| Topic: |
Science > Physics |
| User: |
"PD" |
| Date: |
28 Feb 2006 02:05:34 PM |
| Object: |
Short, cute problem |
In an imaginary world, half of 6 is 4. In that world, what is one-third
of 12?
[I post this as a minor object lesson in showing how math and logic can
be self-consistent without having any bearing on reality, for those who
love to cling to "logic" in asserting what should be true of the world,
regardless whether it is in fact true.]
PD
.
|
|
| User: "Chumly HT" |
|
| Title: Re: Short, cute problem |
28 Feb 2006 02:28:05 PM |
|
|
"PD" <TheDraperFamily@gmail.com> wrote in message
news:1141157134.485774.299380@j33g2000cwa.googlegroups.com...
In an imaginary world, half of 6 is 4. In that world, what is one-third
of 12?
[I post this as a minor object lesson in showing how math and logic can
be self-consistent without having any bearing on reality, for those who
love to cling to "logic" in asserting what should be true of the world,
regardless whether it is in fact true.]
PD
Actually it would not be 4, it would be 3 + 0*j
(or 3 + 0*i for mathematicians)
.
|
|
|
| User: "richard miller" |
|
| Title: Re: Short, cute problem |
28 Feb 2006 03:10:03 PM |
|
|
"Chumly HT" <nospam@invalid.com> wrote in message
news:4404b24b$0$49444$892e7fe2@authen.yellow.readfreenews.net...
"PD" <TheDraperFamily@gmail.com> wrote in message
news:1141157134.485774.299380@j33g2000cwa.googlegroups.com...
In an imaginary world, half of 6 is 4. In that world, what is one-third
of 12?
[I post this as a minor object lesson in showing how math and logic can
be self-consistent without having any bearing on reality, for those who
love to cling to "logic" in asserting what should be true of the world,
regardless whether it is in fact true.]
PD
Actually it would not be 4, it would be 3 + 0*j
(or 3 + 0*i for mathematicians)
or 3 big-Mac and fries if you're an art student
(insert a weak smiley character to symbolize a small degree of irony whilst
not being able to properly convey the satire within the statement)
.
|
|
|
|
|
| User: "Patrick FitzGerald" |
|
| Title: Re: Short, cute problem |
28 Feb 2006 04:39:44 PM |
|
|
On 28 Feb 2006 12:05:34 -0800, "PD" <TheDraperFamily@gmail.com> wrote:
In an imaginary world, half of 6 is 4. In that world, what is one-third
of 12?
I have a Revelation that it would be
6 6 6
Patrick
.
|
|
|
|
| User: "Helmut Wabnig" |
|
| Title: Re: Short, cute problem |
28 Feb 2006 03:40:52 PM |
|
|
On 28 Feb 2006 12:05:34 -0800, "PD" <TheDraperFamily@gmail.com> wrote:
In an imaginary world, half of 6 is 4. In that world, what is one-third
of 12?
It is 5 1/3
w.
.
|
|
|
| User: "Dirk Van de moortel" |
|
| Title: Re: Short, cute problem |
28 Feb 2006 04:26:22 PM |
|
|
"Helmut Wabnig" <...._.--_.-_-..._-._.._--.@.-_---_-._*_.-_-> wrote in message news:aog90254pdm92eicpqe7il96lj603vnd29@4ax.com...
On 28 Feb 2006 12:05:34 -0800, "PD" <TheDraperFamily@gmail.com> wrote:
In an imaginary world, half of 6 is 4. In that world, what is one-third
of 12?
It is 5 1/3
That's what I had as well, but I found it a bit silly
since 12 has the digit 1, which does not exist :-)
Taking 2 as the "zero" I guess?
.... -4 -3 2 3 4 5 6 7 8 9 10 11 12 13 ...
An alternative:
Keeping the number system as is, We could say that
"half" = 2/3, giving 4 as "half" of 6,
and, for instance
"one-third" = 3/4, giving 9 as "one-third" of 12.
