From: mpc755 on
On Oct 9, 12:30 pm, PD <thedraperfam...(a)gmail.com> wrote:
> On Oct 9, 10:06 am, mpc755 <mpc...(a)gmail.com> wrote:
>
> > On Oct 9, 10:52 am, PD <thedraperfam...(a)gmail.com> wrote:
>
> > > On Oct 9, 8:53 am, mpc755 <mpc...(a)gmail.com> wrote:
>
> > > > On Oct 9, 8:57 am, PD <thedraperfam...(a)gmail.com> wrote:
>
> > > > > On Oct 8, 8:34 pm, mpc755 <mpc...(a)gmail.com> wrote:
>
> > > > > > > > > > > > > > > Sorry, I've fouled this up.
>
>
> > Yes, the light from A and B reaches M' at different times, but the
> > light from A' and B' reaches M' simultaneously.
>
> A and A' are a single strike. B and B' are a single strike.

Yes, A and A' are a single strike but A and A' are two different
locations in three dimensional space. A in on the embankment and A' is
on the train.

> The light from A/A' travels through the *same medium* that the
> embankment and the open flatbed train cars are immersed in. The light
> from B/B' does the same thing.
> So how does the light, coming from a single lightning strike (A/A'),
> traveling through a common medium, arrive at the same observer M' both
> simultaneously and not simultaneously as the light from B/B'?

It doesn't. If the train contains open flatbed cars, then you are
implying the medium is stationary relative to the embankment. Meaning
the light travels from B to M' and from A to M'. The marks made by the
lightning strikes are A' and B' are meaningless in this scenario. Even
with the marks made at A' and B', since the medium is stationary
relative to the embankment, all of the light associated with the
lightning strikes travels from A to M' and from B to M'.

> The observer M' either sees the flashes from the strikes at his eyes at
> the same time or he doesn't. He can't do both.
>

Incorrect. If the medium is stationary relative to the embankment in
the embankment frame of reference and the medium is stationary
relative to the train in the train frame of reference the observer at
M' will see the light from the lightning strikes at A' and B'
simultaneously. The light from A and B will have to transition from
the embankment frame of reference to the train frame of reference and
will arrive at M' at different times.

>
>
> > > The train observer has to agree with that.
>
> > Yes, the train observer agrees the light from A and B reaches him at
> > different times, but the light from A' and B' reaches him
> > simultaneously.
>
> A and A' are ONE lightning strike. B and B' are ONE lightning strike.
>

Yes, they are one lightning strike but they occur at two different
locations. A on the embankment and A' on the train. Likewise for the
lightning strike at B/B'.

> Let's say that the ONE lightning strike at A/A' is greenish, and the
> lightning strike at B/B' is yellowish.
>
> The question is simple. There is a guy M' who is going to see the two
> lightning flashes. Does he see the yellowish and greenish ones at the
> same time or at different times? There can only be one answer, as this
> is something that the guy can write down when it happens.
>

If the medium is stationary relative to the train in the train frame
of reference and the medium is stationary relative to the embankment
in the embankment frame of reference the observer at M' is going to
see the yellowish light from A' and the greenish light from B' arrive
simultaneously. He will also see the yellowish light from A and the
greenish light from B arrive at different times.

If the medium is stationary relative to the train in all reference
frames, then the Observer at M' will see a single lighting strike from
A' and a single lightning strike at B' both arrive simultaneously.

If the medium is stationary relative to the embankment in all
reference frames, the Observer at M' will see a single lightning
strike from A and a single lightning strike at B arrive at different
times.

