[TotesNotReptilian]

If you have ever been south of the Equator, you know that the seasons are reversed: December through January are the hottest months, and have the longest daylight hours. Flat earth theory has a halfway decent explanation for this. The radius of the sun's orbit above the earth increases and decreases with the seasons. During the southern summer months, the sun has a larger orbital radius:



This sort of makes sense for the Northern Hemisphere. But as they say, the devil's in the details. Let's look at two cities during the December Solstice:

New York City: 9 hours 15 minutes of daylight
Sao Paulo: 13 hours 35 minutes of daylight

I plotted the location of the sun at sunrise and sunset for each city on a Polar Azimuthal Equidistant Projection Map*:



Notice the location of the sun at sunset for each city. Why does the sun set later for Sao Paulo than for New York City, even though New York City is much closer to the sun?

As you move farther south of Sao Paulo, the days become longer and longer, and the distance from the sun at sunset and sunrise gets farther and farther! In fact, according to this model, in the extreme southern latitudes, much of the northern hemisphere lies between the sun and the southern hemisphere at sunset, despite it being pitch black in many of those northern locations. How is this possible on a flat earth?

* Yes, I know this isn't an official flat earth map. But since there isn't an official map, I'll use this one since it seems to be the most commonly referenced.

Edit: Accidentally posted early. Give me a few minutes. Ok, all better now.

[TotesNotReptilian]

I added Punta Arenas and Los Angeles, which makes it even worse.



Notice that the sun sets for Los Angeles before Punta Arenas, despite Los Angeles being directly between the sun and Punta Arenas at the time. Likewise, the sun rises for Punta Arenas before it rises for Sao Paulo, despite Sao Paulo being directly between the sun and Punta Arenas.

The geometry just doesn't make sense.

[Rounder]

The direction of the rising and setting sun are problematic for FE as well.  Sao Paulo should see the sun rising 26° south of due east, and setting 26° south of due west, but that's not what is shown on the Gleason map.

[rabinoz]

If you have ever been south of the Equator, you know that the seasons are reversed: December through January are the hottest months, and have the longest daylight hours. Flat earth theory has a halfway decent explanation for this. The radius of the sun's orbit above the earth increases and decreases with the seasons. During the southern summer months, the sun has a larger orbital radius:



This sort of makes sense for the Northern Hemisphere. But as they say, the devil's in the details. Let's look at two cities during the December Solstice:

New York City: 9 hours 15 minutes of daylight
Sao Paulo: 13 hours 35 minutes of daylight

I plotted the location of the sun at sunrise and sunset for each city on a Polar Azimuthal Equidistant Projection Map*:

Notice the location of the sun at sunset for each city. Why does the sun set later for Sao Paulo than for New York City, even though New York City is much closer to the sun?

As you move farther south of Sao Paulo, the days become longer and longer, and the distance from the sun at sunset and sunrise gets farther and farther! In fact, according to this model, in the extreme southern latitudes, much of the northern hemisphere lies between the sun and the southern hemisphere at sunset, despite it being pitch black in many of those northern locations. How is this possible on a flat earth?

* Yes, I know this isn't an official flat earth map. But since there isn't an official map, I'll use this one since it seems to be the most commonly referenced.

Edit: Accidentally posted early. Give me a few minutes. Ok, all better now.

Since  I always want to do the right thing!  I did as i was told and looked up "the Wiki"! The nearest I could find was on sunsets, so

The Setting of the Sun
Although the sun is at all times above the earth's surface, it appears in the morning to ascend from the north-east to the noonday position, and thence to descend and disappear, or set, in the north-west. This phenomenon arises from the operation of a simple and everywhere visible law of perspective. A flock of birds, when passing over a flat or marshy country, always appears to descend is it recedes; and if the flock is extensive, the first bird appears lower or nearer to the horizon than the last, although they are at the same actual altitude above the earth immediately beneath them. When a plane flies away from an observer, without increasing or decreasing its altitude, it appears to gradually approach the horizon. In a long row of lamps, the second, supposing the observer to stand at the beginning of the series, will appear lower than the first; the third lower than the second; and so on to the end of the row; the farthest away always appearing the lowest, although each one has the same altitude; and if such a straight line of lamps could be continued far enough, the lights would at length descend, apparently, to the horizon, or to a level with the eye of the observer. This explains how the sun descends into the horizon as it recedes.
Once the lower part of the Sun meets the horizon line, however, it will intersect with the vanishing point and become lost to human perception as the sun's increasingly shallow path creates a tangent beyond the resolution of the human eye. The vanishing point is created when the perspective lines are angled less than one minute of a degree. Hence, this effectively places the vanishing point a finite distance away from the observer.
Usually it is taught in art schools that the vanishing point is an infinite distance away from the observer, as so:

