Here's a simple one that stumps me.

Let's say I am playing a game of paintball and I shoot at someone's back as
they are running away from me. They are within range and the paintball hits
them. However, a recent puzzle I read about claims that's mathematically
impossible, because say he's thirty feet away and running away. The
paintball must travel thirty feet to reach him, but during the time it
traveled thirty feet, he has moved farther away. Let's say he's moved two
inches further. So, now the paintball must travel two inches more--but in
that time my victim has moved still further away. Each time the paintball
travels to where my target was, he has moved out of position. This could
supposedly be calculated out to infinity with the paintball never reaching
the target.

But it does. So what's wrong with the scenario? It's probably something
simple but I don't get it.

Dear Ernie Sty:

"Ernie Sty" <fake_email@yahoo.com> wrote in message
newsZqdnX2HxsqJ1bDbnZ2dnUVZ_gWdnZ2d@giganews.com ...

That is Zeno's paradox, it dates from before the birth of Christ,
and it was a "prank" on one particular school of philosophical
thought.


Solve for when the person running and the paintball are
coincident. Don't mess around with infinite sums where it is not
needed.

David A. Smith

Dear Ernie Sty:

"Ernie Sty" <fake_email@yahoo.com> wrote in message
newsZqdnX2HxsqJ1bDbnZ2dnUVZ_gWdnZ2d@giganews.com ...

That is Zeno's paradox, it dates from before the birth of Christ,
and it was a "prank" on one particular school of philosophical
thought.


Solve for when the person running and the paintball are
coincident. Don't mess around with infinite sums where it is not
needed.

David A. Smith

On Apr 23, 6:58 pm, "Ernie Sty" <[Only registered users see links. ]> wrote:

Look up the paradoxes of Zeno.
This is effectively the same thing as proving that 1/2+1/4+1/8+....
doesn't add up to infinity, it adds up to 2.

In short, the answer is the time that it takes for each successive
step is smaller and smaller. And an infinite series of smaller and
smaller time steps does not necessarily add up to an infinite amount
of time. Though the analysis above makes it look like an infinite
series of steps (it is), it is still a finite amount of time.

PD

On Apr 23, 6:58 pm, "Ernie Sty" <[Only registered users see links. ]> wrote:

Look up the paradoxes of Zeno.
This is effectively the same thing as proving that 1/2+1/4+1/8+....
doesn't add up to infinity, it adds up to 2.

In short, the answer is the time that it takes for each successive
step is smaller and smaller. And an infinite series of smaller and
smaller time steps does not necessarily add up to an infinite amount
of time. Though the analysis above makes it look like an infinite
series of steps (it is), it is still a finite amount of time.

PD

"N:dlzc D:aol T:com (dlzc)" <[Only registered users see links. ]> wrote in message
news:a9cXh.260806$[Only registered users see links. ]...


That's a wholly practical answer. :-)

"N:dlzc D:aol T:com (dlzc)" <[Only registered users see links. ]> wrote in message
news:a9cXh.260806$[Only registered users see links. ]...


That's a wholly practical answer. :-)

"PD" <[Only registered users see links. ]> wrote in message
news:1177435427.117981.323270@r35g2000prh.googlegr oups.com...

I don't understand, but you seem to have explained it very simply. I will
think about your explanation for a while and I suspect I'll get it
eventually. Thank you for explaining it.

Mathematically, will the succession of fractions you mentioned ever really
equal 2? Or will it go on infinitely without ever reaching 2?

Also, is it possible that space can't be divided into smaller and smaller
sections infinitely; that at some point there is a "smallest possible unit"
of space?

"PD" <[Only registered users see links. ]> wrote in message
news:1177435427.117981.323270@r35g2000prh.googlegr oups.com...

I don't understand, but you seem to have explained it very simply. I will
think about your explanation for a while and I suspect I'll get it
eventually. Thank you for explaining it.

Mathematically, will the succession of fractions you mentioned ever really
equal 2? Or will it go on infinitely without ever reaching 2?

Also, is it possible that space can't be divided into smaller and smaller
sections infinitely; that at some point there is a "smallest possible unit"
of space?

Dear Ernie Sty:

"Ernie Sty" <[Only registered users see links. ]> wrote in message
news:[Only registered users see links. ]...
....

When you get to the molecular level, "space" is a really poor
concept. It makes sense to talk about "average bond lengths",
but you don't actually find that exact bond length.

Space and time are like "population mean". Makes good sense when
you have a large statistical population, but means nothing for a
population of "a few".

David A. Smith