there would be surprise at the time of execution, we can eliminate Friday.
It seems like the selection of a hanging day would be a stochastic process, given the word "surprising" in its setup, but the video's explanation treats it as a deterministic problem.
Like Brandon said, sure, you dont know *if* you will make it to Thursday. But that doesnt matter. There are no possible situations where Friday is a day that you will be surprised. If there are absolutely no scenarios where you'd be surprised by your death on that day, you can reliably eliminate that from the pool of days.
Then you just carry that logic down. The issue with this paradox is the concept of being surprised and the assumption that the judge will behave under a certain set of rules in order to surprise you.
Exactly. This is a much more concise statement of the real problem: The judge says "you can't determine what day it'll be," whereupon the prisoner promptly tries to determine what day it'll be. So no wonder he's surprised in the end.
Wow this is scary that academics can't understand something so simple.
Executioner: *Comes to cell*
Prisoner: "You can't surprise me!"
Executioner: "Understandable, have a nice day. "
The flaw in the prisoner’s logic: you only KNOW that the hanging must be on Friday once it is Thursday afternoon, so on Wednesday night the prisoner is yet to be certain of whether it will occur on Thurs or Fri. So in reality, any day other than Friday has potential to be a surprise. It doesn’t matter how many days you look at: if he gave him a window of a month rather than 5 days, it is still only when he has reached the last day of the month that he knows “today must be the day because there are no more days left.”
If he makes it to Thursday afternoon, then he knows the hanging will be on Friday. But once he reaches Wednesday afternoon, he does know it must be on Thursday because it 100% cannot be Friday. If it was Friday, then he would know about it on Thursday afternoon and therefore the hanging couldn't happen.
Can that same logic be applied to Tuesday and Monday?
@@RobbenVaart2 No it can't, this is a paradox only if you view this problem in a certain way. No need to try to disect it.
@@rcutler9 so, if he "KNOWS, 100%" that it CANNOT be friday, and then he go hung on a friday, would that not be surprising to him?
@@RobbenVaart2 no. He will only "know" that he is going to be hanged on Thursday if he makes it to Wednesday alive. But he has no way of knowing if he will be alive that day. There is still the potential of getting hanged Monday, Tuesday, or Wednesday.
He was hung by the Spanish Inquisition. As nobody expects them, it was a complete surprise.
They poked him with the soft cushions to get his confession
Don’t forget the comfy chair!
@@jeffthebracketman *Zooms into Terry Gilliam's Face* "tHe CoMfY cHaIr?!"
Brilliant!
Confess! Confess! Confess!!! I confess! NOT YOU!!!
If the prisoner think he will not be executed because it won’t be a surprise, but then got executed anyway won’t that mean he’s still surprised by the execution?
Good fun. The key word is "surprise".
Even Friday cannot really be excluded, because although logically Friday could not be a surprise if he was not hanged by Thursday and therefore theoretically breach the condition, if he was then hanged, having already felt safe from hanging he would be surprised to have it happen on Friday (including to find that judges are not necessarily logical and have their own prerogatives ie can set the date whenever they feel like regardless of logic.)
Jokes aside, the 'exclude Friday'' argument (as well as the others in sequence) presupposes and assumes not being hung by Thursday - yet he is thinking abut this in the weekend prior ie all possibilities remain open and at the whim of the Judge. For reasons unknown, the arrow of time only flows forward.
I am strongly in the epistemological camp on this one. I would suggest that any pure logic/maths approach to this would have an unrecognised assumption re time order if it found he can't be hanged based on what the Judge proposed.
Prisoner: *Happy noises*
Executioner behind the door : What the hell
Zalkif hahahahaha
I've been thinking of something similar to this, but this is my version: a teacher overhears 2 students arguing. She then splits up the argument and tells one of the students to tell their side of the story. The student can either lie or tell the truth, but the student does not know if the teacher expects them to lie or tell the truth. The student then puts into account that the teacher may expect the student to suspect that they will expect them to lie/tell the truth, so the student then realizes that the teacher could outsmart them even more than them, and so on in an infinite loop.
I acualy though of this paradox myself but then in a different scenario. I knew it had to be some kind of parradox but i dint know that the paradox already existed. So thank you for making me aware.
If the prisoner by logic deduces that he cannot be hanged on the Friday, and believes that he will therefore not be hanged, then being hanged on Friday would come as a surprise on the basis that it was not expected. The end.
It has to be a suprise at the exact moment the executioner knocks at his door thought thats why this solution dosent work. By thursday noon he would know his execution would be friday
@@EpperEcheloN not true - because the prisoner has convinced himself he cannot be hanged.
