In a book about paradoxes I once came across the following two.  
In the book, they were presented as two of the great unsolved 
mysteries of the human mind, but to me the solutions seemed 
easy - too easy, in fact.  So, I'm entering the paradoxes here 
in the hope that someone can enlighten me.  


1. THE UNEXPECTED HANGING 

A judge says to a murderer: "You stand convicted of one of the 
most brutal crimes I've ever seen.  The death penalty is too 
good for you.  But unfortunately it's the worst sentence I can 
pass, so I'm going to have to add a little twist to it.  I'm 
going to tell you that you will be hanged at 8:00 AM some day 
next week, but I won't tell you which day.  It will come as a 
total surprise.  You won't know what day you will be hanged 
until the minute they come to take you away!" 

The murderer's lawyer chuckles to himself, and the murderer 
says, "I'm glad *you* find this funny.  I think it's horrible!" 

The lawyer says, "But don't you see?  They *can't* hang you 
now!  The judge said you would be hanged next week.  That means 
the last day they can possibly hang you is next Saturday, 
right?  But if 8:00 AM Friday comes and goes and you're still 
alive, then you'll *know* the hanging will take place on 
Saturday.  But the judge said it will come as a total surprise, 
so the hanging can't take place on Saturday, and the last day 
it *can* take place is Friday.  But if Friday is the last day, 
and if 8:00 AM Thursday comes and goes and you're still alive, 
then you'll know the hanging will take place on Friday.  But 
the judge said it will come as a total surprise, so the hanging 
can't take place on Friday.  That means the last day it *can* 
take place is Thursday..."  In this way, the lawyer reasons all 
the way back to Sunday, and concludes beyond any doubt that his 
client can't possibly be hanged.  

The murderer, now chuckling like his lawyer, goes to his cell 
on death row.  At 7:55 on Tuesday morning the guards come and 
take him away to be hanged, and, sure enough, it comes as a 
total surprise, just as the judge said it would.


2. NEWCOMBE'S PARADOX

A psychic whose predictions are known to be 90% accurate puts 
two boxes in front of you, marked "A" and "B," and says:

"You can choose either the contents of both boxes, or the 
contents of just box B.  Last night, I predicted which you 
would choose.  If I predicted that you would choose both boxes, 
I put $1,000 in box A and left box B empty.  If I predicted 
that you choose just box B, I put $1,000 in box A and 
$1,000,000 in box B." 

Which do you choose?  Both boxes, or just box B?

Sounds simple at first.  Obviously, you choose just box B 
because you want that $1,000,000.  But wait a minute...  
Whatever the psychic predicted and however much money he put in 
the boxes, that was last night, right?  Either the $1,000,000 
is in box B or it isn't.  Nothing can change that now.  
Certainly no choice you make now is going to have any effect on 
the contents of the boxes.  How could it?  Choosing just box B 
can't make the $1,000,000 appear if it wasn't in there to begin 
with; and choosing both boxes can't make the $1,000,000 
disappear from box B if it's already there.  So, why *not* 
choose both boxes?  Why lose that $1,000 in box A?  

So, which do you choose?  Both boxes, or just box B?

138 responses total.

Choose both. Take the sure thing.

Even as I read the lawyer's logic, I knew it wasn't right.
I don't see where the paradoxes are either.

(as far as Newcombe's Paradox goes, of COURSE you take both boxes!! If the
psychic is wrong, the psychic is REALLY wrong! What's so hard about that?
It's not like the psychic is 100% accurate anyway!)

Are you so sure?  It's given that the psychic is known to be 90%
accurate, and $10,000,000 is far more than ten times $1,000, so if
you believe in playing the odds (as the best gamblers do) ...

(yes I'm sure. No matter what the psychic predicts, the money in the two
boxes isn't going to change, because the psychic has already put it there.
If the psychic predicted wrong, oh well! It'll be the easiest cash I ever
made.)

