The Flat Earth Society
Flat Earth Discussion Boards => Flat Earth Theory => Topic started by: robinofloxley on June 01, 2020, 10:03:35 AM
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I've read a number of posts where latitude and longitude are dismissed by FErs because they are based on a globe earth.
I'd like to unpick this and ask what the actual objections are.
Fundamentally (if you live in the northern hemisphere), your latitude is easily determined. It's simply the altitude of Polaris from your location. It's not an absolute value in miles, km or light years, because to determine that you'd need to know how far away Polaris is and in times past, that wasn't possible to determine. What we do instead is measure the angle from the horizon to the star, because that's easily done and doesn't require you to know any distances.
Longitude is based on time. When was the sun due south at your location compared to when it was due south in Greenwich UK? If that's +1 hour and the sun moves at 15 degrees per hour, then your longitude is 15W.
Both of these are determined easily from the positions and movements of celestial bodies and can be measured with simple instruments (if you consider an accurate timepiece to be a simple instrument).
Neither of these values rely on any preconceived assumption about the shape of the earth.
There is an issue of course if you want to calculate the distance between two points given by latitude/longitude, because that involves spherical geometry and includes an assumption about the shape of the earth.
So is that it? Are latitude/longitude OK by themselves, but the distances are not? What are the actual objections?
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Good description of how we can measure lat and long in the northern part of the world.
However you state the globe theory preconceived assumption that Polaris is at an extreme distance thus its light rays are basically parallel leading to the conclusion that any change in measured angle of elevation to the star is a product of the curvature of this globe .
FE position .This change of angle to Polaris, as we move N or S , allows calculation by geometric method of the approximate distance to the star and its approximate height above the geographic N pole. No assumptions just scientific observation .
It is possible to determine the approximate shape of the earth through the use of precision scientific instruments , sextants , quadrants , zenith sectors and use of geometric surveying technique.
Survey along a meridian and the shape will reveal itself as distance between successive lines of latitude are measured, as will the approximate distance to the pole star - be it near or far.
Geodesy is the applied mathematical method used to map plane geometric survey results onto a sphere . In itself it is not a science .
Geometry is is the measure of earth as the name implies .
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FE position .This change of angle to Polaris, as we move N or S , allows calculation by geometric method of the approximate distance to the star and its approximate height above the geographic N pole. No assumptions just scientific observation.
Right, but the thing I don't understand about FE is that the observations show that for each degree of latitude the angle to Polaris drops by a degree AND degrees of latitude are equidistant. On a FE if light travels in a straight line then that would not be the case, it's simple geometry:
(https://i.ibb.co/QkBknbw/Polaris.jpg)
So is your belief that degrees of latitude are not equidistant? Or is it that light is bending? Or something else?
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Degrees of latitude can only be equidistant on a perfect sphere with parallel light rays from an extremely distant North star.
I should imagine that light bends in an electromagnetic field - problematic because we don't know the true nature of light -and there's atmospheric scattering/diffusion etc.
The coordinate system of gps is based on a math model , not the real shape of earth .
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Good description of how we can measure lat and long in the northern part of the world.
However you state the globe theory preconceived assumption that Polaris is at an extreme distance thus its light rays are basically parallel leading to the conclusion that any change in measured angle of elevation to the star is a product of the curvature of this globe .
No I've not stated anything about the distance to Polaris (extreme or otherwise), other than simply saying that in times past, the distance was not known, but we can however use an angular measurement instead, which works independently of distance. For instance I can measure the angular height of a tree at the bottom of my garden from my current position. It doesn't tell me anything about the actual height of the tree or how far away it is or for that matter, what shape the earth is.
Equally, it doesn't matter whether the light rays from Polaris are parallel or not, just that whenever you measure the angular elevation of Polaris from the same position, you are always going to get the same value and if you move north or south of that position, you will get a different value, which will increase as you move north and decrease as you move south.
It is possible to determine the approximate shape of the earth through the use of precision scientific instruments , sextants , quadrants , zenith sectors and use of geometric surveying technique.
Survey along a meridian and the shape will reveal itself as distance between successive lines of latitude are measured, as will the approximate distance to the pole star - be it near or far.
Geodesy is the applied mathematical method used to map plane geometric survey results onto a sphere . In itself it is not a science .
Geometry is is the measure of earth as the name implies .
I agree with all of the above, however that's jumping ahead somewhat for me, as I'm simply at this point trying to get to the bottom of the objections raised regarding latitude and longitude.
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Degrees of latitude can only be equidistant on a perfect sphere with parallel light rays from an extremely distant North star.
I should imagine that light bends in an electromagnetic field - problematic because we don't know the true nature of light -and there's atmospheric scattering/diffusion etc.
The coordinate system of gps is based on a math model , not the real shape of earth .
Again I agree with all of that, but does that mean latitude and longitude can be used to identify a (unique) position and the problems only arise when you then try and use this as a basis for determining distances? For example, I'm quite satisfied that if you were to give me an arbitrary position in terms of latitude/longitude within say 50 miles of my house, then I'd be able to find my way there and send you a photo and you'd agree we were talking about the same place.
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Degrees of latitude can only be equidistant on a perfect sphere with parallel light rays from an extremely distant North star.
Degrees of latitude have no meaning whatsoever on a flat plane. All you've measured is the angle to polaris. Where would you draw the angle of latitude?
Also, you've skipped completely over people in the South, and how to determine longitude.
EDIT: Let us presume for purposes of this thread that we have an observer on a globe/sphere Earth looking at Polaris;
(https://i.imgur.com/lxhJql5.jpg)
All vertical lines P lead to Polaris. The observer has a horizontal H, and measures 30 degrees above his horizontal as the elevation to Polaris. Simple geometry shows that if his angle E = 30, then the angle between the two radials to the equator and to his position, angle L, also = 30.