Let's boil it down to one day. If the judge said he is to be hanged tomorrow, but when he is hanged, he won't expect it to be that day, then the prisoner will assume that he cannot be hanged, because the Judge's statement is seemingly contradictory. But as a result of him not expecting it, he can therefore be hanged. And the Prisoner makes a false assumption - that the Judge and executioners will keep to the word of the Judge and will only hang him when he isn't expecting to be hanged that day. Back to the 1 day scenario, the prisoner is expecting to be hanged that day, because that is the day the judge said - so he is surprised that the Judge lied by telling him he will be surprised - but in doing so, the judge will be correct - as the prisoner is surprised to be taken away as the judge did not tell the truth that he was expecting the judge to tell.
No, if he gets to noon Thursday and there’s no knock on the door Friday would not be a surprise.
@@slapmyfunkybass it would be a surprise to be hanged on Friday though - because come noon on Thursday he has assumed he can't be hanged. So when he is hanged, he is surprised.
erobed21 depends on how the prisoner interprets the information wouldn’t it? For example come Thursday he would know that his execution is 100% going to be on Friday. However, this contradicts with the idea that it will be a surprise as to when it happens so it can’t happen. The conflict here is that he knows it has to happen that week so it has to be Friday. But also knows it can’t be Friday because he will be expecting it. Either way he is correct.
I don’t understand this video ..
Like at all
Brendon Maximus
Trust me, you’re not the only one
Axiom means the starting point. Does that help?
Brendon Maximus I didn’t either, rewatch the part where he eliminates the days. Now I think I get it.
Brendon Maximus i don‘t too
Mr. Toasty Burger what he says there is dumb too I don‘t understand that these arguments sound like sh*t to me yk
The judge giving an a "weekday of the following week" was to for the hanging crew to get organized. Wednesday was the day they were prepared. The only way to properly get it right is to know the schedule of the hanging crew.
"You will be hanged at noon on a week day during next week with 80% chance of it being a suprise".
Paradox fixed
There is an error in the reasoning here. There are basically 2 statements:
- You will be hanged next week
- The day will come as a surprise to you
By the time you ruled out all 5 days, you cannot just conclude that the other statement (you will be hanged next week) is suddenly no longer valid. Instead, I think you end up in an infinite loop where after ruling out all days, all you can do is say "hey, I don't know what day it is" and start over with removing Friday again.
That still doesn't solve anything of course - but it's a very different situation to analyse.
The prisoner assumed the contradiction proves the first statement wrong, when it really just proves either statement wrong. But the point is: neither was wrong.
the second statement is not garunteed to be true. the prisoner could simply do out with philosiphy and logic and just guess he was hanged wednesday in which case he was correct. in this scenario it is not a paradox the judge was just wrong with his second statement. it is not likely the prisoner will guess which day he is hanged, but it is not impossible as the judge assuems
Hans van Zutphen that’s the reason it’s a paradox
Exactly. If the second statement is false, the first statement can still be true OR false. That factuality of the hanging is not reliant of the factuality of the surprise.
The Judge DID miscalculate in believing the surprise statement was enforceable. (It did ultimately come true, but this was largely by luck - the Prisoner thought five levels of logic deep, but if he'd stopped at two levels or waited until Tuesday afternoon to think it through, he could've assumed he was being hanged on Wednesday. The Judge made an assumption about the Prisoner's thought process.)
But the Prisoner was also mistaken in linking the two statements together, and in assuming that if one is false, the other must also be false.
*Gets hanged on Saturday morning*
Judge: "Too bad you, I lied. Surprise!"
How is that a lie? Saturday would be at the very end of the week, and therefore the judge wouldn't have lied.
He said it had to be a weekday
Friday is only not a surprise on Friday, as Friday is fixed as "the date" only after not being hanged Thursday. Hence, eliminating Thursday can not happen, as it requires two things to both be true when only one can be true: a. The prisoner is still alive on Friday (eliminating Friday as "no longer a surprise") and 2. It's Thursday. In simple terms, Thursday can not be eliminated as no longer a surprise until after Friday is also eliminated, but that can not happen until Friday. Ergo, any day other then Friday is still a surprise on that day.
True. You can’t tell the future, so it’s still a surprise at that point.
Rather than "know", which is ambiguous, it is clearer to say the prisoner will not "be able to compute in advance" the day of the hanging.
What if he says: "I'm sure it's today", every single day
Then his reasoning could be wrong at most 4 times. He has no evidence, no reason to conclude that the hanging is today.
That's how I would do ,if I were the Prisoner ! (Big Brain Time!)