But it's still a bit silly :-)
Dirk Vdm
.
|
|
|
|
| User: "PD" |
|
| Title: Re: Short, cute problem |
28 Feb 2006 04:56:10 PM |
|
|
Helmut Wabnig wrote:
On 28 Feb 2006 12:05:34 -0800, "PD" <TheDraperFamily@gmail.com> wrote:
In an imaginary world, half of 6 is 4. In that world, what is one-third
of 12?
It is 5 1/3
w.
That's an interesting solution, and not the one I came up with. How did
you arrive at it?
FWIW, here is what occured to me:
Draw a number line with two marks at 0 and 6.
Halfway along the line, draw a mark and label it 4.
Now ask: What is the number that should sit halfway between 0 and 4?
PD
.
|
|
|
| User: "Arturo Magidin" |
|
| Title: Re: Short, cute problem |
28 Feb 2006 07:07:22 PM |
|
|
In article <1141167370.651770.257820@t39g2000cwt.googlegroups.com>,
PD <TheDraperFamily@gmail.com> wrote:
Helmut Wabnig wrote:
On 28 Feb 2006 12:05:34 -0800, "PD" <TheDraperFamily@gmail.com> wrote:
In an imaginary world, half of 6 is 4. In that world, what is one-third
of 12?
It is 5 1/3
That's an interesting solution, and not the one I came up with. How did
you arrive at it?
FWIW, here is what occured to me:
Draw a number line with two marks at 0 and 6.
Halfway along the line, draw a mark and label it 4.
Now ask: What is the number that should sit halfway between 0 and 4?
The problem, as I saw it, was that if you say "half of 6 is 4", then I
have no way of knowing if "12" still means "twice 6" or not. Or
whether "4" and '6" still stand for what I think they stand for (so:
is three times 4 the same as twice 6?) Does "half of x is y" mean that
y+y=x, or does it mean something else?
Way too many unknowns. Why would "a mark halfway down the line" mean
half of 6? Why are you free to label it any way you want?
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
magidin@math.berkeley.edu
.
|
|
|
| User: "PD" |
|
| Title: Re: Short, cute problem |
01 Mar 2006 08:39:28 AM |
|
|
Arturo Magidin wrote:
In article <1141167370.651770.257820@t39g2000cwt.googlegroups.com>,
PD <TheDraperFamily@gmail.com> wrote:
Helmut Wabnig wrote:
On 28 Feb 2006 12:05:34 -0800, "PD" <TheDraperFamily@gmail.com> wrote:
In an imaginary world, half of 6 is 4. In that world, what is one-third
of 12?
It is 5 1/3
That's an interesting solution, and not the one I came up with. How did
you arrive at it?
FWIW, here is what occured to me:
Draw a number line with two marks at 0 and 6.
Halfway along the line, draw a mark and label it 4.
Now ask: What is the number that should sit halfway between 0 and 4?
The problem, as I saw it, was that if you say "half of 6 is 4", then I
have no way of knowing if "12" still means "twice 6" or not.
Indeed. And following the algorithm that I suggested, it would seem
that half of 12 is 8, not 6.
Or
whether "4" and '6" still stand for what I think they stand for (so:
is three times 4 the same as twice 6?) Does "half of x is y" mean that
y+y=x, or does it mean something else?
Way too many unknowns. Why would "a mark halfway down the line" mean
half of 6? Why are you free to label it any way you want?
I don't claim my algorithm is unique and I appreciate the ambiguity of
the puzzle as it was posed (in a book about algebra, by the way). I
ascribed some meaning to what "half of" and went from there
PD.
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
magidin@math.berkeley.edu
.
|
|
|
|
|
| User: "PD" |
|
| Title: Re: Short, cute problem |
02 Mar 2006 09:26:37 AM |
|
|
PD wrote:
Helmut Wabnig wrote:
On 28 Feb 2006 12:05:34 -0800, "PD" <TheDraperFamily@gmail.com> wrote:
In an imaginary world, half of 6 is 4. In that world, what is one-third
of 12?
It is 5 1/3
w.
That's an interesting solution, and not the one I came up with. How did
you arrive at it?
FWIW, here is what occured to me:
Draw a number line with two marks at 0 and 6.
Halfway along the line, draw a mark and label it 4.
Now ask: What is the number that should sit halfway between 0 and 4?