Simple geometry tells us that for a sphere, the length of an arc on the surface is consistently the same, whereever the 30 degrees is measured; 30 degrees down from the pole, 30 degrees up from the equator, the arc will be the same length. Equal division of the circumference into equal parts of one degree, etc.
Thus the distance between points can be calculated and used as a basis for navigation, and thus the nautical mile, a length of arc based on subdivision of a degree of latitude or longitude into equal parts, was born.
Observing angle E tells you what angle L is.
All that would appear to happen with the FE angle to polaris diagram above is that you determine the angle to Polaris. Where is the angle of latitude to be drawn?
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Degrees of latitude have no meaning whatsoever on a flat plane. All you've measured is the angle to polaris. Where would you draw the angle of latitude?
Also, you've skipped completely over people in the South, and how to determine longitude.
Here is the problem I'm trying to get to the bottom of. Latitude and longitude are typically dismissed by FEers because they are routinely associated with the despised globe model. I'm trying, for the moment, to unpick that association and ask whether or not you can use latitude and longitude simply to identify a unique location on the earth. From that viewpoint, if we don't care about meaning, does measuring the angle to Polaris on its own - irrespective of model, distance to Polaris, whether or not light travels in straight lines etc. etc. - locate you along a north-south line and when combined with latitude, does that give you a unique location?
I totally get that when you then start talking about distances and whether or not latitude lines are equally spaced, that causes difficulties with the globe vs. flat models. But fundamentally, is there anything wrong (from the FE perspective) with latitude and longitude as an indicator of position?
I'm just not clear what the consensus is (if there is one of course) amongst FEers on this issue.
As far as the southern hemisphere goes, I'd rather stick to the north for now as that's a lot simpler to think about with just Polaris to deal with. Apologies to anyone down south.
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Sorry Robin , I misread your OP about distance to Polaris .
Measuring distances between degrees of latitude taken from the North star will give systematic difference on FE . Surveying these distances along a meridian will indicate which model is closer to the truth.
That the equator is given as 0 degrees midway between the globe geographic poles is an assumption used to model earth as a globe.
In practice it should be possible to survey the distance closely enough to give a true distance between the geographic N pole and the equator since at the pole you are directly beneath the pole star , and at the equator you are directly beneath the path of the sun at equinox .
If you surveyed a fair distance , say from 70N to 40S if possible then you could extrapolate distance southwards to the equator - make a prediction then check this with survey. It becomes harder to track the pole star accurately at lower elevations as you travel towards the equator but the predicted position could be checked against the real one .
This is the simple way to determine the shape of earth . Hope this makes sense
The longitude positions used by gps should be the same in both models but latitudes will differ with shape although by how much will be given by survey .
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If you surveyed a fair distance , say from 70N to 40S if possible then you could extrapolate distance southwards to the equator - make a prediction then check this with survey.
This is the simple way to determine the shape of earth.
...and that's exactly what Norwood did in the 1600s to calculate the circumference.
The French Geodesic Mission repeated the exercise in the 1700s, with a slightly different method, which reinforced Norwood's figure, within reasonable bounds of error for the methods used.
Determining distance from pole to equator is then simple arithmetic. Circ divided by 4.
Since verified by other, progressively more accurate methods.
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Sorry Robin , I misread your OP about distance to Polaris .
Measuring distances between degrees of latitude taken from the North star will give systematic difference on FE . Surveying these distances along a meridian will indicate which model is closer to the truth.
That the equator is given as 0 degrees midway between the globe geographic poles is an assumption used to model earth as a globe.
In practice it should be possible to survey the distance closely enough to give a true distance between the geographic N pole and the equator since at the pole you are directly beneath the pole star , and at the equator you are directly beneath the path of the sun at equinox .
If you surveyed a fair distance , say from 70N to 40S if possible then you could extrapolate distance southwards to the equator - make a prediction then check this with survey. It becomes harder to track the pole star accurately at lower elevations as you travel towards the equator but the predicted position could be checked against the real one .
This is the simple way to determine the shape of earth . Hope this makes sense
The longitude positions used by gps should be the same in both models but latitudes will differ with shape although by how much will be given by survey .
OK, so I hope I've understood your position correctly. You seem happy to accept a position expressed as a latitude/longitude would identify a unique location whatever the shape of the earth and seem OK with the idea of using GPS to obtain a position fix too. That's really what I'm trying to establish, just to see if there is common ground here and it sounds like there is. Any idea whether this is a generally held view within FE? For me, one of the biggest difficulties is understanding where the common ground is in order to have a rational discussion about anything.
I completely agree that if we accept latitude/longitude positions as meaningful and (reasonably) accurate, then measuring a degree or so of either or both would support one model over another. Where we no doubt disagree is that I think these measurements have already been taken and they point to a globe earth.
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GPS is a coordinate system based on a math model , a set of calculations used to determine position , not done by measurement or observation . I don't see the need for GPS . Survey will reveal all.
Measure is required over several degrees . You can't measure just one degree and deduce anything meaningful .
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Robin, this is something I have wondered for a while too. How is Latitude and Longitude a round earth coordinate system as is sometimes claimed here.
As you say if in the northern part of the world you go to a particular place and measure the angle to Polaris it will always be the same, and we call that Latitude and measure it in degrees. If you move North the angle increases and if you move south it decreases.
In the southern part of the world there is a similar spot in the sky that can be used, it is not marked with a convenient star like in the north so it is not as straight forward to make the measurement.
The range of this measure is from 90 degrees North through 0 degrees to 90 degrees South.
As you also say Longitude can be measured in time offset. Again in the northern part of the world how long after the sun is due south from a reference point (Greenwich) is it due south in your location. All you need to measure this is a timepiece set to Greenwich time. This can be measured in hours or minutes for example.
Using these two measures should give a unique and consistent coordinate pair for any location on the Actual Earth.