Martin Alcala then he doesn’t know for sure which make him surprised
He can say hes sure but saying hes sure doesn't make it so.
Since it can only come by surprise, once he says he's sure it's today he simultaneously becomes sure it's NOT today, opening himself up to it being today (hence the paradox)
This just sounds like the prisoner went insane right before he got hanged.
Kudos for executioner politely knocking before killing him
The fact that no day would be a surprise leaves open to the fact that after that deduction was made - every day that he previously erased as a potential surprise would once again be a surprise excluding Friday. The only day that is technically not a surprise by the prisoner's logic would be a Friday - yet, you can also say that as he eliminated Friday as a potential date, if the executioner knocked on Friday, he would be surprised, seeing as his logic was flawed.
"I wouldn't be surprise if you hang me tomorrow"
Solved.
"Ha! Now they can't hang me."
*gets hanged*
"Well I didn't see that coming."
@@GrandSupremeDaddyo "I'm pretty sure that they won't hang me now, but later they will"
I think the only paradox here is the prisoner’s logic. The action of saying that you can’t be hanged on Friday but you CAN be hanged on a Thursday means that when he eliminates Thursday he is contradicting his own logic.
@@Zaz5y that's why I didnt follow that shit logic with longer "suprise" chance.
Isn’t this a simplified version of the “rapture paradox.”
“No man will know the day nor guess the hour.”
So as long as at least one person on the entire planet believes that each separate day of the year may be the rapture, then it would never occur.
@Andrew Elie one man for every hour then
@@georgebrantley776 😂yep we can prolong the time till we are like "ok now we need to go"
@@asanokatana keyword "ususlly"
@@truth24searcha98 Never is the most accurate word
It doesn't say will know, but KNOWS. Secindly, even if it did say that, it's different, because you can only guess or propose an argument for a particular day, but not KNOW it with 100% certainity.
Martin Gardner had a whole chapter on this in the book "The Unexpected Hanging".
In order to not be surprised, the prisoner must:
1. Logically deduce that he will be hanged on a given day.
2. Announce that to the jailer at the start of the daily visit, including his reasoning.
Martin reduces the problem to: "you will be hanged tomorrow and it will be a surprise" with surprise defined as above.
The thing is, that even reducing it to that, the prisoner cannot properly deduce that he will be hanged.
Here's why:
The judge's statement is 3 axioms.
A is "prisoner will be hanged tomorrow"
B is "prisoner cannot deduce A"
If the prisoner tries to deduce relying on A, then he deduces NOT B. But if B is not true, the judge is lying, and A cannot be relied on.
Therefore the prisoner cannot deduce using A. Therefore B is true, and no deduction can be made.
The trick is that the prisoner cannot make any valid deductions based on these premises, and the hanging is always a surprise. The Judge told the truth, in that the prisoner cannot logically conclude that he will be hanged.
It depends on the prisoner’s reasoning. The reason I think so is because his reasoning can change. This particular prisoner’s reasoning concludes that he had escaped his sentence, which means any day would be a surprise. But if he makes a different conclusion, for example that the date of his execution will be on Wednesday, then it won’t come of Wednesday because he would be expecting it.
The prisoner seems to set up his own surprise by way of how he tries to solve the riddle of the judge's sentence, strongly suggesting that the prisoner's original inference against a Friday execution is to blame. From the perspective of Thursday afternoon, there is only one remaining possibility left, leaving a 24-hour warning. But from the perspective of Monday morning, there are still five possibilities. By trying to work backwards in advance, the prisoner erroneously eliminates Thursday as a possibility, since that morning there is still a possibility of execution. Until noon on Thursday, it is still possible to be surprised!
this was the only explaination that made sense, thank you
Yeah this was what i thought, only what makes sense. Logic can’t be beaten like this i mean
Plot twist: The judge was being a prick and decided to just hang him anyway.
The problem arises because you prevent the execution by predicting the execution on that day and then shifting your prediction.
And also there is a contradiction, you can't be executed on the expected day and you know that, so suppose you expected by some logic that you will be executed on day X. Then you can't be executed on day X, since you expected, but now you know that you can't be executed so won't expect to be. But since now you don't expect to be executed on day X, thus you may or may not be executed.
The fact that he was wrong, made him surprised, thus the judge was right
www.reddit.com/r/greentext/comments/e7nruo/anon_watches_clutch_powers/
I've always thought that the paradox is brought about by the reasoning of the prisoner, which works backwards in time, and the experience of the prisoner, which moves forward in time. Can't really explain it, but I think the fallacy is in there.