Clearly water is not level as the horizon shows etc. Curvature of the earth is well known and proven.
If there is any doubt in your mind that water is level, please go perform this experiment.
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?
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.Please provide details of recent experiments.
The Earth is Flat, and that is that.
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.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.
The Earth is Flat, and that is that.
Flat can indeed not be level.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?
Certainly not in the case of water. Unless, of course, it is flowing downstream.Flat can indeed not be level.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?
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.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.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.
The Earth is Flat, and that is that.
Anyway you can't see where the river meets the ocean can you. :)
Certainly not in the case of water. Unless, of course, it is flowing downstream.Flat can indeed not be level.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?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.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.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.
The Earth is Flat, and that is that.
Anyway you can't see where the river meets the ocean can you. :)
We don't have to cherry pick. We just have so much evidence we can well afford to be dainty in our selection.Recent experiments please.
We don't have to cherry pick. We just have so much evidence we can well afford to be dainty in our selection.
Bedford. Level. Experiment. I'd suggest you read some of Lady Blounts replications of it.We don't have to cherry pick. We just have so much evidence we can well afford to be dainty in our selection.
Well, first show some real experiment in written from, with calculations, with measurment on multiple sites with multiple methods on different times of day, with photographic evidence and debunk atmospheric refractions please or take them into account.
After that, you have to face the no map, no stars, no sunsets, problems of Fe mentioning just the basic ones....
We don't have to cherry pick. We just have so much evidence we can well afford to be dainty in our selection.Recent experiments please.
Bedford. Level. Experiment. I'd suggest you read some of Lady Blounts replications of it.We don't have to cherry pick. We just have so much evidence we can well afford to be dainty in our selection.
Well, first show some real experiment in written from, with calculations, with measurment on multiple sites with multiple methods on different times of day, with photographic evidence and debunk atmospheric refractions please or take them into account.
After that, you have to face the no map, no stars, no sunsets, problems of Fe mentioning just the basic ones....
We have a map. Its non-euclidean. A projection of it in euclidean space is a globe. Sunsets and stars are also explained.We don't have to cherry pick. We just have so much evidence we can well afford to be dainty in our selection.Recent experiments please.
It has been recently done by Daniel Shenton. However it should be noted - truth has no expiration date.
Link please. If it's that successful then it would being carried out by many people.Bedford. Level. Experiment. I'd suggest you read some of Lady Blounts replications of it.We don't have to cherry pick. We just have so much evidence we can well afford to be dainty in our selection.
Well, first show some real experiment in written from, with calculations, with measurment on multiple sites with multiple methods on different times of day, with photographic evidence and debunk atmospheric refractions please or take them into account.
After that, you have to face the no map, no stars, no sunsets, problems of Fe mentioning just the basic ones....
We have a map. Its non-euclidean. A projection of it in euclidean space is a globe. Sunsets and stars are also explained.We don't have to cherry pick. We just have so much evidence we can well afford to be dainty in our selection.Recent experiments please.
It has been recently done by Daniel Shenton. However it should be noted - truth has no expiration date.
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.I would dispute your statement. If the Bedford Experiment is real why do these people get different results? (minutes 4-9 at least)
The Earth is Flat, and that is that.
If there is any doubt in your mind that water is level, please go perform this experiment.
Rowbotham repeated his experiments several times over the years but his claims received little attention until, in 1870, a supporter by the name of John Hampden offered a wager that he could show, by repeating Rowbotham's experiment, that the earth was flat. The noted naturalist and qualified surveyor Alfred Russel Wallace accepted the wager. Wallace, by virtue of his surveyor's training and knowledge of physics, avoided the errors of the preceding experiments and won the bet.From wikipedia.
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.
Wikipedia is wrong. Read: Flat Earth: The History of an Infamous Idea. Wallace colluded with the judge and Hampden successfully sued.Distances prove a globe. Or show your measurements.
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.
They did not take into account refraction and the laser was not level. Otherwise they would have noted a greater rise at 500ft and again at their second reading. Flat earthers performed an identical experiment I believe on youtube with wildly different results.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.I would dispute your statement. If the Bedford Experiment is real why do these people get different results? (minutes 4-9 at least)
The Earth is Flat, and that is that.
This is a non-sequitur. Just because you can map something accurately on a round surface does not mean its round.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.
John, FE guys just love commons sense and simple down to earth logic like up us up and down is down so just say it out loud :
The world can be mapped accurately on a globe, without distortion in angles and distances so the shape of earth is at least not flat but, uhm you know maybe spherical
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.Wikipedia is wrong. Read: Flat Earth: The History of an Infamous Idea. Wallace colluded with the judge and Hampden successfully sued.Distances prove a globe. Or show your measurements.
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.
