This paradox is really hard to think through, Mr. Harris should just pretend to fall into Alice's logic trap but split the exam into multiple parts and give it out throughout the week. The students would definitely be surprised. The surprise element is then the format of the exam (parts) and not the days itself.
This only solves the paradox if we accept that there's a 20% chance that the teacher's announcement is false. A Friday announcement (i.e. 20% of the possible days) cannot be a surprise, and as such, it would violate the stated rules. So if we assume on Wednesday evening that the teacher will follow the stated rules, this rules out Friday and leaves only one possible day---which in turn wouldn't be a surprise either. The only way to resolve this is to fix the contradiction in the announcement. This very much sounds like fighting users about software requirements stated in contradictory absolutes.
I'm not aware of any contradiction in the announcement. The announcement says that the exam will be next week. The announcement also says that when the exam does occur, no one will have been in a position to predict it the night before. Both these things can be true. And once the teacher gives a Tuesday exam which surprises everybody, we have confirmation that both things were indeed true.
@@decomplexify Your confirmation argument in this response is only true if the examination was administered Monday through Wednesday. Thursday and Friday still remain problematic based upon the initial conditions. If the teacher has the habit over a period of time of announcing such a "surprise examination" and then limiting the choices of days to only Monday through Wednesday to avoid the apparent paradox then eventually the students would be able to reasonably deduce on Tuesday evening that the examination was going to occur the following day, putting everyone back into the same paradox. No, human behavior cannot be perfectly predicted, but certain behaviors are very strongly correlated. In my doctoral studies there were times where professors never repeated their questions as, in some cases, the prior examinations were handed back to the students after grading and over the years a sizeable library of examination questions had been assembled and was passed down to subsequent classes. The examination questions in the present year often "rhymed" with the prior years, as Mark Twain had said regarding history.
@@r2db I think you may have misunderstood my position! I was just pointing out that the first component of the announcement ("There will be an exam next week") isn't contradicted by the second component ("When the exam does occur, no one will have been in a position to predict it the night before"). The fact that the teacher could fail to surprise us, most obviously by messing up and giving the exam on Friday, is irrelevant to this question of whether the announcement is inherently self-contradictory. The important thing is that the teacher could succeed in surprising us. In other words, it is in his power to make both components of the announcement come true. If you accept that, then you've accepted that the announcement is not self-contradictory. Other things to point out: in the video I didn't suggest that the students had prior experience of this teacher giving surprise exams, so you can take it as a given that they don't. Secondly, in the video I give an analysis of why, even though a surprising Friday exam is impossible, a surprising Thursday exam is not.
Beautiful content, nicely presented. I must admit that halfway through your elimination of the possible attitudes, I almost expected you to start saying that you could clearly not choose the wine in front of you. 😉
What of the scenario where students study beforehand and are prepared for an exam any day of the week? Whether it is a surprise or not is no longer relevant because they were told there would be a 'surprise' exam, meaning It isn't much of a surprise regardless of when it occurs.
There is one key element that is being left out: Mr. Harris must promise that there will be *exactly 1* exam next week. Otherwise there could for example, be an exam on Monday and then also an exam on Friday, both of which are a surprise.
I don't think your solution fits your constraints. I think if you accept the logic that under the given conditions, the last day is impossible, then the same logic will always eliminate the last day. I think there's something wrong with shrinking the interval by cutting out the last day, but I'm not sure what it is. But once you accept that shrinking, I think the rest must follow.
I think the flaw is grounded in the elimination process. According to her the initial day to be eliminated is Friday which makes sense, however, on Wednesday evening she doesn't consider Friday as a possible day at least for a non-surprise exam. In this way she trims the week into having only 4 possible days hence making her conclusion of rulling out Thursday for a surprise exam true. Am I even making sense myself?
What he should have said was 'The earliest point you can know what day the exam will be is at the end of school on Thursday.' And if he wants to be cheeky about it he can add 'I might decide on a day by the roll of a dice, or I might have already decided.' The fault was not in her logic but in the definition of surprise and with it giving himself the limitation of having the surprise having to be be so close to the test being handed out. If his definition is true, she is correct and using the uncertainty that he might be wrong is a cop out and not a solution to the logical paradox.
Basically this solution allows him to say he will give a surprise exam tomorrow and they won't be able to know the night before. Technically he can pretend to die in front of everybody and then show up the next day with a surprise exam. Still not a solution to the logical paradox. The logical paradox is: X is between 1 and 5 I will count from 1 to 5 and tell you when I have reached X. Under no circumstance can you be sure that the next number is X. That is either a lie or a paradox.
If his definition is true, she is correct? That can't be right. We can for example imagine him giving the exam on Tuesday and Alice not having been able to predict this on Monday evening. It's important to realize that the teacher's announcement is entirely correct and Alice is entirely wrong. For clarity, the sequence of events is this: 1) The teacher makes the announcement. 2) On Monday night Alice doesn't know whether the exam will be on Tuesday or not. 3) The teacher gives the exam on Tuesday. 4) Alice has to admit that the announcement was correct on both counts: the exam really did occur "next week", and on the evening before the exam she really had no idea that an exam was coming the following day. The challenge is to figure out where Alice went wrong. She had convinced herself that there was no way the teacher's prediction could be fulfilled. And yet in the scenario described above, the prediction was fulfilled. So there must have been some subtle flaw in her logic - the challenge is to find it.
And he could also wait until Thursday, pretend to die and then give the test anyway. They would be surprised for sure. He could also show up at their home with the test or have the test be about cartoon animals and it would also constitute as a surprise test. You did rule out things like school burning up so I also figured you ruled out that he was using misleading and nonsensical language. His wording makes his claim loose meaning and when he is outside of the boundaries of a verbal contract, he can of course surprise them in any number of ways. "I am holding a stone." doesn't become a true statement just because I then lift up a stone. Logically they would know on Thursday night that it can't be on Friday since that's the only day left and thus it can't be a surprise day. The same is true of every day before that. Basically it is the same as him saying "Tomorrow I will give you a surprise test. By surprise I mean that you can't know the night before if I will give you a test or not." "This sentence is a lie." Was I telling the truth or was I lying?
Can the students only be surprised at the time of the exam? Seems like if the test is given on Friday the surprise occurs when they get the to into Thursday and there is no exam, so the surprise is that the test is given on Friday, but it is revealed on Thursday's class? ;-)
The definition of "surprise" isn't left open-ended in the video, so there's no need to speculate about what might qualify as a surprise. 17 seconds into "Fool the Teacher: The Surprise Exam Paradox Part 1", Alice asks Mr. Harris to clarify what he means by a surprise exam. He says that he is defining a surprise exam as one where, on the evening before the exam, you'll have no way of knowing an exam is happening the next day. A surprise exam as defined in this particular way is what the paradox is about.
I am not a logician but I think the error is in allowing Alice to work backwards through time - the things you come to know on Thursday are not yet known on Wednesday, and so on. So while it is true that you cannot be surprised on Thursday evening if no exam has occurred (p=1 that it will be Friday) this is not true on Wednesday (p=.5) or Tuesday (p=.3) or Monday (p=.25) or Sunday (p=.2) - where p = probability that the exam will be tomorrow.
