Water is Level

If there is any doubt in your mind that water is level, please go perform this experiment.

That is ridiculous! 

Please go perform this experiment ACROSS THE WHOLE OCEAN ALL THE WAY TO THE ANTARCTIC PERIMETER and then, maybe, I will believe it. 

Water is Level

What difference, at this point, does it make?

Wikipedia is wrong. Read: Flat Earth: The History of an Infamous Idea. Wallace colluded with the judge and Hampden successfully sued.

The lawsuit that Hampden successfully tried had nothing to do with the outcome of the bet.  I am sure you know this and if you don't you really, really need to get your facts straight.  The lawsuit was to have the courts void the wager because an arcane law made such wagers illegal.  Whether Wallace colluded, or didn't (he didn't), or whehter Hampden's referee agreed that the water was convex, or didn't (he did) had literally zero relevance to the lawsuit.  However, Hampden was found to have libeled Wallace in a court of law.  If you are going to accuse one side of being dishonest in that infamous case, it is obviously Hampden.

Quote from: inquisitive on June 18, 2016, 02:30:16 PM

Quote from: John Davis on June 18, 2016, 02:07:16 PM

Wikipedia is wrong. Read: Flat Earth: The History of an Infamous Idea. Wallace colluded with the judge and Hampden successfully sued.

No, there is no necessity that since the distances are preserved it must be a globe. Why do you think this is a mathematical fact?  I find it odd you say its not limited to Euclidean geometry too. Math is axiomatic; this means there is no such thing as a mathematical fact just those facts that deduct from the base axioms chosen. If I choose my axioms wisely, there is no reason why what you say must be the case.

Nobody is really talking about it being embedded in higher dimensional space either, at least as far as the map goes.

Distances prove a globe.  Or show your measurements.

They certainly don't prove a globe. At most they prove a non-euclidean surface - a globe is one of  infinitely many such surfaces that would have the same distances. Simply stating it proves a globe doesn't cut the mustard.

Please describe some of these infinite surfaces that have all the same distances and shapes that have been measured with quite good accuracy for centuries. While you are at it show us your Flat Map that has all these correct distances, or do need to delve into Minkowski Space or worse to visualise them.

Mind they are certainly not flat as this Society seems to insist.

It does seem a bit weird that you have invent your own geometry, physics or whatever you want to call it.

Maybe you should get you "physics" accepted by at least a few people before building your whole universe on it!

If there is any doubt in your mind that water is level, please go perform this experiment.

Ok, now you've confused me even more. Apparently you don't believe the earth is non-euclidean flat any more, but normal, generic, euclidean flat.

Also, no, it's not a "verified experiment". The experiment has been repeated many times with different results due to refraction. I remember another asshole doing the same experiment concluded it was concave. Go figure. On the other side, if you live relatively near the sea like I do, you've probably seen distant ships appearing to "sink" below the horizon. All attempts by flat earthers to explain that have failed.

Quote from: sokarul on June 17, 2016, 11:46:43 AM

Quote from: John Davis on June 17, 2016, 10:49:51 AM

Quote from: sokarul on June 17, 2016, 10:35:17 AM

Feel free to pay attention to all the other threads about this. Flat /= level.

This one should be good. Why would you think that flat should not be level?

Flat can indeed not be level. 

Certainly not in the case of water. Unless, of course, it is flowing downstream.

Quote from: Empirical on June 17, 2016, 11:21:09 AM

Quote from: John Davis on June 17, 2016, 10:49:03 AM

How do you explain the results? This is a repeated and verified experiment. It has been published many times over the years, often with photographic evidence.

The Earth is Flat, and that is that.

Diffraction. If you can say that the sun goes over the horizon by perspective, we can say that diffraction allows the flag to still be seen.
Anyway you can't see where the river meets the ocean can you. 

Of course not, the air obstructs my vision before I could have any such luck. Diffraction? oooh so its an illusion now is it? Every time something proves the earth flat every single time it turns out to be diffraction or refraction.  Sounds legit to me.

First of all, it's refraction, not diffraction. Empirical was wrong. But you CAN'T argue it doesn't exist, and the experiment can't be considered accurate since refraction is present.

