The Little Thread Which Grew - the Apollo '73 to Everything But

[Panda Termint]

Re: The old days - Aboard the Apollo - 1973

We are at 511,800 views now, 1,400 more than when I turned off my computer 9 and 1/2 hours ago.

I got what you said on the page count. The answer to the question on thread statistics is difficult to answer yes or no. The truth is that I have put a lot of time and effort into this thread and when readership is high, it pleases me. <snip for brevity...>

Thanks for the answer, it's as good as any other reason and I'm happy that you are happy.

Pro Tip: If you want to quadruple the number of random hits on this thread simply mention nudity more often or get Carmelo back onto the subject of sexual prowess.

At 13,500 replies I'd guess that it is definitely the most posted upon thread here on ESMB so congratulations on keeping it alive and kicking along.

 

[FoTi]

Re: Another Paradox

Okay FoTi (and everyone else)- I am going to give you another paradox to wrap your minds around. This one is called the "UNEXPECTED HANGING".

DESCRIPTION OF THE "UNEXPECTED HANGING" PARADOX

A judge tells a condemned prisoner that he will be hanged at noon on one weekday during the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day. The judge is truthful and the prisoner is informed that if the judge does not keep his word, the prisoner will be set free.

That seems simple enough, right? Wrong!! The way the sentence is phrased creates a major problem, actually a Paradox.

Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts.

He begins by concluding that the "surprise hanging" can't be on Friday, as if he hasn't been hanged by Thursday, there is only one day left - and so it won't be a surprise if he's hanged on Friday. Since the judge's sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday.

He then reasons that the surprise hanging cannot be on Thursday either, because now Friday has been ruled out and if he hasn't been hanged by Wednesday night, the hanging must occur on Thursday, making a Thursday hanging not a surprise either. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all.

The next week, the executioner knocks on the prisoner's door at noon on Wednesday — which, despite all the above, was an utter surprise to him. Everything the judge said came true.

As it turns out, if noon on Thursday passes uneventfully, then the prisoner can demand to be released since he knows for certain that the hanging must be scheduled for Friday and, knowing this, when the hangman shows up at noon, the prisoner will not be surprised.

It can be assumed that prison officials will not want the prisoner to be able to avoid the hanging so they could just rule out Friday as a possible day. However, a clever prisoner will figure this out and so when Thursday morning rolls around, he claims certainty in knowing that the hangman must be coming that day and demands to be released when the hangman shows up because he already deduced the correct day and is not surprised.

From there, the prisoner reason that all the other days of the week can be eliminated in the same manner and so there is not any day of the week on which he can be hung under the terms of the sentence!

Where is the fallacy in this seemingly iron clad logic?
Lakey

Since he is confident that the hanging will not take place at all......the hangman showing up at noon on Wednesday would be a surprise since he thought it wasn't going to happen in the first place.

So.....Lakey.....what's the answer? The fallacy?

I like puzzles.....keep 'em comin'.

 

[FoTi]

Re: So much has changed in only 2 years!

And you don't even have any nudity on this thread (this is a plug for the FCDC thread)

The Anabaptist Jacques

I believe we had a bit of nudity once or twice. There was an incredibly sexy video posted about a very of Swedish looking Super Model types parachute jumping in the nude in Europe somewhere, maybe Germany, because Wagner's "The Ride of the Walkyre" music is playing.

FCDC is right around 300,000 posts which isn't too shabby either.
Lakey

Well....here's some nudity for y'all.

http://www.youtube.com/watch?v=8hytwI3XHfQ

 

[CarmeloOrchards]

Descendants starring George Clooney

[video=youtube;CWHNXJ1K4yA]http://www.youtube.com/watch?v=CWHNXJ1K4yA[/video]


Go see this!
Set in the REAL Hawaii, not Magnum P.I., Hawaii5-0 Hawaii.
Candy, if you're reading this, you will love it! -- pictures of the "hood."

Real people great story excellent writing acting cinematography

Best Oscars for some I'm sure.

 

[DartSmohen]

Re: The old days - Aboard the Apollo - 1973

Thanks Carmelo,

This was a good instant hat.
I am guessing Dart Smohen can name the male standing with Mary Sue !

Otto Roos

 

[Ted]

Re: So much has changed in only 2 years!

Well....here's some nudity for y'all.

http://www.youtube.com/watch?v=8hytwI3XHfQ

I got just 2:02 into the video.

When I saw the old people I thought how ill they looked, not due to being old but being fat with moles and shit. That's my objection to everyone going without clothes. We're more up close and personal to how they really are.

Then my mind wandered and I thought how acceptable would L. Ron Hubbard be if we were to gaze upon his naked body?

Then my mind went

... and I had to turn off the video.

Now I need a session.

Maybe an intensive...

 

[FoTi]

Re: So much has changed in only 2 years!

I got just 2:02 into the video.

When I saw the old people I thought how ill they looked, not due to being old but being fat with moles and shit. That's my objection to everyone going without clothes. We're more up close and personal to how they really are.

Then my mind wandered and I thought how acceptable would L. Ron Hubbard be if we were to gaze upon his naked body?

Then my mind went

... and I had to turn off the video.

Now I need a session.

Maybe an intensive...

LRH Nude?

Here's your session....

http://www.youtube.com/watch?v=0tS9I-oOUJ8&feature=related

 

[Leon]

Re: So much has changed in only 2 years!

I got just 2:02 into the video.

When I saw the old people I thought how ill they looked, not due to being old but being fat with moles and shit. That's my objection to everyone going without clothes. We're more up close and personal to how they really are.

Then my mind wandered and I thought how acceptable would L. Ron Hubbard be if we were to gaze upon his naked body?