However, since man cannot perceive infinity due to human limitations, the perspective lines are modified and placed a finite distance away from the observer as so:

This finite distance to the vanishing point is what allows ships to ascend into horizon and disappear as their hulls intersect with the vanishing point. Every receding star and celestial body in the night sky likewise disappears after intersecting with the vanishing point.

This clearly, and fairly correctly, states that " The vanishing point is created when the perspective lines are angled less than one minute of a degree."

Now the Wiki states that the sun is 32 miles in diameter, so the vanishing point for the sun should be 32/arctan(1' of arc) = 110,008 miles!

Need I say more? The explanations in the Wiki and in Rowbotham are completely ridiculous.

[TotesNotReptilian]

Now the Wiki states that the sun is 32 miles in diameter, so the vanishing point for the sun should be 32/arctan(1' of arc) = 110,008 miles!

Need I say more? The explanations in the Wiki and in Rowbotham are completely ridiculous.

And that's just for the sun to vanish. For it to appear to touch the horizon, the angle between the sun and the horizon would have to be less than 1' of arc. Assuming the sun is 3000 miles above the earth:

3000/arctan(1' of arc) = 10,000,000 miles away. (horizontally)

Yikes.

Edit: 5 posts, 4 major holes in FE theory! We need some Zetetic researchers on this, stat!

[rabinoz]

Now the Wiki states that the sun is 32 miles in diameter, so the vanishing point for the sun should be 32/arctan(1' of arc) = 110,008 miles!

Need I say more? The explanations in the Wiki and in Rowbotham are completely ridiculous.

And that's just for the sun to vanish. For it to appear to touch the horizon, the angle between the sun and the horizon would have to be less than 1' of arc. Assuming the sun is 3000 miles above the earth:

3000/arctan(1' of arc) = 10,000,000 miles away. (horizontally)

Yikes.

Edit: 5 posts, 4 major holes in FE theory! We need some Zetetic researchers on this, stat!

Aha, Eureka!

The Setting of the Sun

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

In addition to this modified law of perspective the remaining light of the sun bouncing around in the atmosphere will be lost by the non transparent atmosphere. After the sun sets the sky is still relatively illuminated. It takes a couple hours for the deep blackness of the night to set in. The cause of night is simply due to a non-transparent atmosphere. As the sun recedes its light is dimmed and lost to the increasing number of atoms and molecules which intersect the light rays.
Take note that at sunset the sun is already dimmed by an order of magnitude compared to its intensity overhead at noonday. At sunset it is possible to look directly at the sun without a straining of the eye, while overhead at noon looking directly at the sun can be quite painful. This severe reduction of intensity at sunset is a striking example of how the atmosphere can reduce the intensity of an object with distance.

It seems that the Northern Hemisphere is closer to the sun, yet doesn't get the requisite number of daylight hours. Now we all know that the atmosphere is much more polluted in the Northern Hemisphere than in the Southern Hemisphere. So with all this "sun bouncing around in the atmosphere" will be lost by the non transparent atmosphere".

  Seems plausible. 

But if the sunset (and sunrise) times are determined by the extremely variable non-transparency atmosphere, How is it possible to predict the time of the sunset to within a couple of minutes at the outside?

[TotesNotReptilian]

Over a week, and no responses. Last call for any flat earthers out there, before I add it to the pile of round earth proofs.

[Luke 22:35-38]

Over a week, and no responses. Last call for any flat earthers out there, before I add it to the pile of round earth proofs.

It is a rather slow site compared to the other site. But that's still no excuse.

[nametaken]

My Favorite Flat Earth Topic! Yay!

Bascially on the flat earth model, you have, as you have shown, 3 'layers' of orbits to the corkscrew 'orbit' path. The 'inner' path seems to move the fastest (less surface area to cover on 'the dome')... the middle path (spring/fall) is the medium speed (slightly more 'surface area' to cover on the dome), and then... DUH DUH DUH! The outer ring, the wiiiiiiiidddeeeeesssssttttt and slowest (weneedtogowider.jpeg).