>
>
> > > Nature doesn't produce two
> > > different measurable outcomes at the same time. There is only one.
> > > Either the light arrives at the same time at M' or it doesn't. The
> > > embankment observer and the train observer have to agree which one of
> > > those two it was.
>
> > > It appears that you are having a slow time getting a grip on what the
> > > Einstein gedanken really says.
>
> > > > > > The water is stationary relative to the train. Pebbles are dropped at
> > > > > > A/A' and B/B'. The wave from A' reaches M. The waves from A' and B'
> > > > > > reach M' simultaneously. The wave from B' reaches M. A and B are
> > > > > > irrelevant in this scenario.
>
> > > > > OK, but there are really only two lightning strikes, and the water
> > > > > doesn't really have time to switch from being stationary relative to
> > > > > the embankment to being stationary relative to the train.
>
> > > > The water doesn't have to switch. The water is stationary relative to
> > > > the embankment in the embankment frame of reference and the water is
> > > > stationary relative to the train in the train frame of reference.
>
> > > But these aren't two different sequences of events. It's the same
> > > train, the same two lightning strikes, and there is only one pool of
> > > water surrounding the embankment and the open train cars. So you tell
> > > me, how can the water be stationary relative to the train AND
> > > stationary relative to the embankment?
>
> > It's the same two lightning strikes, but it is occurring at A on the
> > embankment and A' on the train.
>
> So?
>
>
>
> > You can have a bucket of water that is stationary on the embankment
> > and a bucket of water that is stationary on the train.
>
> Same body of water that the train is immersed in and the embankment is
> immersed in.
> If it's not the same body of water, then there has to be a boundary
> between the two bodies of water. Where is that boundary?
>

If the train contains open flatbed cars, then the water will be
stationary relative to the embankment and the light from the lightning
strikes at A/A' and B/B' will travel from A to M' and from B to M'.

If the train is enclosed and the water is moving with the train in the
train frame of reference and the water on the embankment is stationary
relative to the embankment, then it is the train that is the boundary.

>
>
> > Pebbles are dropped at A, A', B, and B' simultaneously as determined
> > by observers.
>
> That's just it. Whether they are simultaneous or not depends on the
> signals they actually receive at their locations. That is, the
> observers M and M' are not AT the locations A, A', B, B'. They are at
> the places marked M and M'. What they know is what happens where they
> are, and THAT tells them what happens at A, A', B, and B'. They have
> no other way of knowing.

There are observers at A, A', B and B' and they all have clickers and
they all click their clickers when the pebbles hit the water. It is
determined all four observers hit their clickers at the same time.
From: PD on
On Oct 9, 11:54 am, mpc755 <mpc...(a)gmail.com> wrote:
> On Oct 9, 12:35 pm, PD <thedraperfam...(a)gmail.com> wrote:
>
>
>
> > On Oct 9, 11:01 am, mpc755 <mpc...(a)gmail.com> wrote:
>
> > > On Oct 9, 11:06 am, mpc755 <mpc...(a)gmail.com> wrote:
>
> > > > On Oct 9, 10:52 am, PD <thedraperfam...(a)gmail.com> wrote:
>
> > > > > > > > > > > > > > > > > Sorry, I've fouled this up.
>
> > > I missed where you say it is an open train car. If it is an open train
> > > car, which implies the water is stationary relative to the embankment
> > > and not stationary relative to the train,
>
> > Well, hold on a second. Why isn't it possible the water is stationary
> > relative to the train and not stationary relative to the embankment?
>
> The water could be stationary relative to the train and not stationary
> relative to the embankment. In that case, the light from the lightning
> strike at B/B' will travel from B' to M and the light from the
> lightning strike at A/A' will travel from A' to M. The light from A'
> and B' will reach M' simultaneously.

And if this were so, then you'd be able to measure a different speed
of propagation of the signal someplace.

Remember that for BOTH observers M and M', the distance between the
strikes and where the observer is standing is identical. That is, A--M
= M--B, and A--M' = M'--B.
And so if the speed of the signal propagating from A to M and from B
to M is the same, then the time of propagation has to be the same.
So what the observer M SEES (simultaneous or not simultaneous)
determines completely whether the strikes are REALLY simultaneous or
not.
And the same statements hold true for M'.

And here is what is REALLY seen in experiment (or analogous
experiment): M sees the flashes at the same time and M' sees the
flashes at different times.

The only way this can be true is if the speed of propagation from A is
somehow different than the speed of propagation from B.

But measurements in REAL LIFE show that this isn't the case. The speed
is always the same.

I see that this simple gedanken continues to cause you problems and
you're having trouble understanding the point.