I'm not sure I understand your reason for saying that Alice shouldn't be allowed to work backwards through time? We don't have to wait till Thursday evening before we come to know that a Friday surprise exam is impossible. We already know, right now, that a Friday surprise exam is impossible. (You affirmed this in your comment, when you said that there's no way a person who reaches Thursday evening without an exam having taken place can be surprised.) Since Alice knows at the outset that a Friday surprise exam is impossible, she is able to challenge Mr. Harris by getting him to admit that, since he wants to surprise the class, he'll avoid giving the exam on Friday i.e. he'll give the exam between Monday and Thursday. And of course, now that the "real" last possible exam day is Thursday, this reasoning can be repeated.
@@decomplexify Not that she shouldn't be allowed - on Tuesday evening it is not true that we know it cannot be a surprise on Wednesday or Thursday, it is only AFTER it has not already happened that it is not a surprise (forwards in time)...
@@sleepingdragon You have to consider what a paradox is. In a paradox, somebody (in this case Alice) applies a chain of apparently valid reasoning which leads to a conclusion C - while at the same time, if we apply a different chain of apparently valid reasoning we get a conclusion D that directly contradicts conclusion C. Since both chains of reasoning seem equally valid, we're mystified as to why they lead to opposite conclusions. Now, in this case, you have applied a chain of reasoning to reach conclusion D ("a surprise exam is possible") while Alice has applied an entirely different chain of reasoning to reach conclusion C ("a surprise exam cannot happen on any of the five days"). To resolve the paradox, just reiterating your chain of reasoning isn't enough. You have to pinpoint the flaw in Alice's chain of reasoning.
@@decomplexify The paradox requires that something that happens on Thursday (no test) is known on Wednesday - it is true that there can be no surprise on Thursday evening but any test prior to that is a surprise (but less so each day)...
@@sleepingdragon Certainly there can be no surprise once we get to Thursday evening. But it's equally true - according to the reasoning that Alice and Mr. Harris go through - that there can be no surprise once we get to Wednesday evening. The justification for this is as follows. Since both Alice and Mr. Harris agree that a Friday surprise exam is impossible, Alice is able to challenge Mr. Harris by getting him to admit that, since he intends to surprise the class, he won't give the exam on Friday i.e. he'll give the exam between Monday and Thursday. Now that this has been admitted, we can conclude that any student who gets to Wednesday evening without an exam will know that the exam is going to take place on Thursday - and therefore cannot be surprised by a Thursday exam.
I think the problem is the term "next week". Once the teacher defines that the surprising exam is in the "next week", it is not a surprise anymore. Limiting the time period to "next week" eliminates the possibility to have continuous surprises after the last day (Friday) of "next week". Defining "next week" has the same effect as defining "next day". If the teacher says he gives a surprising exam "next day", it is not a surprising exam anymore for a time unit of a "day" unless we further keep that surprise in hours, minutes or even seconds.
You say 'Once the teacher defines that the surprising exam is in the "next week", it is not a surprise anymore.' Consider however that 17 seconds into "Fool the Teacher: The Surprise Exam Paradox Part 1", Alice asks Mr. Harris to clarify what he means by a surprise exam. He says that he is defining a surprise exam as one where, on the evening before the exam, you'll have no way of knowing an exam is happening the next day. A surprise exam as defined in this particular way is what the paradox is about.
@@decomplexify I have a second thought: Surprise depends largely on the level of uncertainty. When Alice moves the bar all the way between Thursday and Friday on Thursday evening as depicted: M, T, W, T || F, Friday is isolated to or narrowed down to its own day and hence decreases its uncertainty as there is no other choice to pick. At that time, Friday is impossible to have surprising exam. However, when Alice moves the bar backward between Wednesday and Thursday on Wednesday as depicted: M, T, W || T, F, the day set on the right of bar has more elements now. Because the set increases elements, it increases uncertainty. It's like the fact that, there is no uncertainty if we can only have one choice, but when we have more elements, the uncertainty increases and we call it "Chance" or "Probability". Friday's certainty relies on its environment or neighborhood or neighbors in its set. If it is a single, it's 100% certain. That's actually what Alice's logic relies on to reach the conclusion that Friday could be excluded from surprising exam in her first round. However, the certainty of Friday not having exam could change when the set includes Thursday on the right of bar. Now we have 50/50 chance for surprising exam to happen on Thursday and Friday. In another word, at that moment, Friday is not a certain element anymore. It has been but it is not now. Just like a healthy cell could turn into a cancer cell. The cell is not an alien cell in our body and it's structure could be same as well, but its remark or behavior could change. I think I wrote too much...
@@ABackZhu Remember, Mr. Harris says that he is defining a surprise exam as one where, on the evening before the exam, you'll have no way of knowing an exam is happening the next day. On this basis, the chance that a Friday surprise exam will occur is 0%. It doesn't matter where the "bar" is: the chance of a Friday surprise exam is 0% regardless of where the bar is. If it's Sunday evening right now, so that the entire week is ahead of us, I can be confident that there's no way a Friday surprise exam can take place. And this is because the notion of a "Friday surprise exam" is simply contradictory.
@@decomplexify I don't think you got what I meant. The domino effect of getting no surprising exam on Thursday is based on the assumption of certainty of having no surprising exam on Friday. If that assumption is not true anymore after the right set has more elements, the whole logic of determining Thursday, Wednesday and so on loses the basis of assumption. Alice neglects the changing status of the "Friday".
@@ABackZhu I understand what you're saying, but what you're saying is not right. Let's back up to what you said in an earlier comment: "When Alice moves the bar all the way between Thursday and Friday... at that time, Friday is impossible to have surprising exam." All right. Let P = the following statement: "If we get to Thursday evening without an exam having taken place yet, at that point I'll be able to conclude that a Friday surprise exam is impossible." I think P is true. And the fact that you've said "When Alice moves the bar all the way between Thursday and Friday... at that time, Friday is impossible to have surprising exam" means that you agree with me about P; you also believe that P is true. Now let's suppose we get to Wednesday evening without an exam having taken place yet. Let's suppose that at that point (Wednesday evening), you say to yourself: "I guess a surprise exam could take place on Friday." This is the same as saying "I guess it's possible that the exam could take place on Friday without me having anticipated it on Thursday evening." And by saying this, you deny that P is true. Therefore it isn't valid for you to say (on Wednesday evening) that a Friday surprise exam might happen - as saying this means saying that P is false, whereas actually you know that P is true. In short: a Friday surprise exam really is impossible! It's just as impossible from the perspective of Wednesday evening as it is from the perspective of Thursday evening.