Remmers is right.  If the psychic is 90% accurate, then when you 
choose both boxes aren't you in effect betting $1,000,000 that 
you got him on a 10% night?  Does that sound very wise to you?

("90% accurate" is how the book worded it, and I've never 
understood why.  Maybe a 90%-accurate psychic supposed to be 
easier to believe in than a 100%-accurate psychic?)  

Well, let's suppose the psychic is known to be 100% accurate.  
What then?  If the psychic was known to be 100% accurate, 
wouldn't you have to choose just box B if you wanted the 
$1,000,000?  If you choose both boxes, aren't you merely 
fulfiling the prediction the psychic made the night before, and 
aren't you guaranteed in that case to find box B empty?

(Remmers is *wrong*! Why would you *not* take *both* boxes? Is there some
sort of penalty that I'm missing as far as TAKING the second box as well?
I'm also trying to figure out what the psychic has to do with ANYTHING.
Am I to believe that with a wave of her/his hand, the psychic can change
the contents of the boxes? The psychic put whatever was going to be in the
boxes into the boxes THE DAY BEFORE. Not now, not a couple of minutes ago,
and most definitely NOT after you choose which boxes to take. This would
be very different if you had to choose between box A and B, but you DON'T.
You *can* take both! You *will* get at LEAST $1,000, no matter what.)

(I don't understand why this is so hard. There are two boxes. Do you take
one or both? That's it. That's the only question being asked, when you get
down to it.)

Its not that easy, carson.  If I choose to take one box there is a 90% chance
that there is a hulluvalota money there.  If I choose both boxes there is
a 90% chance there is 1000 dollars there.  So, I'd choose the one box.

Dangit, got pulled, so I'll finish.  The timing of the psychic is not relevant.
The psychic is correct 90% of the time.  So whichever you choose, the psychic
has a 90% chance of correctly guessing which you will pick.  If you could
somehow change your mind without the psychic knowing then the 90% would drop
accordingly.  I would choose box B.

(It *is* that easy! It's either there or it isn't! Who cares what the
psychic thought yesterday?!? Whatever is going to be in those boxes is
there when you make the selection! It's *not* going to change because
you're trying to outthink some half-baked fortune teller! Sure, I guess
you *could* have spent most of the day before thinking, "gee, that psychic
sure is a nice person. I'll only take one box so that s/he doesn't lose
their life savings", but FOR CRYIN' OUT LOUD, TAKE BOTH BOXES!)


(I guess the point that the one-boxers are trying to make is that if you
want to take both boxes, it will somehow change the contents of the boxes.
While what goes on in your head might have affected *yesterday*, when the
psychic put the money in the boxes, it's not affecting *today*, when
you're actually making the choice. If there's going to be a "hulluvalota"
money in one of the boxes, why wouldn't you take BOTH just to make sure?)


(Please, if I'm REALLY missing something, PLEASE point it out.)

Interesting.  There does seem to be a paradox here after all, or at 
least room for major disagreement.  

It's not exactly as if there's a penalty for taking the second box, 
carson, although it does seem that way.  Your choice isn't what 
determines the contents of the boxes.  The psychic's prediction 
last night is what determined that.  If the psychic is 100% 
accurate, and if you choose both boxes, then obviously that is what 
he must have predicted you would do.  

(Btw, *how* you will reach the decision to choose both boxes is 
irrelevant as far as the psychic is concerned.  Belief in psychic 
ability, unbelief in psychic ability, belief in free will, belief 
in fate, stubbornness, pure logic, pure greed, or whatever - in 
short, your entire thought process - counts for nothing in the 
psychic's mind.  The one and only thing he did was to predict what 
choice you would make.  He is 100% accurate.  Whatever choice you 
make, no matter how you arrive at it, *by definition* has to be the 
very choice he predicted you would make.)  

