What's a boy to do?

On 31 Oct 2006 21:50:30 -0800, "riverman" wrote:


wrote:
On Tue, 31 Oct 2006 23:43:16 +0800, "riverman" wrote:


wrote in message
.. .
On 30 Oct 2006 16:17:56 -0800, "riverman" wrote:


First, list all the ways to throw three darts, A B and C.

ABC
ACB
BAC
BCA
CAB
CBA

Those aren't all the ways...think about it.

Remember, we are looking at a conditional probability; dart B has
already landed farther than dart A. So our list of outcomes is limited
to:

ABC
ACB
CAB

No, it isn't...think about it.

Our 'definition of success' is when dart C lands further than dart A,
which is clearly only the first two arrangements. So the probability of
throwing a third dart that lands farther than the first (given the
second dart has already landed farther than the first), is 2/3.

Its an unsettling conclusion, because people want to make the argument
that the distance from the bullseye affects the probability of each
outcome.

Well, perhaps it's because of that, or perhaps because it's
wrong...think about it.

However, every possible distance affects every outcome
equally, so they are all still equally likely, as counterintuitive as
it may be.

Maybe it would help you get on-target answer-wise if you tied a string
to your finger in exactly the same spot two days in a row...


Thats not possible.

I won't debate that, but it is possible for 2 darts to be the exact same
distance from a target...

HTH,
R

No its not, its a matter of measurement precision.

No, it isn't. Or in the alternative, if it is, neither you or anyone
else could, as an absolute, measure whether C was farther than A or A
was farther than C. And if the latter is the case, your answer, above,
to your own question would still be incorrect.

Look, Myron, I'm not trying to bust your balls, and I'm not a
mathematician, so I've no idea as to what mathematicians consider
"oldies but goodies" or whatever when it comes to such problems,
puzzles, or whatever they call them. Maybe you forgot to give all the
details. But if you're now making/claiming assumptions you didn't state
originally, that's on you, and your answer as written to your own
question, also as written, is just wrong. Stated as you stated it, yes,
it is entirely possible for 2 (or 3 or 154 or "x") darts to be _exactly_
the same distance, especially in the theoretical "math puzzle" sense,
from a target.

Or, if one is going to operate in the completely practical sense and
take the position that even with the most accurate measuring devices
available, there's still no way to say "absolutely _exactly_ the same
distance," then it is equally impossible to state as an absolute that it
is always possible to determine which dart is further from the target.

Another alternative is that you are now assuming, but didn't then, or
did then and didn't disclose, that the darts are really "points," and
that in one axis, occupy a single, discreet plane. But that brings up a
host of problems for your answer, including the theoretical vs.
practical and/or the accuracy-of-measurement issue.

HTH,
R

--riverman

wrote in message
news
On 31 Oct 2006 21:50:30 -0800, "riverman" wrote:

No its not, its a matter of measurement precision.

No, it isn't. Or in the alternative, if it is, neither you or anyone
else could, as an absolute, measure whether C was farther than A or A
was farther than C. And if the latter is the case, your answer, above,
to your own question would still be incorrect.

Look, Myron, I'm not trying to bust your balls, and I'm not a
mathematician, so I've no idea as to what mathematicians consider
"oldies but goodies" or whatever when it comes to such problems,
puzzles, or whatever they call them. Maybe you forgot to give all the
details. But if you're now making/claiming assumptions you didn't state
originally, that's on you, and your answer as written to your own
question, also as written, is just wrong. Stated as you stated it, yes,
it is entirely possible for 2 (or 3 or 154 or "x") darts to be _exactly_
the same distance, especially in the theoretical "math puzzle" sense,
from a target.

Or, if one is going to operate in the completely practical sense and
take the position that even with the most accurate measuring devices
available, there's still no way to say "absolutely _exactly_ the same
distance," then it is equally impossible to state as an absolute that it
is always possible to determine which dart is further from the target.