The way to understand the problem is to realize TIME is involved and the information you have as you progress thru the week changes. So the teacher makes the announcement before the week begins. You cannot use this BACKWARDS REASONING before week begins because you don't yet know the exam has not taken place on Monday or Tuesday etc. That BACKWARDS REASONING would involve using information you don't have!! On Tuesday evening you know exam didn't happen Monday so if it takes place on Wednesday it would be a surprise. Clearly on Thursday evening you know it must take place Friday because you NOW KNOW it's not yet taken place so it's not going to be a surprise. There is no paradox YOU CANNOT USE THIS BACKWARDS REASONING BECAUSE YOU WILL BE USING INFORMATION YOU DON'T HAVE. You cannot (on Sunday or on Monday or on Tuesday etc) reason it will not happen Friday because you don't yet know if it happened on those Monday or Tuesday etc. So in summery teacher makes announcement on Sunday and you start using this reasoning to work out cannot be Friday YOU CANNOT because you are using information you don't have!!!!!!!!!! The exam could be the following day Monday. You cannot use this backwards reasoning because it involves declaring exam didn't happen Monday BUT YOU DON'T YET KNOW WHETHER IT HAPPENED MONDAY. So you cannot use this backwards reasoning because it ALWAYS involves you using information that YOU DON'T HAVE!!!!!!!!!!!!!!!! SORTED!
Another way to think about it is this. The rules of this Surprise Exam must be made very clear on the Sunday. If it's the usual Monday to Friday and will not know evening before then that is NOT POSSIBLE!!!!!! as student points out!!!!! You can still have a surprise exam tho rules would have to be different because if it doesn't happen by Thursday you know it's going to be Friday. That's how it happens in real life if you like. The original surprise exam is NOT POSSIBLE!!!!! and I think everyone was assuming it was, there is no paradox.
If you decouple the surprise happening from the unveiling then you resolve the paradox. If the exam happens Monday, Tuesday, Wednesday or Thursday, the teacher can say: surprise the exam is now. If the exam is Friday, the teacher can say on Thursday: surprise the exam is tomorrow. I feel like it qualifies as a surprise exam.
The paradox is about a very specific, precisely-defined form of "surprise". 17 seconds into "Fool the Teacher: The Surprise Exam Paradox Part 1", Alice asks Mr. Harris to clarify what he means by a surprise exam. He says that he is defining a surprise exam as one where, on the evening before the exam, you'll have no way of knowing an exam is happening the next day. A surprise exam as defined in this particular way is what the paradox is about.
Lets break it down: The teacher makes claim E: "There will be an exam next week". and also claim S: "There is a 100% chance the day of the exam will not be known to you until the day I give the exam." Lets break it down further: The teacher claims: ((EMon or ETue or EWed or EThu or EFri) and S). Combining this with the assumptions about how the passage of time works and so forth, Alice concludes (not EFri) then concludes (not EThu) etc. until she concludes (not EMon) and hence: (Not E). This makes the original claims self contradictory (much like the statement "This statement is a lie".) It just takes longer to get to the contradiction. When our premises lead to a conclusion that is a contradiction, we don't just assume the conclusion is true, we assume one or more of the premises are wrong. So either E is false or S is false or both are false. If E is false, S is not even a statement that has a truth value. If S is false then E can be true without contradiction. However (not S) is the statement: "There is NOT a 100% chance the day of the exam will not be known to you until the day I give the exam." In fact, if the exam is Friday it will not be a surprise. If it is any other day, it will be a surprise. That's how the students were surprised on Wednesday. -------------------- A totally different way of looking at it: What is a surprise? A surprise is when something happens (exam happening on a particular day) when you were reasonably confident it would not happen or had no knowledge of whether it would happen. Alice was 100% sure the exam would not be on Friday (or any other day). She should have then concluded that she would be surprised if the exam actually did occur on ANY of those days.
Hi John, this is a thoughtful argument and you've clearly spent some time thinking the problem through. However, there is a subtle but important flaw in your logic. To pinpoint the flaw, it's helpful to look at an exactly equivalent scenario to the surprise exam scenario. Here is how the philosopher Saul Kripke sets out the scenario: "Consider the case where all fifty-two cards, or at least a large number, are in the deck. Imagine that the experimenter, without telling the subject where it is, assures the subject that he has put the ace [of spades] somewhere in the deck, and that the subject will not know in advance when the ace will come up if the cards are turned up one by one. Can the experimenter guarantee this? It seems clear that he can, say, by putting the ace somewhere in the middle." Kripke goes on to clarify that he means the experimenter has put the ace of spades somewhere in the middle of the deck in advance, before the subject arrived on the scene. So let's imagine that the experimenter shuts his eyes and sticks the card somewhere vaguely in the middle of the deck, and when the subject arrives and the cards are turned over one by one, it turns out that the 34th card turned over is the ace of spades. Just before the ace of spades was turned over, the subject had no idea that the ace of spades was about to appear. Now consider the claim S, which is "There is a 100% chance that just before the ace of spades is turned over, you will not know the ace of spades is about to be turned over." S is absolutely true! There was always a 0% chance that the 52nd card would be the ace of spades; the experimenter ensured that there would be a 0% chance of this when, prior to the subject's arrival on the scene, the experimenter stuck the ace of spades somewhere vaguely in the middle of the deck (rather than right at the end). And so the paradox cannot be resolved by insisting that S is false. S is not false. The paradox has to be resolved in some other way. Resolving it requires close attention to the state of Alice's knowledge - not only what the state of her knowledge is at the outset, but also what the state of her knowledge would be on successive days of the week assuming an exam had not yet taken place.
There is no point in trying to use Propositional Logic and Truth Tables because it's not that type of problem. It involves TIME and changing states of knowledge/information. You are not just dealing with propositions. Anyway I've solved it, see my post at the top.
well ya , a Thursday exam would be a surprise , as on Wednsday evening there are still two days left when you say that it's impossible for a surprise exam to be on Friday that's simply not true as it's only impossible if we are on Thursday evening not on Wednesday evening. As such a Thursday exam would be a surprise, similarly it follows that an exam on any of the days would also be a surprise. from what I understood, the flow is in saying it's "IMPOSSIBLE" for the exam to be on Friday, the fact is it's not "impossible" unless you are on Tuesday evening (that is assuming an exam must take place of course).
It's a bit more complicated than that. Let P = the following statement: "If we get to Thursday evening without an exam having taken place yet, at that point I'll be able to conclude that a Friday surprise exam is impossible." From what you've said above, you believe that P is true. Now let's suppose we get to Wednesday evening without an exam having taken place yet. Let's suppose that at that point (Wednesday evening), you say to yourself: "I guess a surprise exam could take place on Friday." This is the same as saying "I guess it's possible that the exam could take place on Friday without me having anticipated it on Thursday evening." And by saying this, you deny that P is true. Therefore it isn't valid for you to say (on Wednesday evening) that a Friday surprise exam might happen - as saying this means saying that P is false, whereas actually you know that P is true. In short: a Friday surprise exam really is impossible! It's just as impossible from the perspective of Wednesday evening as it is from the perspective of Thursday evening.