The only concession to a circular world (either globe or disc) is in the representation of Longitude not in hours or minutes but rather in four minute increments and refereed to as degrees. This is based on the 24 hours for a cycle of the sun to complete one circle above a disc earth or the earth to complete one rotation in the globe earth. Either way 1/360 of 24 hours is 4 minutes.
I think your main question is, do Flat Earthers agree that these two basic observational measures give a location coordinate pair (latitude and longitude) that is unique and unchanging for a given location on the Earth?
Further that given an latitude and longitude for a location it would be possible to navigate to that point using only the measurement techniques described above. You may not know the distance or the direction, but you could travel north or south to get to the correct latitude, and then travel east or west to get to the right longitude. Not the most efficient path, but it would get you there.
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Robin, this is something I have wondered for a while too. How is Latitude and Longitude a round earth coordinate system as is sometimes claimed here.
As you say if in the northern part of the world you go to a particular place and measure the angle to Polaris it will always be the same, and we call that Latitude and measure it in degrees. If you move North the angle increases and if you move south it decreases.
In the southern part of the world there is a similar spot in the sky that can be used, it is not marked with a convenient star like in the north so it is not as straight forward to make the measurement.
The range of this measure is from 90 degrees North through 0 degrees to 90 degrees South.
As you also say Longitude can be measured in time offset. Again in the northern part of the world how long after the sun is due south from a reference point (Greenwich) is it due south in your location. All you need to measure this is a timepiece set to Greenwich time. This can be measured in hours or minutes for example.
Using these two measures should give a unique and consistent coordinate pair for any location on the Actual Earth.
The only concession to a circular world (either globe or disc) is in the representation of Longitude not in hours or minutes but rather in four minute increments and refereed to as degrees. This is based on the 24 hours for a cycle of the sun to complete one circle above a disc earth or the earth to complete one rotation in the globe earth. Either way 1/360 of 24 hours is 4 minutes.
I think your main question is, do Flat Earthers agree that these two basic observational measures give a location coordinate pair (latitude and longitude) that is unique and unchanging for a given location on the Earth?
Further that given an latitude and longitude for a location it would be possible to navigate to that point using only the measurement techniques described above. You may not know the distance or the direction, but you could travel north or south to get to the correct latitude, and then travel east or west to get to the right longitude. Not the most efficient path, but it would get you there.
This is exactly right and precisely what I'm trying to get to the bottom of. I suspect that two issues are commonly being lumped together: 1) Does latitude/longitude give you a unique and unchanging position (irrespective of shape)? 2) Are distances calculated between two points expressed as latitude/longitude correct?
When you lump these together, it's not surprising that FEers will dismiss latitude/longitude as globe based, because it's hard to accept 2) without accepting a globe, but I don't see 1) as being anywhere near as contentious. Somerled has given an opinion, but I'm having to read between the lines a bit to figure out exactly where he (gender based assumption there) stands on 1). I'm really hoping we'll hear from a few more FEers, I'm genuinely interested to understand their position(s) on this and reasoning.
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About 1. Latitude/longitude gives a unique unchanging position with respect to where you are on earth . The distance between each degree of latitude is dependent on the shape of earth .
That's geometry , not FE or globe theory - a survey along a meridian with respect to the pole star will give the geometric shape whatever that is. That is all that needs to be done .
GPS is not based on a globe earth - it is based on an elipsoid math model we are told. It's not needed for long/lat.
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About 1. Latitude/longitude gives a unique unchanging position with respect to where you are on earth . The distance between each degree of latitude is dependent on the shape of earth .
That's geometry , not FE or globe theory - a survey along a meridian with respect to the pole star will give the geometric shape whatever that is. That is all that needs to be done .
Thanks, that's clear enough, I believe I understand your position on this and agree with it entirely.
GPS is not based on a globe earth
Given the rest of what you say, I'm not sure I understand that.
- it is based on an elipsoid math model we are told.
Agree, but an ellipsoid model of the globe surely?
It's not needed for long/lat.
Agreed, but it can be (amongst other things) used to determine or verify your position in terms of latitude/longitude. For that purpose, I'd say it was accurate enough and a lot quicker and more reliable than the older more traditional methods.
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About GPS - a math model based on assumed globe . That's the point . All surveys are geometric . The shape of earth will be revealed by this method. Why would you use GPS.
All geometric survey then is subjected to the method of geodesy i.e. spherical calculation for the purpose of mapping the results onto globe - it's math modelling again .
GPS could be nothing more than a program designed to remove the spherical calculations to give back the geometric survey results , we could check that after the geometric survey results have determined the shape.
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About GPS - a math model based on assumed globe . That's the point . All surveys are geometric . The shape of earth will be revealed by this method. Why would you use GPS.
If you trust that a GPS device would give you an accurate value for your latitude, you might as well use it. If you don't, or you want to avoid criticism, then either don't use a GPS at all or use it to cross check against another method e.g. angle of Polaris. For myself, I would be happy to just use a GPS device. To convince others, I would probably use a GPS and some other method and record both results for comparison. For a small extra effort you're conducting a secondary experiment comparing GPS with whatever other method you are using. Two for the price of one.
All geometric survey then is subjected to the method of geodesy i.e. spherical calculation for the purpose of mapping the results onto globe - it's math modelling again .
GPS could be nothing more than a program designed to remove the spherical calculations to give back the geometric survey results , we could check that after the geometric survey results have determined the shape.
Makes sense.
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Well , hopefully I've outlined a valid objection which I believe is what you required from an FE point of view .
My objection is not really an FE argument but a geometric one. If I had a GPS device I'd happily use it myself .
Once all distances and angles have been measured then we could input all data and have a geometric positioning system - GPS for short :)
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So where does the signal that my GPS receiver picks up come from?
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Measure is required over several degrees . You can't measure just one degree and deduce anything meaningful .
I refer you back to my previous post.
Norwood measured out the distance from London to York in the 1600s (some 200 miles or so), so according to the textbooks, he measured somewhere around 2.5 degrees of latitude.
