[edby]

It is apparently not uncommon for a plane to fly faster than the speed of sound:

Possibly but you need to provide a convincing explanation of why the same planes fly at significantly higher speeds on southern hemisphere routes, than on northern hemisphere routes.

[edby]

I have flown from Toronto to Vancouver (3,364km) dozens of times.  Depending on wind conditions it takes from less than 4 3/4 hrs to 5 hrs and change.  That fits with that RE data.  You don't have to have taken all these flights yourself either.  Airlines list their average flight times.  You can just google them.

Toronto-Vancouver was one of my pairs. I assumed a time of 5 hours, which agrees with your data.

Of course for any two similar distances, the flight times will vary a lot, as you can see from the graph. For example, an 8,000 km journey could take from 9 hours to 11 hours. This is why the x-y chart is not an exact straight line. But the pattern is very clear. Correlation is 99.58%, which is high by any standard.

[BillO]

- There is no FE map

And that is okay?  You are a proponent of an earth configuration that has no map?

- We can't rely on the distances to be accurate because Lat/Lon relies on spherical coordinates

Is there any way you can explain that statement?

- We can't rely on the flight times to be accurate

On top of all of the above it is also known that on international flights planes regularly use jet streams to quicker get to a destination.

Yes, right.  So?  Flight times vary but the ground speed, which is the thing that varies, is known. So given that flight time is calculated in the usual way:  t=distance/speed, therefore the distance can be calculated as distance=t*speed.  Those distances agree with RE distances, not FE distances - regardless of which 'map' you wish to press into service.

[SphericalEarther]

Latitude : can be derived from the angle from the horizon to Polaris or Sigma Octantis. They are not spherical earth measurements.

Longitude: can be derived from the sun and time, by checking the time when the sun is directly north/south, it is not a spherical earth measurement.

On a globe earth, we have easily defined and calculated distances, and as seen in the graph, flight times match distanced calculated on a globe earth.

We have all the information at our fingertips, yet the FE community has not been able to produce any working map. The monopole map doesn't work and the bi-polar map is hopeless, I really fail to see why FEers would use that instead.

[iamcpc]

There is no map.

Personally I don't understand your claims that there is no map or that no accurate map exists


I have personally used this map to travel North America, South America, Europe, and Asia. How on earth can you claim there is no map or there is no accurate map?

https://www.google.com/maps


1. If no accurate map of the earth exists how am I (and MILLIONS AND MILLIONS of other people) able to accurately travel long distances on a consistent basis using a map?
2. If i'm able to (along with MILLIONS AND MILLIONS of other people) use a map to accurately travel long distances all over the world would that not make that map accurate?
3. If we don't have an accurate map of the earth (and don't know the distances between far cities) how are ships and planes able to navigate long distances?

[ICanScienceThat]

There is no map.

Personally I don't understand your claims that there is no map or that no accurate map exists


I have personally used this map to travel North America, South America, Europe, and Asia. How on earth can you claim there is no map or there is no accurate map?

https://www.google.com/maps


1. If no accurate map of the earth exists how am I (and MILLIONS AND MILLIONS of other people) able to accurately travel long distances on a consistent basis using a map?
2. If i'm able to (along with MILLIONS AND MILLIONS of other people) use a map to accurately travel long distances all over the world would that not make that map accurate?
3. If we don't have an accurate map of the earth (and don't know the distances between far cities) how are ships and planes able to navigate long distances?

He means there is no "Flat Earth" map. Google is a map of the globe.

[edby]

There is no map.

Personally I don't understand your claims that there is no map or that no accurate map exists


I have personally used this map to travel North America, South America, Europe, and Asia. How on earth can you claim there is no map or there is no accurate map?

https://www.google.com/maps


1. If no accurate map of the earth exists how am I (and MILLIONS AND MILLIONS of other people) able to accurately travel long distances on a consistent basis using a map?
2. If i'm able to (along with MILLIONS AND MILLIONS of other people) use a map to accurately travel long distances all over the world would that not make that map accurate?
3. If we don't have an accurate map of the earth (and don't know the distances between far cities) how are ships and planes able to navigate long distances?