@@oximas-oe9vf Ruling out a surprise exam on Wednesday, Tuesday, or Monday would require us first to make the transition from ruling out a Friday surprise exam (which we've done) to ruling out a Thursday surprise exam. The question is whether there's a legitimate way of making this transition. You know, at all times, that a Friday surprise exam is impossible. You also know, at all times, that the teacher is sincere in his intention to make the exam a surprise. None of this means that an EXAM on Friday is impossible. It does mean that, if an exam somehow DOES take place on Friday, the teacher will have have failed in his intention to make the exam a surprise. It's interesting to contemplate what a person's thinking would be on Wednesday evening. On Wednesday evening, you still know all of the above - but does knowing all of the above mean you know what the teacher is going to do? What exactly can you be sure of, and what exactly can't you be sure of, on Wednesday evening? This is a question that the video spends some time exploring. It's tempting to say that on Wednesday evening you'll remain sure that the teacher won't give the exam on Friday and that therefore you'll know the exam is going to be on Thursday. But the video gives an account of why, in fact, you can have no such certainty on Wednesday evening.
I thinking switching out surprise with probability makes it a bit easier to understand. So if he means that there is a probability of 1 that there will be an exam next week. And There probability < 1 that you will know your exam will be the next day. (Aka surprise exam). Then his statement becomes false on Thursday. And her reasoning is false because you only know with 100% probability on Thursday night. I don’t like this paradox because it breaks the rule of what he said that the it would for sure be a surprise any day next week when it’s only a surprise(probability less than 1) for 4 of the days.
Hi Austin, thanks for your comment. In "Fool the Teacher: The Surprise Exam Paradox, Part 1", the phrasing was as follows: "A teacher, Mr. Harris, announces to his class that there's going to be a surprise exam next week." You say: "I don't like this paradox because it breaks the rule of what he said that it would for sure be a surprise any day next week when it's only a surprise (probability less than 1) for 4 of the days." In the teacher's phrasing above, he never said that the exam "would for sure be a surprise any day next week". He never explicitly said, for example: "Even if the exam takes place on Friday, it will be a surprise." He simply said that the exam would take place next week, and that it would be a surprise.
@@HenryLoenwind He did, yes. He said that the exam would take place next week, and that on the evening before the exam, you would have no way of knowing an exam is coming the next day. He did not, however, say: "If the exam occurs on Friday then you won't know on Thursday evening that an exam is coming on Friday." A Friday exam wouldn't be a surprise! Because the teacher wants his prediction to come true, he will simply avoid scheduling the exam for Friday.
So the error is in the first few seconds of video, the student immediate reply to teacher. Think about it - when she says what she does SHE CANNOT BECAUSE SHE IS USING INFORMATION SHE DOESN'T YET HAVE!!!!!!!!
If on Sunday student says "it cannot take place Friday" you ask WHY? Student says "if it didn't take place Monday etc etc etc etc" IF IF IF IF (IT'S STILL ONLY SUNDAY)!!!!!! Cannot use reasoning like that.
So Monday to Friday and will not know evening before. If those are the clear Sunday rules then the student can deduce on the Sunday that as a list of rules it's NOT POSSIBLE!!!!!! because of the Friday problem. Student can appreciate on the Sunday that there is a problem with Fridays which will break the rules, no need to worry about the other days. No backward reasoning needed.
So to keep it simple. On Sunday you cannot reason that it cannot be Friday. That's because to do so involved information that it didn't happen on Monday Tuesday Wednesday Thursday. BUT IT'S STILL ONLY SUNDAY!!!!!! You don't yet know if it happened those days!!!!!! You are using information you don't yet have. YOU CANNOT DO THAT!!!!!! YOU CAN NEVER USE THIS BACKWARDS REASONING BECAUSE IT ALWAYS INVOLVES USING INFORMATION THAT YOU DON'T HAVE!!!!!!!!
I remain completely unconvinced by this example - based on thinking backwards through a logic puzzle. The Puzzle revolves around intent and around the concept of being surprised or not - and deducing backwards from potential future states. maybe the paradox would work better with a better example. because for me, the scenario about a surprise exam isn't about the surprise it's about the exam. and the only night of the week that matters is Sunday Night, when you don't know if monday will have an exam or not. and the question really is should you study on sunday night? and so the question isn't "Do I know if there's a test tomorrow" but did I adequately prepare for a test that I didn't know the day off so i'm not caught off-guard and fail. and yeah, the answer is you should study on Sunday. and the only way for an exam to be a surprise is if you didn't study, especially when you got advanced warning. or in other words, I refuse the premise and substitute it for my own. but for the purposes of finagling the entanglement of surprise, I'm positive that the student is correct, a surprise test is impossible if you think about it recursively - and it's the teacher fault for two things: 1. Claiming a test was definitely going to happen in next 5 days and 2. defining surprised, as a state of mind a student could be in the night before. Making the problem deducable so that surprise is impossible and therefore an exam can't happen. it's one of these problems where concepts of logic and language clash with each other where we focus on the properties of surprise in relation to a test, and the end-results seems dumb and counter-intuitive to people hearing it because we all understand that a surprise exam is a concept in and of it self. and surprise isn't a transitive property of an exam that either exists or not. the paradox is weird because we all understand an exam is possible on friday even if by then its no longer a surprise (again I hope by then you've studied) but in the context of perfect logisticians and logic problems if you can't have an exam be a surprise you can't have a surprise exam, and because the teacher said he would give a surprise exam and not an exam. a surprise exam is impossible to give. Allowing the option for the teacher to fail isn't a logic condition with regards to surprise or exam, and as such the student is right. no surprise exam can be given, and hence the paradox.
I'd rather just lie and make them study till Friday. will falsely announce one more week and then one week on Friday take an exam without announcing about it.
Alice reasoning is good, and there is no resolution to the paradox anymore then there is a resolution to the paradox "this sentence is a lie". The constraints of the problem are self contradictory, and the only way to fix it is to change Mr Harris' statement thereby completely changing the problem (e.g. "suprise exam next week, unless it's on a Friday in which case it clearly won't be a surprise anymore by the time school ends on Thursday").
I have to disagree with you there. Alice's reasoning leads her to the conclusion that Mr. Harris cannot give a surprise exam at all. We know that her conclusion is wrong. The reason we know that her conclusion is wrong is that we can imagine an exam taking place on Tuesday and Alice being surprised by it (she has no way of predicting it on Monday evening). Because her conclusion is wrong, something in her reasoning has to be wrong. As a side note, I would point out that there's nothing contradictory in Mr. Harris saying that there's going to be a surprise exam next week. "This sentence is a lie" can't be assigned a truth value. In contrast, depending on what Mr. Harris does, the exam will either turn out to be a surprise or it won't. His statement will turn out to be true or it won't. There is no indeterminacy to it. If he's rational, he'll give a non-Friday exam (for example, Tuesday) - making it true that the exam is a surprise.
This paradox is really hard to think through, Mr. Harris should just pretend to fall into Alice's logic trap but split the exam into multiple parts and give it out throughout the week. The students would definitely be surprised. The surprise element is then the format of the exam (parts) and not the days itself.
This only solves the paradox if we accept that there's a 20% chance that the teacher's announcement is false. A Friday announcement (i.e. 20% of the possible days) cannot be a surprise, and as such, it would violate the stated rules. So if we assume on Wednesday evening that the teacher will follow the stated rules, this rules out Friday and leaves only one possible day---which in turn wouldn't be a surprise either. The only way to resolve this is to fix the contradiction in the announcement.