Then my mind went

... and I had to turn off the video.

Now I need a session.

Maybe an intensive...

You want to know someting. near Cape Town, which is really my spiritual home, or something like that, there is a beach called Sandy Bay where people have been swimming in the nude fo the last hundred years or so. It's very isolated and you walk for about 20 minutes to get there. That's after driving there and finding parking and all that.

Anyway, I used to frequent the place years ago. Do you know what I most liked about it? It's that soon after you got your clothes off for the first time you realised just how totally unimportant bodies are. So what if one is fat and another skinny and the other has moles or stetch marks ar blotches or whatever. NO ONE CARES. No one gives a damn about it. You go there and you find that nudity is the most incredible leveller of social classes. You get talking to someone and waow what an interesting guy and so you chat away happily for hours, and later maybe you discover he's a brain surgeon professor or a politician or the CEO of some massive mining conglomerate or he's a total nobody from nowhere. What his body looks like and what his wife's titties look like or the saggy bum or whatever - NOBODY GIVES A SHIT. And that is the wonderful thing about nudity.

Body parts only become "unacceptable" because we hide them and declare that no one may see them. Ever. And we go into paroxysms of embarrassment if anyone sees how big or tiny our willies are.

Fact is that no one cares.

 

[lkwdblds]

Re: Another Paradox

Since he is confident that the hanging will not take place at all......the hangman showing up at noon on Wednesday would be a surprise since he thought it wasn't going to happen in the first place.

So.....Lakey.....what's the answer? The fallacy?

I like puzzles.....keep 'em comin'.

Nice try FoTi. You solved a problem but it is not the problem addressed in "The Unexpected Hanging". It's not your fault but rather the problem, as stated on Wikepedia is simply not stated clearly. It did not direct your attention onto the paradox.

Let me replace the Wikepedia statement of the problem with a much better statement made by Martin Gardner in his 1969 book "The Unexpected Hanging"

A convicted man was sentenced on Saturday. "The hanging will take place at noon," said the judge to the prisoner. on one of the five weekdays of next week, but you will not know which day it is until you are so informed on the morning of the day of the hanging."

The judge was known to be a man who always kept his word. The prisoner, accompanied by his lawyer, went back to his cell. As soon as the two men were alone the lawyer broke into a grin. "Don't yoou see?" he exclaimed, "The judge's sentence cannot possibly be carried out."

"I don't see," said the prisoner.

Let me explain. They obviously can't hang you next Friday. Friday is the last day of the week. On Thursday afternoon you would still be alive and you would know with absolute certainty that the hanging would be on Friday. You would know this before your were told so on Friday morning. That would violate the judge's decree.

"True," said the prisoner.

"Friday, then is positively ruled out," continued the lawyer. "This leaves Thursday as the last day they can hang you but they can't hang you on Thursday because by Wednesday afternoon only two days would remain: Thursday and Friday, Since Fiday has already been eliminated, the haning would have to be on Thursday. Your knowledge of that fact would violate the judge's decree again. So Thursday is also out. This leaves Wednesday as the last posible day but Wednesday is out because if you're alive Tuesday afternoon, you'll know that Wednesday is to be the day.

"I get it" said the prisoner, who was beginning to feel much better. In the exact same way I can also eliminate Tuesday. But they can not come Monday either because I now know it will be Monday.

The prisoner is convinced, by what appears to be unimpeachable logic, that he cannot be hanged without contradicting the conditions specified in the judge's sentence. Then on Wednesday morning, to his great surprise, the hangman arrives. Clearly he did not expect him so the judge's decree is seen to be perfectly correct.


Take a look at the problem as stated above, FoTi. I might as well tell you that there is no recognized answer to this problem. It is a paradox; the conditions set forth in the judge's sentencing can't always be carried out.

Four times out of 5, the sentence will work out correctly but in the instance where the hanging is scheduled for Friday, the prisoner will be able to deduce this in advance, thereby violating the judge's decree and the prisoner should be released.

Prison officials can attempt to get around this by never scheduling it for Friday but this introduces new problems. If the judge's decree states that the hanging will occur on Monday through Friday and Friday is always excluded, then the judge's decree has a lie built into it but per the conditions of the paradox, the judge is never allowed to lie.

Mathematically, one explanation is that the prisoner and his lawyer are attempting to apply Inductive reasoning, which is a proven mathematical technique when it is run forwards. In this example, mathematical inductive reasoning is being run backwards and this is not a proven mathematical technique which works every time. On some problems it will work and on some it won't. On this one it doesn't work.

THE KEY TO THE PROBLEM IS THAT THE PRISONER CAN'T OBTAIN TOTAL CERTAINTY UNTIL THE SECOND TO THE LAST DAY HAS PASSED AND HE IS STILL ALIVE. Prison officials could just be spinning a pointer and taking whatever day comes up or they could be trying to manipulate the result by never selecting Friday. If they are not manipulating the date and are relying on random chance for selecting the date of the hanging, then Friday is just as likely to occur as any other date. THERE IS NO WAY THE PRISONER CAN DEDUCE THAT THE DAY WILL BE FRIDAY UNTIL NOON ON THURSDAY HAS PAST AND HE IS STILL ALIVE. The lawyers claim stated above, "Then, Friday is positively ruled out." turns out to be incorrect. In fact, that false assertion leads things into a maze of illogic which culminates in a paradox.

SIMMARY - THE TRUE OUTCOME - If the hanging is set for Monday through Thursday, the sentence can be carried out as decreed by the judge. If the sentence is set for Friday, the prisoner can demand to be set free on Friday because the judges decree is not being followed. If the prison management decide's not to ever use Friday to get around this problem, then the judge is lying when he says the sentence is set for Monday through Friday. The problem states that the judge always tells the truth so the prisoner should be released on the grounds that the judge lied.