He means there is no "Flat Earth" map. Google is a map of the globe.

You have to understand that iamcpc is probably unique in Flat Earth circles in simultaneously holding (i) that distances in Google maps is a totally accurate representation of real distance across the Earth's surface and (ii) that the Earth's surface is flat.

[ICanScienceThat]

You have to understand that iamcpc is probably unique in Flat Earth circles in simultaneously holding (i) that distances in Google maps is a totally accurate representation of real distance across the Earth's surface and (ii) that the Earth's surface is flat.

From what I've seen, that isn't really a very unique perspective.

I think many FEs recognize that google maps and indeed google earth works very well to represent the locations and distances between places on Earth - at least any places near enough to drive between in our everyday experience.

From what I've seen, most FEs expect that we should be able to make a flat map with distances that perfectly match the distances reported by airlines and google earth. It is a rather abstract bit of geometry to understand that this cannot be possible, and I think many FEs are simply not willing to make this leap.

A few FEs have embraced this issue, and those must declare that the distances on google earth are incorrect.

In general, there can be no FE map:
a) If you are in the first group, making such a map disproves your theory, and you are no longer an FE. (TigerDan)
b) If you are in the 2nd group, then making a FE map puts the responsibility upon you to defend it, and that is going to require that you disprove the distances on the globe.

This is going to sound like a criticism, but I don't think it really is... The most common FE philosophy seems to be that as long as we do not present a map, we can continue to say there could be a map. I'm starting to think this is a conscious decision. The possibility that a map could exist so long as we do not present one. I think the common FE thinking is to just let people believe what they want and mostly not to challenge it. Creation of a map is to invite challenge, so to avoid such challenge, one can simply postulate wild ideas that cannot be challenged.

[iamcpc]

He means there is no "Flat Earth" map. Google is a map of the globe.

There are two versions of this map.

The 2D version is clearly flat. It's 2D. The entire map can be printed on a piece of paper. It is NOT a sphere or a globe.

The only way it becomes a "globe" map is if you turn on the satellite setting. You can CLEARLY see the difference between a FLAT paper map and a GLOBE map. If you print this map on a piece of paper you will only be printing a 2D portion of PART of the map.

Here is North America on a map of a GLOBE:




Here is North America on a FLAT paper map (please note that this map makes NO claims about the shape of the earth):

[ICanScienceThat]

I've tried to explain this before. I rather suspect you just don't care, and that is your right.

Because I'm totally OCD about this type of thing, I am compelled to explain it again. Follow along with these steps with me if you like:
1) Open google maps and zoom out to see North America. Make sure you can see the all of Florida and all of Alaska.
2) Take a screenshot, and dump that into some image software (gimp)
3) Go into google earth mode and center the view on the middle of the lower 48.
4) Take a screenshot and dump that into the image software as a new layer
5) Back in google earth, center the view on Alaska.
6) Take a screenshot and dump that as a layer into the image.
7) In the image software, scale the lower 48 picture from the globe to best match the flat map picture. Memorize that scale (it was 33% for me)
Now scale Alaska to that scale. See what you get.


As you can see, Alaska on the flat version is WAY bigger than it is on the globe version. One of these is wrong!

[edby]

Here is North America on a FLAT paper map (please note that this map makes NO claims about the shape of the earth):

Actually if it is constant scale, then it does make claims about the shape of the earth, namely that the earth is flat. A flat map with constant scale can only map a flat surface, nothing else.

However the scale is not constant, as the man above has clearly pointed out.

[iamcpc]

I've tried to explain this before. I rather suspect you just don't care, and that is your right

As you can see, Alaska on the flat version is WAY bigger than it is on the globe version. One of these is wrong!

maps have this thing called a legend.
Per FLAT 2D map legend Alaska is about 800 miles north to south.
About the distance between San Antonio and Kansas City.