I have recently (yesterday) performed an experiment, the results favor a Spherical model.   

I am attempting to measure the dip to the horizon and the accosiated distance to prove a globe model.
An observer close to Earths surface can only see a limited area, bounded by a circle centered on the observer. This circle is called the horizon.

In the spherical Earth model a point on this circle is slightly below the plane drawn through the observer and perpendicular to a line from the observer to the center of the Earth. The angle between this plane and the line from the observer to a point on the horizon is called the dip of the horizon.

In a FE model, many FEers claim that the horizon raises to eye level. (Impossible)

I decided to get hold of a theodolite and make some measurements across a bay in south wales The area has some costal cliffs, And a set of ramps/steps down to the beach . I had a theodolite, and Altimeter, a 10m tape measure and I am measuring the angle the horizon is below the theodolite and the distance that the horizon is away.
The results I am going to show almost certainly show  that the Earth is (approximately) a sphere:

Experement 1

Measure the dip to the horizon at altitudes of 2,5,10,15, 20, 30 and 40 meters altitude
Theodolite set to standard atmosphere for all readings above 5m and sea level (1/7) setting for on the ground at the waters edge and 2 meter reading. remember we have to also allow for refraction, which was visually low on the day.

sea level    = 0.01- 0.03 degrees (reading unstable)
2  m    = 0.04 degrees
5  m   = 0.07 degrees
10 m  = 0.11 degrees
20 m  = 0.17 degrees
30 m  = 0.24 degrees
40 m = 0.32 (Horizon contrast not clear enough for accuracy as hazyness was present)

Experement 2

Measure the Distance to the Horizon in Kilometers from a known altitude

2m   = 4.67
5m   = 8.03
10m = 11.36
20m = 16.05
30m = 19.64
40m = 22.10

Extra
Measure the elevation angle of Polaris
Result: 51.42 degrees

Of course this will be ignored, or called fake. 

More results to come soon, along with Pictures of ships over the horizon complete with measurements, two synchronized videos of sunsets from 2m and 30m altitude and other fun stuff!

Quick question to ponder. If I measured between 3 points in a triangle, why would the measured angles add up to more than 180 degrees?

John Davis, would you please define curvature for me?

The math I am talking about is the one derived from the Zermelo-Fraenkel Axioms (including choice), the ones every mathematician in the world uses. I did not use any other axioms than those mentioned. And yes, this applies to every geometry.

Quote from: John Davis on June 17, 2016, 12:32:55 PM

Quote from: sokarul on June 17, 2016, 11:46:43 AM

Quote from: John Davis on June 17, 2016, 10:49:51 AM

Quote from: sokarul on June 17, 2016, 10:35:17 AM

Feel free to pay attention to all the other threads about this. Flat /= level.

This one should be good. Why would you think that flat should not be level?

Flat can indeed not be level. 

Certainly not in the case of water. Unless, of course, it is flowing downstream.

Quote from: Empirical on June 17, 2016, 11:21:09 AM

Quote from: John Davis on June 17, 2016, 10:49:03 AM

How do you explain the results? This is a repeated and verified experiment. It has been published many times over the years, often with photographic evidence.

The Earth is Flat, and that is that.

Diffraction. If you can say that the sun goes over the horizon by perspective, we can say that diffraction allows the flag to still be seen.
Anyway you can't see where the river meets the ocean can you. 

Of course not, the air obstructs my vision before I could have any such luck. Diffraction? oooh so its an illusion now is it? Every time something proves the earth flat every single time it turns out to be diffraction or refraction.  Sounds legit to me.

First of all, it's refraction, not diffraction. Empirical was wrong. But you CAN'T argue it doesn't exist, and the experiment can't be considered accurate since refraction is present.

If refraction is not real why have ships navigators using "Celestial Navigation" had to allow for it for centuries^[1] as in:

Refraction
Having passed through the vacuum of outer space, the light from the celestial body has to pass through the atmosphere before it is observed using a sextant. The atmosphere tends to bend the path of the light as it passes through, so that the celestial body appears higher in the sky than it would be if there was no atmosphere.

