Marilyn Vos Savant on a famous "paradox"...
Bryan Shelton
I've long been an admirer of Marilyn's. Way back on March 15, 1987 in her
column in Parade Magazine, a reader submitted a very famous "paradox"
to her. It's a tribute to Marilyn's genius that she came up with such an
unusual spin on this puzzle. To be honest, I've never fully understood
her reply and at the time it never generated any comment, much to my
surprise. I'd like to know what the members of these newsgroups think
about her response. Below are the reader's original question and her
answer, in full:
-----------------------------------------------------------------------
"Their is four errers in this sentence." Since the preceding sentence
makes a specific claim --and hence must be either true or false-- I
would like for you to tell me if it's true and explain your choice.
--Dann Walker, Waco, Tx.
I believe the claim is false because I see only three errors. Corrected,
the sentence would read, "*There* *are* four *errors* in this sentence."
We cannot call the word "four" an error any more than we can call the word
"sentence" an error without changing the specific claim itself. If we
could, we may as well say the sentence should read, "*There* *are* four
*ducks* in this *bathtub*" and call the claim true. That is, of course,
if your bathtub does indeed contain four ducks!
Michael Knowlton
Hey, I follow, but.. damn if this isn't the type of thinking that gets
me in trouble at work everyday. I've been conditioned to lie and say;
"dang.. four errors?.. you sure is smart boss.. I swear I didn't see
that there four"
So.. if you take the sentence off of the page and present it to the
larger world.. maybe there ARE four errors?
MK
John Goodwin
On 10 Aug 1997 07:33:01 GMT, Bryan Shelton <br...@shell.c-com.net>
wrote:
>
>I've long been an admirer of Marilyn's. Way back on March 15, 1987 in her
>column in Parade Magazine, a reader submitted a very famous "paradox"
>to her. It's a tribute to Marilyn's genius that she came up with such an
>unusual spin on this puzzle. To be honest, I've never fully understood
>her reply and at the time it never generated any comment, much to my
>surprise. I'd like to know what the members of these newsgroups think
>about her response. Below are the reader's original question and her
>answer, in full:
>
>-----------------------------------------------------------------------
>"Their is four errers in this sentence." Since the preceding sentence
>makes a specific claim --and hence must be either true or false-- I
>would like for you to tell me if it's true and explain your choice.
> --Dann Walker, Waco, Tx.
>
>I believe the claim is false because I see only three errors. Corrected,
>the sentence would read, "*There* *are* four *errors* in this sentence."
>We cannot call the word "four" an error any more than we can call the word
>"sentence" an error without changing the specific claim itself. If we
>could, we may as well say the sentence should read, "*There* *are* four
>*ducks* in this *bathtub*" and call the claim true. That is, of course,
>if your bathtub does indeed contain four ducks!
In general, I would say it is dangererous to construct sentences that
deal with there own meaning.
It is, however dangerous to make any absolute rule.
It is also dangerous to make any statement about the veracity of such
sentences.
It is easy to come up with all sorts of strange oddities if a sentence
relates to its' own meaning.
Consider the following that I have just made up:
"The meaning of this sentence is far from clear"
"This sentence, if translated into French, would mean nothing"
Sometimes sentences of this kind can be amusing, sometimes they can
just give you a headache.
The sentence in your example is interesting because it is on the
borderline between talking about its' own construction, and its' own
meaning (I think).
J.G.
Frank Belsky
Bryan Shelton wrote:
>
> I've long been an admirer of Marilyn's. Way back on March 15, 1987 in her
> column in Parade Magazine, a reader submitted a very famous "paradox"
> to her. It's a tribute to Marilyn's genius that she came up with such an
> unusual spin on this puzzle. To be honest, I've never fully understood
> her reply and at the time it never generated any comment, much to my
> surprise. I'd like to know what the members of these newsgroups think
> about her response. Below are the reader's original question and her
> answer, in full:
>
> -----------------------------------------------------------------------
> "Their is four errers in this sentence." Since the preceding sentence
> makes a specific claim --and hence must be either true or false-- I
> would like for you to tell me if it's true and explain your choice.
> --Dann Walker, Waco, Tx.
>
> I believe the claim is false because I see only three errors. Corrected,
> the sentence would read, "*There* *are* four *errors* in this sentence."
> We cannot call the word "four" an error any more than we can call the word
> "sentence" an error without changing the specific claim itself. If we
> could, we may as well say the sentence should read, "*There* *are* four
> *ducks* in this *bathtub*" and call the claim true. That is, of course,
> if your bathtub does indeed contain four ducks!
Hi,
Corrrecting the fourth error: There are "four" errors, reads the
original sentence. Corrected, it should read, There are "three"... The
fourth error is an error of meaning.
The other three of grammar. Finally, I'm proud to say that I knew
Marilyn when she was an idiot. How do you know that she writes her
columns? If she pays somebody, then that's real genius.
Ron McDermott
Bryan Shelton wrote:
>
> To be honest, I've never fully understood her reply and at the
> time it never generated any comment, much to my surprise. I'd
> like to know what the members of these newsgroups think about
> her response. Below are the reader's original question and her
> answer, in full:
>
> -----------------------------------------------------------------------
> "Their is four errers in this sentence." Since the preceding sentence
> makes a specific claim --and hence must be either true or false-- I
> would like for you to tell me if it's true and explain your choice.
> --Dann Walker, Waco, Tx.
>
> I believe the claim is false because I see only three errors. Corrected,
> the sentence would read, "*There* *are* four *errors* in this sentence."
> We cannot call the word "four" an error any more than we can call the word
> "sentence" an error without changing the specific claim itself. If we
> could, we may as well say the sentence should read, "*There* *are* four
> *ducks* in this *bathtub*" and call the claim true. That is, of course,
> if your bathtub does indeed contain four ducks!
My response, which may be the same as hers after
translation, is that there are three errors of usage
and one error in the statement itself. She seems to
be saying the same thing, and indicating that the
statement error is not of the sentence. Hence the
SENTENCE doesn't have four errors, but the sentence
with its premise DOES...
Erron Speklin
On Thu, 14 Aug 1997 01:06:53 GMT, l...@neutronicstechcorp.com (Lee Kent
Hempfling) wrote:
>On Wed, 13 Aug 1997 12:54:25 GMT, J...@opticon.demon.co.uk (John
>Goodwin) wrote:
>
>>In general, I would say it is dangererous to construct sentences that
>>deal with there own meaning.
>It is?
>>It is, however dangerous to make any absolute rule.
>It is?
>>It is also dangerous to make any statement about the veracity of such
>>sentences.
>It is?
>>It is easy to come up with all sorts of strange oddities if a sentence
>>relates to its' own meaning.
>It is?
>>Consider the following that I have just made up:
>>"The meaning of this sentence is far from clear"
>The meaning of that sentence is very clear. It is far from clear.
>>"This sentence, if translated into French, would mean nothing"
>But it would. It would be like saying :
>This sentence is in English, if translated into French it would mean
>nothing.
>But it would mean something. That it was translated and in doing so
>became redundant. What's wrong with a redundant thing that is wrong
>with its being redundant?
>>Sometimes sentences of this kind can be amusing, sometimes they can
>>just give you a headache.
>Not if you think about them.
>>The sentence in your example is interesting because it is on the
>>borderline between talking about its' own construction, and its' own
>>meaning (I think).
>Which is why it is a paradox..... Which makes it perfectly correct in
>its structure.
>Lee Kent Hempfling
Lee, are you trying to be funny, or serious?
If you are trying to be funny, better luck next time.
If you are trying to be serious, I think you you need to try a little
harder.