Another alternative is that you are now assuming, but didn't then, or
did then and didn't disclose, that the darts are really "points," and
that in one axis, occupy a single, discreet plane. But that brings up a
host of problems for your answer, including the theoretical vs.
practical and/or the accuracy-of-measurement issue.



LOL. Certainly you're busting my balls. At least, I hope so, because
otherwise you sound like you're raving. The probability of two darts landing
a distance that is so close to identical from a target that it is beyond the
ability to be discerned is inversely proportional to the precision of the
measuring device. The more precise our devices, the less likely it is to
happen, and we have some phenominally precise devices, so the likihood of
this happening is relatively zero....that means its so close to zero that it
has no effect on the calculations.

Next, you'll assert that the odds of a coin landing Heads is not 50%,
because we forgot to count the times it lands on its edge. Or gets eaten by
a bird, or something. Those are relatively zero, although a coin landing on
edge is actually possible (I've had it happen twice in my life).

The point of this puzzler was to illustrate that how you approach the answer
is often the key to making something that seems unsolvable, solvable.

Here's a real oldie but goodie. You are racing a slow tortoise, and you give
the tortoise a head start. In the first moments, you run quickly to where
the tortoise started from, but in that time it has moved ahead. So you
continue to run to where it has advanced to....but it has moved ahead a bit
more. So you run to where it is AGAIN, but it has yet again moved ahead!
This proves that you cannot win the race, as you cannot catch the tortoise,
right?

:-)
--riverman

On Wed, 1 Nov 2006 20:47:13 +0800, "riverman" wrote:


wrote in message
news
On 31 Oct 2006 21:50:30 -0800, "riverman" wrote:

No its not, its a matter of measurement precision.

No, it isn't. Or in the alternative, if it is, neither you or anyone
else could, as an absolute, measure whether C was farther than A or A
was farther than C. And if the latter is the case, your answer, above,
to your own question would still be incorrect.

Look, Myron, I'm not trying to bust your balls, and I'm not a
mathematician, so I've no idea as to what mathematicians consider
"oldies but goodies" or whatever when it comes to such problems,
puzzles, or whatever they call them. Maybe you forgot to give all the
details. But if you're now making/claiming assumptions you didn't state
originally, that's on you, and your answer as written to your own
question, also as written, is just wrong. Stated as you stated it, yes,
it is entirely possible for 2 (or 3 or 154 or "x") darts to be _exactly_
the same distance, especially in the theoretical "math puzzle" sense,
from a target.

Or, if one is going to operate in the completely practical sense and
take the position that even with the most accurate measuring devices
available, there's still no way to say "absolutely _exactly_ the same
distance," then it is equally impossible to state as an absolute that it
is always possible to determine which dart is further from the target.

Another alternative is that you are now assuming, but didn't then, or
did then and didn't disclose, that the darts are really "points," and
that in one axis, occupy a single, discreet plane. But that brings up a
host of problems for your answer, including the theoretical vs.
practical and/or the accuracy-of-measurement issue.



LOL. Certainly you're busting my balls. At least, I hope so, because
otherwise you sound like you're raving. The probability of two darts landing
a distance that is so close to identical from a target that it is beyond the
ability to be discerned is inversely proportional to the precision of the
measuring device. The more precise our devices, the less likely it is to
happen, and we have some phenominally precise devices, so the likihood of
this happening is relatively zero....that means its so close to zero that it
has no effect on the calculations.

Next, you'll assert that the odds of a coin landing Heads is not 50%,
because we forgot to count the times it lands on its edge. Or gets eaten by
a bird, or something. Those are relatively zero, although a coin landing on
edge is actually possible (I've had it happen twice in my life).

The point of this puzzler was to illustrate that how you approach the answer
is often the key to making something that seems unsolvable, solvable.

