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TheEngineer

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« Reply #60 on: July 04, 2006, 06:41:57 PM »
Quote from: "Erasmus"
Quote from: "TheEngineer"
However, when one is using a series of points on a coordinate system to determine distances, the points are not interchangeable with other systems without a conversion.

Indeed.  However, it seems to me that nobody was giving coordinates (coordinate-system-dependent) to points, but merely referring to the points themselves (coordinate-system-independent).  "The distance from P to Q" doesn't change when you change coordinate systems and, as far as I can tell, that's what the crux of the argument is here.

The whole basis of the argument here is that the distance CALCULATED from lat/long is different from RE to FE.

"I haven't been wrong since 1961, when I thought I made a mistake."
-- Bob Hudson

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RenaissanceMan

« Reply #61 on: July 04, 2006, 06:46:06 PM »
Quote from: "TheEngineer"
Quote from: "Erasmus"
Quote from: "TheEngineer"
However, when one is using a series of points on a coordinate system to determine distances, the points are not interchangeable with other systems without a conversion.

Indeed.  However, it seems to me that nobody was giving coordinates (coordinate-system-dependent) to points, but merely referring to the points themselves (coordinate-system-independent).  "The distance from P to Q" doesn't change when you change coordinate systems and, as far as I can tell, that's what the crux of the argument is here.

The whole basis of the argument here is that the distance CALCULATED from lat/long is different from RE to FE.

Yes, the distances were calculated from lat/long. That was done because both models use the same measuring system. I meticulously established that both models relied on measurement of lat/long early in the thread and that BOTH models applied them in the same way.

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Erasmus

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« Reply #62 on: July 04, 2006, 06:58:41 PM »
Okay, let's start over.

The two cities in question -- P and Q -- are given a certain latitute and longitude on RE maps.  From this data, RE cartographers compute the great circle distance Dr between P and Q.

Next, FEers convert latitude to radial distance -- hopefully according to r = R arcsin φ, where φ = π/2 - latitude -- and longitude to angle from some standard axis (say, the prime meridian) identically.  Then they compute the straight line distance Df between P and Q.

Lastly, somebody takes a direct measurement Dm of the length of the shortest path from P to Q that doesn't involve digging.

Which of the following do you (anybody, but TheEngineer in particular), are you claiming will be the case?

1)  that the conversion from latitute and longitude to polar coordinates is not the correct one for the geometries in question.

2)  that Dm = Df.

3)  that Dm = Dr.

4)  that the latitude and longitude of cities is faked so that Df = Dr = Dm.  That is, cities are not really where maps claim them to be.
Why did the chicken cross the Möbius strip?

TheEngineer

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« Reply #63 on: July 04, 2006, 07:02:47 PM »
Quote from: "RenaissanceMan"

Yes, the distances were calculated from lat/long. That was done because both models use the same measuring system. I meticulously established that both models relied on measurement of lat/long early in the thread and that BOTH models applied them in the same way.

Maybe I should just stop trying to make things simple, since it still doesn't get through.  The coordinate system that we know as latitude and longitude is based on a spherical coordinate system.  This system's origin is the center of the earth.  Only two of the three dimentions are used because your distance from the center of the earth doesn't really matter.  Now, a flat disk can be represented by spherical coordinates, but now radius must be taken into account, the zenith is now always the same value (0) and the only angle that matters is azimuth.  Since lat/long coordinates use only zenith and azimuth, these same values don't relate to a flat disk.  So, no, the FE and RE don't share the same lat/long system.

"I haven't been wrong since 1961, when I thought I made a mistake."
-- Bob Hudson

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Erasmus

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« Reply #64 on: July 04, 2006, 07:17:57 PM »
Quote from: "TheEngineer"
So, no, the FE and RE don't share the same lat/long system.

True, but we are not merely using spherical coordinates to specify the locations of points on the FE.  Instead, we are imagining that we "unwrap" the round Earth, expanding the south pole to form the circumference, and ending up with a flat Earth.  This is equivalent to the following change of coordinates, where R is the radius of the Earth and Lat ranges from +90° (north pole) to -90° (south pole):

r = R sin (90° - Lat)
θ = Long

In other words, if you apply the above transformation to every point on the Earth, the result will be a picture of the flat Earth.  Now it's just a question of whether you believe this picture to be accurate, especially in the high southern latitudes.  Note that this transformation preserves north-south distances, so if two cities lie along a line of longitude a distance D apart on the round Earth, then they lie along a radius a distance D apart on the flat Earth.