HINT #1 TO OBTAIN MORE UNDERSTANDING - Cut the week to just two days. The judge tells the prisoner that he will be hung on Monday or Tuesday but he will not now which day it is until the hangman arrives at 12:00 noon. This makes things a bit easier to see.

HINT#2 - TO GAIN MORE UNDERSTANDING - Cut the week to just 1 day. The judge tells the prisoner that he will be hung Monday but that he won't know it until the hangman arrives at noon! Think about that for a minute or two and see where it leads you.
Lakey

 

[FoTi]

Re: Another Paradox

Nice try FoTi. You solved a problem but it is not the problem addressed in "The Unexpected Hanging". It's not your fault but rather the problem, as stated on Wikepedia is simply not stated clearly. It did not direct your attention onto the paradox.

Let me replace the Wikepedia statement of the problem with a much better statement made by Martin Gardner in his 1969 book "The Unexpected Hanging"

A convicted man was sentenced on Saturday. "The hanging will take place at noon," said the judge to the prisoner. on one of the five weekdays of next week, but you will not know which day it is until you are so informed on the morning of the day of the hanging."

The judge was known to be a man who always kept his word. The prisoner, accompanied by his lawyer, went back to his cell. As soon as the two men were alone the lawyer broke into a grin. "Don't yoou see?" he exclaimed, "The judge's sentence cannot possibly be carried out."

"I don't see," said the prisoner.

Let me explain. They obviously can't hang you next Friday. Friday is the last day of the week. On Thursday afternoon you would still be alive and you would know with absolute certainty that the hanging would be on Friday. You would know this before your were told so on Friday morning. That would violate the judge's decree.

"True," said the prisoner.

"Friday, then is positively ruled out," continued the lawyer. "This leaves Thursday as the last day they can hang you but they can't hang you on Thursday because by Wednesday afternoon only two days would remain: Thursday and Friday, Since Fiday has already been eliminated, the haning would have to be on Thursday. Your knowledge of that fact would violate the judge's decree again. So Thursday is also out. This leaves Wednesday as the last posible day but Wednesday is out because if you're alive Tuesday afternoon, you'll know that Wednesday is to be the day.

"I get it" said the prisoner, who was beginning to feel much better. In the exact same way I can also eliminate Tuesday. But they can not come Monday either because I now know it will be Monday.

The prisoner is convinced, by what appears to be unimpeachable logic, that he cannot be hanged without contradicting the conditions specified in the judge's sentence. Then on Wednesday morning, to his great surprise, the hangman arrives. Clearly he did not expect him so the judge's decree is seen to be perfectly correct.


Take a look at the problem as stated above, FoTi. I might as well tell you that there is no recognized answer to this problem. It is a paradox; the conditions set forth in the judge's sentencing can't always be carried out.

Four times out of 5, the sentence will work out correctly but in the instance where the hanging is scheduled for Friday, the prisoner will be able to deduce this in advance, thereby violating the judge's decree and the prisoner should be released.

Prison officials can attempt to get around this by never scheduling it for Friday but this introduces new problems. If the judge's decree states that the hanging will occur on Monday through Friday and Friday is always excluded, then the judge's decree has a lie built into it but per the conditions of the paradox, the judge is never allowed to lie.

Mathematically, one explanation is that the prisoner and his lawyer are attempting to apply Inductive reasoning, which is a proven mathematical technique when it is run forwards. In this example, mathematical inductive reasoning is being run backwards and this is not a proven mathematical technique which works every time. On some problems it will work and on some it won't. On this one it doesn't work.

THE KEY TO THE PROBLEM IS THAT THE PRISONER CAN'T OBTAIN TOTAL CERTAINTY UNTIL THE SECOND TO THE LAST DAY HAS PASSED AND HE IS STILL ALIVE. Prison officials could just be spinning a pointer and taking whatever day comes up or they could be trying to manipulate the result by never selecting Friday. If they are not manipulating the date and are relying on random chance for selecting the date of the hanging, then Friday is just as likely to occur as any other date. THERE IS NO WAY THE PRISONER CAN DEDUCE THAT THE DAY WILL BE FRIDAY UNTIL NOON ON THURSDAY HAS PAST AND HE IS STILL ALIVE. The lawyers claim stated above, "Then, Friday is positively ruled out." turns out to be incorrect. In fact, that false assertion leads things into a maze of illogic which culminates in a paradox.

SIMMARY - THE TRUE OUTCOME - If the hanging is set for Monday through Thursday, the sentence can be carried out as decreed by the judge. If the sentence is set for Friday, the prisoner can demand to be set free on Friday because the judges decree is not being followed. If the prison management decide's not to ever use Friday to get around this problem, then the judge is lying when he says the sentence is set for Monday through Friday. The problem states that the judge always tells the truth so the prisoner should be released on the grounds that the judge lied.

HINT #1 TO OBTAIN MORE UNDERSTANDING - Cut the week to just two days. The judge tells the prisoner that he will be hung on Monday or Tuesday but he will not now which day it is until the hangman arrives at 12:00 noon. This makes things a bit easier to see.

HINT#2 - TO GAIN MORE UNDERSTANDING - Cut the week to just 1 day. The judge tells the prisoner that he will be hung Monday but that he won't know it until the hangman arrives at noon! Think about that for a minute or two and see where it leads you.
Lakey

I already got Hint #1.