>
> If the water is stationary relative to the train and not stationary
> relative to the embankment, the lightning strikes at A and B are
> irrelevant in terms of where the light travels from.
>
>
>
> > > then the light from the
> > > lightning strike at A and B will not reach the observer at M'
> > > simultaneously and neither will the light from the lightning strikes
> > > at A' and B'.
>
> > Right.
>
> > But the observer M' then says the following:
> > "OK, I know the following things:
> > 1. The strikes happened at distances that are equally apart from me.
> > 2. The speed of the signal from those two places traveling to me is
> > the same in both cases.
> > 3. The signals did not arrive at the same time."
> > From these bits of information it is OBVIOUS that the strikes
> > originally happened at different times, because the time of
> > propagation of the signal from the strikes to where the observer is
> > standing is identical. If the time of propagation is the same, and
> > they arrived at different times, then they started at different times.
> > No escaping that conclusion.
>
> It sounds as if we are back discussing the water being stationary
> relative to the embankment. If that is the case then the observer at
> M' will not conclude the light traveled from A' and B' to reach him.
> If he does so, then he is incorrect. If the water is stationary
> relative to the embankment the Observer at M' will correctly conclude
> the light from the lightning strike at A/A' traveled from A and the
> light from the lightning strike at B/B' traveled from B.
>
>
>
> > > If the water is stationary relative to the embankment,
> > > the light from the lightning strike at B' will travel from B to M' and
> > > arrive prior to the light from the lightning strike at A' and will
> > > travel from A to M'. A' and B' are irrelevant if we are discussing
> > > 'open train cars' which implies the water is stationary relative to
> > > the embankment.
>
> > > You can replace 'water' with 'aether' in the above paragraph and the
> > > same outcome will occur.
>
> > > > > > If his train thought experiment was correct with equal reference
> > > > > > frames, the light from the lightning strikes at A and B would reach M
> > > > > > and the light from the lightning strikes at A' and B' would reach M'
> > > > > > simultaneously:
>
> > > > > But they DON'T, in real life, as determined in experiment.
>
> > > > I think we can agree on the following:
>
> > > > Pebbles are dropped at A, A', B, and B' simultaneously as determined
> > > > by observers. The water on the embankment is stationary relative to
> > > > the embankment in the embankment frame of reference. The water on the
> > > > train is stationary relative to the train in the train frame of
> > > > reference.
>
> > > > If the waves from A and B reach M simultaneously, then the waves from
> > > > A' and B' reach M' simultaneously. The waves from A and B reach M and
> > > > the waves from A' and B' reach M' at the same time.
>
> > > > If instead of pebbles being dropped into the water, we now have
> > > > flashes occur at A, A', B, and B' simultaneously as determined by
> > > > observers, then due to the results of experiments with water and light
> > > > performed by Fizeau and others, then if the light from A and B reaches
> > > > M simultaneously then the light from A' and B' reaches M'
> > > > simultaneously and the light from A and B reaches M and the light from
> > > > A' and B' reaches M' at the same time.
>
> > > > Now, instead of water being stationary relative to the embankment in
> > > > the embankment frame of reference and water being stationary relative
> > > > to the train in the train frame of reference, we have aether
> > > > stationary relative to the embankment in the embankment frame of
> > > > reference and aether stationary relative to the train in the train
> > > > frame of reference, the results for simultaneously flashes of light at
> > > > A, A', B, and B' will be the same in aether as described above for
> > > > flashes in water.
>
> > > > > >http://www.youtube.com/watch?v=jyWTaXMElUk
>
> > > > > > > > 'Fizeau experiment'http://en.wikipedia.org/wiki/Fizeau_experiment
>
>

From: mpc755 on
On Oct 9, 1:11 pm, PD <thedraperfam...(a)gmail.com> wrote:
> On Oct 9, 11:54 am, mpc755 <mpc...(a)gmail.com> wrote:
>
>
>
> > On Oct 9, 12:35 pm, PD <thedraperfam...(a)gmail.com> wrote:
>
> > > On Oct 9, 11:01 am, mpc755 <mpc...(a)gmail.com> wrote:
>
> > > > On Oct 9, 11:06 am, mpc755 <mpc...(a)gmail.com> wrote:
>
> > > > > On Oct 9, 10:52 am, PD <thedraperfam...(a)gmail.com> wrote:
>
> > > > > > > > > > > > > > > > > > Sorry, I've fouled this up.
>
> > > > I missed where you say it is an open train car. If it is an open train
> > > > car, which implies the water is stationary relative to the embankment
> > > > and not stationary relative to the train,
>
> > > Well, hold on a second. Why isn't it possible the water is stationary
> > > relative to the train and not stationary relative to the embankment?
>
> > The water could be stationary relative to the train and not stationary
> > relative to the embankment. In that case, the light from the lightning
> > strike at B/B' will travel from B' to M and the light from the
> > lightning strike at A/A' will travel from A' to M. The light from A'
> > and B' will reach M' simultaneously.
>
> And if this were so, then you'd be able to measure a different speed
> of propagation of the signal someplace.
>
> Remember that for BOTH observers M and M', the distance between the
> strikes and where the observer is standing is identical. That is, A--M
> = M--B, and A--M' = M'--B.