A calculated Altitude assumes the earth has no atmosphere, so the sextant Altitude has to be corrected for Refraction so that it can be compared to the calculated Altitude. Refraction tables are always included in Almanacs used for celestial navigation.

From Celestial Navigation Terms

Dip/ Height of Eye
The True Horizon is at 90° to the Earth’s gravitational field. It coincides with the
apparent horizon at sea level. However the Apparent Horizon starts to dip below the
horizontal plane as the height of (the observer’s) eye increases.
Dip includes an allowance for Refraction below the horizontal plane.
. . . . . . . . . .
Refraction
The deflection of light as it enters/ passes through the atmosphere is known as Refraction.
Refraction is stable and therefore predictable above about 15°, below that one needs to consider the characteristics of the atmospheric layers through which the light passes at that time. (Taking the altitude of bodies at less than 15° is usually avoided for this reason.)
For altitudes above 15°, a simplified formula is adequate (± 0’.02), Refraction = 0.96/ Tan (Altitude)
Refraction tables make assumptions on the layers for low altitudes and should be treated with caution. +/- 2° is not uncommon at an altitude of 2°.
Refraction is subtracted from the Apparent Altitude to obtain the True Altitude.
 

from: Celestial Navigation Tutorial - NavSoft

Astronomical Refraction
Variability near the horizon
This variability near the horizon is very surprising to the average astronomer, who has been educated to believe that refraction (in the part of the sky where astronomical measurements are usually made) can be calculated accurately from the local atmospheric temperature and pressure. This is true in the part of the sky where Oriani's Theorem holds, but it breaks down very rapidly on approaching the horizon.

In fact, it can be shown that the refraction near the horizon depends mostly on the local temperature gradient, which is much more important than the local temperature itself. For this reason, all the refraction phenomena near the horizon — mirages, dip, terrestrial refraction, etc., as well as the astronomical refraction — are very sensitive to the temperature gradient; and they all vary a great deal more than does the astronomical refraction well up in the sky.

This sensitivity to temperature gradients, which vary a great deal from day to day, is the reason for the apparent “capriciousness” of green flashes (to use the term introduced by Willard J. Fisher.)

From: Astronomical Refraction


[1] Refraction near the horizon has been known and measured centuries ago Tycho Brahe
      made had to be very careful in taking measurements of Mars close to the horizon he needed to determine it's path. 

Here's one replication.

While the non-euclidean model does predict an apparent curvature (though not an actual), it will need to be abandoned or altered if such experiments do indeed falsify it.

John Davis, would you please define curvature for me?

The math I am talking about is the one derived from the Zermelo-Fraenkel Axioms (including choice), the ones every mathematician in the world uses. I did not use any other axioms than those mentioned. And yes, this applies to every geometry.

Those are not the ones every mathematician in the world uses - it is unfair and blatantly incorrect for you to either assume this or present this as fact. Furthermore, they are somewhat irrelevant as they deal more with solving issues present in number and set theory which are largely irrelevant here.

John Davis, I would love to see your non-eucledian map. But if you accept the round-earth maps and say that the globe is simply a projection, then please note that very distance-preserving map also preserves curvature. This is a mathematical fact and not limited to euclidean geometry.

If it applies to every geometry, then I should not be able to supply a geometry where this is not the case. Show me how you derive this 'fact' and how it could possibly relate to every single geometry (an impossible feat.) 

For example, I can make a geometry where every distance equals every other distance, thus preserving distance at the cost of ambiguity or geometries where distance is not an applicable term. These would be two of the many disproofs by example and should already cast significant doubt on your claim that this is mathematical fact. However, without seeing exactly what you are talking about, I have no hope to even discuss the issue.

Quote from: Definitely Not Official on June 19, 2016, 01:12:15 AM

Quote from: John Davis on June 17, 2016, 12:32:55 PM

Quote from: sokarul on June 17, 2016, 11:46:43 AM

Quote from: John Davis on June 17, 2016, 10:49:51 AM

Quote from: sokarul on June 17, 2016, 10:35:17 AM

Feel free to pay attention to all the other threads about this. Flat /= level.

This one should be good. Why would you think that flat should not be level?

Flat can indeed not be level. 

Certainly not in the case of water. Unless, of course, it is flowing downstream.