'Flat earthers performed an identical experiment I believe on youtube with wildly different results.' You believe but cannot find the details. Find details of a recent experiment, what's so difficult about repeating it?They did not take into account refraction and the laser was not level. Otherwise they would have noted a greater rise at 500ft and again at their second reading. Flat earthers performed an identical experiment I believe on youtube with wildly different results.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.I would dispute your statement. If the Bedford Experiment is real why do these people get different results? (minutes 4-9 at least)
The Earth is Flat, and that is that.This is a non-sequitur. Just because you can map something accurately on a round surface does not mean its round.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.
John, FE guys just love commons sense and simple down to earth logic like up us up and down is down so just say it out loud :
The world can be mapped accurately on a globe, without distortion in angles and distances so the shape of earth is at least not flat but, uhm you know maybe spherical
They did not take into account refraction and the laser was not level. Otherwise they would have noted a greater rise at 500ft and again at their second reading. Flat earthers performed an identical experiment I believe on youtube with wildly different results.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.I would dispute your statement. If the Bedford Experiment is real why do these people get different results? (minutes 4-9 at least)
The Earth is Flat, and that is that.This is a non-sequitur. Just because you can map something accurately on a round surface does not mean its round.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.
John, FE guys just love commons sense and simple down to earth logic like up us up and down is down so just say it out loud :
The world can be mapped accurately on a globe, without distortion in angles and distances so the shape of earth is at least not flat but, uhm you know maybe spherical
Flat Closed Finite Non-Euclidean Space.They did not take into account refraction and the laser was not level. Otherwise they would have noted a greater rise at 500ft and again at their second reading. Flat earthers performed an identical experiment I believe on youtube with wildly different results.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.I would dispute your statement. If the Bedford Experiment is real why do these people get different results? (minutes 4-9 at least)
The Earth is Flat, and that is that.This is a non-sequitur. Just because you can map something accurately on a round surface does not mean its round.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.
John, FE guys just love commons sense and simple down to earth logic like up us up and down is down so just say it out loud :
The world can be mapped accurately on a globe, without distortion in angles and distances so the shape of earth is at least not flat but, uhm you know maybe spherical
Yeah because its geoid :D anyway we reach the level of complication that makes the FE crowd uncomfortable and suspicious but just for fun lets continue this scenario. So how could you describe the shape of the earth precisely including the word flat?
Show a map.Flat Closed Finite Non-Euclidean Space.They did not take into account refraction and the laser was not level. Otherwise they would have noted a greater rise at 500ft and again at their second reading. Flat earthers performed an identical experiment I believe on youtube with wildly different results.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.I would dispute your statement. If the Bedford Experiment is real why do these people get different results? (minutes 4-9 at least)
The Earth is Flat, and that is that.This is a non-sequitur. Just because you can map something accurately on a round surface does not mean its round.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.
John, FE guys just love commons sense and simple down to earth logic like up us up and down is down so just say it out loud :
The world can be mapped accurately on a globe, without distortion in angles and distances so the shape of earth is at least not flat but, uhm you know maybe spherical
Yeah because its geoid :D anyway we reach the level of complication that makes the FE crowd uncomfortable and suspicious but just for fun lets continue this scenario. So how could you describe the shape of the earth precisely including the word flat?
Sure beats Oblate Spheroid (Finite Closed Space) in Non-Euclidean curved space where everything is whizzing about in straight lines at magnitude equal to c while simultaneously twirling and bobbing around the sun in some sort of ridiculous celestial race.
Wikipedia is wrong. Read: Flat Earth: The History of an Infamous Idea. Wallace colluded with the judge and Hampden successfully sued.
If there is any doubt in your mind that water is level, please go perform this experiment.
If there is any doubt in your mind that water is level, please go perform this experiment.That is ridiculous!
Water is LevelWhat 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.
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.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.Wikipedia is wrong. Read: Flat Earth: The History of an Infamous Idea. Wallace colluded with the judge and Hampden successfully sued.Distances prove a globe. Or show your measurements.
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.
If there is any doubt in your mind that water is level, please go perform this experiment.
Certainly not in the case of water. Unless, of course, it is flowing downstream.Flat can indeed not be level.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?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.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.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.
The Earth is Flat, and that is that.
Anyway you can't see where the river meets the ocean can you. :)
Certainly not in the case of water. Unless, of course, it is flowing downstream.Flat can indeed not be level.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?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.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.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.
The Earth is Flat, and that is that.
Anyway you can't see where the river meets the ocean can you. :)
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.
RefractionFrom Celestial Navigation Terms (http://www.geoffrey-kolbe.com/C-Nav/terms.htm)
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.
Dip/ Height of Eyefrom: Celestial Navigation Tutorial - NavSoft (http://navsoft.com/Celestial_Navigation_Tutorial.pdf)
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.
Astronomical RefractionFrom: Astronomical Refraction (http://www-rohan.sdsu.edu/~aty/explain/atmos_refr/astr_refr.html)
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.)
John Davis, would you please define curvature for me?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.
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.
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.)
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.Certainly not in the case of water. Unless, of course, it is flowing downstream.Flat can indeed not be level.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?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.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.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.
The Earth is Flat, and that is that.