PD
To extend this a bit further, the mark that is midway between 0 and 4
is 8/3, and the mark that is midway between 0 and 8/3 is then 16/9. I
believe this is a consistent (but non-commutatitve) way of defining the
multiplication.
By this same rule, half of 12 is 8, and with just a little work in
figuring out the nonlinearity of the line, you can deduce that
one-third of 12 is 6.
PD
.
|
|
|
| User: "hanson" |
|
| Title: Relativity a ... Short, cute problem |
02 Mar 2006 11:31:14 AM |
|
|
was ------- Re: Short, cute problem -----------
"PD" <TheDraperFamily@gmail.com> wrote in message
news:1141313197.848555.131570@j33g2000cwa.googlegroups.com...
Helmut Wabnig wrote
In an imaginary world, half of 6 is 4. In that world,
what is one-third of 12?
It is 5 1/3
w.
[PD]
That's an interesting solution, and not the one
I came up with. How did you arrive at it?
FWIW, here is what occured to me:
Draw a number line with two marks at 0 and 6.
Halfway along the line, draw a mark and label it 4.
Now ask: What is the number that should sit halfway between 0 and 4?
To extend this a bit further, the mark that is midway between 0 and 4
is 8/3, and the mark that is midway between 0 and 8/3 is then 16/9. I
believe this is a consistent (but non-commutatitve) way of defining the
multiplication. By this same rule, half of 12 is 8, and with just a little work in
figuring out the nonlinearity of the line, you can deduce that
one-third of 12 is 6.
PD
[hanson]
ahahahaha....see, all those different answers you and a host of
other posters came up with in this thread, in your *imaginary world*,
applying willfully, ad hoc, different rules for the "prediction" of
an outcome?
See how you get into each other's hair over these different
procedures and out comes in your imaginary worlds?...
As long as you keep it in the realm of the unreal, fine...
But the relativists, meaning the Einstein disciples, viciously
advocate to carry such type of mental masturbations over into
the normal, empirically experienced 3DT reality without thought,
qualms and inhibitions.
That makes these relafans out to be CRANKS,... the original
cranks & crack pots! That is cool as long as they stay masturbating
in the darkness of their Albertian cul de sac and keep on ejaculating
in there.... Have fun!... ahahahaha... AHAHAHAHAHA.... ahahahaha....
Androcles just posted a few interesting lines in this regard:
Re: Invalidity of Special Theory of Relativity
"Hexenmeister" <vanquish@broom.Mickey> wrote in message
news:cRxNf.71124$Q22.17@fe1.news.blueyonder.co.uk...
"JanPB" <filmart@gmail.com> wrote in message
news:1141284339.197994.225140@z34g2000cwc.googlegroups.com...
What difference to physics does it make what somebody's expectation
happens to be?
[Androcles]
Exactly.
Physics doesn't give a ***** what Einstein's expectation happens to be.
Time is a universal constant no matter what mathematical games you play
with speed, and experimental evidence from the Cassini probe at Saturn
proves
(PROVES!) that Einstein's guesses are 28 seconds a year off, a far greater
error than 38 microseconds a day from GPS.
Androcles.
[hanson]
then "kk" <mr_kurt_kingston followed up with another interesting observation
in news:1141306846.439034.290760@u72g2000cwu.googlegroups.com...
to which hard core relativist and Einstein disciple Randy Poe answered
in news:1141310704.340660.58790@z34g2000cwc.googlegroups.com...
=== "Synchronized" means only that they are made to
=== agree at the beginning of the experiment. There are
=== no guarantees on what happens after that. There is
=== nothing in a synchronization procedure which
=== has anything to do with any time past t=0."
..... hmm.... ahahaha... AHAHAHAHA... ahahahaha... AHAHAHAA...
So, finally we have it...out of the mouth of the babes of father Einstein:
"... no guarantees on what happens after... time past t=0"... ahahaha...
IOW, in Einstein's world ALL relativity outcomes are equally valid
even if they contravene, .... ahahaha... and since "anything to do with
any time past t=0" then, in Einstein's domains there are no predictions
of any kind and much less with any kind of "guarantee".... ahahahaha....
