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#76 2013-05-04 02:22:58

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Re: The Professor and the Student

Couldn't it be friday too? Because the students know that the test is not going to happen on any day at all


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#77 2013-05-04 02:52:43

alta ego
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Registered: 2012-03-30
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Re: The Professor and the Student

Nice one!

smile

Alta

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#78 2013-05-04 04:11:00

Agnishom
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Re: The Professor and the Student

Ai do not mean to be rude, but I doubt your identity…

Last edited by Agnishom (2013-05-04 04:13:56)


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#79 2013-05-04 05:51:35

alta ego
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Registered: 2012-03-30
Posts: 9

Re: The Professor and the Student

Agnishom wrote:

Ai do not mean to be rude, but I doubt your identity…

What do you mean?  I am who I am.  I recommend you re-read posts 57 and 66.

Alta

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#80 2013-05-04 13:05:29

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,811

Re: The Professor and the Student

Hi Agnishom,

Couldn't it be friday too? Because the students know that the test is not going to happen on any day at all

From post #10:

If the students haven't had their test by the end of Thursday's class they'd know in advance that the test is on Friday (the last day of that week)...hence Friday's elimination in that case.

All days are initially in contention and Friday is eliminated only after Thursday has ended. You can't subsequently apply that position retrospectively to any other days, but that is exactly what the student did.

Imagine, in a real-life scenario, being one of the students, and on one particular day prior to Friday (it doesn't matter which of the four days it is) the professor walks into the room and says, "OK...today is the day I'm giving you the test". Would the students have known in advance which day that was going to be? Obviously not, which is what MIF said re Wednesday in post #3 and Bob has shown in subsequent posts.

Therefore the student's reasoning must be flawed...and if not, I'll be floored! faint

Last edited by phrontister (2013-05-04 21:17:59)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#81 2013-05-04 15:01:26

Agnishom
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Re: The Professor and the Student

Alta Ego,

I am sorry, I thought you're bob


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#82 2013-12-15 14:02:00

nightstrider
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Registered: 2013-12-15
Posts: 3

Re: The Professor and the Student

I've known of this puzzle from elsewhere. The mathematical resolution is that the axiom or setup is paradoxical or contradictory. Assume the axiom is "The test is one day next week, but you won't know in advance which day." The logic of the student is perfectly valid based on the axiom and yet contradicts the axiom. Another paradoxical or contradictory axiom is for example: "The test is one day next week and the test is not next week." or "This statement is false." or "I was lying to you when I said I was lying to you." etc...

As Asimov said: "As far as I am concerned, if, when everything impossible has been eliminated and what remains is supernatural, then someone is lying.” The professor is lying.

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#83 2013-12-15 23:45:09

phrontister
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From: The Land of Tomorrow
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Re: The Professor and the Student

Hi nightstrider,

The professor is lying.

Assuming a standard M-F school week, the only case in which the professor would be lying is if the test isn't set prior to the end of Thursday's class, by which the students would know the day of the test (Friday) in advance. This contradicts the axiom "but you won't know in advance which day”, and immediately rules out Friday as the test day.

However, the previous four days remain as valid options that don't contradict the axiom - as has been reasoned in several posts above and Bob confirmed with his excellent practical demonstration - and when the professor chooses one of these it will be to the great surprise and embarrassment (and probably consternation) of the student, who isn't expecting a test that week and won't have swotted up for it.

Hopefully the other students are with the professor in this, rather than supporting the flawed logic of their peer and ending up with red faces too! smile

Last edited by phrontister (2013-12-16 11:50:17)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#84 2013-12-16 17:21:07

gurthbruins
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Registered: 2010-05-09
Posts: 157

Re: The Professor and the Student

It is true that the professor must be lying.

Everybody has missed the point here. Which they would see if they set up the experiment so that lying was impossible.

The point being that as we cannot know that the professor is not lying, we cannot deduce anything at all.

We cannot know at the end of Thursday that the test will be on Friday, as there may not be a test at all.

And even if we know, somehow, that the professor is not lying, then we still cannot, under any circumstances, deduce that the test will be the next day. A thousand unforeseen events might prevent that.


It's the activity of the intelligence above all that gives charm to existence.

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#85 2013-12-16 20:47:40

alta ego
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Registered: 2012-03-30
Posts: 9

Re: The Professor and the Student

I thought this was totally sorted by Bob Bundy.  Maybe he wasn’t clear enough so I’ll have a go for him.

Let’s call the test availability period,  TAP, measured in days. 

The professor has declared:  Statement   = “…but you won't know in advance which”

So on Sunday evening,

 

As we reach the evening of each day without a test,  TAP reduces by 1 and if we count back one day TAP increases by 1.

Deduction one:  So by Thursday evening

   and so the student deduces that the statement implies  the test cannot take place on Friday, so
 

So far, so good.  But then the student’s logic goes wrong.  The student’s logic, not the professor’s.  Which is at it should be; he is the professor after all.  :)

On Wednesday evening

  .  But the student thinks
  because of deduction one and counting back one day.   And hence the test cannot take place on Wednesday, making
 

But  you cannot use deduction one on Wednesday evening , because deduction one requires that it is Thursday evening  and it isn’t.  You cannot use logic like this.

In post 56 Bob set up a parallel situation involving his next post.  In post 65 he made this post.  No one successfully predicted when he would post, but the post occurred.  He clearly wasn’t lying!

