The Professor and the Student

Agnishom · 2013-05-04 02:22:58

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

alter ego · 2013-05-04 02:52:43

Nice one!

Alter

Last edited by alter ego (2017-11-01 23:22:57)

Agnishom · 2013-05-04 04:11:00

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

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

alter ego · 2013-05-04 05:51:35

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.

Alter

Last edited by alter ego (2017-11-01 23:23:30)

phrontister · 2013-05-04 13:05:29

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!

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

Agnishom · 2013-05-04 15:01:26

Alta Ego,

I am sorry, I thought you're bob

nightstrider · 2013-12-15 14:02:00

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.

phrontister · 2013-12-15 23:45:09

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!

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

gurthbruins · 2013-12-16 17:21:07

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.

alter ego · 2013-12-16 20:47:40

I thought this was totally sorted by Bob Bundy. Maybe he wasnt clear enough so Ill have a go for him.

Lets 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 students logic goes wrong. The students logic, not the professors. 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 isnt. 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 wasnt lying!

He also said he was giving up on the thread thereafter. Thats 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.

Alter ego

Last edited by alter ego (2017-11-01 23:26:03)

phrontister · 2013-12-17 00:46:40

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....

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

gurthbruins · 2013-12-17 00:56:45

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.

anonimnystefy · 2013-12-17 01:35:39

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'.

phrontister · 2013-12-17 01:54:49

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)

phrontister · 2013-12-17 02:01:29

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)

phrontister · 2013-12-18 00:48:21

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.
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
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!!
So Einstine's mind-numbin' logic wasn't worth a zack. Musta bin pullin' a swifty on us, I reckon.
Ciao4niao,
Blogga

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)

phrontister · 2013-12-20 12:51:01

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)

Math Is Fun Forum

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

Re: The Professor and the Student

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

Re: The Professor and the Student

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

Re: The Professor and the Student

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

Re: The Professor and the Student

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

Re: The Professor and the Student

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

Re: The Professor and the Student

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

Re: The Professor and the Student

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

Re: The Professor and the Student

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

Re: The Professor and the Student

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

Re: The Professor and the Student

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

Re: The Professor and the Student

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

Re: The Professor and the Student

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

Re: The Professor and the Student

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

Re: The Professor and the Student

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

Re: The Professor and the Student

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

Re: The Professor and the Student

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

Re: The Professor and the Student

Board footer