Quote from: Empirical on June 17, 2016, 11:21:09 AM

Quote from: John Davis on June 17, 2016, 10:49:03 AM

How do you explain the results? This is a repeated and verified experiment. It has been published many times over the years, often with photographic evidence.

The Earth is Flat, and that is that.

Diffraction. If you can say that the sun goes over the horizon by perspective, we can say that diffraction allows the flag to still be seen.
Anyway you can't see where the river meets the ocean can you. 

Of course not, the air obstructs my vision before I could have any such luck. Diffraction? oooh so its an illusion now is it? Every time something proves the earth flat every single time it turns out to be diffraction or refraction.  Sounds legit to me.

First of all, it's refraction, not diffraction. Empirical was wrong. But you CAN'T argue it doesn't exist, and the experiment can't be considered accurate since refraction is present.

If refraction is not real why have ships navigators using "Celestial Navigation" had to allow for it for centuries^[1] as in:

Quote

Refraction
Having passed through the vacuum of outer space, the light from the celestial body has to pass through the atmosphere before it is observed using a sextant. The atmosphere tends to bend the path of the light as it passes through, so that the celestial body appears higher in the sky than it would be if there was no atmosphere.

A calculated Altitude assumes the earth has no atmosphere, so the sextant Altitude has to be corrected for Refraction so that it can be compared to the calculated Altitude. Refraction tables are always included in Almanacs used for celestial navigation.

From Celestial Navigation Terms

Quote

Dip/ Height of Eye
The True Horizon is at 90° to the Earth’s gravitational field. It coincides with the
apparent horizon at sea level. However the Apparent Horizon starts to dip below the
horizontal plane as the height of (the observer’s) eye increases.
Dip includes an allowance for Refraction below the horizontal plane.
. . . . . . . . . .
Refraction
The deflection of light as it enters/ passes through the atmosphere is known as Refraction.
Refraction is stable and therefore predictable above about 15°, below that one needs to consider the characteristics of the atmospheric layers through which the light passes at that time. (Taking the altitude of bodies at less than 15° is usually avoided for this reason.)
For altitudes above 15°, a simplified formula is adequate (± 0’.02), Refraction = 0.96/ Tan (Altitude)
Refraction tables make assumptions on the layers for low altitudes and should be treated with caution. +/- 2° is not uncommon at an altitude of 2°.
Refraction is subtracted from the Apparent Altitude to obtain the True Altitude.
 

from: Celestial Navigation Tutorial - NavSoft

Quote

Astronomical Refraction
Variability near the horizon
This variability near the horizon is very surprising to the average astronomer, who has been educated to believe that refraction (in the part of the sky where astronomical measurements are usually made) can be calculated accurately from the local atmospheric temperature and pressure. This is true in the part of the sky where Oriani's Theorem holds, but it breaks down very rapidly on approaching the horizon.

In fact, it can be shown that the refraction near the horizon depends mostly on the local temperature gradient, which is much more important than the local temperature itself. For this reason, all the refraction phenomena near the horizon — mirages, dip, terrestrial refraction, etc., as well as the astronomical refraction — are very sensitive to the temperature gradient; and they all vary a great deal more than does the astronomical refraction well up in the sky.

This sensitivity to temperature gradients, which vary a great deal from day to day, is the reason for the apparent “capriciousness” of green flashes (to use the term introduced by Willard J. Fisher.)

From: Astronomical Refraction

Refraction near the horizon is real and very variable, John can scoff all he he likes.

[1] Refraction near the horizon has been known and measured centuries ago Tycho Brahe
      made had to be very careful in taking measurements of Mars close to the horizon he needed to determine it's path.

Obviously refraction is real. However, one must show refraction is actually happening - you are simply assuming it does because the results don't fit with your preexisting view. This is known as confirmation bias.

Here's one replication.

While the non-euclidean model does predict an apparent curvature (though not an actual), it will need to be abandoned or altered if such experiments do indeed falsify it.

Quote from: Kami on June 19, 2016, 02:43:43 AM

John Davis, would you please define curvature for me?

The math I am talking about is the one derived from the Zermelo-Fraenkel Axioms (including choice), the ones every mathematician in the world uses. I did not use any other axioms than those mentioned. And yes, this applies to every geometry.