That is not to say that the psychic is robbing you of your free 
will, or that his prediction somehow forces you to make a certain 
choice.  In fact, you could almost say the opposite: that it's the 
foreknowledge of your choice that forces *him* to make the 
prediction he makes.  So, if you choose just box B, then that has 
to be what he predicted you'd do, and there will be $1,000,000 in 
box B (and $1,000 in box A); and if you choose both boxes, then 
*that* has to be what he predicted you'd do, and there will be 
$1,000 in box A and nothing at all in box B.  

So, I repeat, what's your choice?

I hate to ask a dumb question, since I'm not really following the arguments
here, but even if the psychic is 100% to date what's to say he's going to
be right NOW?  I know, it's probably irrelavant, but I just thought I'd
ask a stupid question.  :-)

That's a very good question.  If a psychic who was 100% accurate predicted
that you'd wear a hat today, couldn't you deliberately avoid wearing
a hat just to confound his prediction?  For that matter, if some
future supercomputer could analyse all of the data in a room you
were in, and caculated the exact position of your left arm 5 seconds
from now, couldn't you deliberately not hold your arm in that position?
Your question comes very close to the heart of this "paradox."

Hint:  What I noticed about "The Unexpected Hanging" is that the 
terms contradict each other.  If the judge simply said that the 
prisoner would be hanged on some unspecified date in the future, 
it would indeed come as a complete surprise when it came, and 
there's no paradox.  But by telling the prisoner that he was 
specifying a last possible day (next Saturday), the judge makes 
it impossible for the hanging to be a surprise if it takes place 
on that day.  The judge is making a promise he can't keep in 
every case: a date can't be both specified and unspecified at the 
same time.  If the prisoner guesses a day at random, he'll 
initially have a 1/7 chance of being right; if he's still alive 
Sunday night, he'll have a 1/6 chance of guessing right; on 
Monday night, a 1/5 chance; Tuesday night, 1/4; Wednesday night, 
1/3; Thursday night, 1/2; and Friday night (and here is where the 
judge messes up), 1/1.  When the lawyer concludes that the 
hanging can't take place on Saturday, he's wrong.  Of course it 
can take place on Saturday; it just won't be a surprise.  

Having figured that one out, I began to suspect that there had to 
be a similar contradiction in the setup for Newcombe's Paradox.  
I *think* I know what it is, but I'd like to hear what others 
have to say first.  

(actually, regarding "The Unexpected Hanging", the reason it was a
surprise was because he had "expected" it, and they killed him anyway. At
least, that's what I'd gathered.)

(I think what we're forgetting about Newcombe's Paradox is that our
decision on which boxes to choose *isn't* going to affect what's already
in the boxes. The $1,000 will either be in box A or B. The other box will
either have $1,000,000 or it will be empty. I'm really failing to see
what's so difficult about this.)

(BTW, the psychic is only *90%* accurate. I guess it's guys like me that
throw the accuracy out. ;) )

Obviously you choose box B.  Why?  Because when you do, the psychic knew
you would, and put a cool million in it for ya.  Well, at least there is a
90% chance that it it there.  Since we gotta believe inb the power of psychics
for this, we gotta think like the psychic put the money there after we made
the choice.  If you were able to alter that, then the 90% would go down
accordingly.

(OBVIOUSLY YOU CHOOSE *BOTH* BOXES!!!)

Not obvious to me.  If the psychic is 100% accurate, then if you
choose box B, then that means she predicted you'd choose box B,
and that means she put $1,000,000 in it.  In other words, if
you choose box B, you are certain to win $1,000,000.  Similarly,
if you chose both boxes, that means she predicted you'd choose
both boxes, and that means you win only $1000.  So "box B" is
a thousand times preferable to "both boxes".

It is very not obvious.  I'd say Box B, probably.

re #17: (She's only *90%* accurate.)