Hint #2.....doesn't make any sense. If the judge tells him that he will be hung Monday....then he already knows when it will happen. Then the judge tells him that he won't know it until the hangman arrives at noon.....but the judge already told him, so he already knows. How could he not know it until the hangman arrives at noon? He also said the hangman would arrive in the morning. Noon is not morning anymore, is it? The judge seems to be aliar or contradicting himself, which leaves the prisoner to go free. No?

Or, did I not get the problem again? If so....what is the problem?

 

[lkwdblds]

Re: Another Paradox

I already got Hint #1.

Hint #2.....doesn't make any sense. If the judge tells him that he will be hung Monday....then he already knows when it will happen. Then the judge tells him that he won't know it until the hangman arrives at noon.....but the judge already told him, so he already knows. How could he not know it until the hangman arrives at noon? He also said the hangman would arrive in the morning. Noon is not morning anymore, is it? The judge seems to be aliar or contradicting himself, which leaves the prisoner to go free. No?

Or, did I not get the problem again? If so....what is the problem?

Hints #1 and #2 are things I found on Google which are not actually part of the problem. I added them in because I thought they were illuminating. You used Hint #2 to show the judge was lying but the judge never actually says the words of Hint #2 so there is no lie there. Also your comments about noon not being morning have NOTHING to do with the problem. The judge says the following, "The hanging will take place at noon," said the judge to the prisoner. on one of the five weekdays of next week, but you will not know which day it is until you are so informed on the morning of the day of the hanging." There are two clauses to his sentence; the prisoner is to be notified in the morning and then to be hung at noon. There is no lie there either.

The idea behind solving the problem is not just to look through the text and try and find items the judge said which might qualify as lies. This is an intelligent approach to solving the problem but the concepts which arise in formulating the problem do not really center around this approach.

ONE OF THE KEY PARAMETERS WE ARE GIVEN IN THE PROBLEM IS THAT THE JUDGE ALWAYS TELLS THE TRUTH. HE WILL NEVER KNOWINGLY LIE. Both of your solutions, yesterday and today focus on finding lies stated by the judge. Finding possible lies by the judge is not really what the problem is about. WHAT THE PROBLEM IS ADDRESSING IS TO FIND A SITUATION WHERE THE CONDITIONS OF THE PROBLEM, AS STATED, CANNOT BE CARRIED OUT THUS FORCING ONE OR MORE OF THE JUDGE'S STATEMENTS TO BECOME LIES, even though the judge never intended them to be lies.

Also, we are looking for why the lawyer's seemingly impeccable logic does not work out and in fact leads to an illogic which MAKES a liar out of the judge .

What happens is that if the prisoner makes it past noon on Thursday and is not hung, then and only then, he can deduce that the hanging is set for Friday and he can demand to be released. At this exact moment, the judge's decree is violated and the sentence, as stated, can't be carried out. TO CARRY OUT THE SENTENCE ON FRIDAY WOULD INADVERTENTLY MAKE A LIAR OUT OF THE JUDGE AND RELEASING THE PRISONER ALSO MAKES A LIAR OUT OF THE JUDGE. Therefore, we have a paradox. An honest judge is made a liar but only if the hanging is scheduled on Friday, the last possible day.

The other item being examined is the problem of why the lawyer's seemingly impeccable logic leads to the conclusion that the hanging can never occur per the judge's decree. This conclusion proves to be false if the hanging is set for any day except Friday. The lawyer took the fact that Friday was eliminated and worked backwards through the earlier days all the way to Monday, showing that those days were not possible either.

THE LAWYER'S LOGIC IN WORKING BACKWARDS LOOKS A LITTLE SUSPECT BUT TRY AS WE MIGHT, WE CAN NOT REALLY SEE ANY APPARENT ERROR IN IT. We are looking for the error in the lawyer's logic. There has to be an error because the sentence put forth by the judges fails to be doable in certain instances.

It turns out that the error made by the lawyer exists but it is subtle and hard to see, even when it is pointed out to people. It goes against the grain of our intuition.

The lawyer's error has to do with the fact that if noon passes on Thursday, then Friday must be the day. The prisoner knows that for certain which violates the judge's decree. The judge's decree can not be carried out.

So Friday can be eliminated after noon passes on Thursday without a hanging. NOW THAT THIS IS ESTABLISHED, THE LAWYER MAKES HIS MISTAKE, HE SAYS "WE CAN NOW ELIMINATE FRIDAY FOR ALL CASES. THIS IMPLIES THAT WE DON'T HAVE TO WAIT UNTIL 1 MINUTE AFTER NOON ON THURSDAY, WE CAN REASON THAT PRISON MANAGEMENT SIMPLY WILL NEVER USE FRIDAY AS THE HANGING DAY."

This sounds totally reasonable. It is hard to find fault with it. Since Friday causes a problem, prison management just won't ever schedule the hanging for Friday. Therefore Thursday is the actual last day for the hanging. At this point we have gone down the tubes, the lawyer is no longer making sense. Why? Because the same argument can now be used to eliminate Thursday, then Wednesday, Tuesday and finally Monday. The lawyer then arrives at the erroneous conclusion that the sentence can't be carried out on any day of the week because the prisoner will already know about it therefore the prisoner will not be hanged.

THE ERROR IN LOGIC -
The lawyer's error occurs as follows: He states that if Thursday at noon passes and the prisoner is still alive, the judge's decree can't be carried out. THIS IS TRUE - SO FAR SO GOOD. Now the lawyer takes the fatal step and declares that Friday can be eliminated in the general case, the prisoner does not have to wait until just after noon on Thursday to know that Friday is out. The prisoner has deduced that Friday simply can't be used as the last day. When that deduction is accepted as true, the lawyer's entire line of reasoning fails.