Those are not the ones every mathematician in the world uses - it is unfair and blatantly incorrect for you to either assume this or present this as fact. Furthermore, they are somewhat irrelevant as they deal more with solving issues present in number and set theory which are largely irrelevant here.

Quote

John Davis, I would love to see your non-eucledian map. But if you accept the round-earth maps and say that the globe is simply a projection, then please note that very distance-preserving map also preserves curvature. This is a mathematical fact and not limited to euclidean geometry.

If it applies to every geometry, then I should not be able to supply a geometry where this is not the case. Show me how you derive this 'fact' and how it could possibly relate to every single geometry (an impossible feat.) 

For example, I can make a geometry where every distance equals every other distance, thus preserving distance at the cost of ambiguity or geometries where distance is not an applicable term. These would be two of the many disproofs by example and should already cast significant doubt on your claim that this is mathematical fact. However, without seeing exactly what you are talking about, I have no hope to even discuss the issue.

LoL Jizm experiment, sounds legit.

I see you ignored my theodolite results!

The witnesses agreed that the Bedford Level was in Wallaces favor? That's mighty odd since one of the judges was noted zeteticist Carpenter.  Here is the tale:

"The atmosphere grew tense. Telescope in place. Walsh and Carpenter stepped forward to check the view. Confused they discovered the six markers along the canal bvank were in disarray; they could not even judge which was which let alone decide whether the line of sight along them was flat or curved. Heated debate ensued, an angry quarrel followed, and the experiment descended into farce while Hampden apparently relaxed enjoying the scene from a nearby barge. It appeared Wallace's simple and conclusive test had been a dismal failure."

The test was repeated elsewhere at Welney Bridge, this time Wallace calculated assuming refraction.

One onlooker said "Oi say, Bill, they want to say the water ain't level. Oi know it is, though, Oi've been 'ere these ten years and Oi know if't ain't level there's no level anywhere!"

The test was done, Carpenter and Wallace both reporting different interpretations of the results.  Wallace wanted to call in the church to support his wacky views, but Carpenter overruled this. That night Hampden found Wallace and demanded he admit he was beaten and to gracefully admit it.

The two referees met the next Monday morning. This led to an altercation that caused the men in blue to show up. Under the conditions, Wallace had to show curvature to both referees. Carpenter was not convinced (obviously.) Not being able to win the bet by the agreed upon rules, they then started bringing in third parties, desperate to take Hampdens hard earned fortune by theft if necessary. They turned to John Henry Walsh. Hardly an impartial judge as he wished to publish the results himself for further fortune.

Fast forward, Walsh and Wallace show up to the meeting early already huddled about discussion concerning the events - colluding to take Hampdens money. It was clear to the witness that "Mr. Walsh had undoubtedly 'had the screw on from Mr Wallace".

Those are not the ones every mathematician in the world uses - it is unfair and blatantly incorrect for you to either assume this or present this as fact. Furthermore, they are somewhat irrelevant as they deal more with solving issues present in number and set theory which are largely irrelevant here.

Okay, to be fair, some mathematicians use other axioms, but they solely work in logic and model theory.
All mathematics working with geometry use ZF. If you think otherwise, please provide an example.

If it applies to every geometry, then I should not be able to supply a geometry where this is not the case. Show me how you derive this 'fact' and how it could possibly relate to every single geometry (an impossible feat.) 

For example, I can make a geometry where every distance equals every other distance, thus preserving distance at the cost of ambiguity or geometries where distance is not an applicable term. These would be two of the many disproofs by example and should already cast significant doubt on your claim that this is mathematical fact. However, without seeing exactly what you are talking about, I have no hope to even discuss the issue.

If you define a geometry where every distance equals every other distance, then you would not find a distance-preserving map to another geometry where this is not the case. So no, this is not a disproof. If you want proof that distance-preserving maps preserves curvature, please provide a definition of curvature I can work with.

Edit: I notice there might be a slight misunderstanding. In mathematics, a map is a function from one space (with a certain geometry) to another one.