Again, I ask - if you accept positioning of places by reference to degrees of latitude or longitude, where are you drawing the angle?
Definition; "an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle".
Where is your endpoint, the vertex of the angle?
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As far as the southern hemisphere goes, I'd rather stick to the north for now as that's a lot simpler to think about with just Polaris to deal with. Apologies to anyone down south.
Anyway, it's not really different, it just takes a little more effort to determine the latitude since there is no bright star at the southern celestial pole.
I suspect that two issues are commonly being lumped together: 1) Does latitude/longitude give you a unique and unchanging position (irrespective of shape)? 2) Are distances calculated between two points expressed as latitude/longitude correct?
When you lump these together, it's not surprising that FEers will dismiss latitude/longitude as globe based, because it's hard to accept 2) without accepting a globe, but I don't see 1) as being anywhere near as contentious. Somerled has given an opinion, but I'm having to read between the lines a bit to figure out exactly where he (gender based assumption there) stands on 1). I'm really hoping we'll hear from a few more FEers, I'm genuinely interested to understand their position(s) on this and reasoning.
Actually, I don't see how 1) could be rebutted. As you said, latitude can be determined with the position of the celestial pole in the sky, and longitude can be determined by calculating the difference between solar noon in Greenwich and local solar noon. Travel west and solar noon will happen later, travel east and it will happen sooner. Travel north and Polaris will appear higher in the sky until you reach the north pole and you see it directly overhead. Travel south and Polaris will appear lower until you reach the Equator and it appears on the horizon, and if you keep on travelling south you can repeat with the southern celestial pole. Latitude and longitude are not just arbitrary values, they have a meaning that can be easily verified by anybody: this fact alone is already a strong argument for a spherical Earth, both latitude and longitude being angular measurements.
Then comes 2). As seen in another thread, values given by online maps are generally accepted as accurate - or at least, no one has proved them wrong. And we've seen they're based on formulas such as haversine or Vincenty's.
Conclusion: we can determine a latitude and longitude of any point on Earth, and we can determine the distance between any two points on Earth knowing their latitude and longitude using a formula that calculates distances on a sphere or an oblate spheroid. It would be a very intriguing coincidence if this worked without the Earth being a globe.
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As far as the southern hemisphere goes, I'd rather stick to the north for now as that's a lot simpler to think about with just Polaris to deal with. Apologies to anyone down south.
Anyway, it's not really different, it just takes a little more effort to determine the latitude since there is no bright star at the southern celestial pole.
I suspect that two issues are commonly being lumped together: 1) Does latitude/longitude give you a unique and unchanging position (irrespective of shape)? 2) Are distances calculated between two points expressed as latitude/longitude correct?
When you lump these together, it's not surprising that FEers will dismiss latitude/longitude as globe based, because it's hard to accept 2) without accepting a globe, but I don't see 1) as being anywhere near as contentious. Somerled has given an opinion, but I'm having to read between the lines a bit to figure out exactly where he (gender based assumption there) stands on 1). I'm really hoping we'll hear from a few more FEers, I'm genuinely interested to understand their position(s) on this and reasoning.
Actually, I don't see how 1) could be rebutted. As you said, latitude can be determined with the position of the celestial pole in the sky, and longitude can be determined by calculating the difference between solar noon in Greenwich and local solar noon. Travel west and solar noon will happen later, travel east and it will happen sooner. Travel north and Polaris will appear higher in the sky until you reach the north pole and you see it directly overhead. Travel south and Polaris will appear lower until you reach the Equator and it appears on the horizon, and if you keep on travelling south you can repeat with the southern celestial pole. Latitude and longitude are not just arbitrary values, they have a meaning that can be easily verified by anybody: this fact alone is already a strong argument for a spherical Earth, both latitude and longitude being angular measurements.
I agree with most of what you say here, but to determine your latitude you measure the distance from the horizon to Polaris and since we don't (or at least didn't hundreds of years ago) know the distance to Polaris, we can't figure out an absolute distance, so it makes perfect sense to me to measure the angular distance and use that. In fact I can't think of any alternative. That angular measurement could be observed on a flat earth just as well. Similar argument for longitude.
So my argument is that just measuring latitude/longitude and asserting this gives you a unique position you can always find your way back to, isn't (by itself) predicated on a spherical earth model. So I think there is potential for agreement between both sides on this point.
I've frequently seen arguments dismissed out of hand with FErs saying things like "oh you're using latitude/longitude, they're based on an assumption of a globe so your argument is invalid". I was hoping by splitting the whole latitude/longitude question into two points, one independent of model and the other not, that I could find out if FErs could at least agree on 1). Unfortunately, with the exception of somerled, nobody else from that side appears to be interested enough to engage, which is disappointing.
Then comes 2). As seen in another thread, values given by online maps are generally accepted as accurate - or at least, no one has proved them wrong. And we've seen they're based on formulas such as haversine or Vincenty's.
Conclusion: we can determine a latitude and longitude of any point on Earth, and we can determine the distance between any two points on Earth knowing their latitude and longitude using a formula that calculates distances on a sphere or an oblate spheroid. It would be a very intriguing coincidence if this worked without the Earth being a globe.
Yes indeed, but I can't imagine many FErs agreeing that distances calculated using spherical trig are going to be valid. iamcpc went to a lot of effort to avoid the obvious conclusion that Bing maps distances are based on a spherical model.
Ideally I'd like to hear a bunch of FErs say "yes, latitude and longitude work and give you a fixed, unique position. No you can't calculate distances with them because...". At least that would clarify their position.
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Just to make my position clear .
I am not taking a FE or RE stance on latitude . A survey of length of successive degrees of latitude along a meridian , with respect to the pole star , will give a clear indication of the shape of the land . It's just geometry . If you don't know the distance to the pole then it can be calculated from those results .
This is the point , the results are determined by measurement not theory. Any coordinate system will give unique values to each point but if want them to conform to the real shape of earth then you have to deduce that shape .