Heck, I'm willing to go completely real-world application. I've
witnessed throws for the first throw in which two darts were close
enough to the same distance from the bull that those throwing simply
re-threw. Heck, I, and every other darts-thrower out there, has hit the
rings and dividers - I'm willing to call that "the same distance
target." Take a 12" piece of string, tie loops in both ends, put a dart
through one loop and a marker in the other. Stick the dart into a board
and use the setup as a compass to mark a circular line. I'm willing to
call that "the same distance." There are darts players out there that
could hit such a line fairly consistently. As such, I've no problem
accepting the premise that in any given three-dart string, two could
well hit such a line. And I didn't bring up measurement precision, you
did.

IAC, given the "puzzle" as you stated it, and your answer as you stated
it, your answer was and is wrong.

HTH,
R

wrote in message
...
On Wed, 1 Nov 2006 20:47:13 +0800, "riverman" wrote:


wrote in message
news
On 31 Oct 2006 21:50:30 -0800, "riverman" wrote:

No its not, its a matter of measurement precision.

No, it isn't. Or in the alternative, if it is, neither you or anyone
else could, as an absolute, measure whether C was farther than A or A
was farther than C. And if the latter is the case, your answer, above,
to your own question would still be incorrect.

Look, Myron, I'm not trying to bust your balls, and I'm not a
mathematician, so I've no idea as to what mathematicians consider
"oldies but goodies" or whatever when it comes to such problems,
puzzles, or whatever they call them. Maybe you forgot to give all the
details. But if you're now making/claiming assumptions you didn't state
originally, that's on you, and your answer as written to your own
question, also as written, is just wrong. Stated as you stated it, yes,
it is entirely possible for 2 (or 3 or 154 or "x") darts to be _exactly_
the same distance, especially in the theoretical "math puzzle" sense,
from a target.

Or, if one is going to operate in the completely practical sense and
take the position that even with the most accurate measuring devices
available, there's still no way to say "absolutely _exactly_ the same
distance," then it is equally impossible to state as an absolute that it
is always possible to determine which dart is further from the target.

Another alternative is that you are now assuming, but didn't then, or
did then and didn't disclose, that the darts are really "points," and
that in one axis, occupy a single, discreet plane. But that brings up a
host of problems for your answer, including the theoretical vs.
practical and/or the accuracy-of-measurement issue.



LOL. Certainly you're busting my balls. At least, I hope so, because
otherwise you sound like you're raving. The probability of two darts
landing
a distance that is so close to identical from a target that it is beyond
the
ability to be discerned is inversely proportional to the precision of the
measuring device. The more precise our devices, the less likely it is to
happen, and we have some phenominally precise devices, so the likihood of
this happening is relatively zero....that means its so close to zero that
it
has no effect on the calculations.

Next, you'll assert that the odds of a coin landing Heads is not 50%,
because we forgot to count the times it lands on its edge. Or gets eaten
by
a bird, or something. Those are relatively zero, although a coin landing
on
edge is actually possible (I've had it happen twice in my life).

The point of this puzzler was to illustrate that how you approach the
answer
is often the key to making something that seems unsolvable, solvable.

Heck, I'm willing to go completely real-world application. I've
witnessed throws for the first throw in which two darts were close
enough to the same distance from the bull that those throwing simply
re-threw. Heck, I, and every other darts-thrower out there, has hit the
rings and dividers - I'm willing to call that "the same distance
target." Take a 12" piece of string, tie loops in both ends, put a dart
through one loop and a marker in the other. Stick the dart into a board
and use the setup as a compass to mark a circular line. I'm willing to
call that "the same distance." There are darts players out there that
could hit such a line fairly consistently. As such, I've no problem
accepting the premise that in any given three-dart string, two could
well hit such a line. And I didn't bring up measurement precision, you
did.

IAC, given the "puzzle" as you stated it, and your answer as you stated
it, your answer was and is wrong.

OK, whats the right answer then?

--riverman

On Wed, 1 Nov 2006 21:44:30 +0800, "riverman" wrote:


wrote in message
.. .
On Wed, 1 Nov 2006 20:47:13 +0800, "riverman" wrote:


wrote in message
news On 31 Oct 2006 21:50:30 -0800, "riverman" wrote:

No its not, its a matter of measurement precision.