However, the transformation does distort east-west distances.  You now have the option of deciding which information you believe to be incorrect: the measured east-west distances between points, or the longitudes of those points.  Certainly either of those data can be empirically verified.
Why did the chicken cross the Möbius strip?

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Easter_Bunny

• 16
« Reply #65 on: July 04, 2006, 07:20:52 PM »
I have driven from Adelaide to Sydney, though I went via Melbourne so wasn't a straight path. However I have also driven from Adelaide to Perth via the Nullabor Desert.

This goes along the world longest straight stretch of road http://en.wikipedia.org/wiki/Nullarbor_Plain

I can tell you Adelaide and Perth are about 2700km apart (1677miles), and close to the same distance from the equator. We did the drive in 2 days. Under a FE model they would be closer to 6000km apart. There is no way I could drive this far in 2 days.

As for FE not distorting the sizes of the continents, surely it must as there is approximately 105 minutes between the sun rising in Adelaide and rising in perth.

24*60=1440
105/1440=0.0729
0.0729*360 =26.25 degrees apart (adelaide and perth)

At circumference of 57600 miles at 34 degrees south according to FE model.

26.25/360 = 0.0729
57600 * 0.729 = 4200 miles

4200 miles apart , 6762km apart.

there is no way adelaide is 4200 miles from Perth.

TheEngineer

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« Reply #66 on: July 04, 2006, 07:23:53 PM »
Erasmus-
No transformations were made.  I stated earlier that without a transformation, the same coordinates can't be used - we are arguing the same point!  Now, the calculations that were made used coordinates from one system in another without the transformations, which is why the distances were off.

"I haven't been wrong since 1961, when I thought I made a mistake."
-- Bob Hudson

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Easter_Bunny

• 16
« Reply #67 on: July 04, 2006, 07:32:09 PM »
Sorry exact Coordinates of the cities.

Adelaide, Australia  34  55 S  138  36 E
Perth, Australia  31  57 S  115  52 E

Also Longitude is an observed phenomenon, you can measure it yourself if you think it is false.
1. Observe the difference between the sun rising in two places at the same lattitude. eg 105 minutes

2. There is 1440  minutes in a day, so divide the observed time difference by the length of a day. eg 105/1440 = 0.0729

3. The flat earth is a circle with 360 degrees. To fing out how big the "segment" 105 minutes is, multiply 0.0729 by 360.
eg. 360*0.0729 = 26.25

thus the two cities are roughly 26.25 degrees apart by rough calculations. The actual difference is 23 degrees using the coordinates above.

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RenaissanceMan

« Reply #68 on: July 04, 2006, 07:32:15 PM »
Quote from: "TheEngineer"
Erasmus-
No transformations were made.  I stated earlier that without a transformation, the same coordinates can't be used - we are arguing the same point!  Now, the calculations that were made used coordinates from one system in another without the transformations, which is why the distances were off.

The sun is the sun. The earth is the earth. The sun traverses over the earth in a repeatable, measurable way. What part of that is not clear?

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Erasmus

• The Elder Ones
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« Reply #69 on: July 04, 2006, 07:47:18 PM »
So I got the transformation wrong before: the radial distance of a point from the hub is R * (π/2 - latitude).

Anyway point A (latitude = -34.5°, longitude = 138.5°) -- taking the radius of the Earth to be 6400 km -- has FE polar coordinates (r = 13907 km, θ = 138.5°), or FE cartesian coordinates (x = -10416 km, y = 9214.9 km).

Point B (latitude = -34.5°, longitude = 151°) has FE polar coordinates (r = 13907 km, θ = 151°) or FE cartesian coordinates (x = -12163 km, y = 6742.1 km).

So the FE displacement between points A and B is given by (Δx = 1747.6 km, Δy = 2472.8 km).  The FE distance along this displacement is sqrt( ΔxΔx + ΔyΔy ) = 3028.0 km.

This is a pretty significant difference from Easter_Bunny's measurement of 2700 km.  Note that his measurement is an upper bound on the actual distance, since the road he took may have been longer -- but not shorter -- than the shortest path.