This very much sounds like fighting users about software requirements stated in contradictory absolutes.
I'm not aware of any contradiction in the announcement. The announcement says that the exam will be next week. The announcement also says that when the exam does occur, no one will have been in a position to predict it the night before. Both these things can be true. And once the teacher gives a Tuesday exam which surprises everybody, we have confirmation that both things were indeed true.
@@decomplexify Your confirmation argument in this response is only true if the examination was administered Monday through Wednesday. Thursday and Friday still remain problematic based upon the initial conditions. If the teacher has the habit over a period of time of announcing such a "surprise examination" and then limiting the choices of days to only Monday through Wednesday to avoid the apparent paradox then eventually the students would be able to reasonably deduce on Tuesday evening that the examination was going to occur the following day, putting everyone back into the same paradox. No, human behavior cannot be perfectly predicted, but certain behaviors are very strongly correlated. In my doctoral studies there were times where professors never repeated their questions as, in some cases, the prior examinations were handed back to the students after grading and over the years a sizeable library of examination questions had been assembled and was passed down to subsequent classes. The examination questions in the present year often "rhymed" with the prior years, as Mark Twain had said regarding history.
@@r2db I think you may have misunderstood my position! I was just pointing out that the first component of the announcement ("There will be an exam next week") isn't contradicted by the second component ("When the exam does occur, no one will have been in a position to predict it the night before").
The fact that the teacher could fail to surprise us, most obviously by messing up and giving the exam on Friday, is irrelevant to this question of whether the announcement is inherently self-contradictory. The important thing is that the teacher could succeed in surprising us. In other words, it is in his power to make both components of the announcement come true. If you accept that, then you've accepted that the announcement is not self-contradictory.
Other things to point out: in the video I didn't suggest that the students had prior experience of this teacher giving surprise exams, so you can take it as a given that they don't. Secondly, in the video I give an analysis of why, even though a surprising Friday exam is impossible, a surprising Thursday exam is not.
This sort of makes my brain hurt. I would „surprise“ them with an exam on on Tuesday and then surprise them with another exam in Friday - Surprise!
Beautiful content, nicely presented. I must admit that halfway through your elimination of the possible attitudes, I almost expected you to start saying that you could clearly not choose the wine in front of you. 😉
What of the scenario where students study beforehand and are prepared for an exam any day of the week? Whether it is a surprise or not is no longer relevant because they were told there would be a 'surprise' exam, meaning It isn't much of a surprise regardless of when it occurs.
There is one key element that is being left out:
Mr. Harris must promise that there will be *exactly 1* exam next week.
Otherwise there could for example, be an exam on Monday and then also an exam on Friday, both of which are a surprise.
I don't think your solution fits your constraints. I think if you accept the logic that under the given conditions, the last day is impossible, then the same logic will always eliminate the last day. I think there's something wrong with shrinking the interval by cutting out the last day, but I'm not sure what it is. But once you accept that shrinking, I think the rest must follow.
I think you need to be a bit more precise about which part of the discussion starting at 5:46 I've got wrong!
I think the flaw is grounded in the elimination process. According to her the initial day to be eliminated is Friday which makes sense, however, on Wednesday evening she doesn't consider Friday as a possible day at least for a non-surprise exam. In this way she trims the week into having only 4 possible days hence making her conclusion of rulling out Thursday for a surprise exam true. Am I even making sense myself?
You don't need to worry about making sense, see below I've solved the problem and explained the solution.
Sorted
Wow nice to see more videos from you
What he should have said was 'The earliest point you can know what day the exam will be is at the end of school on Thursday.' And if he wants to be cheeky about it he can add 'I might decide on a day by the roll of a dice, or I might have already decided.'
The fault was not in her logic but in the definition of surprise and with it giving himself the limitation of having the surprise having to be be so close to the test being handed out. If his definition is true, she is correct and using the uncertainty that he might be wrong is a cop out and not a solution to the logical paradox.
Basically this solution allows him to say he will give a surprise exam tomorrow and they won't be able to know the night before. Technically he can pretend to die in front of everybody and then show up the next day with a surprise exam.
Still not a solution to the logical paradox.
The logical paradox is:
X is between 1 and 5
I will count from 1 to 5 and tell you when I have reached X.
Under no circumstance can you be sure that the next number is X.
That is either a lie or a paradox.
If his definition is true, she is correct? That can't be right. We can for example imagine him giving the exam on Tuesday and Alice not having been able to predict this on Monday evening. It's important to realize that the teacher's announcement is entirely correct and Alice is entirely wrong. For clarity, the sequence of events is this: 1) The teacher makes the announcement. 2) On Monday night Alice doesn't know whether the exam will be on Tuesday or not. 3) The teacher gives the exam on Tuesday. 4) Alice has to admit that the announcement was correct on both counts: the exam really did occur "next week", and on the evening before the exam she really had no idea that an exam was coming the following day.
The challenge is to figure out where Alice went wrong. She had convinced herself that there was no way the teacher's prediction could be fulfilled. And yet in the scenario described above, the prediction was fulfilled. So there must have been some subtle flaw in her logic - the challenge is to find it.
And he could also wait until Thursday, pretend to die and then give the test anyway. They would be surprised for sure. He could also show up at their home with the test or have the test be about cartoon animals and it would also constitute as a surprise test. You did rule out things like school burning up so I also figured you ruled out that he was using misleading and nonsensical language. His wording makes his claim loose meaning and when he is outside of the boundaries of a verbal contract, he can of course surprise them in any number of ways. "I am holding a stone." doesn't become a true statement just because I then lift up a stone.
Logically they would know on Thursday night that it can't be on Friday since that's the only day left and thus it can't be a surprise day. The same is true of every day before that. Basically it is the same as him saying "Tomorrow I will give you a surprise test. By surprise I mean that you can't know the night before if I will give you a test or not."
"This sentence is a lie."
Was I telling the truth or was I lying?
Can the students only be surprised at the time of the exam? Seems like if the test is given on Friday the surprise occurs when they get the to into Thursday and there is no exam, so the surprise is that the test is given on Friday, but it is revealed on Thursday's class? ;-)
The definition of "surprise" isn't left open-ended in the video, so there's no need to speculate about what might qualify as a surprise. 17 seconds into "Fool the Teacher: The Surprise Exam Paradox Part 1", Alice asks Mr. Harris to clarify what he means by a surprise exam. He says that he is defining a surprise exam as one where, on the evening before the exam, you'll have no way of knowing an exam is happening the next day. A surprise exam as defined in this particular way is what the paradox is about.
I am not a logician but I think the error is in allowing Alice to work backwards through time - the things you come to know on Thursday are not yet known on Wednesday, and so on. So while it is true that you cannot be surprised on Thursday evening if no exam has occurred (p=1 that it will be Friday) this is not true on Wednesday (p=.5) or Tuesday (p=.3) or Monday (p=.25) or Sunday (p=.2) - where p = probability that the exam will be tomorrow.
