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The Coffee Shop

  • Thread starter The Fallen Angel
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You originally stated that the test might occur on any of the five days next week at random, as has been discussed, but you were bounced by Connie into changing your terms of reference and you agreed that it must be a surprise. You have limited yourself to five days and the students have inferred that a ‘surprise’ test cannot occur on Friday. They proceed to infer that you really limit yourself to four days by changing your ToRs in this way. They conclude that a ‘surprise’ test cannot occur on Thursday, either, and that you have ever decreasing opportunities to launch a ‘true’ surprise in the manner described.

And yet….you surprised them!

You surprised them because the students erroneously converted their risk into your opportunity. Each day that they fail to swot up they take an increasing risk of getting caught out. You can merrily agree with Connie that even though it is a surprise test, if she hasn’t swotted up by Thursday evening she will definitely be caught out, and she will only have herself to blame when you take her out into the yard and give her a damn good thrashing for failing the test. The students all know that anyway, so do you. But you retain the element of uncertainty that you might choose Friday, and so their logic collapses.
 
Wragg134 said:
You originally stated that the test might occur on any of the five days next week at random, as has been discussed, but you were bounced by Connie into changing your terms of reference and you agreed that it must be a surprise. You have limited yourself to five days and the students have inferred that a ‘surprise’ test cannot occur on Friday. They proceed to infer that you really limit yourself to four days by changing your ToRs in this way. They conclude that a ‘surprise’ test cannot occur on Thursday, either, and that you have ever decreasing opportunities to launch a ‘true’ surprise in the manner described.

And yet….you surprised them!

You surprised them because the students erroneously converted their risk into your opportunity. Each day that they fail to swot up they take an increasing risk of getting caught out. You can merrily agree with Connie that even though it is a surprise test, if she hasn’t swotted up by Thursday evening she will definitely be caught out, and she will only have herself to blame when you take her out into the yard and give her a damn good thrashing for failing the test. The students all know that anyway, so do you. But you retain the element of uncertainty that you might choose Friday, and so their logic collapses.
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You score several points in your argument which have been noted. What exactly is a surprise test?
 
melissa said:
You score several points in your argument which have been noted. What exactly is a surprise test?
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The true definition of a surprise is an event of which one has no prior warning. You've already told them that the test is next week so the test is not a true surprise. Holding the test on Friday does not give them any more warning than they already have; does not make it more or less of a surprise than it already is.
 
The meaning of a word is its use, and in ordinary language 'surprise' is (like most things) relative, not absolute.
Supposing Melissa announced on the first day of term that she would set the test one morning during the term,
but she will not say when or give any further reminders. If she actually sets the test the following day,
when there are still around 50 more maths lessons still to come, would it not be (relatively) surprising?

This reminds me of a story some years ago when a philosopher (Cambridge, needless to say) saw on his bar of chocolate that if he was not absolutely satisfied, he could ask for his money back. He requested a refund on the grounds that, while he was quite, even very, satisfied with the chocolate, he was not absolutely satisfied. The judge ruled against him as he failed to identify in what way it was less than satisfactory. :D
 
Eulalia said:
The meaning of a word is its use, and in ordinary language 'surprise' is (like most things) relative, not absolute.
Supposing Melissa announced on the first day of term that she would set the test one morning during the term,
but she will not say when or give any further reminders. If she actually sets the test the following day,
when there are still around 50 more maths lessons still to come, would it not be (relatively) surprising?

This reminds me of a story some years ago when a philosopher (Cambridge, needless to say) saw on his bar of chocolate that if he was not absolutely satisfied, he could ask for his money back. He requested a refund on the grounds that, while he was quite, even very, satisfied with the chocolate, he was not absolutely satisfied. The judge ruled against him as he failed to identify in what way it was less than satisfactory. :D
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Excellent, good story! :D

To drive home the point from the exercise, the suggestion that the test can't be a surprise if it occurs on Friday is invalid because holding the test on Friday gives the students no more prior warning than they already have.
 
Wragg134 said:
The true definition of a surprise is an event of which one has no prior warning. You've already told them that the test is next week so the test is not a true surprise. Holding the test on Friday does not give them any more warning than they already have; does not make it more or less of a surprise than it already is.
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But...Tree argued that if they had not had the test by Thurs then I must have chosen Friday. Since that would be clear to all by the end of the lesson on Thurs then it would come as no surprise to have it on Friday which would go against what I agreed with Connie and hence they can deduce that I would never have chosen Friday. The class are all capable of logical deduction and by similar logic they rule out all the other days!!
 
melissa said:
But...Tree argued that if they had not had the test by Thurs then I must have chosen Friday. Since that would be clear to all by the end of the lesson on Thurs then it would come as no surprise to have it on Friday which would go against what I agreed with Connie and hence they can deduce that I would never have chosen Friday. The class are all capable of logical deduction and by similar logic they rule out all the other days!!
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If we define the test as needing to be on a day when the students do not get up in the morning knowing, with absolute certainty, that they have a test, we need to discuss the meaning of the word ‘certainty’ within the terms of this exercise.