If you cannot provide how you derived this, perhaps you can at least cite a source that I can procure so we can continue to discuss this. You are likely right that there is some sort of confusion going on, but its impossible for me to know to what depth this confusion exists without knowledge of your claim.

I have recently (yesterday) performed an experiment, the results favor a Spherical model.   

I am attempting to measure the dip to the horizon and the accosiated distance to prove a globe model.
An observer close to Earths surface can only see a limited area, bounded by a circle centered on the observer. This circle is called the horizon.

In the spherical Earth model a point on this circle is slightly below the plane drawn through the observer and perpendicular to a line from the observer to the center of the Earth. The angle between this plane and the line from the observer to a point on the horizon is called the dip of the horizon.

In a FE model, many FEers claim that the horizon raises to eye level. (Impossible)

I decided to get hold of a theodolite and make some measurements across a bay in south wales The area has some costal cliffs, And a set of ramps/steps down to the beach . I had a theodolite, and Altimeter, a 10m tape measure and I am measuring the angle the horizon is below the theodolite and the distance that the horizon is away.
The results I am going to show almost certainly show  that the Earth is (approximately) a sphere:

Experement 1

Measure the dip to the horizon at altitudes of 2,5,10,15, 20, 30 and 40 meters altitude
Theodolite set to standard atmosphere for all readings above 5m and sea level (1/7) setting for on the ground at the waters edge and 2 meter reading. remember we have to also allow for refraction, which was visually low on the day.

sea level    = 0.01- 0.03 degrees (reading unstable)
2  m    = 0.04 degrees
5  m   = 0.07 degrees
10 m  = 0.11 degrees
20 m  = 0.17 degrees
30 m  = 0.24 degrees
40 m = 0.32 (Horizon contrast not clear enough for accuracy as hazyness was present)

Experement 2

Measure the Distance to the Horizon in Kilometers from a known altitude

2m   = 4.67
5m   = 8.03
10m = 11.36
20m = 16.05
30m = 19.64
40m = 22.10

Extra
Measure the elevation angle of Polaris
Result: 51.42 degrees

Of course this will be ignored, or called fake. 

More results to come soon, along with Pictures of ships over the horizon complete with measurements, two synchronized videos of sunsets from 2m and 30m altitude and other fun stuff!

Quick question to ponder. If I measured between 3 points in a triangle, why would the measured angles add up to more than 180 degrees?

Bravo! You just added measurements to what I have been saying all along when the "curved horizon" topic keeps coming up:
(https://www.theflatearthsociety.org/forum/index.php?topic=66717.msg1779776#msg1779776)

A quite good book dealing with this topic would be "Riemannian Manifolds - an introduction to curvature" by John M. Lee.
The definition of curvature there is quite complicated, though, but it can be applied to abstract geometries. There are easier definitions, but they can not be used everywhere.
But this definition of curvature is the one Einstein used to describe general relativity.

The witnesses agreed that the Bedford Level was in Wallaces favor? That's mighty odd since one of the judges was noted zeteticist Carpenter.  Here is the tale:

"The atmosphere grew tense. Telescope in place. Walsh and Carpenter stepped forward to check the view. Confused they discovered the six markers along the canal bvank were in disarray; they could not even judge which was which let alone decide whether the line of sight along them was flat or curved. Heated debate ensued, an angry quarrel followed, and the experiment descended into farce while Hampden apparently relaxed enjoying the scene from a nearby barge. It appeared Wallace's simple and conclusive test had been a dismal failure."

The test was repeated elsewhere at Welney Bridge, this time Wallace calculated assuming refraction.

One onlooker said "Oi say, Bill, they want to say the water ain't level. Oi know it is, though, Oi've been 'ere these ten years and Oi know if't ain't level there's no level anywhere!"

The test was done, Carpenter and Wallace both reporting different interpretations of the results.  Wallace wanted to call in the church to support his wacky views, but Carpenter overruled this. That night Hampden found Wallace and demanded he admit he was beaten and to gracefully admit it.

The two referees met the next Monday morning. This led to an altercation that caused the men in blue to show up. Under the conditions, Wallace had to show curvature to both referees. Carpenter was not convinced (obviously.) Not being able to win the bet by the agreed upon rules, they then started bringing in third parties, desperate to take Hampdens hard earned fortune by theft if necessary. They turned to John Henry Walsh.