Getting to the point again, you can conclude:

1)  The cities are not really at the latitudes/longitudes that cartographers would have us believe.
has polar
2)  Easter_Bunny's measurement is wrong.

3)  The Earth is not flat.

Which do you conclude?
Why did the chicken cross the Möbius strip?

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Easter_Bunny

• 16
« Reply #70 on: July 04, 2006, 08:08:35 PM »
Erasmus I'm talking about Adelaide and PERTH, not Sydney, just because there is a road that goes fairly straight from Perth to Adelaide.

Sorry if there was any confusion.

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Erasmus

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« Reply #71 on: July 04, 2006, 08:10:16 PM »
Quote from: "Easter_Bunny"
Erasmus I'm talking about Adelaide and PERTH, not Sydney, just because there is a road that goes fairly straight from Perth to Adelaide.

Sorry if there was any confusion.

Er, that's okay.  It's a similar argument.  Feel free to run the numbers again using my coordinate transformation.
Why did the chicken cross the Möbius strip?

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RenaissanceMan

« Reply #72 on: July 04, 2006, 08:17:52 PM »
Erasmus, you've made an error, there.

You calculated the distance between Adalaide and Sydney. and... interestingly, came up with very close to the number I did for the FE model before.

Check those Longitudes again.

The distance from Perth to Adelaide is MUCH higher according to the FE.

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Easter_Bunny

• 16
« Reply #73 on: July 04, 2006, 08:29:20 PM »
Quote from: "Erasmus"
Quote from: "Easter_Bunny"
Erasmus I'm talking about Adelaide and PERTH, not Sydney, just because there is a road that goes fairly straight from Perth to Adelaide.

Sorry if there was any confusion.

Er, that's okay.  It's a similar argument.  Feel free to run the numbers again using my coordinate transformation.

Actually Perth to Adelaide is about double the distance than Adelaide Sydney. Also are you saying my view and calculations on the falt earth model are wrong? Or are you agreeing and saying the flat earth model can't be correct?

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Erasmus

• The Elder Ones
• 4242
« Reply #74 on: July 04, 2006, 08:42:35 PM »
Quote from: "RenaissanceMan"
Erasmus, you've made an error, there.

You calculated the distance between Adalaide and Sydney. and... interestingly, came up with very close to the number I did for the FE model before.

Aha.  Yes.  Using the more accurate longitudes, I find the FE distance from Adelaide to Sydney to be 3013.9 km, and the FE distance from Adelaide to Perth to be 5456.5 km.  This of course only make Easter_Bunny's measurements all the more striking.

On the other hand, according to this formula for the great circle distance on a sphere, the RE distance from Adelaide to Perth is 3185.8 km, which is noticeably greater than Easter_Bunny's upper-bound estimate.

Hm.
Why did the chicken cross the Möbius strip?

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RenaissanceMan

« Reply #75 on: July 04, 2006, 08:45:08 PM »
Quote from: "Erasmus"
So I got the transformation wrong before: the radial distance of a point from the hub is R * (π/2 - latitude).

Anyway point A (latitude = -34.5°, longitude = 138.5°) -- taking the radius of the Earth to be 6400 km -- has FE polar coordinates (r = 13907 km, θ = 138.5°), or FE cartesian coordinates (x = -10416 km, y = 9214.9 km).

Point B (latitude = -34.5°, longitude = 151°) has FE polar coordinates (r = 13907 km, θ = 151°) or FE cartesian coordinates (x = -12163 km, y = 6742.1 km).

So the FE displacement between points A and B is given by (Δx = 1747.6 km, Δy = 2472.8 km).  The FE distance along this displacement is sqrt( ΔxΔx + ΔyΔy ) = 3028.0 km.

This is a pretty significant difference from Easter_Bunny's measurement of 2700 km.  Note that his measurement is an upper bound on the actual distance, since the road he took may have been longer -- but not shorter -- than the shortest path.

Getting to the point again, you can conclude:

1)  The cities are not really at the latitudes/longitudes that cartographers would have us believe.Which do you conclude?

has polar
2)  Easter_Bunny's measurement is wrong.

3)  The Earth is not flat.