It never fails to leave me with a smirk. I feel it coming on now. Imagine a pancake. A kind of big one. The surface area near the 'middle' of the pancake is small, can be navigated fast. The outter edge though, if you go the same speed as in the middle, is much slower and takes longer to traverse.

Only problem with OP's post is not posting the time of year, you see. Obviously with a sun that has 3 orbital paths to go between sometimes he/she shows up late, early, or not at all (OOPS!). Busy guy/gall can't be everywhere at once. I have seen FE try to say... IM TRYING NOT TO LAUGH that the sun SPEEDS UP on the outer ring to keep appearance of same speed. But this OP implies it does go 'slower' maybe on the outer ring? If anything that actually PROVES Flat Earth then; though the reported sunrise direction does sound like checkmate to me.

[TotesNotReptilian]

Nametaken, I'm pretty sure you completely missed the point of my post.

Only problem with OP's post is not posting the time of year, you see.

I did specify the time of year. December solstice. December 21. Northern winter, southern summer.

the sun SPEEDS UP on the outer ring to keep appearance of same speed.

Yes, it would have to speed up to make it around the longer loop in the same 24 hour period. This is yet another problem with the FE model. However, that wasn't the point of my post.

But this OP implies it does go 'slower' maybe on the outer ring? If anything that actually PROVES Flat Earth then;

I am fairly sure I did not imply anything of the sort. Even if I did, how on earth would that prove that the earth is flat? I merely plotted the location of the sun during sunrise/sunset for each city, based on the amount of daylight they receive. The goal was to highlight some geometric problems with the flat earth model.

though the reported sunrise direction does sound like checkmate to me.

yep

[nametaken]

I made a few edits to the post for clarity and to fix a few mistakes.

Nametaken, I'm pretty sure you completely missed the point of my post.

That's what I'm best at. On google Earth, all of your points of sunrise and sunset are mapped concisely. Simply fire it up and navigate to the point of sunrise and spin towards the corresponding town, and you will feel like the sun, just as you have depicted. Interesting trick, about which way the sun rises from.

I caught the fact that you listed December right after I posted. But I had too much fun writing that. I probably do owe a slight apology there, but it sure was fun. That is a nice diagram. Wish I made it myself to be honest, I might have been slightly jealous.

Yes, it would have to speed up to make it around the longer loop in the same 24 hour period. This is yet another problem with the FE model. However, that wasn't the point of my post.

It has to move faster to cover more area in the same amount of time, but that still means it spends more time in the sky in December. The only inconsistency I see is with sun rise direction to be honest (FE Model); but it uses shady logic. The sun doesn't actually appear from over another continent, as the image you put will seem to show (illusion). Basic geometry, if I may borrow your image... What these people might see:

Proof I'm not a FE shill I made a mistake: old one I messed up:
http://i.imgur.com/r9OE9bA.jpg

Real One:


The black lines are what these people in each city should see... not the rising from another continent. The sunrise and sunset are time-based, not location based in the image you provided. Unless like you said I am missing the point entirely. Simple geometry. Although that leaves the issue of sunset direction for the FE model it seems, so my diagram may be incorrect.

As you admit, that scale is incorrect and not official FE Map. So we are both shooting in the dark on that one. In FE model, as I stated above, in winter the sun moves much, much slower in the 'southern hemisphere'. So the daylight cycle is accurate on both model's as far as I can tell; that's not a problem with the FE model, nor the globe. The sun gives the Southern Hemisphere more December love in both models. Though for People in Punta, I imagine the sun seems to move VERY slow considering that margin of window they have.

I am fairly sure I did not imply anything of the sort. Even if I did, how on earth would that prove that the earth is flat? I merely plotted the location of the sun during sunrise/sunset for each city, based on the amount of daylight they receive. The goal was to highlight some geometric problems with the flat earth model.

Regardless, the FE model implies that it appears to go 'slower' in southern hemisphere, due to more area to cover. This argument automatically implies that at the outset. It's not an argument otherwise. I should have said 'proof of longer days this time of year favors neither flat earth nor globe model' instead of 'if anything it proves flat earth'. I meant, it's not an argument for or against either model, as both models sufficiently account for it.