SIDEBAR - Trying to explain something like this as clearly as possible and in as few words as possible leads to the explainer gaining more understanding of the problem himself.
Lakey

 

[CarmeloOrchards]

Happy Thanksgiving from Wednesday Addams

[video=youtube;ccj2BH25c0I]http://www.youtube.com/watch?v=ccj2BH25c0I&feature=player_embedded#![/video]

I approve this video

 

[FoTi]

Re: Another Paradox

..

 

[FoTi]

Re: Another Paradox

Hints #1 and #2 are things I found on Google which are not actually part of the problem. I added them in because I thought they were illuminating. You used Hint #2 to show the judge was lying but the judge never actually says the words of Hint #2 so there is no lie there. Also your comments about noon not being morning have NOTHING to do with the problem. The judge says the following, "The hanging will take place at noon," said the judge to the prisoner. on one of the five weekdays of next week, but you will not know which day it is until you are so informed on the morning of the day of the hanging." There are two clauses to his sentence; the prisoner is to be notified in the morning and then to be hung at noon. There is no lie there either.

The idea behind solving the problem is not just to look through the text and try and find items the judge said which might qualify as lies. This is an intelligent approach to solving the problem but the concepts which arise in formulating the problem do not really center around this approach.

ONE OF THE KEY PARAMETERS WE ARE GIVEN IN THE PROBLEM IS THAT THE JUDGE ALWAYS TELLS THE TRUTH. HE WILL NEVER KNOWINGLY LIE. Both of your solutions, yesterday and today focus on finding lies stated by the judge. Finding possible lies by the judge is not really what the problem is about. WHAT THE PROBLEM IS ADDRESSING IS TO FIND A SITUATION WHERE THE CONDITIONS OF THE PROBLEM, AS STATED, CANNOT BE CARRIED OUT THUS FORCING ONE OR MORE OF THE JUDGE'S STATEMENTS TO BECOME LIES, even though the judge never intended them to be lies.

Also, we are looking for why the lawyer's seemingly impeccable logic does not work out and in fact leads to an illogic which MAKES a liar out of the judge .

What happens is that if the prisoner makes it past noon on Thursday and is not hung, then and only then, he can deduce that the hanging is set for Friday and he can demand to be released. At this exact moment, the judge's decree is violated and the sentence, as stated, can't be carried out. TO CARRY OUT THE SENTENCE ON FRIDAY WOULD INADVERTENTLY MAKE A LIAR OUT OF THE JUDGE AND RELEASING THE PRISONER ALSO MAKES A LIAR OUT OF THE JUDGE. Therefore, we have a paradox. An honest judge is made a liar but only if the hanging is scheduled on Friday, the last possible day.

The other item being examined is the problem of why the lawyer's seemingly impeccable logic leads to the conclusion that the hanging can never occur per the judge's decree. This conclusion proves to be false if the hanging is set for any day except Friday. The lawyer took the fact that Friday was eliminated and worked backwards through the earlier days all the way to Monday, showing that those days were not possible either.

THE LAWYER'S LOGIC IN WORKING BACKWARDS LOOKS A LITTLE SUSPECT BUT TRY AS WE MIGHT, WE CAN NOT REALLY SEE ANY APPARENT ERROR IN IT. We are looking for the error in the lawyer's logic. There has to be an error because the sentence put forth by the judges fails to be doable in certain instances.

It turns out that the error made by the lawyer exists but it is subtle and hard to see, even when it is pointed out to people. It goes against the grain of our intuition.

The lawyer's error has to do with the fact that if noon passes on Thursday, then Friday must be the day. The prisoner knows that for certain which violates the judge's decree. The judge's decree can not be carried out.

So Friday can be eliminated after noon passes on Thursday without a hanging. NOW THAT THIS IS ESTABLISHED, THE LAWYER MAKES HIS MISTAKE, HE SAYS "WE CAN NOW ELIMINATE FRIDAY FOR ALL CASES. THIS IMPLIES THAT WE DON'T HAVE TO WAIT UNTIL 1 MINUTE AFTER NOON ON THURSDAY, WE CAN REASON THAT PRISON MANAGEMENT SIMPLY WILL NEVER USE FRIDAY AS THE HANGING DAY."

This sounds totally reasonable. It is hard to find fault with it. Since Friday causes a problem, prison management just won't ever schedule the hanging for Friday. Therefore Thursday is the actual last day for the hanging. At this point we have gone down the tubes, the lawyer is no longer making sense. Why? Because the same argument can now be used to eliminate Thursday, then Wednesday, Tuesday and finally Monday. The lawyer then arrives at the erroneous conclusion that the sentence can't be carried out on any day of the week because the prisoner will already know about it therefore the prisoner will not be hanged.

THE ERROR IN LOGIC -
The lawyer's error occurs as follows: He states that if Thursday at noon passes and the prisoner is still alive, the judge's decree can't be carried out. THIS IS TRUE - SO FAR SO GOOD. Now the lawyer takes the fatal step and declares that Friday can be eliminated in the general case, the prisoner does not have to wait until just after noon on Thursday to know that Friday is out. The prisoner has deduced that Friday simply can't be used as the last day. When that deduction is accepted as true, the lawyer's entire line of reasoning fails.

SIDEBAR - Trying to explain something like this as clearly as possible and in as few words as possible leads to the explainer gaining more understanding of the problem himself.
Lakey

Lakey....I don't understand why you posted a riddle/puzzle/paradox here that someone wrote that has no known answer that doesn't make any sense and can't be figured out. What's the point ?????????