I conclude that you didn't use Easter_Bunny's basis of measurement. He measured between PERTH and ADELAIDE. You measured between ADELAIDE and SYDNEY. Huge difference.

Your FE calculation between Adelaide and Sydney is 3028 km. The map distance is 1200 km. Giving a FE to RE error factor of 2.5 to 1 at that latitude as I have been saying all through this thread.

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RenaissanceMan

« Reply #76 on: July 04, 2006, 08:58:38 PM »
Quote from: "Erasmus"
Quote from: "RenaissanceMan"
Erasmus, you've made an error, there.

You calculated the distance between Adalaide and Sydney. and... interestingly, came up with very close to the number I did for the FE model before.

Aha.  Yes.  Using the more accurate longitudes, I find the FE distance from Adelaide to Sydney to be 3013.9 km, and the FE distance from Adelaide to Perth to be 5456.5 km.  This of course only make Easter_Bunny's measurements all the more striking.

On the other hand, according to this formula for the great circle distance on a sphere, the RE distance from Adelaide to Perth is 3185.8 km, which is noticeably greater than Easter_Bunny's upper-bound estimate.

Hm.

You must think I'm stupid. The great circle calculation works on a round earth by calculating the minimal distance between point A and point B if you travel in an arc using the earth's curvature and rotation to shorten the traveled distance.

It is NOT the straight line distance between two points, which is what we are talking about. We are ASSUMING you are traveling by car.

The fact remains. The error factor between the Flat Earth model and actual maps USED EVERY DAY is 2.5 to 1 in south Australia.

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Erasmus

• The Elder Ones
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« Reply #77 on: July 04, 2006, 09:08:54 PM »
Quote from: "RenaissanceMan"
You must think I'm stupid.

No, I don't; stop being so argumentative.

Quote
The great circle calculation works on a round earth by calculating the minimal distance between point A and point B if you travel in an arc using the earth's curvature and rotation to shorten the traveled distance.

That's not true.  The great circle distance has nothing to do with the rotation of the sphere in question.  "Straight line" distance on a sphere means great circle distance, unless you plan on digging through the Earth, which I sense is not what you mean since you refer to distance travelled by a car.

Mostly I'm agreeing with you, except apparently on terminology.  Pretend for a second that you don't think I'm an FEer, and suddenly you'll be a lot less confused.
Why did the chicken cross the Möbius strip?

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RenaissanceMan

« Reply #78 on: July 04, 2006, 09:20:34 PM »
Quote from: "Erasmus"
Quote from: "RenaissanceMan"
You must think I'm stupid.

No, I don't; stop being so argumentative.

Quote
The great circle calculation works on a round earth by calculating the minimal distance between point A and point B if you travel in an arc using the earth's curvature and rotation to shorten the traveled distance.

That's not true.  The great circle distance has nothing to do with the rotation of the sphere in question.  "Straight line" distance on a sphere means great circle distance, unless you plan on digging through the Earth, which I sense is not what you mean since you refer to distance travelled by a car.

Mostly I'm agreeing with you, except apparently on terminology.  Pretend for a second that you don't think I'm an FEer, and suddenly you'll be a lot less confused.

Sorry, I slightly overreacted. I was thinking of something else. However, there was no reason to pull yet another set of formulas into the mix. The already established error of 2.5 to 1 is MORE than adequate.

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Erasmus

• The Elder Ones
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« Reply #79 on: July 04, 2006, 09:21:51 PM »
Quote from: "RenaissanceMan"
Sorry, I slightly overreacted. I was thinking of something else. However, there was no reason to pull yet another set of formulas into the mix. The already established error of 2.5 to 1 is MORE than adequate.

Well, TheEngineer seemed to be ... tangling up the discussion, so I thought I'd try to "reset" it.
Why did the chicken cross the Möbius strip?

TheEngineer

• Planar Moderator
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• GPS does not require satellites.
« Reply #80 on: July 04, 2006, 09:37:22 PM »
If the transformations were previously taken into account, I appologize; I missed it.

"I haven't been wrong since 1961, when I thought I made a mistake."
-- Bob Hudson

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• 551
« Reply #81 on: July 04, 2006, 10:59:55 PM »
The FEers have gotten quiet in this thread all of a sudden.