Per the GLOBE map the same is true. It does not matter if your map shows a GIANT square mile or a tiny square mile. As long as the legend shows the distance it's still a square mile.

[iamcpc]

It is apparently not uncommon for a plane to fly faster than the speed of sound:

Possibly but you need to provide a convincing explanation of why the same planes fly at significantly higher speeds on southern hemisphere routes, than on northern hemisphere routes.

Tom had just said that no flat earth map exists. Hemisphere is a round earth term. Tom's flat earth model has no idea the routes those planes are or are not taking.

[edby]

maps have this thing called a legend.
Per FLAT 2D map legend Alaska is about 800 miles north to south.
About the distance between San Antonio and Kansas City.

The legend will state the scale of the map, correct. And for small areas (i.e. the size of a state) the scale will be almost constant.

This does not work for larger areas. See below. One line measures the distance between San Antonio and Kansas City, 1046.72 km. The other measures the length of the border between Alaska and Canada, 1,126.51km. The distances measured are roughly the same, you agree?

But the length on the map is different. Measured on my screen, San Antonio to Kansas City is about 4cm, Alaska-Canada border about 7cm. So the scale for the border is nearly twice that of San Antonio to Kansas City.

You will probably object that we could redraw the map so the scale was constant. However there is a geometrical theorem that says that this is impossible. Happy to go into that. First, do you agree that the map is not constant scale throughout?

[edit] Indeed we have discussed this before. https://forum.tfes.org/index.php?topic=9955.msg157186#msg157186

What Gauss discovered was that even the inhabitants of a world which was perpetually covered in cloud could discover whether they were living on a flat surface or not, simply by measuring distances.

I.e. if you believe that Google maps is accurate, then logically you must believe that it is a map of a curved surface. This is fundamental.

[edby]

Hemisphere is a round earth term.

OK, remove the term 'hemisphere' from what I wrote. Do we agree that Australia is in the South of the world, and Norway (e.g.) in the North?

[inquisitive]

It's not the same.

(i) I collected the data myself (ii) there are many more data points (more than 350 in all) (iii) I used the proper formula to compute the RE predicted distance between the locations. The other experimenter used a piece of string and a globe, from memory.

If the data is based on the spherical coordinate system of Latitude and Longitude, which you admit is based on the idea that the earth is a sphere, then the results are invalid until you can demonstrate that the system and model is correct.

WGS84 proves this.

[Tumeni]

https://erenow.com/common/shorthistory/6.html

"For half a century people had been trying to work out the size of the Earth, mostly by making very exacting measurements. One of the first such attempts was by an English mathematician named Richard Norwood. As a young man Norwood had travelled to Bermuda ...  In the early seventeenth century Bermuda was well known among ships’ captains for being hard to locate. The problem was that the ocean was big, Bermuda small and the navigational tools for dealing with this disparity hopelessly inadequate. There wasn’t even yet an agreed length for a nautical mile. Over the breadth of an ocean the smallest miscalculations would become magnified so that ships often missed Bermuda-sized targets by dismayingly large margins. Norwood, whose first love was trigonometry and thus angles, decided to bring a little mathematical rigour to navigation, and to that end he determined to calculate the length of a degree.

Starting with his back against the Tower of London, Norwood spent two devoted years marching 208 miles north to York, repeatedly stretching and measuring a length of chain as he went, all the while making the most meticulous adjustments for the rise and fall of the land and the meanderings of the road. The final step was to measure the angle of the sun at York at the same time of day and on the same day of the year as he had made his first measurement in London. From this, he reasoned he could determine the length of one degree of the Earth’s meridian and thus calculate the distance around the whole. It was an almost ludicrously ambitious undertaking—a mistake of the slightest fraction of a degree would throw the whole thing out by miles—but in fact, as Norwood proudly declaimed, he was accurate to “within a scantling”—or, more precisely, to within about six hundred yards. In metric terms, his figure worked out at 110.72 kilometres per degree of arc.