No, it isn't. Or in the alternative, if it is, neither you or anyone
else could, as an absolute, measure whether C was farther than A or A
was farther than C. And if the latter is the case, your answer, above,
to your own question would still be incorrect.

Look, Myron, I'm not trying to bust your balls, and I'm not a
mathematician, so I've no idea as to what mathematicians consider
"oldies but goodies" or whatever when it comes to such problems,
puzzles, or whatever they call them. Maybe you forgot to give all the
details. But if you're now making/claiming assumptions you didn't state
originally, that's on you, and your answer as written to your own
question, also as written, is just wrong. Stated as you stated it, yes,
it is entirely possible for 2 (or 3 or 154 or "x") darts to be _exactly_
the same distance, especially in the theoretical "math puzzle" sense,
from a target.

Or, if one is going to operate in the completely practical sense and
take the position that even with the most accurate measuring devices
available, there's still no way to say "absolutely _exactly_ the same
distance," then it is equally impossible to state as an absolute that it
is always possible to determine which dart is further from the target.

Another alternative is that you are now assuming, but didn't then, or
did then and didn't disclose, that the darts are really "points," and
that in one axis, occupy a single, discreet plane. But that brings up a
host of problems for your answer, including the theoretical vs.
practical and/or the accuracy-of-measurement issue.



LOL. Certainly you're busting my balls. At least, I hope so, because
otherwise you sound like you're raving. The probability of two darts
landing
a distance that is so close to identical from a target that it is beyond
the
ability to be discerned is inversely proportional to the precision of the
measuring device. The more precise our devices, the less likely it is to
happen, and we have some phenominally precise devices, so the likihood of
this happening is relatively zero....that means its so close to zero that
it
has no effect on the calculations.

Next, you'll assert that the odds of a coin landing Heads is not 50%,
because we forgot to count the times it lands on its edge. Or gets eaten
by
a bird, or something. Those are relatively zero, although a coin landing
on
edge is actually possible (I've had it happen twice in my life).

The point of this puzzler was to illustrate that how you approach the
answer
is often the key to making something that seems unsolvable, solvable.

Heck, I'm willing to go completely real-world application. I've
witnessed throws for the first throw in which two darts were close
enough to the same distance from the bull that those throwing simply
re-threw. Heck, I, and every other darts-thrower out there, has hit the
rings and dividers - I'm willing to call that "the same distance
target." Take a 12" piece of string, tie loops in both ends, put a dart
through one loop and a marker in the other. Stick the dart into a board
and use the setup as a compass to mark a circular line. I'm willing to
call that "the same distance." There are darts players out there that
could hit such a line fairly consistently. As such, I've no problem
accepting the premise that in any given three-dart string, two could
well hit such a line. And I didn't bring up measurement precision, you
did.

IAC, given the "puzzle" as you stated it, and your answer as you stated
it, your answer was and is wrong.

OK, whats the right answer then?

Give a person a fish, and they'll eat for the day, teach a person to
fish, and you'll morally and financially ruin them...no, wait...that's
not the one I was looking for...aha - teach a person to fish, and
they'll eat for a lifetime.

HTH,
R

--riverman

wrote in message
news
On Wed, 1 Nov 2006 21:44:30 +0800, "riverman" wrote:

OK, whats the right answer then?

Give a person a fish, and they'll eat for the day, teach a person to
fish, and you'll morally and financially ruin them...no, wait...that's
not the one I was looking for...aha - teach a person to fish, and
they'll eat for a lifetime.

HA! HA! HA! HA! HA! HA! HA! HA!

He doesn't have a clue what the question is......much less the right answer!

HA! HA! HA! HA! HA! HA! HA! HA!

Wolfgang

"riverman" wrote in message ...

wrote in message
...
On Wed, 1 Nov 2006 20:47:13 +0800, "riverman" wrote:


wrote in message
news On 31 Oct 2006 21:50:30 -0800, "riverman" wrote:

No its not, its a matter of measurement precision.