Poe, you made an extremely profound admission here... ahahahaha...
Under these circumstances I will join the hordes of master-con Albert.
Thanks for the laughs!... AHAHAHAHAHA... ahahahanson
.
|
|
|
|
|
|
|
| User: "" |
|
| Title: Re: Short, cute problem |
28 Feb 2006 05:37:13 PM |
|
|
PD wrote:
In an imaginary world, half of 6 is 4. In that world, what is one-third
of 12?
I'd guess 5, using the rule 1/m (*) n = (m+n)/m (with m=2 and n=6
in your first example).
[I post this as a minor object lesson in showing how math and logic can
be self-consistent without having any bearing on reality, for those who
love to cling to "logic" in asserting what should be true of the world,
regardless whether it is in fact true.]
PD
.
|
|
|
| User: "" |
|
| Title: Re: Short, cute problem |
28 Feb 2006 09:29:56 PM |
|
|
Lets see. 1/2 of 6 is 4.
This could mean that 1/2 * x = x - 2,
or it could mean that x - 2 = 2 * x.
These are not consistent statements. So, the only reasonable thing to
do is to take you literally.
Since half of 6 is ordinarily 3, but you say it's 4, then the result is
dilated as arithmetic is performed -> 0.
For delta 1/2 * 6, range is dilated s.t. f(x) = 4/3 * f(x)
So, the most reasonable assumption for 1/3 of 12 is that 1/3 * 12 = 4/3
* 4 = 16/3 = 5.33333
Of course, there are other answers, but I dont agree with any of them.
.
|
|
|
| User: "" |
|
| Title: Re: Short, cute problem |
01 Mar 2006 12:07:51 AM |
|
|
Is there any reason why 1/0 must be "undefined" instead of saying that
there are "infinitely many wrong solutions" ?
Maybe I'm splitting hairs here, but it really seems like you could view
it slightly differently and still have arithmetic remaining intact.
.
|
|
|
| User: "Robert Low" |
|
| Title: Re: Short, cute problem |
01 Mar 2006 01:13:12 AM |
|
|
wrote:
Is there any reason why 1/0 must be "undefined" instead of saying that
there are "infinitely many wrong solutions" ?
What do you mean by 'solution'? (And 'wrong solution',
for that matter.) But whatever you mean, in what sense
is saying that 0x=1 has infinitely many wrong solutions
any more help than 1x=2 has infinitely many wrong solutions?
Maybe I'm splitting hairs here, but it really seems like you could view
it slightly differently and still have arithmetic remaining intact.
So do it and present that as an alternative.
.
|
|
|
|
| User: "Robert Israel" |
|
| Title: Re: Short, cute problem |
01 Mar 2006 01:22:02 AM |
|
|
In article <1141193271.475261.249360@e56g2000cwe.googlegroups.com>,
<RadicalLibertarian@hotmail.com> wrote:
Is there any reason why 1/0 must be "undefined" instead of saying that
there are "infinitely many wrong solutions" ?
1/0 is not a question, so there's no such thing as "a solution" to it,
right or wrong.
"What is 1/0?" is a question.
It has infinitely many wrong solutions, but so do most other questions.
Robert Israel
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.
|
|
|
| User: "" |
|
| Title: Re: Short, cute problem |
01 Mar 2006 09:58:02 PM |
|
|
If one sets a = b, where a =/= b, then you can derive division by zero
or all kinds of wierd things.
Let 1 = 2, and see what happens.
Now, we dont say that 1 = 2 is "undefinfed", but 1/0 sure is.
So, what's so special about 1/0 that it gets this white glove treatment
? We dont roll out the red carpet for 1 = 2 ?
.
|
|
|
| User: "" |
|
| Title: Re: Short, cute problem |
02 Mar 2006 12:55:46 AM |
|
|
wrote:
If one sets a = b, where a =/= b, then you can derive division by zero
or all kinds of wierd things.
Let 1 = 2, and see what happens.
Now, we dont say that 1 = 2 is "undefinfed", but 1/0 sure is.
I'm pretty sure I've never said that anything was "undefinfed", or
"definfed"
for that matter. Not to mention "finfed".