>-------
Erron Speklin
John Goodwin
Read Lee's responses again. I think that you will find them wryly
amusing if you consider them for a little.
J.G.
Chris Menzel
Bryan Shelton <br...@shell.c-com.net> writes:
> I've long been an admirer of Marilyn's. Way back on March 15, 1987 in her
> column in Parade Magazine, a reader submitted a very famous "paradox"
> to her. It's a tribute to Marilyn's genius that she came up with such an
> unusual spin on this puzzle. To be honest, I've never fully understood
> her reply and at the time it never generated any comment, much to my
> surprise. I'd like to know what the members of these newsgroups think
> about her response. Below are the reader's original question and her
> answer, in full:
>
> -----------------------------------------------------------------------
> "Their is four errers in this sentence." Since the preceding sentence
> makes a specific claim --and hence must be either true or false-- I
> would like for you to tell me if it's true and explain your choice.
> --Dann Walker, Waco, Tx.
>
> I believe the claim is false because I see only three errors. Corrected,
> the sentence would read, "*There* *are* four *errors* in this sentence."
> We cannot call the word "four" an error any more than we can call the word
> "sentence" an error without changing the specific claim itself.
Seems to me she avoids the problem simply by choosing too narrow a
notion of an error. The idea isn't that "four" is an error, but that,
at first sight anyway, there is an error in *what the sentence says*
(which gives us a fourth error, in which case what the sentence says
is no longer in error, but then we're back to three errors, and off we
go down the bunny trail). But we can just make things more explicit
and Marilyn's answer won't wash.
There are both syntactic and semantic senses of "containing an error"
that can apply to written sentences. Syntactically, a sentence
contains an error if is contains a misspelled word (or a gramatical
mistake, etc.). Semantically, it contains an error if it says
something that isn't true, e.g., Reagan and Carter were both
democratic presidents. So say generally that a sentence *contains an
error* if it contains either a syntactic or semantic error, and that
the number of errors it contains is the total number of such. (We'd
have to be a little more precise about the number of semantic errors a
sentence can contain, but let's suppose that when the only problem is
that the sentence is false, there is exactly one semantic error.) So,
for example, "Regan and Carter were both democratic prezidents"
contains 3 errors, two syntactic and one semantic.
But now consider the sentence "This sentense contanes four errers."
Marilyn's response, which allowed only syntactic errors, will no
longer work. You can't pin down a definite truth value for the
sentence.
-chris
cme...@tamu.edu
Lee Kent Hempfling
It is?
It is?
It is?
>J.G.
>
Lee Kent Hempfling
Neutronics Technologies Corporation (USA)
ad...@neutronicstechcorp.com
Voice: 501-782-9999
http://www.neutronicstechcorp.com
A proud member of http://www.internetscipark.com
Martin Paul Bishop
The first three errors are red herrings -
"This sentence is false"
is enough
If its false its true
If its true its false
wow is that a paradox
hey lets get real and stop playing with words
gimme a REAL physical paradox
no hyperthetical ones like black holes and worm holes
Martin (Bubs) Bishop
G. Mark Stewart
Bryan Shelton (br...@shell.c-com.net) wrote:
: I've long been an admirer of Marilyn's. Way back on March 15, 1987 in her
: column in Parade Magazine, a reader submitted a very famous "paradox"
: to her. It's a tribute to Marilyn's genius that she came up with such an
: unusual spin on this puzzle. To be honest, I've never fully understood
: her reply and at the time it never generated any comment, much to my
: surprise. I'd like to know what the members of these newsgroups think
: about her response. Below are the reader's original question and her
: answer, in full:
: -----------------------------------------------------------------------
: "Their is four errers in this sentence." Since the preceding sentence
: makes a specific claim --and hence must be either true or false-- I
: would like for you to tell me if it's true and explain your choice.
: --Dann Walker, Waco, Tx.
: I believe the claim is false because I see only three errors. Corrected,
: the sentence would read, "*There* *are* four *errors* in this sentence."
: We cannot call the word "four" an error any more than we can call the word
: "sentence" an error without changing the specific claim itself. If we
: could, we may as well say the sentence should read, "*There* *are* four
: *ducks* in this *bathtub*" and call the claim true. That is, of course,
: if your bathtub does indeed contain four ducks!
Unless you can call a word which constitutes an error an errer.
Lee Kent Hempfling
>>-------
>Erron Speklin
>
No... but if you missed it, I can understand that.
Lee Kent Hempfling
But it sooooo much fuuuun.
Lee Kent Hempfling
>
>Read Lee's responses again. I think that you will find them wryly
>amusing if you consider them for a little.
>
>J.G.
>
I was beginning to think everyone took things too seriously. ;-)
Lee Kent Hempfling
On 14 Aug 1997 17:52:00 -0500, cme...@philebus.tamu.edu (Chris
Menzel) wrote:
>Seems to me she avoids the problem simply by choosing too narrow a
>notion of an error.
Thank you. But be careful.. she 'IS' the smartest living person......
>
>-chris
>cme...@tamu.edu
Lee Kent Hempfling
On 15 Aug 1997 03:44:41 GMT, tim...@is.dal.ca (Snowmit) wrote:
What fun.... what diversion... what a waste of time... but who cares..
what fun.....
>This a self-referential sentence
>
Nice title
>Thit sentence is not self-referential because 'thit' is not a word.
>-Douglas Hofstadter
>
But it is, since it refers to itself.
>This sentence has cabbage six words.
>-David Moser
thats right
>This gubblick contains many nonsklarkish English flutzpahs, but the overall
>pluggandisp can
>be glorked from context.
>-David Moser
>
I'd say that too.. very well written.
Sometimes its difficult to gleam pluggandisp from meer passages. It is
brilliant that the gubblick was able to insert many nonsklarkish
English flutzpahs to arrive at a single part of the pluggandisp from
context. There have been less reliable means of glorking.
>Does this sentence remind you of Agatha Christie?
>-Ann Trail
>
yep.
>If the meanings of 'true' and 'false' were switched, then this sentence
>wouldn't be false.
>-Pete Maclean
>
It sure would.
>You have of course, just begun the sentence that you have just finished
>reading.
>-Peter Brigham
>
How true that is.
>If you think this sentence is confusing, then change one pig.
>-Uilliam Bricken Jr.
>
I bet that would be confusing, especially to the pig.
>Although this sentence begins with the word 'because', it is false.
>-Douglas Hofstadter
>
Which is true.
>The world will little note nor long remember what we say here.
>-Abraham Lincoln
>
Gee... how could he have known.... but being humble causes such
things...
>I particularily like the Abraham Lincoln one. I wonder if he intended it
>to end up being what it became...
>
he was very humble and honestly believed his remarks scribbled on a
scrap of paper were worth the scrap of paper..
>Of course, let us never forget the words of St Paul:
>One of themselves, even a prophet of their own said, the Cretans are always
>liars, evil beasts, slow bellies. This witness is true...
> (Titus 1:12-13)
>
Since it was relayed that one of their own said it, I'd tend to
believe the witness as saying what he knew... if the second hand
reporting was accurate.
>Good luck with that headache!
>--
>
Thank you, it too will pass
jr...@no.spam.fastlane.net.no.spam
In sci.math Lee Kent Hempfling <l...@neutronicstechcorp.com> wrote:
> On 14 Aug 1997 17:52:00 -0500, cme...@philebus.tamu.edu (Chris
> Menzel) wrote:
> >Seems to me she avoids the problem simply by choosing too narrow a
> >notion of an error.
> Thank you. But be careful.. she 'IS' the smartest living person......