Correct, at the time of the lightning strikes.

> And so if the speed of the signal propagating from A to M and from B
> to M is the same, then the time of propagation has to be the same.
> So what the observer M SEES (simultaneous or not simultaneous)
> determines completely whether the strikes are REALLY simultaneous or
> not.
> And the same statements hold true for M'.
>

Correct, for M' and the lightning strikes at A' and B'.

> And here is what is REALLY seen in experiment (or analogous
> experiment): M sees the flashes at the same time and M' sees the
> flashes at different times.
>

M sees the flashes at the same time if the medium is stationary
relative to him.

M' sees the flashes at different times from A and B because the light
has traveled different distances from A and B to M'. M' is moving
relative to A and B.

> The only way this can be true is if the speed of propagation from A is
> somehow different than the speed of propagation from B.
>

Incorrect. M' sees the light from B prior to the light from A because
M' is hastening towards B and away from A.

> But measurements in REAL LIFE show that this isn't the case. The speed
> is always the same.
>

Yes, the speed of light is always 'c'. But what you do not understand
is where the light emanates from is dependent on the relative motion
of the medium it was created in and is traveling through. See Fizeau
experiment (http://en.wikipedia.org/wiki/Fizeau_experiment)

> I see that this simple gedanken continues to cause you problems and
> you're having trouble understanding the point.
>
From: PD on
On Oct 9, 12:08 pm, mpc755 <mpc...(a)gmail.com> wrote:
> On Oct 9, 12:30 pm, PD <thedraperfam...(a)gmail.com> wrote:
>
>
>
> > On Oct 9, 10:06 am, mpc755 <mpc...(a)gmail.com> wrote:
>
> > > On Oct 9, 10:52 am, PD <thedraperfam...(a)gmail.com> wrote:
>
> > > > On Oct 9, 8:53 am, mpc755 <mpc...(a)gmail.com> wrote:
>
> > > > > On Oct 9, 8:57 am, PD <thedraperfam...(a)gmail.com> wrote:
>
> > > > > > On Oct 8, 8:34 pm, mpc755 <mpc...(a)gmail.com> wrote:
>
> > > > > > > > > > > > > > > > Sorry, I've fouled this up.
>
> > > Yes, the light from A and B reaches M' at different times, but the
> > > light from A' and B' reaches M' simultaneously.
>
> > A and A' are a single strike. B and B' are a single strike.
>
> Yes, A and A' are a single strike but A and A' are two different
> locations in three dimensional space. A in on the embankment and A' is
> on the train.

No, they are not. You have not read the gedanken carefully. A lighting
strike hits in ONE place, not two. A and A' are two labels for the
same point. In the original gedanken, A and A' label the point where
the train meets the track at one end of the train. That is ONE POINT.

Please reread it and pay more attention than what you have been doing
so far.

>
> > The light from A/A' travels through the *same medium* that the
> > embankment and the open flatbed train cars are immersed in. The light
> > from B/B' does the same thing.
> > So how does the light, coming from a single lightning strike (A/A'),
> > traveling through a common medium, arrive at the same observer M' both
> > simultaneously and not simultaneously as the light from B/B'?
>
> It doesn't. If the train contains open flatbed cars, then you are
> implying the medium is stationary relative to the embankment.

No, I'm not. There's no such implication at all. What you know is true
is that there is ONE medium, not two.