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I am not taking a FE or RE stance on latitude . A survey of length of successive degrees of latitude along a meridian , with respect to the pole star , will give a clear indication of the shape of the land. It's just geometry . If you don't know the distance to the pole then it can be calculated from those results .
This is the point , the results are determined by measurement not theory. Any coordinate system will give unique values to each point but if want them to conform to the real shape of earth then you have to deduce that shape .
"degrees of latitude along a meridian" has no meaning on FE. As mentioned earlier, where would you draw the angle between the two vectors?
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Just to make my position clear .
I am not taking a FE or RE stance on latitude . A survey of length of successive degrees of latitude along a meridian , with respect to the pole star , will give a clear indication of the shape of the land . It's just geometry . If you don't know the distance to the pole then it can be calculated from those results .
This is the point , the results are determined by measurement not theory. Any coordinate system will give unique values to each point but if want them to conform to the real shape of earth then you have to deduce that shape .
No, I get that. I think I understand your position well enough. Without wishing to put words in your mouth, I'd say you were happy enough to accept my proposition 1) - that you can use latitude/longitude in either model to pinpoint an exact position and as for 2) potentially you can determine whether or not you can calculate accurate distance from latitude/longitude, well then, that can be checked/investigated by taking survey measurements along a meridian.
As I said, I was hoping to get a range of opinions from flat earthers on 1) & 2) separately, but not much engagement so far.
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"degrees of latitude along a meridian" has no meaning on FE. As mentioned earlier, where would you draw the angle between the two vectors?
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A meridian is any straight line from N to S - not hard to understand .
Just to make my position clear .
I am not taking a FE or RE stance on latitude . A survey of length of successive degrees of latitude along a meridian , with respect to the pole star , will give a clear indication of the shape of the land . It's just geometry . If you don't know the distance to the pole then it can be calculated from those results .
This is the point , the results are determined by measurement not theory. Any coordinate system will give unique values to each point but if want them to conform to the real shape of earth then you have to deduce that shape .
No, I get that. I think I understand your position well enough. Without wishing to put words in your mouth, I'd say you were happy enough to accept my proposition 1) - that you can use latitude/longitude in either model to pinpoint an exact position and as for 2) potentially you can determine whether or not you can calculate accurate distance from latitude/longitude, well then, that can be checked/investigated by taking survey measurements along a meridian.
As I said, I was hoping to get a range of opinions from flat earthers on 1) & 2) separately, but not much engagement so far.
For proposition 1 i'd have to say no . What your saying ,it seems to me , is that you can use any coordinate system . Well you can , and it is true that each will give unique results . But there is only one coordinate system which can rightly be called a latitude/longitude coordinate system - the angle of latitude as measured from the pole star . All other coordinate systems are based on math models - not reality .
Pole star latitude/longitude system cannot fit both FE or RE model . It will fit only one .
You can distort the results of survey by applying a set of calculations which will enable you to map earth as any shape you wish but it won't be reality .
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"degrees of latitude along a meridian" has no meaning on FE. As mentioned earlier, where would you draw the angle between the two vectors?
A meridian is any straight line from N to S - not hard to understand.
I understand perfectly what a meridian is, but it's the "degrees of latitude" applicable TO the meridian that I'm querying. Where do you draw the angle that's formed by the two vectors connecting the end points of the meridian to the point where the angle of latitude or longitude is defined?
EDIT - where is point C, if the 30 degrees of meridian is defined by the angle between vectors CA and CB?
(https://i.imgur.com/nnJx4ys.jpg)
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Point C is the pole star. Where is N - S on your diagram
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Point C is the pole star. Where is N - S on your diagram
Point C is below the ground.
I thought it was clear that the meridian is line AB, across the surface, and, following convention, the area above that line is sky, and the area below is terra firma.
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"degrees of latitude along a meridian" has no meaning on FE. As mentioned earlier, where would you draw the angle between the two vectors?
A meridian is any straight line from N to S - not hard to understand .
Just to make my position clear .
I am not taking a FE or RE stance on latitude . A survey of length of successive degrees of latitude along a meridian , with respect to the pole star , will give a clear indication of the shape of the land . It's just geometry . If you don't know the distance to the pole then it can be calculated from those results .
This is the point , the results are determined by measurement not theory. Any coordinate system will give unique values to each point but if want them to conform to the real shape of earth then you have to deduce that shape .
No, I get that. I think I understand your position well enough. Without wishing to put words in your mouth, I'd say you were happy enough to accept my proposition 1) - that you can use latitude/longitude in either model to pinpoint an exact position and as for 2) potentially you can determine whether or not you can calculate accurate distance from latitude/longitude, well then, that can be checked/investigated by taking survey measurements along a meridian.
As I said, I was hoping to get a range of opinions from flat earthers on 1) & 2) separately, but not much engagement so far.
For proposition 1 i'd have to say no . What your saying ,it seems to me , is that you can use any coordinate system . Well you can , and it is true that each will give unique results . But there is only one coordinate system which can rightly be called a latitude/longitude coordinate system - the angle of latitude as measured from the pole star . All other coordinate systems are based on math models - not reality .
Pole star latitude/longitude system cannot fit both FE or RE model . It will fit only one .
You can distort the results of survey by applying a set of calculations which will enable you to map earth as any shape you wish but it won't be reality .
OK, sorry, I thought we were on the same page. Seems not to be the case. Let me have another go at explaining. I won't bother with 2), I'll just stick with proposition 1) for now, see if there is some common ground or not.