He also said he was giving up on the thread thereafter.  That’s why he has asked me to remind everyone about what he said; so he can maintain the position that he was not lying.  

I am, of course, happy to assist him.  smile

Alta ego

Last edited by alta ego (2013-12-16 20:50:13)

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#86 2013-12-17 00:46:40

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,811

Re: The Professor and the Student

From the OP's first post: "Who is right, the professor or the student?" I'll stay with the original question and let the newly-raised one of lying go...at least until we all understand that it's the professor who is right.

I agree with the reasoning of MathsIsFun, Bob and Alta ego, in which no one has yet identified any actual logic flaws...but all three have spotted the logic flaws committed by the student. Hmmm.... smile

Last edited by phrontister (2013-12-17 00:57:22)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#87 2013-12-17 00:56:45

gurthbruins
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Registered: 2010-05-09
Posts: 157

Re: The Professor and the Student

You have simply ignored my arguments and presented your own, which I find
invalid and unconvincing.

We certainly do not have to wait until Thursday night to know the test can't be on Friday. We know that at the start already.  For the simple reason that we already cannot possibly imagine the test occurring on the Friday. For obvious reasons. If you ignore the objections that I made in my last post, which are of course that we never know anything and can make no deductions whatsoever.


It's the activity of the intelligence above all that gives charm to existence.

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#88 2013-12-17 01:35:39

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 14,845

Re: The Professor and the Student

There is no reason that the test cannot be on Friday. Seems nobody read my posts from before. It depends on how you define the word 'expected'.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#89 2013-12-17 01:54:49

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,811

Re: The Professor and the Student

gurthbruins wrote:

You have simply ignored my arguments...

The thrust of those arguments was 'lying', which subject, against my better judgment, I chose to pursue in answer to nightstrider's post. That new subject is one of many that could be thrown into the ring, but I'd much rather concentrate on the question in your first post.

...and presented your own, which I find invalid and unconvincing.

I merely said that I was in agreement with the reasoning of M, B and AE.

If you ignore the objections that I made in my last post, which are of course that we never know anything and can make no deductions whatsoever.

To me, those objections and your similar comment in post #31 were obviously too hypothetical and not connected to obtaining a proper answer to your first post's question for me to feel that I needed to respond.

Last edited by phrontister (2013-12-19 20:29:23)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#90 2013-12-17 02:01:29

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,811

Re: The Professor and the Student

Hi stefy,

I did read them when you posted them, but I've forgotten their content. I'll reread them.

It depends on how you define the word 'expected'.

One definition is "considered likely or probable to happen or arrive".

'expected' doesn't appear in the thread but 'expect' does. It isn't in the puzzle wording and has quite a different meaning from the puzzle's "we'll know in advance".

Last edited by phrontister (2013-12-20 18:53:07)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#91 2013-12-18 00:48:21

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,811

Re: The Professor and the Student

Hi all,

Thursday can't be eliminated the student's way. Consider the following scenario:

Ok...so here I am, Blogga, waitin' nervously with the rest of the class on Wednesday of TEST WEEK for Prof to announce that the test is today (TAP, TAP...can't stop me fingers from TAPPIN'). Y'see, I kinda believe the first bit of what that dude Einstine said, that the test can't be on Thursday or Friday, but I'm not the sharpest tool in the shed when it comes to stuff like that 'n so I missed gettin' a handle on the rest of what 'e was rabbitin' on about...however it went. dunno

Anyways, the test wasn't yesterday or the day before, so if Einstine's right it must be today. Here's hopin' I swotted enough!! (fingers crossed)

I'll upd8ya l8a with me marks...

Ciao4niao,
Blogga wave

UPDATE SURPRISE!!: So now it's Thursday, but blow me down, we didn't 'ave the test yesterday after all!! Everyone's bin talkin' about it 'n sayin' we shoulda listened to Einstine, cos 'e'd figgered it all out 'n said we can't 'ave the test at all (that bit of what 'e'd said'd gone whoosh waaay over me 'ead at the time, but now the way me mates put it, it makes sense).

But then...BAM! Prof announced this arvo that the test is today!!! Didn't see that one comin', that's for sure!! And no one else did, neither!! eek

So Einstine's mind-numbin' logic wasn't worth a zack. down Musta bin pullin' a swifty on us, I reckon. shame

Ciao4niao,
Blogga wave

The same scenario (with the necessary adjustments) can be applied to Tuesday and Wednesday, and a variation of it to Monday. This is just another way of showing that all days prior to Friday are 'possible days' until the professor chooses one of them as the test day.

Last edited by phrontister (2013-12-21 00:59:43)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#92 2013-12-20 12:51:01

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,811

Re: The Professor and the Student

I think this may help explain why the student's logic doesn't work:

Causality (cause and effect): "The cause must be prior to the effect" - David Hume

Retrocausality: "Any of several hypothetical phenomena or processes that reverse causality, allowing an effect to occur before its cause. It is primarily a thought experiment in philosophy of science based on elements of physics, addressing the question: Can the future affect the present, and can the present affect the past? - Wikipedia article

Friday's elimination by the student's logic is valid, but that result cannot in any way affect the state of prior days (other than hypothetically/fancifully). The rest of the logic therefore is flawed, and hence it fails.

This is borne out by the arguments and practical demonstrations of Bob, alta ego, MIF and Blogga.

So...the professor is right.

Last edited by phrontister (2013-12-20 21:41:19)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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