Nope! Looks like both models check out. Though it looks a little funny for sunset direction on FE model. The downside of not having a official FE map, maybe? I'm assuming it has to do with sunrise/sunset angles on globe model assuming the lat/long gets smaller on globe, when in fact, they get larger on FE model, meaning a translation is required. I may simply be missing something, I admit.

#TIL

[Rama Set]

Nametaken, the last time the OP was edited was August 3rd. You missed the date originally. It's your mistake, not TotesNotReptilian's. You should probably apologize too.

[nametaken]

Nametaken, the last time the OP was edited was August 3rd. You missed the date originally. It's your mistake, not TotesNotReptilian's. You should probably apologize too.

True didn't see that. Didn't realize how slow this forum moves, this was the second post I saw in this board, and assumed it was recent. That is my bad. I probably won't post here anymore anyway. Every other post I made in the past here similarly had a response asking me to either apologize or leave; typically because my posts were poor quality anyway. That's [the literal reason] why I left last time (though I typically welcome that type of response on most boards). I meant, what I said above, was I edited my post several times due to errors in post-posting proofreading, not anyone else's. This is the only forum I've ever received a ban warning flag from in my entire life. I only responded here mainly because I saw the words "last call"; tbh I'm arguing a point I don't even agree with here (and failing apparently anyway, so I'll stop), I just challenge accepted it since TNR did me the same favor. In that capacity TNR did a much better job than I did of that, and I didn't even have to sit through a 2 hour movie like I forced [them] to. As for whatever mess I tried to convey above, for that I will sincerely apologize; I am still trying to make heads and tails of it myself (hence the edits).

This is the first forum I've ever had anyone address me by my username, I've never seen that before but I see it constantly here. Anyone else notice that?

[Rounder]

tbh I'm arguing a point I don't even agree with here (and failing apparently anyway, so I'll stop)...As for whatever mess I tried to convey above, for that I will sincerely apologize; I am still trying to make heads and tails of it myself (hence the edits).

I am quite confused, I'll admit. 

This is the first forum I've ever had anyone address me by my username, I've never seen that before but I see it constantly here. Anyone else notice that?

How else would we address you?  We don't know your real name.  When conversations become lively, calling out usernames is a good way for us to be sure the intended recipient of a given comment is understood by all.

[rabinoz]

I made a few edits to the post for clarity and to fix a few mistakes.

Nametaken, I'm pretty sure you completely missed the point of my post.

That's what I'm best at. On google Earth, all of your points of sunrise and sunset are mapped concisely. Simply fire it up and navigate to the point of sunrise and spin towards the corresponding town, and you will feel like the sun, just as you have depicted. Interesting trick, about which way the sun rises from.

I caught the fact that you listed December right after I posted. But I had too much fun writing that. I probably do owe a slight apology there, but it sure was fun. That is a nice diagram. Wish I made it myself to be honest, I might have been slightly jealous.

Yes, it would have to speed up to make it around the longer loop in the same 24 hour period. This is yet another problem with the FE model. However, that wasn't the point of my post.

It has to move faster to cover more area in the same amount of time, but that still means it spends more time in the sky in December. The only inconsistency I see is with sun rise direction to be honest (FE Model); but it uses shady logic. The sun doesn't actually appear from over another continent, as the image you put will seem to show (illusion). Basic geometry, if I may borrow your image... What these people might see:

Proof I'm not a FE shill I made a mistake: old one I messed up:
http://i.imgur.com/r9OE9bA.jpg

Real One:

The black lines are what these people in each city should see... not the rising from another continent. The sunrise and sunset are time-based, not location based in the image you provided. Unless like you said I am missing the point entirely. Simple geometry. Although that leaves the issue of sunset direction for the FE model it seems, so my diagram may be incorrect.

As you admit, that scale is incorrect and not official FE Map. So we are both shooting in the dark on that one. In FE model, as I stated above, in winter the sun moves much, much slower in the 'southern hemisphere'. So the daylight cycle is accurate on both model's as far as I can tell; that's not a problem with the FE model, nor the globe. The sun gives the Southern Hemisphere more December love in both models. Though for People in Punta, I imagine the sun seems to move VERY slow considering that margin of window they have.