I assume this is sarcasm. Remember, she is also the "genius" who offered
the following "proof" that Andrew Weil could not have solved Fermat's Last
Theorem (even unashamed of embarrassment enough to publish it in a
paperback book!):
1. It has been proven that you cannot square the circle.
2. Andrew Weil's proof uses hyperbolic geometry.
3. The circle can be squared using hyperbolic geometry.
4. (1) and (3) imply that hyperbolic geometry is thus invalid.
5. (4) and (2) imply that Andrew Weil's proof is thus invalid.
Gosh. And to think that those mathematicians out there brewing up a pot
of coffee and hunkering down to review his voluminous proof are just
wasting their time!
For a bonus point: Who can explain what is wrong with the above "proof"
in just one sentence?
--
Jonathan R. Fox
Bryan Shelton
In sci.logic Frank Belsky <fj...@idt.net> wrote:
: > <<Statement of the paradox and Marilyn's reply snipped>>
: Hi,
: Corrrecting the fourth error: There are "four" errors, reads the
: original sentence. Corrected, it should read, There are "three"... The
: fourth error is an error of meaning. The other three of grammar.
But doesn't an "error of meaning" COUNT as an "error"? The original
sentence doesn't stipulate what KIND of errors it's referring to,
just errors in general. So the fact that there are "only" three
errors, ITSELF is an error, right? So now there are indeed FOUR
errors, right? But now that there are FOUR errors after all, the
sentence now makes a correct statement, which means the word "four"
is no longer an error, which brings the sentence back down to THREE
errors. And on and on... You DO understand the paradox?
What I really want to know is, what do you think of Marilyn's reply?
Is it valid in its attempt to circumvent the paradoxical nature
of the sentence?
Bryan
William L. Bahn
jr...@no.spam.fastlane.net.no.spam wrote in article
<5t4v9j$7...@news.cybernews.net>...
Knowing very little (O.K., nothing really) about squaring circles using
hyperbolic geometry, I will tackle it from a more generic standpoint:
If I rely on theory A to prove theory B and theory A later turns out to be
invalid, that only means that my proof of theory B is now open for
question, it does not mean that it is automatically invalid.
A footnote in my Diffy-Q book made a good point related to this when it was
going over Laplace Transforms. In the section on the conditions necessary
for the existence of the Laplace Transform for a given function, it made
note that if you use a Transform to solve a set of differential equations
and can verify the validity of the solution from the solution itself
(which, of course, is very straightforward when dealing with differential
equations) then the need to show the validity of the solution method is
removed - except, of course, during college examinations.
Bryan Shelton
In sci.logic John Goodwin <J...@opticon.demon.co.uk> wrote:
: > <<Statement of the paradox and Marilyn's reply snipped>>
: In general, I would say it is dangererous to construct sentences that
: deal with there own meaning.
: It is, however dangerous to make any absolute rule.
: It is also dangerous to make any statement about the veracity of such
: sentences.
: It is easy to come up with all sorts of strange oddities if a sentence
: relates to its' own meaning.
: Consider the following that I have just made up:
: "The meaning of this sentence is far from clear"
: "This sentence, if translated into French, would mean nothing"
: Sometimes sentences of this kind can be amusing, sometimes they can
: just give you a headache.
: The sentence in your example is interesting because it is on the
: borderline between talking about its' own construction, and its' own
: meaning (I think).
John, you're giving me your reflections (and they are quite interesting)
on the general difficulties involved in self-referential "paradoxes"
like the one submitted to Marilyn. However, what I really want to know
is, what do you think of her REPLY? She seems to be attempting
to circumvent the paradox in some oblique way by denying the self-
reference itself. Do you think her reasoning is valid? Please reply!
Bryan
Bryan Shelton
In sci.logic Martin Paul Bishop <mar...@mouette.win-uk.net> wrote:
: The first three errors are red herrings -
: "This sentence is false" is enough
: If its false its true
: If its true its false
: wow is that a paradox
: hey lets get real and stop playing with words
: gimme a REAL physical paradox
: no hyperthetical ones like black holes and worm holes
I've had to point this out several times now:
The issue is NOT how to resolve that well-known paradox; it can't
be resolved any more than any other of the self-referential paradoxes.
What interests me greatly is WHAT DO YOU MAKE OF MARILYN'S REPLY
to the paradox?! Is it valid? Does she make a logical point?
Or is she blowing smoke?
Bryan
Lee Kent Hempfling
On 16 Aug 1997 19:33:07 GMT, jr...@no.spam.fastlane.net.no.spam wrote:
>For a bonus point: Who can explain what is wrong with the above "proof"
>in just one sentence?
Godel.
John Goodwin
On 16 Aug 1997 22:50:05 GMT, Bryan Shelton <br...@shell.c-com.net>
wrote:
>In sci.logic John Goodwin <J...@opticon.demon.co.uk> wrote:
I don't want to start a flame war, but the answer is: Not much.
It seems to be a lot of unfocused prodding at the problem. There is
plenty of carefully reasoned theory about the issues raised, and this
does not seem to add something.
I must say, however, that I have never heard of this person, and do
not know the level of the audience at whom she was aiming, so the
above might be a little unfair.
J.G.
Robert Vienneau
Consider the sentence "Colorless green ideas sleep furiously."
There are four errors in this sentence.
The context determines what "this sentence" refers to. It need not
refer to the sentence "There are four errors in this sentence."
--
Robert Vienneau Try my Mac econ simulation
removethis!rv...@future.dreamscape.com game, Bukharin, at
ftp://csf.colorado.edu/econ/authors/Vienneau.Robert/Bukharin.sea
Whether strength of body or of mind, or wisdom, or virtue, are always
found...in proportion to the power or wealth of a man [is] a question
fit perhaps to be discussed by slaves in the hearing of their
masters, but highly unbecoming to reasonable and free men in search
of the truth. -- Rousseau
David Kastrup
Bryan Shelton <br...@shell.c-com.net> writes:
> In sci.logic Frank Belsky <fj...@idt.net> wrote:
>
> : > <<Statement of the paradox and Marilyn's reply snipped>>
>
> : Hi,
>
> : Corrrecting the fourth error: There are "four" errors, reads the
> : original sentence. Corrected, it should read, There are "three"... The
> : fourth error is an error of meaning. The other three of grammar.
>
> But doesn't an "error of meaning" COUNT as an "error"? The original
> sentence doesn't stipulate what KIND of errors it's referring to,
> just errors in general.
So you'd say the sentence "This sentence contains one
arflebarflegloop." is a paradox because it is really meant to say
"This sentence contains one error." and fails?
The problem is that you are trying to locate the falseness in
"errors", but a logically false sentence can have its "error"
everywhere, and perhaps even multiple versions of this? Perhaps the
sentence was meant to be "This sentence contains more than one error,
to be sure." and is entirely correct because half of it sounds
different?
--
David Kastrup Phone: +49-234-700-5570
Email: d...@neuroinformatik.ruhr-uni-bochum.de Fax: +49-234-709-4209
Institut für Neuroinformatik, Universitätsstr. 150, 44780 Bochum, Germany
Bryan Shelton
In sci.logic David Kastrup <d...@mailhost.neuroinformatik.ruhr-uni-bochum.de> wrote:
: Bryan Shelton <br...@shell.c-com.net> writes:
: > But doesn't an "error of meaning" COUNT as an "error"? The original
: > sentence doesn't stipulate what KIND of errors it's referring to,
: > just errors in general.
: So you'd say the sentence "This sentence contains one
: arflebarflegloop." is a paradox because it is really meant to say
: "This sentence contains one error." and fails?
Not at all. Why would you think there's a paradox anywhere in there?