So, what's so special about 1/0 that it gets this white glove treatment
? We dont roll out the red carpet for 1 = 2 ?
1 = 2 is an equation, which happens to be false. 1/0 is an expression,
not
an equation.
Robert Israel
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.
|
|
|
| User: "" |
|
| Title: Re: Short, cute problem |
04 Mar 2006 10:16:41 PM |
|
|
wrote:
RadicalLibertarian@hotmail.com wrote:
If one sets a = b, where a =/= b, then you can derive division by zero
or all kinds of wierd things.
Let 1 = 2, and see what happens.
Now, we dont say that 1 = 2 is "undefinfed", but 1/0 sure is.
I'm pretty sure I've never said that anything was "undefinfed", or
"definfed"
for that matter. Not to mention "finfed".
So, what's so special about 1/0 that it gets this white glove treatment
? We dont roll out the red carpet for 1 = 2 ?
1 = 2 is an equation, which happens to be false. 1/0 is an expression,
not
an equation.
Is it still an equation if it's false ?
Robert Israel
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.
|
|
|
| User: "Arturo Magidin" |
|
| Title: Re: Short, cute problem |
04 Mar 2006 11:07:56 PM |
|
|
In article <1141532201.800866.101660@t39g2000cwt.googlegroups.com>,
<RadicalLibertarian@hotmail.com> wrote:
israel@math.ubc.ca wrote:
[.snip.]
1 = 2 is an equation, which happens to be false. 1/0 is an expression,
not an equation.
Is it still an equation if it's false ?
Yes; an equation is a special kind of expression; one of its main
requirements, and the reason it is called an 'equation", is that it
must state that certain things are equal. In standard symbols, it must
contain a "=" sign.
And what does "false" mean? There are perfectly reasonable situations in
which the standard interpretation of "1=2" is that it is true in the
model.
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
magidin@math.berkeley.edu
.
|
|
|
| User: "" |
|
| Title: Re: Short, cute problem |
05 Mar 2006 12:20:01 AM |
|
|
In article <dudrnc$1l3h$1@agate.berkeley.edu>, (Arturo Magidin) writes:
In article <1141532201.800866.101660@t39g2000cwt.googlegroups.com>,
<RadicalLibertarian@hotmail.com> wrote:
israel@math.ubc.ca wrote:
[.snip.]
1 = 2 is an equation, which happens to be false. 1/0 is an expression,
not an equation.
Is it still an equation if it's false ?
Yes; an equation is a special kind of expression; one of its main
requirements, and the reason it is called an 'equation", is that it
must state that certain things are equal. In standard symbols, it must
contain a "=" sign.
It is worth to remember, too, that an equation in general is a
statement which is nearly always false. For example the equation
x^2 = 4
is false for nearly all values of x, with 2 and -2 being the
exceptions. Said exceptions (i.e those entities for which the
statment happens to be true) are the solutions of the equation. And
yes, it is possible for an equation to be always false (i.e. no
solutions).
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
.
|
|
|
|
|
|
| User: "" |
|
| Title: Re: Short, cute problem |
05 Mar 2006 12:05:40 AM |
|
|
wrote:
RadicalLibertarian@hotmail.com wrote:
Now, we dont say that 1 = 2 is "undefinfed", but 1/0 sure is.
I'm pretty sure I've never said that anything was "undefinfed", or
"definfed"
for that matter. Not to mention "finfed".
Isn't that someone who dines exclusively on shark soup?
Cheers - Chas
.
|
|
|
|
|
|
|
|
|
|
| User: "QCD Apprentice" |
|
| Title: Re: Short, cute problem |
28 Feb 2006 02:26:25 PM |
|
|
PD wrote:
In an imaginary world, half of 6 is 4. In that world, what is one-third
of 12?
[I post this as a minor object lesson in showing how math and logic can
be self-consistent without having any bearing on reality, for those who
love to cling to "logic" in asserting what should be true of the world,
regardless whether it is in fact true.]
I presume you mean you're defining a new "addition" operator such that 4
and 4 is 6?
.
|
|
|
|
|
Related Articles |
|
|