I'm not sure I understand your reason for saying that Alice shouldn't be allowed to work backwards through time? We don't have to wait till Thursday evening before we come to know that a Friday surprise exam is impossible. We already know, right now, that a Friday surprise exam is impossible. (You affirmed this in your comment, when you said that there's no way a person who reaches Thursday evening without an exam having taken place can be surprised.) Since Alice knows at the outset that a Friday surprise exam is impossible, she is able to challenge Mr. Harris by getting him to admit that, since he wants to surprise the class, he'll avoid giving the exam on Friday i.e. he'll give the exam between Monday and Thursday. And of course, now that the "real" last possible exam day is Thursday, this reasoning can be repeated.
@@decomplexify Not that she shouldn't be allowed - on Tuesday evening it is not true that we know it cannot be a surprise on Wednesday or Thursday, it is only AFTER it has not already happened that it is not a surprise (forwards in time)...
@@sleepingdragon You have to consider what a paradox is. In a paradox, somebody (in this case Alice) applies a chain of apparently valid reasoning which leads to a conclusion C - while at the same time, if we apply a different chain of apparently valid reasoning we get a conclusion D that directly contradicts conclusion C. Since both chains of reasoning seem equally valid, we're mystified as to why they lead to opposite conclusions. Now, in this case, you have applied a chain of reasoning to reach conclusion D ("a surprise exam is possible") while Alice has applied an entirely different chain of reasoning to reach conclusion C ("a surprise exam cannot happen on any of the five days"). To resolve the paradox, just reiterating your chain of reasoning isn't enough. You have to pinpoint the flaw in Alice's chain of reasoning.
@@decomplexify The paradox requires that something that happens on Thursday (no test) is known on Wednesday - it is true that there can be no surprise on Thursday evening but any test prior to that is a surprise (but less so each day)...
@@sleepingdragon Certainly there can be no surprise once we get to Thursday evening. But it's equally true - according to the reasoning that Alice and Mr. Harris go through - that there can be no surprise once we get to Wednesday evening. The justification for this is as follows. Since both Alice and Mr. Harris agree that a Friday surprise exam is impossible, Alice is able to challenge Mr. Harris by getting him to admit that, since he intends to surprise the class, he won't give the exam on Friday i.e. he'll give the exam between Monday and Thursday. Now that this has been admitted, we can conclude that any student who gets to Wednesday evening without an exam will know that the exam is going to take place on Thursday - and therefore cannot be surprised by a Thursday exam.
Every time a military surprise attack succeeds, this is what happened
You could do some tasks on thursday and reveal on friday, that these tasks from thursday will be count as an exam…. Surprise… you already did it 😂
I think the problem is the term "next week". Once the teacher defines that the surprising exam is in the "next week", it is not a surprise anymore. Limiting the time period to "next week" eliminates the possibility to have continuous surprises after the last day (Friday) of "next week". Defining "next week" has the same effect as defining "next day". If the teacher says he gives a surprising exam "next day", it is not a surprising exam anymore for a time unit of a "day" unless we further keep that surprise in hours, minutes or even seconds.
You say 'Once the teacher defines that the surprising exam is in the "next week", it is not a surprise anymore.' Consider however that 17 seconds into "Fool the Teacher: The Surprise Exam Paradox Part 1", Alice asks Mr. Harris to clarify what he means by a surprise exam. He says that he is defining a surprise exam as one where, on the evening before the exam, you'll have no way of knowing an exam is happening the next day. A surprise exam as defined in this particular way is what the paradox is about.
@@decomplexify I have a second thought: Surprise depends largely on the level of uncertainty. When Alice moves the bar all the way between Thursday and Friday on Thursday evening as depicted: M, T, W, T || F, Friday is isolated to or narrowed down to its own day and hence decreases its uncertainty as there is no other choice to pick. At that time, Friday is impossible to have surprising exam. However, when Alice moves the bar backward between Wednesday and Thursday on Wednesday as depicted: M, T, W || T, F, the day set on the right of bar has more elements now. Because the set increases elements, it increases uncertainty. It's like the fact that, there is no uncertainty if we can only have one choice, but when we have more elements, the uncertainty increases and we call it "Chance" or "Probability". Friday's certainty relies on its environment or neighborhood or neighbors in its set. If it is a single, it's 100% certain. That's actually what Alice's logic relies on to reach the conclusion that Friday could be excluded from surprising exam in her first round. However, the certainty of Friday not having exam could change when the set includes Thursday on the right of bar. Now we have 50/50 chance for surprising exam to happen on Thursday and Friday. In another word, at that moment, Friday is not a certain element anymore. It has been but it is not now. Just like a healthy cell could turn into a cancer cell. The cell is not an alien cell in our body and it's structure could be same as well, but its remark or behavior could change. I think I wrote too much...
@@ABackZhu Remember, Mr. Harris says that he is defining a surprise exam as one where, on the evening before the exam, you'll have no way of knowing an exam is happening the next day. On this basis, the chance that a Friday surprise exam will occur is 0%. It doesn't matter where the "bar" is: the chance of a Friday surprise exam is 0% regardless of where the bar is. If it's Sunday evening right now, so that the entire week is ahead of us, I can be confident that there's no way a Friday surprise exam can take place. And this is because the notion of a "Friday surprise exam" is simply contradictory.
@@decomplexify I don't think you got what I meant. The domino effect of getting no surprising exam on Thursday is based on the assumption of certainty of having no surprising exam on Friday. If that assumption is not true anymore after the right set has more elements, the whole logic of determining Thursday, Wednesday and so on loses the basis of assumption. Alice neglects the changing status of the "Friday".
@@ABackZhu I understand what you're saying, but what you're saying is not right. Let's back up to what you said in an earlier comment: "When Alice moves the bar all the way between Thursday and Friday... at that time, Friday is impossible to have surprising exam."
All right. Let P = the following statement: "If we get to Thursday evening without an exam having taken place yet, at that point I'll be able to conclude that a Friday surprise exam is impossible."
I think P is true. And the fact that you've said "When Alice moves the bar all the way between Thursday and Friday... at that time, Friday is impossible to have surprising exam" means that you agree with me about P; you also believe that P is true.
Now let's suppose we get to Wednesday evening without an exam having taken place yet. Let's suppose that at that point (Wednesday evening), you say to yourself: "I guess a surprise exam could take place on Friday." This is the same as saying "I guess it's possible that the exam could take place on Friday without me having anticipated it on Thursday evening." And by saying this, you deny that P is true.
Therefore it isn't valid for you to say (on Wednesday evening) that a Friday surprise exam might happen - as saying this means saying that P is false, whereas actually you know that P is true.
In short: a Friday surprise exam really is impossible! It's just as impossible from the perspective of Wednesday evening as it is from the perspective of Thursday evening.
The way to understand the problem is to realize TIME is involved and the information you have as you progress thru the week changes.
So the teacher makes the announcement before the week begins. You cannot use this BACKWARDS REASONING before week begins because you don't yet know the exam has not taken place on Monday or Tuesday etc. That BACKWARDS REASONING would involve using information you don't have!!
On Tuesday evening you know exam didn't happen Monday so if it takes place on Wednesday it would be a surprise.
Clearly on Thursday evening you know it must take place Friday because you NOW KNOW it's not yet taken place so it's not going to be a surprise.