No, it isn't. Or in the alternative, if it is, neither you or anyone
else could, as an absolute, measure whether C was farther than A or A
was farther than C. And if the latter is the case, your answer, above,
to your own question would still be incorrect.

Look, Myron, I'm not trying to bust your balls, and I'm not a
mathematician, so I've no idea as to what mathematicians consider
"oldies but goodies" or whatever when it comes to such problems,
puzzles, or whatever they call them. Maybe you forgot to give all the
details. But if you're now making/claiming assumptions you didn't
state
originally, that's on you, and your answer as written to your own
question, also as written, is just wrong. Stated as you stated it,
yes,
it is entirely possible for 2 (or 3 or 154 or "x") darts to be
_exactly_
the same distance, especially in the theoretical "math puzzle" sense,
from a target.

Or, if one is going to operate in the completely practical sense and
take the position that even with the most accurate measuring devices
available, there's still no way to say "absolutely _exactly_ the same
distance," then it is equally impossible to state as an absolute that
it
is always possible to determine which dart is further from the target.

Another alternative is that you are now assuming, but didn't then, or
did then and didn't disclose, that the darts are really "points," and
that in one axis, occupy a single, discreet plane. But that brings up
a
host of problems for your answer, including the theoretical vs.
practical and/or the accuracy-of-measurement issue.



LOL. Certainly you're busting my balls. At least, I hope so, because
otherwise you sound like you're raving. The probability of two darts
landing
a distance that is so close to identical from a target that it is beyond
the
ability to be discerned is inversely proportional to the precision of the
measuring device. The more precise our devices, the less likely it is to
happen, and we have some phenominally precise devices, so the likihood of
this happening is relatively zero....that means its so close to zero that
it
has no effect on the calculations.

Next, you'll assert that the odds of a coin landing Heads is not 50%,
because we forgot to count the times it lands on its edge. Or gets eaten
by
a bird, or something. Those are relatively zero, although a coin landing
on
edge is actually possible (I've had it happen twice in my life).

The point of this puzzler was to illustrate that how you approach the
answer
is often the key to making something that seems unsolvable, solvable.

Heck, I'm willing to go completely real-world application. I've
witnessed throws for the first throw in which two darts were close
enough to the same distance from the bull that those throwing simply
re-threw. Heck, I, and every other darts-thrower out there, has hit the
rings and dividers - I'm willing to call that "the same distance
target." Take a 12" piece of string, tie loops in both ends, put a dart
through one loop and a marker in the other. Stick the dart into a board
and use the setup as a compass to mark a circular line. I'm willing to
call that "the same distance." There are darts players out there that
could hit such a line fairly consistently. As such, I've no problem
accepting the premise that in any given three-dart string, two could
well hit such a line. And I didn't bring up measurement precision, you
did.

IAC, given the "puzzle" as you stated it, and your answer as you stated
it, your answer was and is wrong.

OK, whats the right answer then?

--riverman


You could have an almost infinite amount of darts the exact same distance
from the center. The only limiting number is how big the circle is from the
center and how big of diameter is the dart. There are an infinite number of
points equidistant from the center point. And it depends on neither the
precision or accuracy of the measurement. And in your measurement of the
distance it would be more accuracy and not precision. Precision only gives
more numbers after the decimal point.

"Calif Bill" wrote in message
.net...

You could have an almost infinite amount of darts the exact same distance
from the center.

No, actually, in practice you can't even have two.

The only limiting number is how big the circle is from the center and how
big of diameter is the dart.

English isn't even your second language, is it?

There are an infinite number of points equidistant from the center point.

Ah now, HERE'S a startling revelation! There's going to be quite a buzz in
geometric circles (if you'll pardon the expression) when word of this gets
out!

And it depends on neither the precision or accuracy of the measurement.

What does?

Hm....