 

[lkwdblds]

Re: Another Paradox

Lakey....I don't understand why you posted a riddle/puzzle/paradox here that someone wrote that has no known answer that doesn't make any sense and can't be figured out. What's the point ?????????

FoTi, first thing, the paradox does have an answer, the answer does make sense and it can be figured out. I cover all 3 of these points in my last post.

I put it up because you liked the last two puzzles and wanted more. I was interested in what people might come up with for answers, especially you. Your approach was interesting, scanning the problem just trying to show that the judge was a habitual liar. That shows high intelligence but went off on a tangent without actually confronting the problem.

I DID NOT INTEND TO GIVE THE ANSWER BUT JUST LEAVE IT FOR YOU AND OTHERS TO FIGURE IT OUT.

When it seemed as if you were not really getting the essence of the problem, I added more and more information trying to state the problem more clearly so that you would understand what it is all about, appreciate its fine nuances, and come up with your own solution. I was really interested to see what you might come up with and hoped someone else might comment on it.

On the second go around, you came up with the same answer as you did the first time AND NOBODY ELSE SEEMED TO BE INTERESTED. I started to just clarify the problem for you some more so you could work out your own solution but then, on the spur of the moment, I just decided to give the solution and be done with it.

I have owned the Martin Gardner book with this problem, since 1969. I knew the answer but really didn't have a full conceptual understanding of it. I decided to see if it is on the Internet and it is. I read two of the articles to gain some new points of view.

In writing up the answer, I did edit after edit, trying to get it as concise as possible. I even got out the Martin Gardner book and reread the problem. I am sharper in math now than when I first read about the problem in 1969. In the process of writing up the answer, I learned more of the essence of the problem and actually gained full conceptual understanding for myself.

This problem and paradox is pretty advanced and is probably only appreciated by people with high math and puzzle solving backgrounds and aptitudes. These are people who study and work puzzles just for fun and for the mental exercise and the insights which that provides.
Lakey

 

[FoTi]

Re: Another Paradox

Lakey....I don't understand why you posted a riddle/puzzle/paradox here that someone wrote that has no known answer that doesn't make any sense and can't be figured out. What's the point ?????????

Hints #1 and #2 are things I found on Google which are not actually part of the problem. I added them in because I thought they were illuminating. You used Hint #2 to show the judge was lying but the judge never actually says the words of Hint #2 so there is no lie there. Also your comments about noon not being morning have NOTHING to do with the problem. The judge says the following, "The hanging will take place at noon," said the judge to the prisoner. on one of the five weekdays of next week, but you will not know which day it is until you are so informed on the morning of the day of the hanging." There are two clauses to his sentence; the prisoner is to be notified in the morning and then to be hung at noon. There is no lie there either.

The idea behind solving the problem is not just to look through the text and try and find items the judge said which might qualify as lies. This is an intelligent approach to solving the problem but the concepts which arise in formulating the problem do not really center around this approach.

ONE OF THE KEY PARAMETERS WE ARE GIVEN IN THE PROBLEM IS THAT THE JUDGE ALWAYS TELLS THE TRUTH. HE WILL NEVER KNOWINGLY LIE. Both of your solutions, yesterday and today focus on finding lies stated by the judge. Finding possible lies by the judge is not really what the problem is about. WHAT THE PROBLEM IS ADDRESSING IS TO FIND A SITUATION WHERE THE CONDITIONS OF THE PROBLEM, AS STATED, CANNOT BE CARRIED OUT THUS FORCING ONE OR MORE OF THE JUDGE'S STATEMENTS TO BECOME LIES, even though the judge never intended them to be lies.

Also, we are looking for why the lawyer's seemingly impeccable logic does not work out and in fact leads to an illogic which MAKES a liar out of the judge .

What happens is that if the prisoner makes it past noon on Thursday and is not hung, then and only then, he can deduce that the hanging is set for Friday and he can demand to be released. At this exact moment, the judge's decree is violated and the sentence, as stated, can't be carried out. TO CARRY OUT THE SENTENCE ON FRIDAY WOULD INADVERTENTLY MAKE A LIAR OUT OF THE JUDGE AND RELEASING THE PRISONER ALSO MAKES A LIAR OUT OF THE JUDGE. Therefore, we have a paradox. An honest judge is made a liar but only if the hanging is scheduled on Friday, the last possible day.

The other item being examined is the problem of why the lawyer's seemingly impeccable logic leads to the conclusion that the hanging can never occur per the judge's decree. This conclusion proves to be false if the hanging is set for any day except Friday. The lawyer took the fact that Friday was eliminated and worked backwards through the earlier days all the way to Monday, showing that those days were not possible either.

THE LAWYER'S LOGIC IN WORKING BACKWARDS LOOKS A LITTLE SUSPECT BUT TRY AS WE MIGHT, WE CAN NOT REALLY SEE ANY APPARENT ERROR IN IT. We are looking for the error in the lawyer's logic. There has to be an error because the sentence put forth by the judges fails to be doable in certain instances.

It turns out that the error made by the lawyer exists but it is subtle and hard to see, even when it is pointed out to people. It goes against the grain of our intuition.

The lawyer's error has to do with the fact that if noon passes on Thursday, then Friday must be the day. The prisoner knows that for certain which violates the judge's decree. The judge's decree can not be carried out.

So Friday can be eliminated after noon passes on Thursday without a hanging. NOW THAT THIS IS ESTABLISHED, THE LAWYER MAKES HIS MISTAKE, HE SAYS "WE CAN NOW ELIMINATE FRIDAY FOR ALL CASES. THIS IMPLIES THAT WE DON'T HAVE TO WAIT UNTIL 1 MINUTE AFTER NOON ON THURSDAY, WE CAN REASON THAT PRISON MANAGEMENT SIMPLY WILL NEVER USE FRIDAY AS THE HANGING DAY."

