"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".

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

Zeno's paradox.
An infinite number of steps can add up to a finite number, which was
something that was incomprehensible to some Greeks.
1/2 + 1/4 + 1/8 + 1/16 + ..... = 1, not infinity.

Here, the intervals of time are getting smaller and smaller and
smaller. Even though there's an infinite number of them, they add up
to a finite time.

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

Zeno's paradox.
An infinite number of steps can add up to a finite number, which was
something that was incomprehensible to some Greeks.
1/2 + 1/4 + 1/8 + 1/16 + ..... = 1, not infinity.

Here, the intervals of time are getting smaller and smaller and
smaller. Even though there's an infinite number of them, they add up
to a finite time.

On Apr 24, 1:50 pm, "Ernie Sty" <[Only registered users see links. ]> wrote:

*Mathematically*, no, any *finite* set of terms never quite adds to 2.

But here is where you get into tricky ground, because you are taking a
real situation (runner, paintball) and analyzing it with a
mathematical *model*. In the *model*, you are breaking down a physical
process into a set of steps. The place where the conceptual breakdown
is then thinking that the *reality* really does operate according to
the artifice of this model. That is, does the paintball *really* have
to take the first step, then the second step, then the third step, and
so on? This is where the brain fools you, because you are tempted to
think that just because you've *mentally* broken down the path into an
infinite number of steps, the paintball really does have to execute an
infinite number of steps. In other words, you are forcing a mental
concept and trying to turn it into a reality. The paintball doesn't
know anything about steps. It just goes from here to the runner. So if
you run into a conceptual roadblock, the first thing you should do is
check whether what's blocking about the model really has any reality.
This should have been flagged for you by the bogus question, "What's
the smallest possible physical step through space?" There ARE NO steps
the paintball takes in reality. There are only steps in your model.
Don't try to ascribe too much reality to your model without good
reason.

On Apr 24, 1:50 pm, "Ernie Sty" <[Only registered users see links. ]> wrote:

*Mathematically*, no, any *finite* set of terms never quite adds to 2.

But here is where you get into tricky ground, because you are taking a
real situation (runner, paintball) and analyzing it with a
mathematical *model*. In the *model*, you are breaking down a physical
process into a set of steps. The place where the conceptual breakdown
is then thinking that the *reality* really does operate according to
the artifice of this model. That is, does the paintball *really* have
to take the first step, then the second step, then the third step, and
so on? This is where the brain fools you, because you are tempted to
think that just because you've *mentally* broken down the path into an
infinite number of steps, the paintball really does have to execute an
infinite number of steps. In other words, you are forcing a mental
concept and trying to turn it into a reality. The paintball doesn't
know anything about steps. It just goes from here to the runner. So if
you run into a conceptual roadblock, the first thing you should do is
check whether what's blocking about the model really has any reality.
This should have been flagged for you by the bogus question, "What's
the smallest possible physical step through space?" There ARE NO steps
the paintball takes in reality. There are only steps in your model.
Don't try to ascribe too much reality to your model without good
reason.