For proposition 1, this is just about latitude/longitude. That's the only coordinate system I'm talking about. The units are degrees, either expressed as degrees-minutes-seconds (and fractions thereof) or decimal degrees, whichever you like, no preference on my part. Latitude to be measured however you like really. Quite happy with angular distance from horizon to Polaris (or equivalent in the southern hemisphere), measured with a sextant, quadrant, backstaff, or something else, whatever you prefer, so long as the values it gives are sensible. For longitude, I'd suggest time difference between either the sun or a suitable star transiting due south at a fixed meridian (I'd suggest Greenwich, but flexible on that) and same event occurring at the observer's position. Time difference converted to an angle based on the sun moving at 15 degrees per hour or the sidereal day length if using a star transit. But any sensible method to measure longitude acceptable.
I'm not suggesting a coordinate system based on math calculations, just observations, so long as you don't consider converting a time difference to an angle for longitude to be a math calculation in the sense I think you mean it.
If you are happy with the basic idea of latitude and longitude and you want to suggest suitable equipment and/or methodology, I'm pretty confident we can find agreement there.
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Latitude is determined by measure of the angle of pole star above the horizontal plane form position of measure , not the horizon . The plane is found by plumbline and level , the angle of elevation by sextant and quadrant .
Use the stars to determine the meridian . Zenith sector, transit scope , survey instruments . You need to see the pole star . It's not visible during daylight which is why I wouldn't use the sun . Every star will cross the meridian at it's zenith . You will then have a meridian along which you will also have observed and measured degrees of latitude given by the pole star - that point above the geographical N point . Call it whatever you want .
These observations will reveal the shape of earth according to these measurements of latitude along that meridian . It's all survey of land and sky .
You can then plot other meridian position using the fact that the sun completes it's 360 degree journey in 24 hrs. Also will be able to check any predictions.
This is all in the North where the pole star is visible . Once that's done we can move south.
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Latitude is determined by measure of the angle of pole star above the horizontal plane form position of measure , not the horizon . The plane is found by plumbline and level , the angle of elevation by sextant and quadrant.
So where is the angle formed by two vectors? If you say you are at 30 degrees N, where is that angle drawn?
If it's the angle between your horizontal and the pole star, then all you have determined is the elevation of the pole star from your position.
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Take a reading at 30N , take a reading from 29N , measure accurately the distance between the points - and carry it on like so .
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Take a reading at 30N , take a reading from 29N , measure accurately the distance between the points - and carry it on like so .
So what are the two vector lines which form the angle of latitude?
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Latitude is determined by measure of the angle of pole star above the horizontal plane form position of measure , not the horizon . The plane is found by plumbline and level , the angle of elevation by sextant and quadrant .
Use the stars to determine the meridian . Zenith sector, transit scope , survey instruments . You need to see the pole star . It's not visible during daylight which is why I wouldn't use the sun . Every star will cross the meridian at it's zenith . You will then have a meridian along which you will also have observed and measured degrees of latitude given by the pole star - that point above the geographical N point . Call it whatever you want .
OK, well that's my proposition 1 then. Quite happy with the equipment and methodology. So really that's all my proposition 1 is about. I believe this is compatible with either flat or globe earth, it's just a set of observations you make, it doesn't by itself tell you what shape the earth is. So my question to anybody who believes in a flat earth is, do any of you have a problem with this and if so, what is it?
I take it you and I at least can now agree that this is an acceptable method / co-ordinate system for describing a position somewhere, anywhere on earth?
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Yeah nice , we agree about the equipment and methodology , and you are correct this is indeed compatible with flat or globe earth .
I disagree with your next bit. The set of geometric observations you make will tell you , without preconception , which shape is a better fit for a model of earth .
On a perfect sphere with the pole star at immense distance , light rays would be parallel to the axis of the globe and all degrees of latitude should be equal distance apart since they are governed by the curve of the sphere.
On an oblate sphere ,same distant polestar, degrees of latitude will lengthen to the North.
On a plain degrees of latitude will shorten to the North only if the polestar is relatively close .
God knows about the pearoid.
It's probably impossible to get true accurate readings due to the diffraction /diffusion etc caused by the air but the general shape should be discernable.
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Yeah nice , we agree about the equipment and methodology , and you are correct this is indeed compatible with flat or globe earth .
I disagree with your next bit. The set of geometric observations you make will tell you , without preconception , which shape is a better fit for a model of earth .
On a perfect sphere with the pole star at immense distance , light rays would be parallel to the axis of the globe and all degrees of latitude should be equal distance apart since they are governed by the curve of the sphere.
On an oblate sphere ,same distant polestar, degrees of latitude will lengthen to the North.
On a plain degrees of latitude will shorten to the North only if the polestar is relatively close .
God knows about the pearoid.
It's probably impossible to get true accurate readings due to the diffraction /diffusion etc caused by the air but the general shape should be discernable.
What I mean is, you can determine your position and that by itself doesn't force you to accept a particular model. It's only if you start measuring distances between pairs of locations that the realities of the model need to be considered and I think it's this follow on measuring that's the real problem for FE believers, but it's hard to tell because the argument always seems to be along the lines of "can't use latitude/longitude because that's based on a globe". Well I'm just saying that actually, if you limit yourself to determining position, and put aside the tricky topic of distance, then all you are doing is using some pretty basic instruments to make some simple to understand observations.
I completely agree that if you start measuring distances, that will lead you to draw conclusions about the shape of the earth and if you lump the two together (position+distance), then you just get the standard "can't use that, it's based on a globe" response.
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I don't get your point . Last line of your OP .
"So is that it? Are latitude/longitude OK by themselves, but the distances are not? What are the actual objections?"
I have put forward the objections . Why should FE accept an ellipsoid model coordinate system as being suitable to describe earth ?
GPS and the globe are not latitude longitude systems of earth , yet they are offered up as proof of a globe because by RE . Why do you think that doesn't deserve objection ?
RE is fond of telling us FE distances don't add up on their imaginary model . This is why the distances are important .
Your last sentence makes no sense - can't fathom that out.
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I don't get your point . Last line of your OP .
"So is that it? Are latitude/longitude OK by themselves, but the distances are not? What are the actual objections?"