Tree made a statement of certainty about the ‘Fridayness’ of the test. “It cannot be Friday….because if it is we would know by Thursday afternoon.”

Therefore the ‘Fridayness’ of the test becomes certain only on Thursday afternoon. Does Tree, by the assertion, achieve absolute certainty that the test will not occur on Friday? In fact he does not, because although you look worried, you do not absolutely agree with him that the test cannot be on Friday. (If you had done that, you would have resolved the status of Friday before the week begins!)

If Wednesday afternoon comes, and the test still hasn’t happened, could the students get up on Thursday morning and be absolutely certain that the test will happen that morning? No, they can’t, because the certainty of the Friday test is still, at that point, dependent upon whether or not it occurs on Thursday. Because you have retained the right to say ‘never mind that they’ll get 24 hours notice, I’m still keeping the option of a test on Friday’, certainty about Friday remains unresolved until that moment on Thursday when you can no longer have a test that day.

It’s like Schrodinger’s cat, which exists inside a closed, opaque, soundproof box in a state of ‘alive deadness’ until either we open the box and discover whether it is dead or alive, or until a defined moment in time arrives when it cannot be alive any longer. The algebra test box opens only when:

· The test occurs, or

· Thursday afternoon comes and the test has not occurred.

On Wednesday afternoon it may be that neither of those conditions have been met. The box remains closed.
 
You have really entered into the spirit of this even introducing some Philosophy. I did say there was no clear cut solution. When I post my attempt I'll attach one of many papers which have been published on the subject.
TARGET You are on 32 and Eulalia 33
 
Could you please clarify one point in your argument. Assuming that it is now Thursday evening and they have not had a test. When it comes to Friday morning would your students
A. Expect a test because it is the only day left.
B.Not expect a test because it would no longer be a surprise test which would presumably contradict the initial condition.
 
"It’s like Schrodinger’s cat, which exists inside a closed, opaque, soundproof box in a state of ‘alive deadness’ until either we open the box and discover whether it is dead or alive, or until a defined moment in time arrives when it cannot be alive any longer."


I know ... it's off topic but it kinda isn't. ;)
 
LittleSiss said:
"It’s like Schrodinger’s cat, which exists inside a closed, opaque, soundproof box in a state of ‘alive deadness’ until either we open the box and discover whether it is dead or alive, or until a defined moment in time arrives when it cannot be alive any longer."


I know ... it's off topic but it kinda isn't. ;)
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Pp is a rabid BBT fan. This is one of his favouites. He hasn't checked the episode but wasn't there a comment from Penny about not having "to open the box to know there was all kinds of dead in there" or words to that effect?
 
melissa said:
Could you please clarify one point in your argument. Assuming that it is now Thursday evening and they have not had a test. When it comes to Friday morning would your students
A. Expect a test because it is the only day left.
B.Not expect a test because it would no longer be a surprise test which would presumably contradict the initial condition.
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A. You said the test would occur next week.

BTW you were right -it does your head in :rolleyes:
 
Tree has only commented that he wants to be served coffee, he was going to fry Connie in an electric chair, and ask if we should crucify all the ladies...

Where did anyone see me have deep thoughts on this riddle???:confused:

Tree
 
melissa said:
If they expect the test then why did they believe Tree when he said it could not occur on the Friday?
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Well, you've just shown that, in fact, even when Friday comes, there is still doubt about the test, maybe Tree was right, maybe he was wrong, so Tree, thinking he created certainty about Friday, in fact did the exact opposite, and facilitated Friday as a possibility for a surprise test..

Anyone know where I can get something for a headache? Mind you, Melissa did warn me.....
 
Wragg134 said:
Well, you've just shown that, in fact, even when Friday comes, there is still doubt about the test, maybe Tree was right, maybe he was wrong, so Tree, thinking he created certainty about Friday, in fact did the exact opposite, and facilitated Friday as a possibility for a surprise test..

Anyone know where I can get something for a headache? Mind you, Melissa did warn me.....
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..which post did I say that? I'm trying to write a story here!!!
 
thehangingtree said:
..which post did I say that? I'm trying to write a story here!!!
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In between bouts of algebra, you mean? :rolleyes:

I can imagine you as a great mathematician, Tree....you can compute the correct length of a nail or rope to the nearest millimetre!!:D
 
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