Anyway you can't see where the river meets the ocean can you. :)
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:QuoteRefractionFrom Celestial Navigation Terms (http://www.geoffrey-kolbe.com/C-Nav/terms.htm)
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.QuoteDip/ Height of Eyefrom: Celestial Navigation Tutorial - NavSoft (http://navsoft.com/Celestial_Navigation_Tutorial.pdf)
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.
QuoteAstronomical RefractionFrom: Astronomical Refraction (http://www-rohan.sdsu.edu/~aty/explain/atmos_refr/astr_refr.html)
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.)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.
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?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.
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.QuoteJohn 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.
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.
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.)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.
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.
I have recently (yesterday) performed an experiment, the results favor a Spherical model. 8)Bravo! You just added measurements to what I have been saying all along when the "curved horizon" topic keeps coming up:
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?
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".
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.
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?
Here's one replication.
I take it then you are referring to Gauss' Theorema Egregium?Stick with the basics.
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?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.
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.QuoteJohn 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.
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 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.
The source is The Flat Earth: A History of an Infamous Idea. It is written by Christine Garwood, the expert on Flat Earth history.
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?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?
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.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?
Here's one replication.
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.
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.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.
I have. The map is a globe.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.
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.
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.Certainly not in the case of water. Unless, of course, it is flowing downstream.Flat can indeed not be level.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?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.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.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.
The Earth is Flat, and that is that.
Anyway you can't see where the river meets the ocean can you. :)
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:QuoteRefractionFrom Celestial Navigation Terms (http://www.geoffrey-kolbe.com/C-Nav/terms.htm)
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.QuoteDip/ Height of Eyefrom: Celestial Navigation Tutorial - NavSoft (http://navsoft.com/Celestial_Navigation_Tutorial.pdf)
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.
QuoteAstronomical RefractionFrom: Astronomical Refraction (http://www-rohan.sdsu.edu/~aty/explain/atmos_refr/astr_refr.html)
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.)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.
You know, by not making the wild assumption that the suns rays are parallel and the earth is round.
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.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.I have. The map is a globe.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.
You know, by not making the wild assumption that the suns rays are parallel and the earth is round.
The round earth was not an assumption, it was a conclusion. Back then, the parallel nature of solar light rays was an assumption, but now it's also a conclusion. Taking the earth to be flat is no less of an assumption. The Eratosthenes experiment also gives different results for how far away the sun is assuming a flat earth depending on how you carry it out.
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.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.I have. The map is a globe.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.
Where are you getting that everything travels at light speed from?
You know, by not making the wild assumption that the suns rays are parallel and the earth is round.
The round earth was not an assumption, it was a conclusion. Back then, the parallel nature of solar light rays was an assumption, but now it's also a conclusion. Taking the earth to be flat is no less of an assumption. The Eratosthenes experiment also gives different results for how far away the sun is assuming a flat earth depending on how you carry it out.
The round earth was an assumption. The conclusion was its supposed diameter.
It is obvious that the base fact of the matter is that light casts a shadow that has an angle based off its source. You need not assume the earth is flat. You find this out empirically because it looks flat.
Latitude
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.
You know, by not making the wild assumption that the suns rays are parallel and the earth is round.
The round earth was not an assumption, it was a conclusion. Back then, the parallel nature of solar light rays was an assumption, but now it's also a conclusion. Taking the earth to be flat is no less of an assumption. The Eratosthenes experiment also gives different results for how far away the sun is assuming a flat earth depending on how you carry it out.
The round earth was an assumption. The conclusion was its supposed diameter.
It is obvious that the base fact of the matter is that light casts a shadow that has an angle based off its source. You need not assume the earth is flat. You find this out empirically because it looks flat.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.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.I have. The map is a globe.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.
Where are you getting that everything travels at light speed from?
The magnitude of the 4-vector.
You know, by not making the wild assumption that the suns rays are parallel and the earth is round.
The round earth was not an assumption, it was a conclusion. Back then, the parallel nature of solar light rays was an assumption, but now it's also a conclusion. Taking the earth to be flat is no less of an assumption. The Eratosthenes experiment also gives different results for how far away the sun is assuming a flat earth depending on how you carry it out.
The round earth was an assumption. The conclusion was its supposed diameter.
It is obvious that the base fact of the matter is that light casts a shadow that has an angle based off its source. You need not assume the earth is flat. You find this out empirically because it looks flat.
I dare you to replicate that experiment from a number of latitude pairs, not just one. If the earth is flat, obviously, they should all give the same answer for the sun's height.
So what are the heights and sizes of the sun and moon?I dare you to replicate that experiment from a number of latitude pairs, not just one. If the earth is flat, obviously, they should all give the same answer for the sun's height.
"The sun's height doesn't change" - this is an unfounded assumption. I don't see why that would be obvious. I don't trust the wiki which is why I'm trashing it. Much of it is complete garbage and makes fun of the flat earth and its proponents rather than acts as a good source of information.