This sounds totally reasonable. It is hard to find fault with it. Since Friday causes a problem, prison management just won't ever schedule the hanging for Friday. Therefore Thursday is the actual last day for the hanging. At this point we have gone down the tubes, the lawyer is no longer making sense. Why? Because the same argument can now be used to eliminate Thursday, then Wednesday, Tuesday and finally Monday. The lawyer then arrives at the erroneous conclusion that the sentence can't be carried out on any day of the week because the prisoner will already know about it therefore the prisoner will not be hanged.

THE ERROR IN LOGIC -
The lawyer's error occurs as follows: He states that if Thursday at noon passes and the prisoner is still alive, the judge's decree can't be carried out. THIS IS TRUE - SO FAR SO GOOD. Now the lawyer takes the fatal step and declares that Friday can be eliminated in the general case, the prisoner does not have to wait until just after noon on Thursday to know that Friday is out. The prisoner has deduced that Friday simply can't be used as the last day. When that deduction is accepted as true, the lawyer's entire line of reasoning fails.

SIDEBAR - Trying to explain something like this as clearly as possible and in as few words as possible leads to the explainer gaining more understanding of the problem himself.
Lakey

If the prisoner has deduced that Friday simply can't be used as the last day and that deduction is accept4ed as true......why does the lawyer's entire line of reasoning fail?

Also....

You said...."Take a look at the problem as stated above, FoTi. I might as well tell you that there is no recognized answer to this problem. It is a paradox; the conditions set forth in the judge's sentencing can't always be carried out."

I guess I don't see how it is a paradox. You stated in your original post on this that the judge said that it would happen on any weekday. If the judge or whomever made the decision of the day never even figured Friday into the plan, then Friday would be irrelevant. So...does this make the lawyer's logic a fallacy because he arbitrarily added Friday into the equation?

Then you say ... "FoTi, first thing, the paradox does have an answer, the answer does make sense and it can be figured out. I cover all 3 of these points in my last post."

This seems like double talk to me. ???????

The only way I can see that the prisoner would be surprised on Wednesday was because he bought the lawyer's logic and deduced that it would never happen, so it surprised him when the hangman did show up. So, if the prisoner knew per the judge that he would die on any one of the weekdays during that week, why was he surprised when the hangman showed up at noon on Wednesday? Also seems to me if he was following the lawyer's logic that he would have been expecting the hangman to show up on Wednesday and would not have been surprised at all.

What is the point of all this anyway?

I can't believe I'm doing this at 5:30am on Sunday morning. I must have lost my mind.

 

[RogerB]

Re: Another Paradox

If the prisoner has deduced that Friday simply can't be used as the last day and that deduction is accept4ed as true......why does the lawyer's entire line of reasoning fail?

Also....

You said...."Take a look at the problem as stated above, FoTi. I might as well tell you that there is no recognized answer to this problem. It is a paradox; the conditions set forth in the judge's sentencing can't always be carried out."

I guess I don't see how it is a paradox. You stated in your original post on this that the judge said that it would happen on any weekday. If the judge or whomever made the decision of the day never even figured Friday into the plan, then Friday would be irrelevant. So...does this make the lawyer's logic a fallacy because he arbitrarily added Friday into the equation?

Then you say ... "FoTi, first thing, the paradox does have an answer, the answer does make sense and it can be figured out. I cover all 3 of these points in my last post."

This seems like double talk to me. ???????

The only way I can see that the prisoner would be surprised on Wednesday was because he bought the lawyer's logic and deduced that it would never happen, so it surprised him when the hangman did show up. So, if the prisoner knew per the judge that he would die on any one of the weekdays during that week, why was he surprised when the hangman showed up at noon on Wednesday? Also seems to me if he was following the lawyer's logic that he would have been expecting the hangman to show up on Wednesday and would not have been surprised at all.

What is the point of all this anyway?

I can't believe I'm doing this at 5:30am on Sunday morning. I must have lost my mind.

Err, umm, I always thought that getting one's attention hung up on things was one way of losing (at least a part of) one's mind

R

 

[CarmeloOrchards]

Last Week

Last week, I was going to be in LA to finish a construction project. I didn't make it.

My son, who lives in Nor Cal and works across the continent, in NYC's house got burgled. And while I was killing a hornets' nest so that the septic tank could be pumped, I got stung stang and abused by the little critters even in the dark.

When the venom or whatever it is called fell into my bloodstream, I ended up sleeping 36 hours straight. In Pain. Unconscious. I can't even tell you if it was clear or raining outside for that period. I'm recovering. Should be in LA on Tuesday.

In the meantime I missed Dave and Aida's party of international exes. Can someone post pics and stories?

 

[lkwdblds]

Re: Another Paradox

If the prisoner has deduced that Friday simply can't be used as the last day and that deduction is accept4ed as true......why does the lawyer's entire line of reasoning fail?

I answer this in the in the last paragraph of this post!

Also....

You said...."Take a look at the problem as stated above, FoTi. I might as well tell you that there is no recognized answer to this problem. It is a paradox; the conditions set forth in the judge's sentencing can't always be carried out."

I guess I don't see how it is a paradox. You stated in your original post on this that the judge said that it would happen on any weekday. If the judge or whomever made the decision of the day never even figured Friday into the plan, then Friday would be irrelevant. So...does this make the lawyer's logic a fallacy because he arbitrarily added Friday into the equation?