There is no paradox YOU CANNOT USE THIS BACKWARDS REASONING BECAUSE YOU WILL BE USING INFORMATION YOU DON'T HAVE.
You cannot (on Sunday or on Monday or on Tuesday etc) reason it will not happen Friday because you don't yet know if it happened on those Monday or Tuesday etc.
So in summery teacher makes announcement on Sunday and you start using this reasoning to work out cannot be Friday YOU CANNOT because you are using information you don't have!!!!!!!!!!
The exam could be the following day Monday. You cannot use this backwards reasoning because it involves declaring exam didn't happen Monday BUT YOU DON'T YET KNOW WHETHER IT HAPPENED MONDAY.
So you cannot use this backwards reasoning because it ALWAYS involves you using information that YOU DON'T HAVE!!!!!!!!!!!!!!!!
SORTED!
Another way to think about it is this. The rules of this Surprise Exam must be made very clear on the Sunday.
If it's the usual Monday to Friday and will not know evening before then that is NOT POSSIBLE!!!!!! as student points out!!!!!
You can still have a surprise exam tho rules would have to be different because if it doesn't happen by Thursday you know it's going to be Friday. That's how it happens in real life if you like.
The original surprise exam is NOT POSSIBLE!!!!! and I think everyone was assuming it was, there is no paradox.
If you decouple the surprise happening from the unveiling then you resolve the paradox. If the exam happens Monday, Tuesday, Wednesday or Thursday, the teacher can say: surprise the exam is now. If the exam is Friday, the teacher can say on Thursday: surprise the exam is tomorrow. I feel like it qualifies as a surprise exam.
The paradox is about a very specific, precisely-defined form of "surprise". 17 seconds into "Fool the Teacher: The Surprise Exam Paradox Part 1", Alice asks Mr. Harris to clarify what he means by a surprise exam. He says that he is defining a surprise exam as one where, on the evening before the exam, you'll have no way of knowing an exam is happening the next day. A surprise exam as defined in this particular way is what the paradox is about.
Lets break it down: The teacher makes claim E: "There will be an exam next week". and also claim S: "There is a 100% chance the day of the exam will not be known to you until the day I give the exam."
Lets break it down further: The teacher claims: ((EMon or ETue or EWed or EThu or EFri) and S). Combining this with the assumptions about how the passage of time works and so forth, Alice concludes (not EFri) then concludes (not EThu) etc. until she concludes (not EMon) and hence: (Not E). This makes the original claims self contradictory (much like the statement "This statement is a lie".) It just takes longer to get to the contradiction. When our premises lead to a conclusion that is a contradiction, we don't just assume the conclusion is true, we assume one or more of the premises are wrong.
So either E is false or S is false or both are false. If E is false, S is not even a statement that has a truth value. If S is false then E can be true without contradiction. However (not S) is the statement: "There is NOT a 100% chance the day of the exam will not be known to you until the day I give the exam." In fact, if the exam is Friday it will not be a surprise. If it is any other day, it will be a surprise. That's how the students were surprised on Wednesday.
--------------------
A totally different way of looking at it: What is a surprise? A surprise is when something happens (exam happening on a particular day) when you were reasonably confident it would not happen or had no knowledge of whether it would happen. Alice was 100% sure the exam would not be on Friday (or any other day). She should have then concluded that she would be surprised if the exam actually did occur on ANY of those days.
Hi John, this is a thoughtful argument and you've clearly spent some time thinking the problem through. However, there is a subtle but important flaw in your logic. To pinpoint the flaw, it's helpful to look at an exactly equivalent scenario to the surprise exam scenario. Here is how the philosopher Saul Kripke sets out the scenario:
"Consider the case where all fifty-two cards, or at least a large number, are in the deck. Imagine that the experimenter, without telling the subject where it is, assures the subject that he has put the ace [of spades] somewhere in the deck, and that the subject will not know in advance when the ace will come up if the cards are turned up one by one. Can the experimenter guarantee this? It seems clear that he can, say, by putting the ace somewhere in the middle." Kripke goes on to clarify that he means the experimenter has put the ace of spades somewhere in the middle of the deck in advance, before the subject arrived on the scene.
So let's imagine that the experimenter shuts his eyes and sticks the card somewhere vaguely in the middle of the deck, and when the subject arrives and the cards are turned over one by one, it turns out that the 34th card turned over is the ace of spades. Just before the ace of spades was turned over, the subject had no idea that the ace of spades was about to appear.
Now consider the claim S, which is "There is a 100% chance that just before the ace of spades is turned over, you will not know the ace of spades is about to be turned over." S is absolutely true! There was always a 0% chance that the 52nd card would be the ace of spades; the experimenter ensured that there would be a 0% chance of this when, prior to the subject's arrival on the scene, the experimenter stuck the ace of spades somewhere vaguely in the middle of the deck (rather than right at the end).
And so the paradox cannot be resolved by insisting that S is false. S is not false. The paradox has to be resolved in some other way. Resolving it requires close attention to the state of Alice's knowledge - not only what the state of her knowledge is at the outset, but also what the state of her knowledge would be on successive days of the week assuming an exam had not yet taken place.
There is no point in trying to use Propositional Logic and Truth Tables because it's not that type of problem. It involves TIME and changing states of knowledge/information. You are not just dealing with propositions.
Anyway I've solved it, see my post at the top.
well ya , a Thursday exam would be a surprise , as on Wednsday evening there are still two days left
when you say that it's impossible for a surprise exam to be on Friday that's simply not true
as it's only impossible if we are on Thursday evening not on Wednesday evening.
As such a Thursday exam would be a surprise,
similarly it follows that an exam on any of the days would also be a surprise.
from what I understood, the flow is in saying it's "IMPOSSIBLE" for the exam to be on Friday, the fact is it's not "impossible"
unless you are on Tuesday evening (that is assuming an exam must take place of course).
It's a bit more complicated than that.
Let P = the following statement: "If we get to Thursday evening without an exam having taken place yet, at that point I'll be able to conclude that a Friday surprise exam is impossible."
From what you've said above, you believe that P is true.
Now let's suppose we get to Wednesday evening without an exam having taken place yet. Let's suppose that at that point (Wednesday evening), you say to yourself: "I guess a surprise exam could take place on Friday." This is the same as saying "I guess it's possible that the exam could take place on Friday without me having anticipated it on Thursday evening." And by saying this, you deny that P is true.
Therefore it isn't valid for you to say (on Wednesday evening) that a Friday surprise exam might happen - as saying this means saying that P is false, whereas actually you know that P is true.
In short: a Friday surprise exam really is impossible! It's just as impossible from the perspective of Wednesday evening as it is from the perspective of Thursday evening.
@@decomplexify Hmmm interesting, Using the same logic why isn't a Tuesday exam impossible then?
@@oximas-oe9vf Ruling out a surprise exam on Wednesday, Tuesday, or Monday would require us first to make the transition from ruling out a Friday surprise exam (which we've done) to ruling out a Thursday surprise exam. The question is whether there's a legitimate way of making this transition.