I have put forward the objections . Why should FE accept an ellipsoid model coordinate system as being suitable to describe earth ?
GPS and the globe are not latitude longitude systems of earth , yet they are offered up as proof of a globe because by RE . Why do you think that doesn't deserve objection ?
RE is fond of telling us FE distances don't add up on their imaginary model . This is why the distances are important .
Your last sentence makes no sense - can't fathom that out.
Somehow or other I'm just not managing to explain myself very well and I keep trying different ways to say the same thing. All I can do is keep trying I guess. I don't honestly think there's much if any disagreement with each other. Anyway here goes...
Latitude and longitude pre-date GPS by centuries, so by all means discard any arguments based on GPS, not that I'm using any here.
If you were completely lost, but you had a basic set of instruments (and I think we agree what those are), none of which rely on a globe to function (you just point them at things and measure angles or check timings), you could determine your latitude and longitude. If I had the same basic set of instruments, plus a compass, and you could tell me your position, then in theory I could find you. I just need to travel north or south until we're at the same latitude and then east or west until we're at the same longitude and we should meet. Distances don't matter. This process just works whether the earth is a globe or flat - correct?
So from my point of view, for this purpose and this purpose only, nobody can object to latitude/longitude. But they do. Frequently I come across "you can't use latitude/longitude because it's based on a globe". Well how is this based on a globe? Don't go talking about measuring distances, we only have these basic instruments, we have no means to measure any distances.
In order to determine the truth of this, I'm discarding GPS, spherical geometry, everything globe related. Pretend humanity had never even considered the idea that the world was a globe, pretend we've never invented the ruler or tape measure or even the concept of a distance. Is determining your position (latitude/longitude) possible? Well clearly it is. Is it useful? Again, clearly it is. Why then is it constantly rejected in arguments?
I think it's because latitude/longitude have just become forever associated with the globe and that's what's causing the problem for those who don't believe in the globe.
You keep bringing up distances, well you keep objecting to a point I'm just not making. Leave distances out of it and then tell me what's wrong with latitude/longitude.
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"I think it's because latitude/longitude have just become forever associated with the globe and that's what's causing the problem for those who don't believe in the globe."
You've answered your own question there. Plane measurements associated with a globe through spherical calculations . That's the objection.
From your OP.
"Fundamentally (if you live in the northern hemisphere), your latitude is easily determined. It's simply the altitude of Polaris from your location. It's not an absolute value in miles, km or light years, because to determine that you'd need to know how far away Polaris is and in times past, that wasn't possible to determine. What we do instead is measure the angle from the horizon to the star, because that's easily done and doesn't require you to know any distances."
Point 1 . You assume Polaris is known to be a vast distance and point 2 - you assume that in past times the distance to Polaris wasn't possible to measure .
See Brahe's model for the distance to the stars for one example and I'm sure triangulation of distance has been around for a long time .
Point 3. We do not measure elevation of Polaris from the horizon - we measure elevation from the horizontal plane
If you make a post containing assumptions you are confusing the issue.
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"I think it's because latitude/longitude have just become forever associated with the globe and that's what's causing the problem for those who don't believe in the globe."
You've answered your own question there. Plane measurements associated with a globe through spherical calculations . That's the objection.
Well I've taken a guess at what the objections might be, but I want to know if that's what FErs actually object to, or is it something else?
From your OP.
"Fundamentally (if you live in the northern hemisphere), your latitude is easily determined. It's simply the altitude of Polaris from your location. It's not an absolute value in miles, km or light years, because to determine that you'd need to know how far away Polaris is and in times past, that wasn't possible to determine. What we do instead is measure the angle from the horizon to the star, because that's easily done and doesn't require you to know any distances."
Point 1 . You assume Polaris is known to be a vast distance and point 2 - you assume that in past times the distance to Polaris wasn't possible to measure .
No, we've been here before and this has been addressed already..
Good description of how we can measure lat and long in the northern part of the world.
However you state the globe theory preconceived assumption that Polaris is at an extreme distance thus its light rays are basically parallel leading to the conclusion that any change in measured angle of elevation to the star is a product of the curvature of this globe .
No I've not stated anything about the distance to Polaris (extreme or otherwise), other than simply saying that in times past, the distance was not known, but we can however use an angular measurement instead, which works independently of distance. For instance I can measure the angular height of a tree at the bottom of my garden from my current position. It doesn't tell me anything about the actual height of the tree or how far away it is or for that matter, what shape the earth is.
Equally, it doesn't matter whether the light rays from Polaris are parallel or not, just that whenever you measure the angular elevation of Polaris from the same position, you are always going to get the same value and if you move north or south of that position, you will get a different value, which will increase as you move north and decrease as you move south.
To which you replied...
Sorry Robin , I misread your OP about distance to Polaris .
See Brahe's model for the distance to the stars for one example and I'm sure triangulation of distance has been around for a long time .
Point 3. We do not measure elevation of Polaris from the horizon - we measure elevation from the horizontal plane
If you make a post containing assumptions you are confusing the issue.
I'm no sailor and I've never used a sextant, however my understanding of how these are normally used when in open water is that you adjust two images until they overlap. One of the images is the celestial object, sun, moon, planet or star and the other is the horizon. Determining the horizontal plane on a rolling ship is not easy. I'm not going to bother arguing about this though, it's detail, it doesn't fundamentally change the methodology, it would just lead to very slightly different results. If I'm wrong, then I'm wrong and quite happy to concede the point. To me it's a fairly unimportant detail to the overall process.
So just to reiterate. I don't assume the distance to Polaris is known to be a vast distance. The distance is utterly irrelevant if all you are doing is measuring its angular height above a datum (horizon or horizontal plane, I don't really care). I don't care if the light rays are parallel either. That won't stop you measuring an angle. Yes, I do assume that in ancient times we had no way to determine the distance to a star. I believe Tycho Brahe proposed measuring stellar parallax, but didn't have equipment capable of doing so. But again, whether they could or couldn't measure stellar distances is completely irrelevant to a method which uses angles, not distances, so I'll happily ditch that assumption and say in times past, people may or may not have been able to measure stellar distances, but since we're using angles, it makes no difference whether they did or whether they didn't.