I am fairly sure I did not imply anything of the sort. Even if I did, how on earth would that prove that the earth is flat? I merely plotted the location of the sun during sunrise/sunset for each city, based on the amount of daylight they receive. The goal was to highlight some geometric problems with the flat earth model.

Regardless, the FE model implies that it appears to go 'slower' in southern hemisphere, due to more area to cover. This argument automatically implies that at the outset. It's not an argument otherwise. I should have said 'proof of longer days this time of year favors neither flat earth nor globe model' instead of 'if anything it proves flat earth'. I meant, it's not an argument for or against either model, as both models sufficiently account for it.

Nope! Looks like both models check out. Though it looks a little funny for sunset direction on FE model. The downside of not having a official FE map, maybe? I'm assuming it has to do with sunrise/sunset angles on globe model assuming the lat/long gets smaller on globe, when in fact, they get larger on FE model, meaning a translation is required. I may simply be missing something, I admit.

#TIL

You blithely say "Though it looks a little funny for sunset direction on FE model."

No, it's not a little funny, it's massively wrong.

The simple fact that Flat Earther's will not address is the in the south of the Equator at the Summer Equinox the sun rises south of East.
Just a few places:

Location		Sunrise Azimuth		FE Sunrise Dir
Brisbane, Australia		117°, or 27° South of East				I know this one, I live here!
São Paulo, Brazil		115°, or 25° South of East		23°, or 67° North of East
Puntas Arenas, Chile		133°, or 43° South of East		39°, 51° North of East

To me this is quite a big argument against the FE theory of the sun's movement, and ultimately against the whole FE hypothesis.

[nametaken]

The simple fact that Flat Earther's will not address is the in the south of the Equator at the Summer Equinox the sun rises south of East.
Just a few places:

Location		Sunrise Azimuth		FE Sunrise Dir
Brisbane, Australia		117°, or 27° South of East				I know this one, I live here!
São Paulo, Brazil		115°, or 25° South of East		23°, or 67° North of East
Puntas Arenas, Chile		133°, or 43° South of East		39°, 51° North of East

To me this is quite a big argument against the FE theory of the sun's movement, and ultimately against the whole FE hypothesis.

Heh. Can't hold a debate without both perspectives is all.

As I already stated, the difference here we are all ignoring is the fact that 'degree' doesn't mean anything on the FE!

FE degrees are different from Globe degrees in Southern Hemisphere due to lattitude/longitude getting longer instead of shorter. That's all. It's a matter of translation. Don't ask me for the translation! I wouldn't know. I don't defend the FE model, only misrepresentations of it. I never went so far as to learn this 'translation'.

Example:



flat earth would be more like this:

http://i65.tinypic.com/1zbqv79.png


I know I'm the only one arguing for the FE model. I'm not claiming to be FE'r. I'm just pointing out the misrepresentation of the FE model. Actually, this argument has a better smoking gun against the flat earth, I was thinking about making a topic on myself. It is this; yes the sun works funny in the southern hemisphere. But if the sun works funny... the stars are a bloody circus. I have wasted a lot of time trying to figure out how the southern hemisphere (or hell, the equatorial at that) stars work in the FE model for months... and I'm not better off. Here is a good example (starts at 3:26. To prevent going off topic, I can make a separate thread if anyone wants to share their humorous reactions to this.

For personal tastes, I like to use both models when I approach understanding of things. However like many others, I am still a dabbler on the FE model, but don't mind pointing out mistakes where I find them. That is golden 

[TotesNotReptilian]

First of all, there is no need to apologize. I suspect Rama misread your comment.

As I already stated, the difference here we are all ignoring is the fact that 'degree' doesn't mean anything on the FE!

Sure it does. A "degree" is just a unit of measurement of angles. In this case, it means the exact same thing on the flat earth as it does on the round earth. Both models have a North. The degree that the sun rises/sets at is measured as an angle from due North. We aren't talking about latitude/longitude degrees. The fact that the measured angle doesn't agree with the model's angle is hard evidence that the model is wrong.

I know I'm the only one arguing for the FE model. I'm not claiming to be FE'r. I'm just pointing out the misrepresentation of the FE model. Actually, this argument has a better smoking gun against the flat earth, I was thinking about making a topic on myself. It is this; yes the sun works funny in the southern hemisphere. But if the sun works funny... the stars are a bloody circus.