The judge's decision has to apply in the GENERAL case. That means it must work no matter which of the 5 days is picked. The judge states that the hanging will occur one weekday, MTWTF, during the following week, and that the prisoner will not know in advance which of those 5 days it will be. There is a chance it will be Friday, in which case the judge's decree can't be fulfilled. If it is any of the other 4 days the decree can be fulfilled. The lawyer has deduced that none of the 5 days are possible when the truth is that 4 of the 5 days are possible, therefore there is a fallacy in his logic.

There are two issues. #1 The lawyer's deduction that the decree can't be carried out on any of the 5 days is wrong. #2 The judge's decree can be carried out on 4 of the 5 days; all days but Friday.

Then you say ... "FoTi, first thing, the paradox does have an answer, the answer does make sense and it can be figured out. I cover all 3 of these points in my last post."

This seems like double talk to me. ???????

par·a·dox [ párrə dòks ]
1.something absurd or contradictory: a statement, proposition, or situation that seems to be absurd or contradictory, but in fact is or may be true
2.self-contradictory statement: a statement or proposition that contradicts itself
3.person of opposites: a person with seemingly self-contradictory qualities

I am using definition #2. We have a judge's sentence which contradicts itself on occasion, though not always. Wikepedia and other sources state that there is no known and accepted cut and dry explanation for this. This is not to say that such an explanation doesn't exist. By your pressing me with your various challenges, I believe that I now have full 100% conceptual understanding of the problem and have uncovered the true explanation.

Your criticism above about double talk has some merit in it. When I first brought the problem to your attention, the pundits said there was no actual solution and I agreed with them. Due to your pressing me with your various challenges, I believe that I now have soved the problem by uncovering the true solution (which I explain in the last paragraph of this post). It was me changing my mind, mid stream, which caused the double talk to occur. Sorry if that double talk irked you!

The only way I can see that the prisoner would be surprised on Wednesday was because he bought the lawyer's logic and deduced that it would never happen, so it surprised him when the hangman did show up. So, if the prisoner knew per the judge that he would die on any one of the weekdays during that week, why was he surprised when the hangman showed up at noon on Wednesday? Also seems to me if he was following the lawyer's logic that he would have been expecting the hangman to show up on Wednesday and would not have been surprised at all.

Your first sentence contains the answer to your question. The lawyer used what looks like impeccable logic to convince the prisoner that he could not be hung on any of the 5 days. THE PRISONER BOUGHT THE LAWYERS EXPLANATION AND CAME TO BELIEVE WITH CERTAINTY THAT THE HANGING COULD NOT OCCUR! Of course when the hangman showed up on Wednesday, the prisoner was caught completely off guard and was very surprised. Therefore, the judge's decree was observed successfully.

Your second sentence's question is answered from what you said in your first sentence - "The prisoner bought the lawyer's logic." He started out following the judge's logic but bought his lawyer's logic, changed his mind, and stopped believing what the judge had said.

What is the point of all this anyway?

You liked the first two puzzles I gave you and you asked for more. The point was to satisfy your request by supplying you with a puzzle which I believe to be the most challenging of all the ones I have seen. You appeared to me to be having trouble grasping what the puzzle was all about (correct me if I am wrong). I decided to stay with it and attempt to convey the enigma of the puzzle with sufficient clarity so that you could recognize the contradictions which the puzzle brings to mind.

I can't believe I'm doing this at 5:30am on Sunday morning. I must have lost my mind.

FoTi: Sorry, if the problem has you in a tizzy. This is advanced puzzle math. It's not for everyone. Like many things mathematical, a minority of people, such as me, do this stuff just for pleasure, challenge, and mental exercise. Once in a while some new subtle insights may be gained by a person. It takes a lot of time to really get involved in this type of stuff. I do not recommend it for everybody. For at least 99% of the population, spending time on this type of puzzle is a big WASTE OF TIME.

I am retired right now, live alone, and my family is grown, I've got spare time on my hands for the first time since being a small kid. I want to thank you because your persistent questioning challenged me to explain the problem in more and more detail. As a result, I believe that I have full and total 100% conceptual understanding of this problem.

Its not an intelligence thing. Getting involved in a problem such as this and spending hours on it is not a very intelligent thing to do in the first place! There is aptitude involved. Regardless of one's intelligence some people have the aptitude to kick these type of problems around and have fun doing so. Look at all the puzzle books on the magazine racks in the stores. Most productive people avoid spending serkious amounts of time on puzzles believing it is a waste of time. For the most part, they are right.

AT LAST A FURTHER ANALYSIS OF THE LAWYER'S ERROR AND A FINAL SOLUTION!!
The lawyer puts himself in time at a future 12:01 pm Thursday without the hanging taking place. The lawyer sees that if that scenario occurs, the hanging can't take place the next day without the prisoner knowing it in advance which violates the judge's decree.

The lawyer now applies a reverse mathematical induction process to predict a future scenario. He takes information which would be gained after a forthcoming 12:01 pm Thursday and applies that information to deduce outcomes for days in the future which will occur before the forthcoming Thursday.

Mathematical induction is designed to take present time outcome and extend it further out from that point. The lawyer is attempting to forecast a future event by using a reverse mathematical inductive process.

ILLEGAL FORM OF MENTAL TIME TRAVEL? - THE PARADOX SOLVED?
The lawyer looks to the future to see what conditions might exist on some future Thursday at 12:01 pm. Now if he extended those conditions further into the future, his logic would be correct. However, he attempts to extend those conditions backwards to days still in the future but which will occur before that future Thursday. This is faulty logic and a real no-no. Any answers obtained by doing this must be paradoxical.

Lakey

 

[FoTi]

Re: Another Paradox

Err, umm, I always thought that getting one's attention hung up on things was one way of losing (at least a part of) one's mind

R