If you presented me with the sentence and asked me if its claim is
true or false, I would reply, "I don't know. It contains a word that's
unfamiliar to me". If you then assured me that its author typed the
last word at the very moment he was having a minor stroke, and the
word came out garbled as he was attempting to type "error", then I
would be persuaded to say that the claim is true, since there would
then be ONE egregious spelling error. But there would STILL be no
"paradox" involved. I'm not sure what your point is!
I think it's good to point out here that even Marilyn exercised
*caution* in her reply. She was careful to say, "I *believe* the
claim is false because I *see* only three errors..." She was humble
enough to imply that she might have failed to recognize SOME errors.
: The problem is that you are trying to locate the falseness in
: "errors", but a logically false sentence can have its "error"
: everywhere, and perhaps even multiple versions of this? Perhaps the
: sentence was meant to be "This sentence contains more than one error,
: to be sure." and is entirely correct because half of it sounds
: different?
Oh yes, you can certainly go and complicate things as much as possible
and make it extremely difficult to pin down just EXACTLY how many errors
there are in a sentence, but this is totally irrelevent. Let's just
confine ourselves to simple, straightforward sentences which are clear
FROM THEIR CONTEXT where their errors lie. The original sentence
submitted to Marilyn is such a sentence. It has three obvious spelling
and grammar errors and one slightly less obvious semantic error, but
that last one is the real meat of the problem. I'm not interested in
anyone's ability to come up with unlimited shades of meaning which would
only make our job more difficult, I'm only interested in THE VALIDITY OF
MARILYN'S response to the paradox itself.
Bryan
Bryan Shelton
In sci.logic Ron McDermott <rom...@ibm.net> wrote:
: > <<The statement of the paradox and Marylin's reply snipped>>
: My response, which may be the same as hers after
: translation, is that there are three errors of usage
: and one error in the statement itself. She seems to
: be saying the same thing, and indicating that the
: statement error is not of the sentence. Hence the
: SENTENCE doesn't have four errors, but the sentence
: with its premise DOES...
But what kind of sense does it make to say that the "statement error"
is not "of the sentence"? What about THIS sentence: "Adolf Hitler
was President of the United States of America". Would anybody in his
right mind try to say that there is no error in this sentence? That
the "premise" is in error, but somehow the sentence itself is perfectly
error-free?
I don't believe that Marilyn is attacking the paradox from this
particular angle; that is, I don't think she's trying to give preference
to one particular KIND of error over another. Rather, she seems to be
attempting to apply some kind of oblique LOGICAL reasoning to persuade
us that we can't really consider that particularly nasty FOURTH error
as being legitimate. What do YOU think?
Bryan
Bryan Shelton
In sci.logic Chris Menzel <cme...@philebus.tamu.edu> wrote:
: > <<Statement of the paradox and Marilyn's reply snipped>>
: Seems to me she avoids the problem simply by choosing too narrow a
: notion of an error. The idea isn't that "four" is an error, but that,
: at first sight anyway, there is an error in *what the sentence says*
: (which gives us a fourth error, in which case what the sentence says
: is no longer in error, but then we're back to three errors, and off we
: go down the bunny trail). But we can just make things more explicit
: and Marilyn's answer won't wash.
This seems to be the strong consensus; namely, that Marilyn is using
too narrow a notion of "error". However, that one sentence keeps coming
back to haunt me: "We cannot call the word 'four' an error any more than
we can call the word 'sentence' an error without changing the specific
claim itself". This suggests to me that she is well aware of ALL notions
and kinds of "errors", but for some oblique logical reason that escapes
me, she thinks the paradoxical "four" cannot be considered in this
particular context.
: <<snip>>
: But now consider the sentence "This sentense contanes four errers."
: Marilyn's response, which allowed only syntactic errors, will no
: longer work. You can't pin down a definite truth value for the
: sentence.
Chris, you've lost me now. How does THIS sentence differ substantively
from the original? Please explain!
Bryan
Alan Morgan
In article <5t4v9j$7...@news.cybernews.net>,
<jr...@no.spam.fastlane.net.no.spam> wrote:
[Vos Savant's "proof"]
>1. It has been proven that you cannot square the circle.
>2. Andrew Weil's proof uses hyperbolic geometry.
>3. The circle can be squared using hyperbolic geometry.
>4. (1) and (3) imply that hyperbolic geometry is thus invalid.
>5. (4) and (2) imply that Andrew Weil's proof is thus invalid.
>
>Gosh. And to think that those mathematicians out there brewing up a pot
>of coffee and hunkering down to review his voluminous proof are just
>wasting their time!
>
>For a bonus point: Who can explain what is wrong with the above "proof"
>in just one sentence?
I'll bite. It is not true that you can't square the circle. It
is true that you can't square the circle in Euclidean geometry.
The fact that you can do it in hyperbolic geometry does not make
hyperbolic geometry invalid any more than being able to express
2/3 using real numbers but not integers makes real numbers invalid.
Okay, so I used more than one sentence. Do I have the right idea?
Alan
John Goodwin
On 18 Aug 1997 19:50:00 GMT, ika...@alumni.caltech.edu (Ilias
Kastanas) wrote:
>In article <5t4v9j$7...@news.cybernews.net>,
> <jr...@no.spam.fastlane.net.no.spam> wrote:
>>In sci.math Lee Kent Hempfling <l...@neutronicstechcorp.com> wrote:
>>> On 14 Aug 1997 17:52:00 -0500, cme...@philebus.tamu.edu (Chris
>>> Menzel) wrote:
>>
>>> >Seems to me she avoids the problem simply by choosing too narrow a
>>> >notion of an error.
>>
>>> Thank you. But be careful.. she 'IS' the smartest living person......
>>
>>I assume this is sarcasm. Remember, she is also the "genius" who offered
>>the following "proof" that Andrew Weil could not have solved Fermat's Last
>>Theorem (even unashamed of embarrassment enough to publish it in a
>>paperback book!):
>>
>>1. It has been proven that you cannot square the circle.
>>2. Andrew Weil's proof uses hyperbolic geometry.
>>3. The circle can be squared using hyperbolic geometry.
>>4. (1) and (3) imply that hyperbolic geometry is thus invalid.
>>5. (4) and (2) imply that Andrew Weil's proof is thus invalid.
>>
>>Gosh. And to think that those mathematicians out there brewing up a pot
>>of coffee and hunkering down to review his voluminous proof are just
>>wasting their time!
>>
>>For a bonus point: Who can explain what is wrong with the above "proof"
>>in just one sentence?
>
>
>
> I am distressed to admit that it is vacuously _correct_ ... as
>it refers to "Andrew Weil" ...
Sometimes, concise answers can be confusing.
I cannot determine the meaning of your post.
Please elucidate.
J.G.
> Ilias
>
>
John Goodwin
On Mon, 18 Aug 1997 19:52:58 +0100, Chris Marriott
<ch...@chrism.demon.co.uk> wrote:
>In article <5ta2e0$2v4$1...@Radon.Stanford.EDU>, Alan Morgan
><amo...@Xenon.Stanford.EDU> writes
>>I'll bite. It is not true that you can't square the circle. It
>>is true that you can't square the circle in Euclidean geometry.
>>The fact that you can do it in hyperbolic geometry does not make
>>hyperbolic geometry invalid any more than being able to express
>>2/3 using real numbers but not integers makes real numbers invalid.
>
>You can express 2/3 using real numbers; it just so happens that you
>can't do so if you choose to use 10 as your number base.
>
>In base 3 arithmetic, for example, 2/3 is exactly represented as the
>real number "0.2".
The interesting thing, that nobody (yet) seems to have noticed, is
that you evidently *can* express two thirds using real numbers. It's
easy.
Look:
2/3
See?
J.G.