[Somewhere up there I tried to simplify the problem by asking
everyone to assume the psychic is 100% accurate.  If she's 90%
accurate, then you have to add "nine times out of ten" to the
statements in remmers' response #17.  That doesn't make your
choice any more obvious, unless I'm missing something.]

I agree.  To figure out how much money you would get on average simply multiply
by .9.  It doesn't really change anything.

(I really don't know how I can make this any clearer. You *can't* remove
the fact that the psychic is *90%* accurate if you're going to base your
guess on the psychic's prediction. My point couldn't care less *what* the
psychic predicted. The money is going to be in the boxes or it isn't.)


(I bet the reason that the psychic only claims *90%* accuracy is so that
when you people choose "only box B" [It still seems stupid to me, but I
digress], and there is only $1,000 in it, the psychic can say, "oops!
those pesky little fates...")

Then you are changing the situation.  This problem mandates acceptance of the
psychic.  It is fundamental, and cannot be looked at as a skam.  If you remove
the psychic then you must choose both boxes, because that is the only way
money will be there for sure.  If you keep the psychic there is money in the
box you pick 90% of teh time.  Not bad, eh?

(jason242, please type "only 0" after reading this and look at the
original paradox. I haven't changed the situation. There is no need to
accept the psychic's word as gold. There's no reason to even believe in
psychics for the sake of the problem. I'm simply trying to show why I
agree so strongly with the sentiments expressed in #0 in regards to why
anyone would pick both boxes. I don't think the psychic's prediction is at
all relevant at the time of the choosing of the boxes because the money is
already in the boxes and the amounts are not going to change because of
your choice of boxes.)

The psychic's prediction is relevant because it affected her choice
of what to put in the boxes.

(but it shouldn't affect your choice, because the money is already in the
boxes.)

Ok, carson, I did like you asked.  I still cannot see why you dismiss the
psychic.  When the psychic places the money is not relevant.  She might as
well place it a split second before you decide.  If you choose box B, there
is a 90% chance that you are now a millionaire.  Why?  Because the pychic
had a 90% chance of guessing correctly.  Try replacing the psychic with an
extremely lucky person, I think the basis of fortune telling is throwing you.

but is there a one hundred percent chance of you getting the $1000?

(I think it VERY relevant that the psychic put the money in the boxes
BEFORE the actual guessing, because it means that the money is already in
the boxes and won't be changed because of your guess, should you choose
something other than what the psychic predicted. Would the timing of the
psychic putting the money in the boxes be relevant if the psychic had
"predicted" after you'd vocalized your choice and THEN put the money in
the boxes? I'd hope so.)

(I think the problem is that the rest of you are trying to look at it from
a probability standpoint, when probability doesn't enter into this at all.
I'm going to work on a table to show my point.)

Carson, the 90% is very important.  What you propse is to alter that.  When 
analyzing a problem the 'A' #1 mistake people make is they alter the given
information.  The psychic was, is, and always will be 90% correct reguardless
of your decision.

(the *90%* {emphasis, lest we forget AGAIN> "accuracy" isn't important
because it's *not* *100%*. The psychic does not know what you will pick.
The psychic is using whatever abilities possessed to make a *guess*. These
abilities are not *100%*. The psychic is not predicting a future "as is".
I can see the reasoning in trying to outthink the psychic if you had known
before the money was put in the boxes that the psychic was going to put
money in the boxes based on your decision, but not what's said and done.)

(Here's a question: which choice is more greedy, box B or both boxes?)