In 1637, Norwood’s masterwork of navigation, The Seaman’s Practice, was published and found an immediate following. It went through seventeen editions and was still in print twenty-five years after his death.

... The momentum for determining the Earth’s circumference passed to France. There, the astronomer Jean Picard devised an impressively complicated method of triangulation involving quadrants, pendulum clocks, zenith sectors and telescopes (for observing the motions of the moons of Jupiter). After two years of trundling and triangulating his way across France, in 1669 he announced a more accurate measure of 110.46 kilometres for one degree of arc. ...

... chose the Andes because they needed to measure near the equator, to determine if there really was a difference in sphericity there, and because they reasoned that mountains would give them good sightlines. In fact, the mountains of Peru were so constantly lost in cloud that the team often had to wait weeks for an hour’s clear surveying. ... But Bouguer and La Condamine were nothing if not tenacious, and they stuck to the task for nine and a half long, grim, sun-blistered years. Shortly before concluding the project, word reached them that a second French team, taking measurements in northern Scandinavia (and facing notable discomforts of their own, from squelching bogs to dangerous ice floes), had found that a degree was in fact longer near the poles, as Newton had promised. The Earth was 43 kilometres stouter when measured equatorially than when measured from top to bottom around the poles."

So, how does one measure one degree of meridian on a flat Earth?

[AATW]

This is going to sound like a criticism, but I don't think it really is... The most common FE philosophy seems to be that as long as we do not present a map, we can continue to say there could be a map. I'm starting to think this is a conscious decision. The possibility that a map could exist so long as we do not present one. I think the common FE thinking is to just let people believe what they want and mostly not to challenge it. Creation of a map is to invite challenge, so to avoid such challenge, one can simply postulate wild ideas that cannot be challenged.

Agreed. I see that sort of reasoning a lot on here. It's like claiming to have discovered a square number which is also a prime number but then refusing to state the number. You can then spend all day saying "Well it can't be 5 - that's a prime number but it's not a square number", "It can't be 9, that's a square number but it divides by 3 so it's not a prime number". And I can say "I'm not thinking of 5 or 9". Rinse and repeat. So long as no map of a flat earth is produced they can keep pretending that one could exist. It's telling that Tom's argument was:

If the data is based on the spherical coordinate system of Latitude and Longitude, which you admit is based on the idea that the earth is a sphere, then the results are invalid until you can demonstrate that the system and model is correct.

When it's the result which demonstrates the model is correct. Or, more accurately, it gives confidence in that model.

[Tom Bishop]

It's telling that Tom's argument was:

If the data is based on the spherical coordinate system of Latitude and Longitude, which you admit is based on the idea that the earth is a sphere, then the results are invalid until you can demonstrate that the system and model is correct.

When it's the result which demonstrates the model is correct. Or, more accurately, it gives confidence in that model.

It's geometrically a spherical coordinate system. Any distance recorded is done under the assumption of a sphere. Many of the youtube arguments are trying to show that a spherical coordinate system can make a sphere. It's circular reasoning.

[edby]

It's telling that Tom's argument was:

If the data is based on the spherical coordinate system of Latitude and Longitude, which you admit is based on the idea that the earth is a sphere, then the results are invalid until you can demonstrate that the system and model is correct.

When it's the result which demonstrates the model is correct. Or, more accurately, it gives confidence in that model.

It's geometrically a spherical coordinate system. Any distance recorded is done under the assumption of a sphere. Many of the youtube arguments are trying to show that a spherical coordinate system can make a sphere. It's circular reasoning.

I think we are totally agreed that the distances derived from the coordinates using the Haversine formula, assume spherical earth.

The coordinates are not in themselves spherical though. They are just measurements based on direct observation of the sun's position. It's the formula that assumes a sphere, not the coordinates.

Given that, they should show minimal correlation with flight times on our flat earth, for the times do not depend directly on the shape of the earth, but rather the actual distance travelled. Do you agree?