Chris Marriott
In article <5ta2e0$2v4$1...@Radon.Stanford.EDU>, Alan Morgan
<amo...@Xenon.Stanford.EDU> writes
>I'll bite. It is not true that you can't square the circle. It
>is true that you can't square the circle in Euclidean geometry.
>The fact that you can do it in hyperbolic geometry does not make
>hyperbolic geometry invalid any more than being able to express
>2/3 using real numbers but not integers makes real numbers invalid.
You can express 2/3 using real numbers; it just so happens that you
can't do so if you choose to use 10 as your number base.
In base 3 arithmetic, for example, 2/3 is exactly represented as the
real number "0.2".
Chris
----------------------------------------------------------------
Chris Marriott, Microsoft Certified Solution Developer.
SkyMap Software, U.K. e-mail: ch...@skymap.com
Visit our web site at http://www.skymap.com
Ilias Kastanas
In article <5t4v9j$7...@news.cybernews.net>,
<jr...@no.spam.fastlane.net.no.spam> wrote:
>In sci.math Lee Kent Hempfling <l...@neutronicstechcorp.com> wrote:
>> On 14 Aug 1997 17:52:00 -0500, cme...@philebus.tamu.edu (Chris
>> Menzel) wrote:
>
>> >Seems to me she avoids the problem simply by choosing too narrow a
>> >notion of an error.
>
>> Thank you. But be careful.. she 'IS' the smartest living person......
>
>I assume this is sarcasm. Remember, she is also the "genius" who offered
>the following "proof" that Andrew Weil could not have solved Fermat's Last
>Theorem (even unashamed of embarrassment enough to publish it in a
>paperback book!):
>
>1. It has been proven that you cannot square the circle.
>2. Andrew Weil's proof uses hyperbolic geometry.
>3. The circle can be squared using hyperbolic geometry.
>4. (1) and (3) imply that hyperbolic geometry is thus invalid.
>5. (4) and (2) imply that Andrew Weil's proof is thus invalid.
>
>Gosh. And to think that those mathematicians out there brewing up a pot
>of coffee and hunkering down to review his voluminous proof are just
>wasting their time!
>
>For a bonus point: Who can explain what is wrong with the above "proof"
>in just one sentence?
I am distressed to admit that it is vacuously _correct_ ... as
it refers to "Andrew Weil" ...
Ilias
Alan Morgan
In article <33f8c535....@news.demon.co.uk>,
John Goodwin <J...@opticon.demon.co.uk> wrote:
>On Mon, 18 Aug 1997 19:52:58 +0100, Chris Marriott
><ch...@chrism.demon.co.uk> wrote:
>
>><amo...@Xenon.Stanford.EDU> writes
>>>I'll bite. It is not true that you can't square the circle. It
>>>is true that you can't square the circle in Euclidean geometry.
>>>The fact that you can do it in hyperbolic geometry does not make
>>>hyperbolic geometry invalid any more than being able to express
>>>2/3 using real numbers but not integers makes real numbers invalid.
>>
>>You can express 2/3 using real numbers; it just so happens that you
>>can't do so if you choose to use 10 as your number base.
Hey, I never said you couldn't. I picked a bad example because
everyone assumed that there was some point to the number being
non-terminating. There wasn't. All I was saying is that 2/3 (or
1/2 if you prefer) is a valid operation over the reals but invalid
over the integers. This does not make the reals somehow invalid.
Just as being able to square the circle in hyperbolic geometry but
not in Euclidean does not make hyperbolic geometry invalid.
That, IMHO, is the flaw in Vos Savant's reasoning.
Alan
Óscar Martín
Snowmit wrote:
> Self referential sentences and partially self-referential sentences are
> great fun. I was first introduced to the things in a column by Douglas
> Hofstadter which ran in Scientific American. The column can be found in
> his book Metamagical Themas.
>
> But enough plugging. Here are some more of those things.
Well, here's my little contribution (I hope my english is good enough...
er, mine, not this sentence's):
1) If this condition is in a different tense, this sentence would be
grammatical.
2) If you change the word at the end of this sentence for its
opposite, it will become true.
(Just a one-sentence statement of the famous two-sentences
paradox.)
3) Fill in the _____.
4) I wish I was a complete
5a) The truth of the statement in the line next to my end depends on
the width of your news-reader.
Your news-reader is really wide.
5b) The truth of the statement in the line next to my end depends on
the width of your news-reader. 1=1.
1=0.
8) Sentence out of order. (Use another, please.)
6) I've tried hard to write a non self-referential sentence, but I'm
not sure whether I have got it.
7) This paragraph has the same meaning as the one below it... Hey!
Hey, please, write a paragraph below me! I want to have a meaning!
Bryan L. Dumka
On 17 Aug 1997 00:39:47 GMT, Bryan Shelton <br...@shell.c-com.net>
wrote:
>In sci.logic Chris Menzel <cme...@philebus.tamu.edu> wrote:
>
>: > <<Statement of the paradox and Marilyn's reply snipped>>
>
>
>: <<snip>>
>: But now consider the sentence "This sentense contanes four errers."
>: Marilyn's response, which allowed only syntactic errors, will no
>: longer work. You can't pin down a definite truth value for the
>: sentence.
>
>Chris, you've lost me now. How does THIS sentence differ substantively
>from the original? Please explain!
>
>Bryan
By forcing the focus to the particular sentence quoted. There is no
ambiguity about what sentence is being referred to by the four errors.
There is no longer a possible sentence, not in view, that the errors
may refer to, as there is when 'this sentence' is the object in the
original example.
Another way of dealing with the problem is to correct the sentence to
read: 'There were four errors in this sentence.'
If you count number and tense corrections to the verb as separate
errors, you create a TRUE and accurate statement.
Bryan L. Dumka
»»»»-------------------»
'Pluralitas non est ponenda sine necessitate.'
William of Ockham (c. 1280-1349)
Chris Menzel
: : But now consider the sentence "This sentense contanes four errers."
: : Marilyn's response, which allowed only syntactic errors, will no
: : longer work. You can't pin down a definite truth value for the
: : sentence.
: Chris, you've lost me now. How does THIS sentence differ substantively
: from the original? Please explain!
Substantively it doesn't. I changed the original sentence slightly
because in my attempt to clarify things I explicitly defined what it
is for a sentence to "contain n errors", for some number n. So I
simply rephrased the original so it would use that defined
expression. It was was a stylistic change only.
-chris
cme...@tamu.edu
Martin Paul Bishop
As I pointed out above it is easy to use words to lie or otherwise
bend a truth to the point where ther whole sentence is meaningless
(or a "paradox").I do not accept this as a paradox and I feel that
anyone wasting time trying to find proof in it is blowing smoke.
BTW in a recent copy of FOCUS magazine (Is it available in the
USA?) there was an article proving (in the eyes of certain
scientists) that time travel is possible. They state that this
requires a massive amount of antimatter.
I have tried to get permission to post some or all of this article
but have as yet received no response from the publishers.
Do I believe it ? Does that matter (anti or otherwise!)
The article's title is Time Travel yes, it can be done
It appeared on pages104 thru 108 of FOCUS August 1997
The publishers e-mail is: Fo...@tower.telme.com
See if you can get a better response
Regards
Martin (Bubs) Bishop
____________________________________________________________________
It takes just one dream to evaluate the chance of choice
Jon Anderson
____________________________________________________________________
jr...@no.spam.fastlane.net.no.spam
In sci.math Ilias Kastanas <ika...@alumni.caltech.edu> wrote:
> In article <5t4v9j$7...@news.cybernews.net>,
> <jr...@no.spam.fastlane.net.no.spam> wrote:
> >I assume this is sarcasm. Remember, she is also the "genius" who offered
> >the following "proof" that Andrew Weil could not have solved Fermat's Last
> >Theorem (even unashamed of embarrassment enough to publish it in a
> >paperback book!):
> >
> >1. It has been proven that you cannot square the circle.