You know, at all times, that a Friday surprise exam is impossible. You also know, at all times, that the teacher is sincere in his intention to make the exam a surprise.
None of this means that an EXAM on Friday is impossible. It does mean that, if an exam somehow DOES take place on Friday, the teacher will have have failed in his intention to make the exam a surprise.
It's interesting to contemplate what a person's thinking would be on Wednesday evening. On Wednesday evening, you still know all of the above - but does knowing all of the above mean you know what the teacher is going to do? What exactly can you be sure of, and what exactly can't you be sure of, on Wednesday evening? This is a question that the video spends some time exploring.
It's tempting to say that on Wednesday evening you'll remain sure that the teacher won't give the exam on Friday and that therefore you'll know the exam is going to be on Thursday. But the video gives an account of why, in fact, you can have no such certainty on Wednesday evening.
Ok, Monday it is.
I thinking switching out surprise with probability makes it a bit easier to understand.
So if he means that there is a probability of 1 that there will be an exam next week. And There probability < 1 that you will know your exam will be the next day. (Aka surprise exam).
Then his statement becomes false on Thursday. And her reasoning is false because you only know with 100% probability on Thursday night.
I don’t like this paradox because it breaks the rule of what he said that the it would for sure be a surprise any day next week when it’s only a surprise(probability less than 1) for 4 of the days.
His statement should be
“There will be test next week, and it can happen on any day so make sure you study” haha
Hi Austin, thanks for your comment. In "Fool the Teacher: The Surprise Exam Paradox, Part 1", the phrasing was as follows: "A teacher, Mr. Harris, announces to his class that there's going to be a surprise exam next week."
You say: "I don't like this paradox because it breaks the rule of what he said that it would for sure be a surprise any day next week when it's only a surprise (probability less than 1) for 4 of the days."
In the teacher's phrasing above, he never said that the exam "would for sure be a surprise any day next week". He never explicitly said, for example: "Even if the exam takes place on Friday, it will be a surprise." He simply said that the exam would take place next week, and that it would be a surprise.
@@decomplexify I'm pretty sure he clarified that surprise means "you won't know it the evening before" wen asked about it...
@@HenryLoenwind He did, yes. He said that the exam would take place next week, and that on the evening before the exam, you would have no way of knowing an exam is coming the next day. He did not, however, say: "If the exam occurs on Friday then you won't know on Thursday evening that an exam is coming on Friday." A Friday exam wouldn't be a surprise! Because the teacher wants his prediction to come true, he will simply avoid scheduling the exam for Friday.
So the error is in the first few seconds of video, the student immediate reply to teacher. Think about it - when she says what she does SHE CANNOT BECAUSE SHE IS USING INFORMATION SHE DOESN'T YET HAVE!!!!!!!!
If on Sunday student says "it cannot take place Friday" you ask WHY?
Student says "if it didn't take place Monday etc etc etc etc"
IF IF IF IF (IT'S STILL ONLY SUNDAY)!!!!!!
Cannot use reasoning like that.
You cannot use this BACKWARDS REASONING to say it cannot be Friday because it ALWAYS INVOLVES USING INFORMATION THAT YOU DON'T HAVE!!!!!!!!!!!!
So Monday to Friday and will not know evening before. If those are the clear Sunday rules then the student can deduce on the Sunday that as a list of rules it's NOT POSSIBLE!!!!!! because of the Friday problem.
Student can appreciate on the Sunday that there is a problem with Fridays which will break the rules, no need to worry about the other days. No backward reasoning needed.
So to keep it simple. On Sunday you cannot reason that it cannot be Friday. That's because to do so involved information that it didn't happen on Monday Tuesday Wednesday Thursday.
BUT IT'S STILL ONLY SUNDAY!!!!!!
You don't yet know if it happened those days!!!!!!
You are using information you don't yet have. YOU CANNOT DO THAT!!!!!!
YOU CAN NEVER USE THIS BACKWARDS REASONING BECAUSE IT ALWAYS INVOLVES USING INFORMATION THAT YOU DON'T HAVE!!!!!!!!
I remain completely unconvinced by this example - based on thinking backwards through a logic puzzle. The Puzzle revolves around intent and around the concept of being surprised or not - and deducing backwards from potential future states. maybe the paradox would work better with a better example. because for me, the scenario about a surprise exam isn't about the surprise it's about the exam. and the only night of the week that matters is Sunday Night, when you don't know if monday will have an exam or not. and the question really is should you study on sunday night?
and so the question isn't "Do I know if there's a test tomorrow" but did I adequately prepare for a test that I didn't know the day off so i'm not caught off-guard and fail. and yeah, the answer is you should study on Sunday. and the only way for an exam to be a surprise is if you didn't study, especially when you got advanced warning.
or in other words, I refuse the premise and substitute it for my own.
but for the purposes of finagling the entanglement of surprise, I'm positive that the student is correct, a surprise test is impossible if you think about it recursively - and it's the teacher fault for two things: 1. Claiming a test was definitely going to happen in next 5 days and 2. defining surprised, as a state of mind a student could be in the night before. Making the problem deducable so that surprise is impossible and therefore an exam can't happen. it's one of these problems where concepts of logic and language clash with each other where we focus on the properties of surprise in relation to a test, and the end-results seems dumb and counter-intuitive to people hearing it because we all understand that a surprise exam is a concept in and of it self. and surprise isn't a transitive property of an exam that either exists or not. the paradox is weird because we all understand an exam is possible on friday even if by then its no longer a surprise (again I hope by then you've studied) but in the context of perfect logisticians and logic problems if you can't have an exam be a surprise you can't have a surprise exam, and because the teacher said he would give a surprise exam and not an exam. a surprise exam is impossible to give. Allowing the option for the teacher to fail isn't a logic condition with regards to surprise or exam, and as such the student is right. no surprise exam can be given, and hence the paradox.
I'd rather just lie and make them study till Friday. will falsely announce one more week and then one week on Friday take an exam without announcing about it.
Alice reasoning is good, and there is no resolution to the paradox anymore then there is a resolution to the paradox "this sentence is a lie". The constraints of the problem are self contradictory, and the only way to fix it is to change Mr Harris' statement thereby completely changing the problem (e.g. "suprise exam next week, unless it's on a Friday in which case it clearly won't be a surprise anymore by the time school ends on Thursday").
I have to disagree with you there. Alice's reasoning leads her to the conclusion that Mr. Harris cannot give a surprise exam at all. We know that her conclusion is wrong. The reason we know that her conclusion is wrong is that we can imagine an exam taking place on Tuesday and Alice being surprised by it (she has no way of predicting it on Monday evening).
Because her conclusion is wrong, something in her reasoning has to be wrong.
As a side note, I would point out that there's nothing contradictory in Mr. Harris saying that there's going to be a surprise exam next week. "This sentence is a lie" can't be assigned a truth value. In contrast, depending on what Mr. Harris does, the exam will either turn out to be a surprise or it won't. His statement will turn out to be true or it won't. There is no indeterminacy to it. If he's rational, he'll give a non-Friday exam (for example, Tuesday) - making it true that the exam is a surprise.
I belive I actually solved it and it's pretty simple