Fast forward, Walsh and Wallace show up to the meeting early already huddled about discussion concerning the events - colluding to take Hampdens money. It was clear to the witness that "Mr. Walsh had undoubtedly 'had the screw on from Mr Wallace".

Read the court transcript.

It says witnesses stated curvature was shown.

I would appreciate to see your source.  I will supply what I found in letters to the editor by both sides.  Was rather difficult to find so got to sort through some searches again from various libraries and other sources that have made copies of periodical from around that time available. Wallace also wrote about the ordeal in something wrote and was published.  Which also took me some time to track down.

I suspect similar to the wiki from the other site stating the court ruled Wallace had cheated your source is at least a bit misleading. 

From memory so not sure I am correct there was a last minute change of one of the judges and both sides came to an agreement to who would be acceptable.

When there was a disagreement between the judges and of course Wallace and Hampden they decided to get an local optician to judge.  Who judged Wallace to have proven curvature. 

The end result was Hampden signed an agreement that Wallace proved curvature. This part I am sure of since it was offered as evidence during the court hearing.

I take it then you are referring to Gauss' Theorema Egregium?

I take it then you are referring to Gauss' Theorema Egregium?

This book introduces sectional curvature. Gauss' curvature is a special case of this, but sectional curvature can be applied in more general manners.

Here's one replication.

Well it's nice that their carers let them play out for the night on their own, but at what point in this drivel are we meant to see proof of a flat earth?

I take it then you are referring to Gauss' Theorema Egregium?

Stick with the basics.

A spinning earth refers to relative to the sun.  It's clear what this means.

Measure the angle of the sun from different positions at different times of day.  These plot to show a round earth.

Measured distances successfully plot on the round earth we know.

Exactly what do you not believe about a round earth?

Here's one replication.

While the non-euclidean model does predict an apparent curvature (though not an actual), it will need to be abandoned or altered if such experiments do indeed falsify it.

Quote from: Kami on June 19, 2016, 02:43:43 AM

John Davis, would you please define curvature for me?

The math I am talking about is the one derived from the Zermelo-Fraenkel Axioms (including choice), the ones every mathematician in the world uses. I did not use any other axioms than those mentioned. And yes, this applies to every geometry.

Those are not the ones every mathematician in the world uses - it is unfair and blatantly incorrect for you to either assume this or present this as fact. Furthermore, they are somewhat irrelevant as they deal more with solving issues present in number and set theory which are largely irrelevant here.

Quote

John Davis, I would love to see your non-eucledian map. But if you accept the round-earth maps and say that the globe is simply a projection, then please note that very distance-preserving map also preserves curvature. This is a mathematical fact and not limited to euclidean geometry.

If it applies to every geometry, then I should not be able to supply a geometry where this is not the case. Show me how you derive this 'fact' and how it could possibly relate to every single geometry (an impossible feat.) 

For example, I can make a geometry where every distance equals every other distance, thus preserving distance at the cost of ambiguity or geometries where distance is not an applicable term. These would be two of the many disproofs by example and should already cast significant doubt on your claim that this is mathematical fact. However, without seeing exactly what you are talking about, I have no hope to even discuss the issue.

Using the wrong tools for the job does not provide valid results.  You need proper surveying equipment capable of precise measurements for this task, not some dude holding a mirror and bouncing a laser off of it.

And while I'm thinking of it, how do I know they even did the experiment as they describe?  I saw none of their measurements.  Did they even make any?  And at no point did I see the laser unless it was filmed up close.  I don't know what this is supposed to prove, other than improper equipment doesn't give good results... 

Quote from: John Davis on June 19, 2016, 08:22:07 AM

I take it then you are referring to Gauss' Theorema Egregium?

This book introduces sectional curvature. Gauss' curvature is a special case of this, but sectional curvature can be applied in more general manners.

Sure - but it seems his Theorema Egregium is what states that you can find curvature based off distances. From wikipedia: "If a curved surface is developed upon any other surface whatever, the measure of curvature in each point remains unchanged."