> >2. Andrew Weil's proof uses hyperbolic geometry.
> >3. The circle can be squared using hyperbolic geometry.
> >4. (1) and (3) imply that hyperbolic geometry is thus invalid.
> >5. (4) and (2) imply that Andrew Weil's proof is thus invalid.
> I am distressed to admit that it is vacuously _correct_ ... as
> it refers to "Andrew Weil" ...
Yes, I was horrified to discover my error the moment I had sent this post
into the vast realm of irretrievability. I am surprised how long it
actually took for someone to point out my goof.
Apologies to Andrew Wiles.
--
Jonathan R. Fox
jr...@no.spam.fastlane.net.no.spam
In sci.math Alan Morgan <amo...@Xenon.Stanford.EDU> wrote:
> In article <5t4v9j$7...@news.cybernews.net>,
> <jr...@no.spam.fastlane.net.no.spam> wrote:
> [Vos Savant's "proof"]
> >1. It has been proven that you cannot square the circle.
> >2. Andrew Weil's proof uses hyperbolic geometry.
> >3. The circle can be squared using hyperbolic geometry.
> >4. (1) and (3) imply that hyperbolic geometry is thus invalid.
> >5. (4) and (2) imply that Andrew Weil's proof is thus invalid.
> >
> >Gosh. And to think that those mathematicians out there brewing up a pot
> >of coffee and hunkering down to review his voluminous proof are just
> >wasting their time!
> >
> >For a bonus point: Who can explain what is wrong with the above "proof"
> >in just one sentence?
> I'll bite. It is not true that you can't square the circle. It
> is true that you can't square the circle in Euclidean geometry.
> The fact that you can do it in hyperbolic geometry does not make
> hyperbolic geometry invalid any more than being able to express
> 2/3 using real numbers but not integers makes real numbers invalid.
> Okay, so I used more than one sentence. Do I have the right idea?
That is exactly the answer I was looking for. You cannot square the
circle in Euclidean geometry -- that is what statement (1) is referring
to. Vos Savant thought that applies to all geometries.
--
Jonathan R. Fox
Ilias Kastanas
In article <33f8c5b4....@news.demon.co.uk>,
John Goodwin <J...@opticon.demon.co.uk> wrote:
>On 18 Aug 1997 19:50:00 GMT, ika...@alumni.caltech.edu (Ilias
>>>I assume this is sarcasm. Remember, she is also the "genius" who offered
>>>the following "proof" that Andrew Weil could not have solved Fermat's Last
>>>Theorem (even unashamed of embarrassment enough to publish it in a
>>>paperback book!):
>>>
>>>1. It has been proven that you cannot square the circle.
>>>2. Andrew Weil's proof uses hyperbolic geometry.
>>>3. The circle can be squared using hyperbolic geometry.
>>>4. (1) and (3) imply that hyperbolic geometry is thus invalid.
>>>5. (4) and (2) imply that Andrew Weil's proof is thus invalid.
>>>
>>>Gosh. And to think that those mathematicians out there brewing up a pot
>>>of coffee and hunkering down to review his voluminous proof are just
>>>wasting their time!
>>>
>>>For a bonus point: Who can explain what is wrong with the above "proof"
>>>in just one sentence?
>>
>>
>> I am distressed to admit that it is vacuously _correct_ ... as
>>it refers to "Andrew Weil" ...
>
>Sometimes, concise answers can be confusing.
>I cannot determine the meaning of your post.
>Please elucidate.
There is Andrew Wiles... and there is Andre Weil...
Ilias
John Goodwin
On 20 Aug 1997 05:48:54 GMT, ika...@alumni.caltech.edu (Ilias
Kastanas) wrote:
Ah, it all becomes clear. spelling never was my strong point!
J.G.
Zyryab
On 20 Aug 1997, Blake Wilfong wrote:
>In sci.logic Bryan Shelton <br...@shell.c-com.net> wrote:
>[quoting Marilyn's Parade column]
>: "Their is four errers in this sentence." Since the preceding sentence
>: makes a specific claim --and hence must be either true or false-- I
>: would like for you to tell me if it's true and explain your choice.
>: --Dann Walker, Waco, Tx.
>
>: I believe the claim is false because I see only three errors. Corrected,
>: the sentence would read, "*There* *are* four *errors* in this sentence."
>: We cannot call the word "four" an error any more than we can call the word
>: "sentence" an error without changing the specific claim itself. If we
>: could, we may as well say the sentence should read, "*There* *are* four
>: *ducks* in this *bathtub*" and call the claim true. That is, of course,
>: if your bathtub does indeed contain four ducks!
>[Bryan requests an explanation of Maralyn's explanation.]
>
>This is a question for William Safire, not Marilyn Vos Savant.
Since I think it's masochistic to think about things like that,
Maybe it's a better question for Marylin Manson :)
>Check a
>Webster's dictionary; you'll find that intent or belief is key in deciding
>whether something is an error. If I say, "Adolf Hitler was a president
>of the United States," I err only if I believe he really was. Otherwise
>I am merely lying. This may be what Marilyn is trying to say.
I don't think so. The above statements refer to you lying or
being in error. The sentence in question refers to itself. When
you say "Adolph Hitler was a president of the US" your intent may
determine whether you're lying or just in error, but your
statement is definitely false (as far as I know)
>Another related possibility: Marilyn may be saying that we can't decide
>whether there is a fourth error because we can't assume we know the
>author's intent. Perhaps the sentence was meant to read, "There are four
>cheeses in this sandwich." In that case, the sentence contains four
>errors, and its truth or falsehood is unknown. Again, no paradox.
Ok, let's go with intent. I think it's obvious that the person
who sent in the letter was sending it to her as an example of a
paradox, so there's the intent, right? In any case, paradoxes
like "this sentence is false" have become so popular that even
Parade readers have heard of them by now. I think what Marylin is
trying to do is impress the Parade readers by showing
them that she thinks about things differently than they, and
since she *is* the smartest person alive, she has to be right.
>(In other words, we could argue, "The author meant to say 'three' instead
>of 'four'. That is a fourth error." But we have no proof of this.
>We could equally well argue, "The author meant to say 'cheeses' instead of
>'errers' and 'sandwich' instead of 'sentence'.")
I completely agree with you on this point. Except I meant
"disagree" instead of "agree", and "the following" instead of
"this" :)
If Marylin was the smartest person on earth, she'd know that
having the highest IQ score doesn't make one the smartest person
on earth.
-Zyryab
-=-=-=-=-=-=-=-=-=-=-
www.stickwigglies.com
-=-=-=-=-=-=-=-=-=-=-
The following people have recently sent me junk e-mail.
Note to e-mail harvesters: Don't use these addresses.
pa...@webcom.com, reachm...@baltmd.com, cybe...@nevwest.com
offsho...@answerme.com , appli...@answerme.com
adha...@bogo.co.uk, bee...@scs.unr.edu
Peter Hallowes
Blake Wilfong wrote:
>
> In sci.logic Bryan Shelton <br...@shell.c-com.net> wrote:
> [quoting Marilyn's Parade column]
> : "Their is four errers in this sentence." Since the preceding sentence
> : makes a specific claim --and hence must be either true or false-- I
> : would like for you to tell me if it's true and explain your choice.
> : --Dann Walker, Waco, Tx.
>
> : I believe the claim is false because I see only three errors. Corrected,
> : the sentence would read, "*There* *are* four *errors* in this sentence."