> Meaning
> the light travels from B to M' and from A to M'. The marks made by the
> lightning strikes are A' and B' are meaningless in this scenario. Even
> with the marks made at A' and B', since the medium is stationary
> relative to the embankment, all of the light associated with the
> lightning strikes travels from A to M' and from B to M'.
>
> > The observer M' either sees the flashes from the strikes at his eyes at
> > the same time or he doesn't. He can't do both.
>
> Incorrect. If the medium is stationary relative to the embankment in
> the embankment frame of reference and the medium is stationary
> relative to the train in the train frame of reference the observer at
> M' will see the light from the lightning strikes at A' and B'
> simultaneously. The light from A and B will have to transition from
> the embankment frame of reference to the train frame of reference and
> will arrive at M' at different times.
>
>
>
> > > > The train observer has to agree with that.
>
> > > Yes, the train observer agrees the light from A and B reaches him at
> > > different times, but the light from A' and B' reaches him
> > > simultaneously.
>
> > A and A' are ONE lightning strike. B and B' are ONE lightning strike.
>
> Yes, they are one lightning strike but they occur at two different
> locations. A on the embankment and A' on the train. Likewise for the
> lightning strike at B/B'.
>
> > Let's say that the ONE lightning strike at A/A' is greenish, and the
> > lightning strike at B/B' is yellowish.
>
> > The question is simple. There is a guy M' who is going to see the two
> > lightning flashes. Does he see the yellowish and greenish ones at the
> > same time or at different times? There can only be one answer, as this
> > is something that the guy can write down when it happens.
>
> If the medium is stationary relative to the train in the train frame
> of reference and the medium is stationary relative to the embankment
> in the embankment frame of reference the observer at M' is going to
> see the yellowish light from A' and the greenish light from B' arrive
> simultaneously. He will also see the yellowish light from A and the
> greenish light from B arrive at different times.

OK, and this is where you get a little loony.

You say that the observer M' will see the green flash and the yellow
flash at the same time AND not at the same time?

This kind of odd behavior you describe has never been observed in
experiment.

>
> If the medium is stationary relative to the train in all reference
> frames, then the Observer at M' will see a single lighting strike from
> A' and a single lightning strike at B' both arrive simultaneously.
>
> If the medium is stationary relative to the embankment in all
> reference frames, the Observer at M' will see a single lightning
> strike from A and a single lightning strike at B arrive at different
> times.
>
>
>
>
>
> > > > Nature doesn't produce two
> > > > different measurable outcomes at the same time. There is only one.
> > > > Either the light arrives at the same time at M' or it doesn't. The
> > > > embankment observer and the train observer have to agree which one of
> > > > those two it was.
>
> > > > It appears that you are having a slow time getting a grip on what the
> > > > Einstein gedanken really says.
>
> > > > > > > The water is stationary relative to the train. Pebbles are dropped at
> > > > > > > A/A' and B/B'. The wave from A' reaches M. The waves from A' and B'
> > > > > > > reach M' simultaneously. The wave from B' reaches M. A and B are
> > > > > > > irrelevant in this scenario.
>
> > > > > > OK, but there are really only two lightning strikes, and the water
> > > > > > doesn't really have time to switch from being stationary relative to
> > > > > > the embankment to being stationary relative to the train.
>
> > > > > The water doesn't have to switch. The water is stationary relative to
> > > > > the embankment in the embankment frame of reference and the water is
> > > > > stationary relative to the train in the train frame of reference.
>
> > > > But these aren't two different sequences of events. It's the same
> > > > train, the same two lightning strikes, and there is only one pool of
> > > > water surrounding the embankment and the open train cars. So you tell
> > > > me, how can the water be stationary relative to the train AND
> > > > stationary relative to the embankment?
>
> > > It's the same two lightning strikes, but it is occurring at A on the
> > > embankment and A' on the train.
>
> > So?
>
> > > You can have a bucket of water that is stationary on the embankment
> > > and a bucket of water that is stationary on the train.
>
> > Same body of water that the train is immersed in and the embankment is
> > immersed in.
> > If it's not the same body of water, then there has to be a boundary
> > between the two bodies of water. Where is that boundary?
>
> If the train contains open flatbed cars, then the water will be
> stationary relative to the embankment and the light from the lightning
> strikes at A/A' and B/B' will travel from A to M' and from B to M'.
>
> If the train is enclosed and the water is moving with the train in the
> train frame of reference and the water on the embankment is stationary
> relative to the embankment, then it is the train that is the boundary.

There is no enclosure implied in the gedanken. Please reread it
carefully.