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Rick_James

• The Elder Ones
• 4311
• Rick <3 Gayer
« Reply #82 on: July 05, 2006, 12:08:40 AM »
Lol they're just waiting for the thread to peter out so it gets lost into oblivion and we forget about it 8-)

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RenaissanceMan

« Reply #83 on: July 05, 2006, 06:28:08 AM »
Quote from: "Erasmus"
Quote from: "RenaissanceMan"
Erasmus, you've made an error, there.

You calculated the distance between Adalaide and Sydney. and... interestingly, came up with very close to the number I did for the FE model before.

Aha.  Yes.  Using the more accurate longitudes, I find the FE distance from Adelaide to Sydney to be 3013.9 km, and the FE distance from Adelaide to Perth to be 5456.5 km.  This of course only make Easter_Bunny's measurements all the more striking.

On the other hand, according to this formula for the great circle distance on a sphere, the RE distance from Adelaide to Perth is 3185.8 km, which is noticeably greater than Easter_Bunny's upper-bound estimate.

Hm.

You know, I thought those numbers looked cooked, but the great circle calculations are fairly complicated. The number you cite is from Perth to SYDNEY, not Adalaide. The 'great circle' distance from Perth to Adelaide is only 2100 km, while the flat earth calculation of the same distance is 5456 km. Look at that! When I use the correct coordinates, the distance error is 2.5 to 1.

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RenaissanceMan

« Reply #84 on: July 05, 2006, 02:02:12 PM »
LOL This is funny... I've been reading Samuel Rowbotham's "Not a globe" but not in chapter order...

I picked the cities of Adelaide and Sydney because they matched criteria I was looking for... but now I find that Rowbotham ALSO used those two cities in his work! His distance calculations are catastrophically off, but not as bad as the current FE calculations as his 'world' was much smaller. (52,800 miles in cicrumference as opposed to 78,222 for the current model) Samuel also used the wrong longitude delta for Sydney and Adelaide, I guess he figured noone would notice.

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Rick_James

• The Elder Ones
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• Rick <3 Gayer
« Reply #85 on: July 06, 2006, 02:22:04 AM »
Is he an FE'er by any chance  :wink:

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RenaissanceMan

« Reply #86 on: July 06, 2006, 08:23:30 AM »
Quote from: "Rick_James"
Is he an FE'er by any chance  :wink:

Yes, Samuel Rowbotham is considered to be the 'Father of modern Flat Earthism" He cruised England in the late 19th century, his book, "Earth, not a globe" was written in 1881 and included all of his previous bullshit, along with expanded notes on the 'mecahnics' of heavenly bodies in relation to the flat earth.

The scientific method wasn't good enough for Samuel, so he invented his own.. the 'Zetetic method' that expanded upon the scientific method by allowing the concepts of unverifiability and circular logic. He was, however, an acomplished debator that reportedly steamrollered all opponents.

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Rick_James

• The Elder Ones
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• Rick <3 Gayer
« Reply #87 on: July 06, 2006, 03:47:31 PM »
Quote
....was written in 1881 and included all of his previous bullshit,

Well Put. I might see if I can find that book for a bit of on-topic research.

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Xargo

• 670
« Reply #88 on: July 06, 2006, 03:51:11 PM »
Quote from: "RenaissanceMan"
LOL This is funny... I've been reading Samuel Rowbotham's "Not a globe" but not in chapter order...

I picked the cities of Adelaide and Sydney because they matched criteria I was looking for... but now I find that Rowbotham ALSO used those two cities in his work! His distance calculations are catastrophically off, but not as bad as the current FE calculations as his 'world' was much smaller. (52,800 miles in cicrumference as opposed to 78,222 for the current model) Samuel also used the wrong longitude delta for Sydney and Adelaide, I guess he figured noone would notice.

Surprised?
quot;Earth is flat because there is a conspiracy, and there is a conspiracy because the Earth is flat" - Makes sense, duh.

http://theflatearthsociety.org/forum/index.php?topic=2955.0

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RenaissanceMan

« Reply #89 on: July 06, 2006, 04:38:46 PM »
Quote from: "Rick_James"
Quote
....was written in 1881 and included all of his previous bullshit,

Well Put. I might see if I can find that book for a bit of on-topic research.

Here you go, it's on line!

http://www.sacred-texts.com/earth/za/index.htm