> : We cannot call the word "four" an error any more than we can call the word
> : "sentence" an error without changing the specific claim itself. If we
> : could, we may as well say the sentence should read, "*There* *are* four
> : *ducks* in this *bathtub*" and call the claim true. That is, of course,
> : if your bathtub does indeed contain four ducks!
> [Bryan requests an explanation of Maralyn's explanation.]
>
> Webster's dictionary; you'll find that intent or belief is key in deciding
> whether something is an error. If I say, "Adolf Hitler was a president
> of the United States," I err only if I believe he really was. Otherwise
> I am merely lying. This may be what Marilyn is trying to say.
>
> no errors at all, just deliberate misspelling and word substitution.
> There is no paradox, and the sentence is simply false.
>
> Another related possibility: Marilyn may be saying that we can't decide
> whether there is a fourth error because we can't assume we know the
> author's intent. Perhaps the sentence was meant to read, "There are four
> cheeses in this sandwich." In that case, the sentence contains four
> errors, and its truth or falsehood is unknown. Again, no paradox.
>
> of 'four'. That is a fourth error." But we have no proof of this.
> We could equally well argue, "The author meant to say 'cheeses' instead of
> 'errers' and 'sandwich' instead of 'sentence'.")
Hold on a second. A sentence can't have any semantic interpretation
unless it is syntactically correct - unless we disregard constructive
logic and resort to heuristics, in which case the above sentence
requires analysis using a natural language algorithm; all current
natural language algorithms being not very good.
Peter
Mike Oliver
In article <5uo2u1$341$1...@uhura1.phoenix.net>,
Bryan Shelton <br...@shell.c-com.net> wrote:
>Here is my favorite example of a simple goof made by Marilyn vos Savant
>herself: remember that silly puzzle that goes, "If a chicken and a half
>can lay an agg and a half in a day and a half, how long would it take
>ONE chicken to lay ONE egg"? Marilyn announced to her readers in one
>of her columns that all her life she had never understood the point
>of this problem whose answer was OBVIOUSLY "one"!!
Actually, it looks to me as though MvS has a point here. Since
the half-a-chicken is dead, it doesn't lay any eggs at all, so
the live chicken is laying an egg per day.
Though I don't really want to be around when she lays the half-an-egg.
--
Disclaimer: I could be wrong -- but I'm not. (Eagles, "Victim of Love")
Finger for PGP public key, or visit http://www.math.ucla.edu/~oliver.
1500 bits, fingerprint AE AE 4F F8 EA EA A6 FB E9 36 5F 9E EA D0 F8 B9
G. Mark Stewart
Bryan Shelton (br...@shell.c-com.net) wrote:
: In sci.logic G. Mark Stewart <gm...@grayfox.svs.com> wrote:
: : dlo...@inlink.nospam.com wrote:
: : : Why do people seemingly _have_ to come up with paradoxes, puzzles and
: : : logic traps to try and ensnare Mensans and scientists?
: : Because it's the only thing that does. And it makes the little people
: : feel closer to us, thus encouraging brotherhood and love.
: Or to put it without using your amusing hubris, it gives a real thrill
: to catch the intellectually high-and-mighty in puzzles and logic traps.
: Kinda shows that EVERYONE puts his pants on one leg at a time, and that
: EVERYONE will make simple mistakes occasionally.
Do you realize that hubris was originally Greek for an offense of the
gods?
And don't you think that to be the object of others' efforts to overcome
intelligence is in itself an ego boost?
And do you realize that Marily vos Savant is generally considered to be
a bit of a goof on r.o.m., due not only to her studying IQ tests to boost
her score, but to her penchant for blunders?
And do you think I should ask more questions in this post and use it as
a puzzle itself to trip up more Mensans and scientists?
Is six questions enough?
Or is seven?
GMS
http://www.svs.com/users/gmark
: Here is my favorite example of a simple goof made by Marilyn vos Savant
: herself: remember that silly puzzle that goes, "If a chicken and a half
: can lay an agg and a half in a day and a half, how long would it take
: ONE chicken to lay ONE egg"? Marilyn announced to her readers in one
: of her columns that all her life she had never understood the point
: of this problem whose answer was OBVIOUSLY "one"!! Yes, the great
: Marilyn vos Savant, listed in Guinness under "Highest IQ", having
: scored an IQ of about 230 as a child, completely and ignominiously
: tripped up on a common childhood riddle! (Other readers eventually
: explained it to her) There is some comfort knowing that we're ALL
: pretty much in the same boat...
: Bryan
Wayne Dyer
dlo...@inlink.nospam.com <dlo...@inlink.nospam.com> done wrote:
>
> Everything snipped
>
> Why do people seemingly _have_ to come up with paradoxes, puzzles and
> logic traps to try and ensnare Mensans and scientists?
Keeps 'em distracted and away from the keg.
-W-
"Three of one, two of each, BAH! Pump it up & hand me a cup!"
dlo...@inlink.nospam.com
On 5 Sep 1997 04:48:01 GMT, Bryan Shelton <br...@shell.c-com.net>
wrote:
>In sci.logic G. Mark Stewart <gm...@grayfox.svs.com> wrote:
>
>: dlo...@inlink.nospam.com wrote:
>: : Why do people seemingly _have_ to come up with paradoxes, puzzles and
>: : logic traps to try and ensnare Mensans and scientists?
>
>: Because it's the only thing that does. And it makes the little people
>: feel closer to us, thus encouraging brotherhood and love.
>
>Or to put it without using your amusing hubris, it gives a real thrill
>to catch the intellectually high-and-mighty in puzzles and logic traps.
>Kinda shows that EVERYONE puts his pants on one leg at a time, and that
>EVERYONE will make simple mistakes occasionally.
Did it ever occur to you that _most_ of us like to think of ourselves
as 'Joe Average'.
>
>Here is my favorite example of a simple goof made by Marilyn vos Savant
>herself: remember that silly puzzle that goes, "If a chicken and a half
>can lay an agg and a half in a day and a half, how long would it take
>ONE chicken to lay ONE egg"? Marilyn announced to her readers in one
>of her columns that all her life she had never understood the point
>of this problem whose answer was OBVIOUSLY "one"!! Yes, the great
>Marilyn vos Savant, listed in Guinness under "Highest IQ", having
>scored an IQ of about 230 as a child, completely and ignominiously
>tripped up on a common childhood riddle! (Other readers eventually
>explained it to her) There is some comfort knowing that we're ALL
>pretty much in the same boat...
Some of us are not into puzzles and conundrums and get annoyed when
people pop all these things at us. Some of us are also more verbally
oriented than mathematically oriented and are not very good at math
type puzzles. Each of us is different with different strengths and
weakness.
>
>Bryan
Lee Rudolph
>>Or to put it without using your amusing hubris, it gives a real thrill
>>to catch the intellectually high-and-mighty in puzzles and logic traps.
>>Kinda shows that EVERYONE puts his pants on one leg at a time,
I've never understood that idiom (so I'm diverting this thread to
alt.usage.english). On either common reading of "pants" (American
English: equivalent to "trousers"; British English: equivalent to
Am.Eng. "underpants"), I would find it either difficult or impossible
(for geometric, not topological, reasons) to "put my pants on one leg
at a time". Surely I am not alone in putting on my pants both legs
simultaneously?
Lee Rudolph
dlo...@inlink.nospam.com
On 5 Sep 1997 04:48:01 GMT, Bryan Shelton <br...@shell.c-com.net>
wrote:
>In sci.logic G. Mark Stewart <gm...@grayfox.svs.com> wrote:
>
>: dlo...@inlink.nospam.com wrote:
>: : Why do people seemingly _have_ to come up with paradoxes, puzzles and
>: : logic traps to try and ensnare Mensans and scientists?