>
>
>
> > > Pebbles are dropped at A, A', B, and B' simultaneously as determined
> > > by observers.
>
> > That's just it. Whether they are simultaneous or not depends on the
> > signals they actually receive at their locations. That is, the
> > observers M and M' are not AT the locations A, A', B, B'. They are at
> > the places marked M and M'. What they know is what happens where they
> > are, and THAT tells them what happens at A, A', B, and B'. They have
> > no other way of knowing.
>
> There are observers at A, A', B and B' and they all have clickers and
> they all click their clickers when the pebbles hit the water. It is
> determined all four observers hit their clickers at the same time.

How is it determined that they hit their clickers at the same time?
What procedure would you need to ensure that?
I want you to think about this very carefully...

From: PD on
On Oct 9, 12:17 pm, mpc755 <mpc...(a)gmail.com> wrote:
> On Oct 9, 1:11 pm, PD <thedraperfam...(a)gmail.com> wrote:
>
>
>
> > On Oct 9, 11:54 am, mpc755 <mpc...(a)gmail.com> wrote:
>
> > > On Oct 9, 12:35 pm, PD <thedraperfam...(a)gmail.com> wrote:
>
> > > > On Oct 9, 11:01 am, mpc755 <mpc...(a)gmail.com> wrote:
>
> > > > > On Oct 9, 11:06 am, mpc755 <mpc...(a)gmail.com> wrote:
>
> > > > > > On Oct 9, 10:52 am, PD <thedraperfam...(a)gmail.com> wrote:
>
> > > > > > > > > > > > > > > > > > > Sorry, I've fouled this up.
>
> > > > > I missed where you say it is an open train car. If it is an open train
> > > > > car, which implies the water is stationary relative to the embankment
> > > > > and not stationary relative to the train,
>
> > > > Well, hold on a second. Why isn't it possible the water is stationary
> > > > relative to the train and not stationary relative to the embankment?
>
> > > The water could be stationary relative to the train and not stationary
> > > relative to the embankment. In that case, the light from the lightning
> > > strike at B/B' will travel from B' to M and the light from the
> > > lightning strike at A/A' will travel from A' to M. The light from A'
> > > and B' will reach M' simultaneously.
>
> > And if this were so, then you'd be able to measure a different speed
> > of propagation of the signal someplace.
>
> > Remember that for BOTH observers M and M', the distance between the
> > strikes and where the observer is standing is identical. That is, A--M
> > = M--B, and A--M' = M'--B.
>
> Correct, at the time of the lightning strikes.

Or any time. The track observer could do it all afterwards if he
wanted to. He just marks the location where he was standing and then
goes to look for the scorch mark on the track and he measures the
distance from where he was standing to the scorch mark. Then he does
the same for the other scorch mark.
The train observer can do the same thing.

>
> > And so if the speed of the signal propagating from A to M and from B
> > to M is the same, then the time of propagation has to be the same.
> > So what the observer M SEES (simultaneous or not simultaneous)
> > determines completely whether the strikes are REALLY simultaneous or
> > not.
> > And the same statements hold true for M'.
>
> Correct, for M' and the lightning strikes at A' and B'.

A' and B' happen at the same locations as A and B. A and A' are two
different labels applied to the same point. Same for B and B'.

>
> > And here is what is REALLY seen in experiment (or analogous
> > experiment): M sees the flashes at the same time and M' sees the
> > flashes at different times.
>
> M sees the flashes at the same time if the medium is stationary
> relative to him.
>
> M' sees the flashes at different times from A and B because the light
> has traveled different distances from A and B to M'. M' is moving
> relative to A and B.

M' cannot see the flashes at the same time AND at different times. It
has to be one or the other. There is only one green flash and he will
see it only once, and there is only one yellow flash and he will see
it only once. When he sees the green and yellow flashes, does he see
them at the same time or at different times? He doesn't see the green
flash twice or the yellow flash twice.

>
> > The only way this can be true is if the speed of propagation from A is
> > somehow different than the speed of propagation from B.
>
> Incorrect. M' sees the light from B prior to the light from A because
> M' is hastening towards B and away from A.
>
> > But measurements in REAL LIFE show that this isn't the case. The speed
> > is always the same.
>
> Yes, the speed of light is always 'c'. But what you do not understand
> is where the light emanates from is dependent on the relative motion
> of the medium it was created in and is traveling through. See Fizeau
> experiment (http://en.wikipedia.org/wiki/Fizeau_experiment)
>
> > I see that this simple gedanken continues to cause you problems and
> > you're having trouble understanding the point.
>
>