I'll review sectional curvature - its been a long time since Uni. On first look though, it seems to not be applicable in this case - but I'll give it a proper read through and refreshing.

Read the court transcript.

It says witnesses stated curvature was shown.

I would appreciate to see your source.  I will supply what I found in letters to the editor by both sides.  Was rather difficult to find so got to sort through some searches again from various libraries and other sources that have made copies of periodical from around that time available. Wallace also wrote about the ordeal in something wrote and was published.  Which also took me some time to track down.

I suspect similar to the wiki from the other site stating the court ruled Wallace had cheated your source is at least a bit misleading. 

From memory so not sure I am correct there was a last minute change of one of the judges and both sides came to an agreement to who would be acceptable.

When there was a disagreement between the judges and of course Wallace and Hampden they decided to get an local optician to judge.  Who judged Wallace to have proven curvature. 

The end result was Hampden signed an agreement that Wallace proved curvature. This part I am sure of since it was offered as evidence during the court hearing.

The source is The Flat Earth: A History of an Infamous Idea. It is written by Christine Garwood, the expert on Flat Earth history.

They certainly didn't agree who would be acceptable. Hampden could have signed an agreement saying the earth was round for all I care, and this would still be cheating. Unless Carpenter himself agreed, then the wager was lost. Its clear the other side was using some shady tactics - colluding without the presence of all the judges (Carpenter), trying to get Carpenter and Hampden arrested, and insisting Carpenter be replaced despite him being approved to be judge. This is ignoring that the first attempt was already an utter failure.

I'll pull the source out again when I get home and review it. It certainly doesn't outright state they were cheating - she keeps a very neutral stance throughout the book. However it does say "they had no other choice" than to find a judge which certainly is not the case.

I'll also take a look at the court transcript.

Quote from: John Davis on June 19, 2016, 08:22:07 AM

I take it then you are referring to Gauss' Theorema Egregium?

Stick with the basics.

A spinning earth refers to relative to the sun.  It's clear what this means.

Measure the angle of the sun from different positions at different times of day.  These plot to show a round earth.

Measured distances successfully plot on the round earth we know.

Exactly what do you not believe about a round earth?

Like this?

Quote from: John Davis on June 19, 2016, 07:21:42 AM

Here's one replication.

Well it's nice that their carers let them play out for the night on their own, but at what point in this drivel are we meant to see proof of a flat earth?

Jeran would not have been able to see the light(and even us in the video) at that height above water if the Earth was curved and water not level.

Try shadows of sticks at 5 locations.

That's how you get this:

You know, by not making the wild assumption that the suns rays are parallel and the earth is round.

You know, by not making the wild assumption that the suns rays are parallel and the earth is round.

Because magic is so much better. A magical force keeps the sun above the earth. The magic also makes the orbits diameter shrink and expand in basically a rate for thousands of years.

You know, by not making the wild assumption that the suns rays are parallel and the earth is round.

All observations and measurements show a round earth.  Please provide a flat earth map.

Quote from: John Davis on June 20, 2016, 10:00:45 AM

You know, by not making the wild assumption that the suns rays are parallel and the earth is round.

Because magic is so much better. A magical force keeps the sun above the earth. The magic also makes the orbits diameter shrink and expand in basically a rate for thousands of years.

A magical force bends space and time and makes everything travel at (or rather have a magnitude) of lightspeed. All the while, it is also causing the planets to spin about like whirling tops, making the moon rotate at the exact right rate to not appear to rotate at all, and then there's that old dark matter leprechaun. The mechanism for this magic ? Nobody knows.

Quote from: John Davis on June 20, 2016, 10:00:45 AM

You know, by not making the wild assumption that the suns rays are parallel and the earth is round.

All observations and measurements show a round earth.  Please provide a flat earth map.

I have. The map is a globe.

Obviously refraction is real. However, one must show refraction is actually happening - you are simply assuming it does because the results don't fit with your preexisting view. This is known as confirmation bias.

Distant objects beyond the horizon sink toward the horizon as the distance between the objects and observer increases, or the observer gets closer to the surface.  Depending on the temperatures, refraction occurs (laser beams are also affected).  This is the result if people doing these tests actually tried it from multiple elevations.