Yep. The south celestial pole is the next item on my agenda.

Yes, it would have to speed up to make it around the longer loop in the same 24 hour period. This is yet another problem with the FE model. However, that wasn't the point of my post.

It has to move faster to cover more area in the same amount of time, but that still means it spends more time in the sky in December. The only inconsistency I see is with sun rise direction to be honest (FE Model); but it uses shady logic. The sun doesn't actually appear from over another continent, as the image you put will seem to show (illusion). Basic geometry, if I may borrow your image... What these people might see:

I think you still completely missed the point of my post. Yes, the sun is physically over a different continent/ocean when it rises/sets for these cities. The outer yellow circle represents the physical path of the sun over a 24 hour period on December 21. Each spot represents the physical location of the sun when the corresponding city sees a sunrise or sunset.

[rabinoz]

The simple fact that Flat Earther's will not address is the in the south of the Equator at the Summer Equinox the sun rises south of East.
Just a few places:

Location		Sunrise Azimuth		FE Sunrise Dir
Brisbane, Australia		117°, or 27° South of East				I know this one, I live here!
São Paulo, Brazil		115°, or 25° South of East		23°, or 67° North of East
Puntas Arenas, Chile		133°, or 43° South of East		39°, 51° North of East

To me this is quite a big argument against the FE theory of the sun's movement, and ultimately against the whole FE hypothesis.

Heh. Can't hold a debate without both perspectives is all.

As I already stated, the difference here we are all ignoring is the fact that 'degree' doesn't mean anything on the FE!

FE degrees are different from Globe degrees in Southern Hemisphere due to lattitude/longitude getting longer instead of shorter. That's all. It's a matter of translation. Don't ask me for the translation! I wouldn't know. I don't defend the FE model, only misrepresentations of it. I never went so far as to learn this 'translation'.

I haven't the time or inclination (I feel a bit like "death warmed up" at the moment), but I beg to differ on degrees being different on the flat earth map.

I have not been misrepresenting the FE position at all.

As on the Globe, on the flat earth map "parallels" of latitudes are measured north or south of the equator with the North Pole being 90° N and the limit of the "Ice Rim" being 90° S.
The meridians of longitude on the flat earth map are straight lines radiating from the North Pole, with 0° through Greenwich, exactly as on the globe.

The co-ordinates of any point on that map are the same in degrees of latitude and longitude as on the globe.  The spacing of latitude lines (close to 111 km per degree) is the same as on the globe, though the spacing of the lines of longitude continually increases from zero at the North Pole to a maximum at the "rim".

At a particular location, North is towards the North Pole and East is 90° clockwise from that.
In any case, I was interested if the difference in directions of sunrise on the FW map compared to what we actually observe and that difference is massive.

On the diagrams, you gave, the shapes of the earth are quite different, but the lat, long of any location is exactly the same numbers on each.

[Rounder]

As I already stated, the difference here we are all ignoring is the fact that 'degree' doesn't mean anything on the FE!

Sure it does. A "degree" is just a unit of measurement of angles. In this case, it means the exact same thing on the flat earth as it does on the round earth. Both models have a North. The degree that the sun rises/sets at is measured as an angle from due North. We aren't talking about latitude/longitude degrees.

Actually we are talking about lat and long degrees.  Your degree of latitude = the elevation angle of the sun on the equinox.  Even the Wiki agrees:

To locate your latitude on the flat earth, it's important to know the following fact: The degrees of the earth's latitude are based upon the angle of the sun in the sky at noon equinox.
That's why 0° N/S sits on the equator where the sun is directly overhead, and why 90° N/S sits at the poles where the sun is at a right angle to the observer. At 45 North or South from the equator, the sun will sit at an angle 45° in the sky. The angle of the sun past zenith is our latitude.
Knowing that as you recede North or South from the equator at equinox, the sun will descend at a pace of one degree per 69.5 miles, we can even derive our distance from the equator based upon the position of the sun in the sky.

One of the major problems with the FE model is the fact that on a flat surface the angle of elevation to a fixed object in the sky would not be a constant mileage per degree.  The further away from zero one travels north or south, the further you should have to travel to get another degree of elevation change to the sun.

[Rama Set]

First of all, there is no need to apologize. I suspect Rama misread your comment.

You are totally right.  Nametaken, I am the one who needs to apologize.