>
>: Because it's the only thing that does. And it makes the little people
>: feel closer to us, thus encouraging brotherhood and love.
>
>Or to put it without using your amusing hubris, it gives a real thrill
>to catch the intellectually high-and-mighty in puzzles and logic traps.
>Kinda shows that EVERYONE puts his pants on one leg at a time, and that
>EVERYONE will make simple mistakes occasionally.
>
>Here is my favorite example of a simple goof made by Marilyn vos Savant
>herself: remember that silly puzzle that goes, "If a chicken and a half
>can lay an agg and a half in a day and a half, how long would it take
>ONE chicken to lay ONE egg"? Marilyn announced to her readers in one
>of her columns that all her life she had never understood the point
>of this problem whose answer was OBVIOUSLY "one"!! Yes, the great
>Marilyn vos Savant, listed in Guinness under "Highest IQ", having
>scored an IQ of about 230 as a child, completely and ignominiously
>tripped up on a common childhood riddle! (Other readers eventually
>explained it to her) There is some comfort knowing that we're ALL
>pretty much in the same boat...
And BTW, it can't be all that common, I've never heard of it.
>
>Bryan
neiGHBor
I like paradoxes not becasue I want to trip people up with them, but
because they teach me something. Resolving the paradox makes you
smarter, it shows you where your errors were.
Jeffrey Lockshin
How about this one:
Head over heels in love.
Isn't your head always over your heels?...
Being bilingual, I can think of dozens of these illogical statements.
Now, let's get back to math, and leave THESE puzzles for the
linguists.
Jeff
Eric Dew
>
>> >Here is my favorite example of a simple goof made by Marilyn vos Savant
>> >herself: remember that silly puzzle that goes, "If a chicken and a half
>> >can lay an agg and a half in a day and a half, how long would it take
>> >ONE chicken to lay ONE egg"? Marilyn announced to her readers in one
>> >of her columns that all her life she had never understood the point
>> >of this problem whose answer was OBVIOUSLY "one"!! Yes, the great
>> >Marilyn vos Savant, listed in Guinness under "Highest IQ", having
>> >scored an IQ of about 230 as a child, completely and ignominiously
>> >tripped up on a common childhood riddle! (Other readers eventually
>> >explained it to her) There is some comfort knowing that we're ALL
>> >pretty much in the same boat...
First off, this ain't a paradox.
Second, shouldn't the answer be 1-1/2 days? I mean, if 1.5 chickens can
lay 1.5 eggs in 1.5 days, then 3 chickens can lay 3 eggs also in 1.5 days,
where each chicken lays one egg in 1.5 days. So, the answer should be 1.5
days. Ain't that correct?
EDEW
Peter Hallowes
Firstly, there is no mention that it is a paradox.
Secondly, yes.
> EDEW
Russ Grossman
To me also this is a simple problem amenable to canceling and
indeed the correct answer is that it takes 1.5 days for 1 chicken
to lay 1 egg. It is immediately obvious. I don't see the catch
unless you get all wound up about talking about 1/2 a chicken
which you have to assume is merely a quantitative abstraction
since we know that 1/2 a chicken can't lay anything. If Marilyn
expressed the reasons for her answer than she's correct (e.g. a 1/2
chicken isn't going to lay anything).
However, I would have made a different assumption that the 1/2 chicken
was merely an abstraction just as the 1/2 egg is an abstraction and
therefore I get 1.5 instead of 1. To assume that the 1/2 chicken is
not an abstraction, but, then to accept the 1/2 egg as an abstraction
seems inconsistent to me. Then again, the speaker has really left
it up to the listener to provide the assumptions and Marilyn just chose
the one that she wanted perhaps for discussion purposes just like this.
IQ is one measure of intelligence. Another important measure
is EQ, emotional quotient, since knowledge must be organized in
a framework of love, beauty and compassion. I very much like
Occam's razor. It's part of my framework because simplicity is
beauty.
Since we can only go on the information presented, you have to make
some assumptions. Using Occam's razor it is simpliest to use only 1
assumption, not 2. Therefore, to assume that both are abstractions is
the simpliest answer and the one that is most probably right and the
one that the speaker is most probably expecting. To produce 2
assumptions tends to go against the simpliest solution.
I would have answered 1.5 days, but, then again I'm not Marilyn and
I'm sure the world is thankful for that ;^)
Regards,
Russ
kem...@de.ibm.com
In <edewEG7...@netcom.com>, ed...@netcom.com (Eric Dew) writes:
>
>>
>>> >Here is my favorite example of a simple goof made by Marilyn vos Savant
>>> >herself: remember that silly puzzle that goes, "If a chicken and a half
>>> >can lay an agg and a half in a day and a half, how long would it take
>>> >ONE chicken to lay ONE egg"? Marilyn announced to her readers in one
>>> >of her columns that all her life she had never understood the point
>>> >of this problem whose answer was OBVIOUSLY "one"!! Yes, the great
>>> >Marilyn vos Savant, listed in Guinness under "Highest IQ", having
>>> >scored an IQ of about 230 as a child, completely and ignominiously
>>> >tripped up on a common childhood riddle! (Other readers eventually
>>> >explained it to her) There is some comfort knowing that we're ALL
>>> >pretty much in the same boat...
>
>First off, this ain't a paradox.
>
>Second, shouldn't the answer be 1-1/2 days? I mean, if 1.5 chickens can
>lay 1.5 eggs in 1.5 days, then 3 chickens can lay 3 eggs also in 1.5 days,
>where each chicken lays one egg in 1.5 days. So, the answer should be 1.5
>days. Ain't that correct?
>
>EDEW
and a million chickens lay a million (or should I use billions,trillions?) of eggs a day
though how many eggs do we get per second ?
Keith Tarrant
"Their is four errers in this sentence."
This is like "what is the square root of 4".
Not a paradox. Just a question with two answers:
Three errors in the sentence, but then the sentence as a whole is
false because of the counting error.
- OR-
Four errors in the sentence, including the counting error, and then
sentence as a whole is true.
Call me simplistic, but the question was not designed to be solved
with higher mathmatics. It was just designed to have a neat answer.
keith tarrant
And Marilyn doesn't claim to be the smartest person in the world.
She "only" claims to have the highest score on the Sanford-Binet IQ
test.
Still, she's an impressive woman, even with the rare mistake.
Jim Nastos
Keith Tarrant wrote:
>
> "Their is four errers in this sentence."
>
> This is like "what is the square root of 4".
>
> Not a paradox. Just a question with two answers:
The first of the above is not a question.. thus, it has no 'answers.'
This is merely a statement, and it has interpretations.
The statement is either TRUE, or FALSE.
> Call me simplistic, but the question was not designed to be solved
> with higher mathmatics. It was just designed to have a neat answer.
I can call you other things, as well.
You see, the paradoxical thing here is that once you have identified
the three errors in the sentence, you claim that the interpretation of
the
statement is false - jence, the fourth error, making it true. But then
you claim the statement is true? The fourth error that was believed
to be there is no longer there.
What came first: the chicken or the egg?
Jim
Jason
Jim Nastos wrote:
> What came first: the chicken or the egg?
>
> Jim
This is how we find out how paradoxes are resolvable. To solve this, you
must limit the definition of either a chicken or the egg.
According to evolution, the egg came first. Naturally, the first
fully-chicken chicken came out of the egg of a slightly different bird.
In other words, we must limit the egg to a place either before or after
the chicken.
If the egg MUST be an egg laid by a chicken, then the chicken came first.
If the chicken MUST have come out of an egg, the egg came first.
paradoxes simply point out problems caused by ambiguity in our thought
patterns.
Jason
--
This is a lie.