Do you have any idea at all what this little charade is about?

And in your measurement of the distance it would be more accuracy and not
precision.

What would be?

Precision only gives more numbers after the decimal point.

And your contention here is that there is no difference we need bother
ourselves about between 6 inches and 6.99.*

Wolfgang
*particularly stupid......even for billie.

Calif Bill wrote:


You could have an almost infinite amount of darts the exact same distance
from the center. The only limiting number is how big the circle is from the
center and how big of diameter is the dart. There are an infinite number of
points equidistant from the center point. And it depends on neither the
precision or accuracy of the measurement. And in your measurement of the
distance it would be more accuracy and not precision. Precision only gives
more numbers after the decimal point.

Bill:
I'm not sure where to start, but there are a lot of little details in
your assertations that are erroneous. There's some truth also, so don't
lose hope :-)

First of all, yes the definition of a circle states there are an
infinite number of points in a plane that are equidistant from a given
point, but the liklihood of getting even two darts to land on that
circle is slim. (Just how slim is discussed in the second paragraph
below.) We don't even have to agree on how slim for now, but the the
more darts you want to have land on that circle, the less likely it is
to happen, and it approaches zero as the number of darts gets larger
and larger. Although the phrase 'almost infinite' is actually
meaningless, I assume you mean we are looking at numbers that are
growing huge beyond comprehension, so the liklihood of it happening is
shrinking tiny beyond comprehension.

Secondly, it IS a matter of precision, not accuracy. We don't care what
the actual distance from the center is, what we do care about is
whether or not two darts have the same measurement from the center,
even if that measurement is wrong. If we use an inaccurate tool, then
we might get a wrong amount (a broken ruler might show each dart to be
10.55 cm from the center, while they are both actually much less that
that). That's 'inaccurate', but if the numbers match, then we can still
assert that they are the same distance. If we use a ruler with really
fat indicator lines, we might get both measuring 10.55 cm, however if
we used a vernier caliper, calibrated or not, we might get one of them
measuring 10.550000000000001 cm and the other measuring
10.550000000000002 cm. Those are measures of high PRECISION, and my
assertation is that, no matter how the darts land, we can always use
more precise measuring devices until we find where the numbers vary.
And they always will, even if we have to go to electron microscope
levels. Just as no two snowflakes are alike, no two darts can land the
same distance from the center.

Now, I appreciate that some people might have an ingrained prejudice
against math because it doesn't always conform to their intuition (and
this might be you, or it might not). But when faced with something that
doesn't seem to 'fit' what we want to believe, there are two choices:
find out the rules of math and learn to analyze things according to
those rules, including learning the constraints and limitations and the
meaning of those, or else continue to assert that what we believe is
right because it 'feels right' to us, and use poorly structured
arguments or misnomers to claim that nothing has any validity, so we
can't possibly be wrong. That way lies madness.

--riverman

riverman wrote:
....If we use a ruler with really
fat indicator lines, we might get both measuring 10.55 cm, however if
we used a vernier caliper, calibrated or not, we might get one of them
measuring 10.550000000000001 cm and the other measuring
10.550000000000002 cm. Those are measures of high PRECISION, and my
assertation is that, no matter how the darts land, we can always use
more precise measuring devices until we find where the numbers vary....

If you can REALLY measure things on a scale several orders of magnitude
short of an angstrom, I REALLY wanna come play in your shop!

For the benefit of those who don't know what a vernier caliper is (a
friend of mine....who should have known better.....once thought a
micrometer I handed him was some sort of special application c-clamp
and proceeded to see how tight he could crank it.....I nearly smacked
his ****in' hea......well, never mind about that), suffice it to say
that the numbers displayed above were used for effect but Myron's point
is indisputable. Precision measuring instruments these days are such
that finding two darts whose distance from a given point is so close
that the difference can't be measured is vanishingly small. The REAL
difficulty (whether in a pub or a laboratory) would be in getting
agreement on exactly where to measure from.

Wolfgang