Wow! A chance to do something productive on GREX!
Let me see if I can sum up both sides of this debate (even though its already
been done, Hey, we can never be two clear) The one boxers foster the belief
that by choosing both boxes it becomes more likely that ipso facto there was no
money in B, due to the psychic's knowledge of your choice (or high probability
thereof).  This view isn't influenced at all by the issue of time, more
specifically, when the psychic actually placed the s. The two boxer(s) (are
there others besides carson) see time as a definate player.  They don't believe
that the contents of the boxes could possibly change,  ipso facto.  If the
boxes were transparent, they might argue then one would know the contents, and
it would be impossible for box Balways have contained the opposite amount.
Surprisingly enough, both of these views are valid.  That is why it is known as
a paradox.  Lest we forget, a paradox is a statement or predicament which is
self contradictory in nature.  Paradoxes don't mean the end of the world, or
logic as we know it, for that matter, they just force us to look back and see
that some original assumptions were false.  In this case it is the belief in
knowledge of the physical future.  Obviously if man has knowledge of the future
then he also has the ability to act on his knowledge and falsify it.  This is
the PARADOX Newcombe found.   Again, paradoxes CAN exist.  They simply chalenge
our previous notions.  There is no need for the shouting match.

By the way, can we enter our own paradoxes here or do we just have to discuss
those elaborated initially.  Is anyone still reading this...answer me!!!

(obviously he's been listening to the goat.)

:)

carson, maybe i can help.  there is $1000 in box a.  this is a given.
now the question is, is there $1,000,000 in box b?  if you choose box
b only, there is a 90% chance of it containing the $$, because there
is a 90% chance that the psychic predicted correctly.  if you pick
both boxes, there is a 90% chance that you get $1000, and a 10% chance
that you get $1,001,000.  so, if you pick both, you get money, but if
you pick just b, there is a greater chance that you get more money.
does this help?

That makes it sound like your choice is what determines the
contents of the boxes, which is the problem many people have
with this.  If the boxes were transparent and you were blindfold,
would everyone else in the room see the contents change when
you made your choice?  It actually *has* been argued that the
contents of the boxes are indeterminate, by the way.  That seems
just a bit farfetched.

Here's a question:  If we have free will, can anyone predict the
future?  Or stated another way: In a universe where it is possible
to foresee the future with 90% accuracy, can there be such a
thing as free will?  

yes, your choice determins what is in the boxes, because the psychic
put is the money based on your choice.  you can't change the money
with your choice, because only your final choice affects the position
of the money.  changing your choice has no effect, the psychic knew
that you would change your choice (90% of the time)

(dang, you misunderstand. The psychic did not base what amount of money
will be in the boxes on your choice, but rather on his *prediction* of
your choice. This is a key difference.)

Re #36:  So, if you were blindfolded and the boxes were made of lucite,
what the other people in the room would see before you make your choice
would be a kind of indeterminate shimmer, a Heisenbergian haze inside
box B, which would resolve either into $1,000,000 or into nothing,
when you make your choice, depending on what your choice is?  

I'll have you know, carson, that all that I wrote was of my own creation,
and none of it was influenced in the slightest by a goat, or any other
barnyard animal (for that matter).  Did anyone even read what I wrote?

In the case of the transparent boxes, if one fosters a true belief in
pshychic knowledge of the future, then depending on your choice, the 
spectators will have always seen $1,000,000 or will have always seen nothing.
That's the whole idea behind the ipso facto change.  If I went back in time
and murdered Adolf Hitler, people won't notice a sudden change ("Wow, we
remember the Holocaust even though it never happened"), neither will Hitler
be in a Heisenbergian haze (I can only assume you're refering to his 
uncertainty principal, even though the connection seems a litle streched)
until the moment I do or do not shoot him.  He will just have never been
what he was.  In the same way, the contents of box B will have always
been, to all spectators, whatever it was finally.  That is the One Boxers'
point (or at least some of them).

To answer your question carson, I've already stated that psychic knowledge
of a physical future can't exist.  Therefore your hypothetical situation is
invalid.  It doesn't matter wheather one would have free will or not.  It 
just wouldn't be.

By the way, carson.  I haven't been in contact with any goats since the day
I was forced onto GREX.   SO THERE!!!!!!!!!!!

- Backtalk version 1.3.30 - Copyright 1996-2006, Jan Wolter and Steve Weiss