I think “pop quiz” implies that the time of its administration cannot be known to the takers. If the time is known then it ceases to be “pop” and is just a regular quiz.
I don’t know how this logic doesn’t follow.
Assumptions:
there will be a pop quiz next week
the teacher does not tell the students which day it will be on, but will simply “surprise” them with it
initialy there are only 5 options for which days it can be given (Monday through Friday)
if the day becomes known prior to the quiz it ceases to be a “surprise”
Implications:
1a) If the test is not given by Thursday it will not be a surprise because Friday is the only other option
1b) thus Friday is no longer an option for a surprise
1c) now there are only 4 days in which the test can be a surprise
…
2c) now only 3 days
…
3c) now 2
… etc.
For each iteration, apply this logic to the final day in the set of days in which a surprise can occur. The set will converge to zero.
Granted on the previous Friday the students will not know what day next week the quiz will be on. They only know that there will be one.
The moral here is i think that if you tell student that there will be a quiz next week, the day of the week mathematically cannot be a surprise.
The reason you can’t take this logic passed the first iteration (where we scratch Friday off the list as a possible day for a surprise quiz) is because any further iterations require additional assumptions - namely, that the teacher knows that the students are expecting the test on Thurseday at the latest. But all that was explicitely layd out in the problem description was that the teacher announced that any time this week there will be a surprise quiz. That could include Friday. We have no right to assume that any of the students know it won’t be Friday, nor do we have the right to assume the teacher expects the students to know this.
The critical point here is not only what day the quiz will be on, but that IT WILL BE A SURPRISE.
A Friday quiz logically cannot be a surprise because the students will know its on Friday. the knowledge of the quiz’s administration day is logically NOT a “pop” quiz.
The only thing that’s a “surprise” is something completely unexpected. Therefore, to give a pop quiz, a teacher must necessarily not forewarn the students about it. If that occurs, then the “pop”-part of the quiz is ambiguous. It’s not a “pop”-quiz, to me, unless I hear the teacher say, “Guess what you lazy fuck heads? We’re going to have a quiz worth 10% of your term points right now and you won’t pass this quiz unless you are completely up-to-date with the class materials.” The teacher / professor then lets out a maniacal laugh that sounds of a demonic nature. Then, and only then, would I agree and say, “Yes, in fact this is a pop quiz (and I’m fucked)!”
So, this is not a paradox. The only “paradox” here is the clueless context to which you cannot differentiate a normal quiz from a “pop”-quiz, and that is rather inept comparison to make.
Now, by assuming when the previously announced “pop quiz” is going to take place, the probability remains between how intelligent the student can predict the date in agreement with the teacher following through with the verbal commitment and actively giving out the so-called “pop quiz”. This is not a “pop quiz” in the sense that the teacher is a moron. A “pop quiz”, like I’ve already stated, is a complete surprise (except to the teacher who has made plans around it).
Perhaps this is a good example of Heidegger’s thesis that reason is the stiff-necked adversary of thought. You say:
“1. It needs to be given by thursday because then you’d know it would be on Friday. (so Friday is out because its later than Thursday)”
It is you who counts Friday out. The original promise, that the quiz will be given on a day between Sunday and Saturday, still stands.
When the quiz hasn’t been given as late as Thursday afternoon (after school has ended), according to your reasoning it cannot be given anymore, as you’ve counted Friday out. So you’re convinced it will never be given. What surprise when it’s given on Friday after all, then!
Apart from what I just said (which I came up with quite some time ago), there is another even more blatant flaw in your reasoning.
Time is not in itself divided into segments. If the quiz hasn’t been given as late as Thursday afternoon, after school, then it has to be given on Friday, unless the teacher breaks his promise. Very well. Now you can divide Friday’s school day into segments. Say the quiz cannot take less than ten minutes (you will have to assume this). Then it cannot be given in the last ten minutes. And it cannot be given in the before-last ten minutes, for the same reason it could not be given on Thursday. But what if the teacher let’s this quiz pop up at fifteen minutes before time?
You will see that, no matter how small the segments are into which you divide the school day, the teacher can always start the quiz somewhere in the middle of such a segment.
Logic divides all things into segments – therein consists its falsification.
That’s where you’re mistaken. Unless he specifically said the entire quiz would be given on one day, it might start somewhere on Monday and be continued and finished on Thursday, for instance.
It is true – and this renders my before-last post moot – that if the only element of surprise consists in on what day it will be given (and therefore will be given in its entirety on one day), it will be no surprise anymore if it hasn’t been given by Thursday afternoon. However, as I said, by your very counting Friday out it could still be a surprise on Friday.
No, Friday is counted out BECAUSE it can’t be a surprise on that day. If you don’t get the quiz on Thursday then you know it will be on Friday. Ergo, not a surprise on Friday.
Sure you might not know what day the quiz will be on when the teacher tells you the week prior. But during quiz week, if the teacher is planning secretly to give it on Friday, when Thursday comes and the quiz hasn’t been given on Thursday, then you’ll know it has to be Friday negating the “surprise/pop” aspect.
But wait. You mean you still expect a quiz on Friday, even though it won’t be a surprise? But the teacher said he was going to give a pop quiz (i.e., a surprise quiz). So if you’ve stripped it of its pop aspect, the whole premise “teacher is going to give a pop quiz this week” is annulled. So you have to rule out the pop quiz, and cannot expect a non-pop quiz to be given (as nothing was said about any non-pop quiz). So you don’t expect a quiz on Friday, which will make any quiz given on that day a surprise for you.
The probability of something not happening reduces to zero given a certain time frame,
or
The probability of something happening increases to 100% given a certain time frame.
If it not given by the end of Thursday… it was still a surprise but… the probability of it happening on Friday is 100%.
Once this probability of 100% then the quiz has ceased to become a surprise.
By your logic, the Pop Quiz cannot exist… ever… Even if the Pop Quiz is announced one second before you take the Pop Quiz.
In this second it ceases to be a surprise and is 100% reality.
The key issue here is time… the fact that one second or one day passes is irrelevant to the surprise nature of the quiz.
Anticipation… is a prediction
Surprise… by definition occupies a single instant in time (less than one billionth of a second).
Shock… on the other hand is reactionary and lasts longer.
If the Pop Quiz is on Friday… then surprise came into and out of existence in less than a billionth of second, as you anticipated wrongly.
Shock then sets in as you probably failed.