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What happened in the 1600s? Quoting from Bryson's abbreviated account;
".. one revelation became almost immediately controversial.
This was the suggestion that the Earth is not quite round. According to Newton’s theory, the centrifugal force of the Earth’s spin should result in a slight flattening at the poles and a bulging at the equator, which would make the planet slightly oblate. That meant that the length of a degree of meridian wouldn’t be the same in Italy as it was in Scotland. Specifically, the length would shorten as you moved away from the poles. This was not good news for those people whose measurements of the planet were based on the assumption that it was a perfect sphere, which was everyone.
For half a century people had been trying to work out the size of the Earth, mostly by making very exacting measurements. One of the first such attempts was by an English mathematician named Richard Norwood. As a young man Norwood had travelled to Bermuda with a diving bell modelled on Halley’s device, intending to make a fortune scooping pearls from the seabed. The scheme failed because there were no pearls and anyway Norwood’s bell didn’t work, but Norwood was not one to waste an experience. In the early seventeenth century Bermuda was well known among ships’ captains for being hard to locate. The problem was that the ocean was big, Bermuda small and the navigational tools for dealing with this disparity hopelessly inadequate. There wasn’t even yet an agreed length for a nautical mile. Over the breadth of an ocean the smallest miscalculations would become magnified so that ships often missed Bermuda-sized targets by dismayingly large margins. Norwood, whose first love was trigonometry and thus angles, decided to bring a little mathematical rigour to navigation, and to that end he determined to calculate the length of a degree.
Starting with his back against the Tower of London, Norwood spent two devoted years marching 208 miles north to York, repeatedly stretching and measuring a length of chain as he went, all the while making the most meticulous adjustments for the rise and fall of the land and the meanderings of the road. The final step was to measure the angle of the sun at York at the same time of day and on the same day of the year as he had made his first measurement in London. From this, he reasoned he could determine the length of one degree of the Earth’s meridian and thus calculate the distance around the whole. It was an almost ludicrously ambitious undertaking—a mistake of the slightest fraction of a degree would throw the whole thing out by miles—but in fact, as Norwood proudly declaimed, he was accurate to “within a scantling”—or, more precisely, to within about six hundred yards. In metric terms, his figure worked out at 110.72 kilometres per degree of arc.
In 1637, Norwood’s masterwork of navigation, The Seaman’s Practice, was published and found an immediate following. It went through seventeen editions and was still in print twenty-five years after his death. "
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How is a Nautical Mile defined on FE?
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Somerled,
sorry to come in to this discussion rather late. I just like to make sure that I understand your position in response the OP's original question :
a) you support the idea that a latitude/longitude coordinate system allows us to uniquely identify each and every point on earth. And we could use the elevation angle of polaris to clearly identify the latitude and the time difference w.r.t Greenwich (position of sun in the sky) as a measure of longitude.
b) if we look up on the internet latitude and longitude for a particular place on earth people living there would confirm these numbers by measuring the elevation angle of polaris and time difference to Greenwich. Well, at least you and I could do that as well as others on this thread making small allowances for our measurement errors.
Thank you for your response
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Coming to this rather late. As people have noted, there are two separate questions. (i) Is it possible to make celestial observations that uniquely identify our position on the earth, (ii) can we use these observations to infer the distance between two different positions.
Regarding the first, Polaris can be used, but is not necessary. The standard method is to observe the time when the altitude of the sun as at its highest (zenith), which requires knowing the time at any place in the world. (Knowing the time was a famous problem of longitude).
This tells us the longitude. Then determine (using a sextant) the altitude of the sun at zenith. This tells us the latitude. The method works equally well in the Southern hemisphere.
Latitude and longitude make no assumptions about the shape of the land. Flat Earth believers could use the method.
Question (ii) is whether, knowing the latitude and longitude of two different points, we could mathematically determine the distance between the points. FE navigators could work this out also, if they used the standard model used by RE navigators. They could just say “well it’s a model, and it works, we don’t really know why”.
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Doesn't the altitude of the sun at it highest point during a day depend on the time of the year ? Maybe at one of the equinoxes you would be a good choice ?
Would love to hear from the FE folks too.
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Doesn't the altitude of the sun at it highest point during a day depend on the time of the year ? Maybe at one of the equinoxes you would be a good choice ?
Yes, I think if you are in a suitable (well north of the equator) static location and you aren't in a hurry, personally I'd use the Polaris method for latitude. The sun changes its altitude during the day and throughout the year and you really don't want to look directly at it. Polaris just sits there, unmoving and you can look straight at it. If you're on the open sea, south of the equator and it's daytime, use the sun for sure.
But really whatever works for you, so long as it gives you the right answer. The key idea here is, however you choose to do it, you end up with a pair of angles which uniquely define your position and that would work, globe or flat.
Would love to hear from the FE folks too.
Yes, it's a bit pointless all us RErs discussing this because we're not going to disagree (I assume). Disappointing that we're not hearing much from them.
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Doesn't the altitude of the sun at its highest point during a day depend on the time of the year ?
It does, and is known as the Declination. You can get that number from tables, but again it does not depend on any assumption about the shape of the earth. You can simply observe the declination each day at local noon (i.e. at zenith) and note it down, so you have a number for each day of the year.
Then take a sighting with the sextant to find the altitude of the sun at local noon. Latitude then given by the following formula:
LAT = 90 - ALT + DEC
Simple. Involves no assumptions about the shape of the earth, so FE and RE should agree on the latitude for any point on the earth. Likewise, if they know London (Greenwich) time, they both agree on the longitude.
Where they will profoundly disagree is on the distance implied between two points on the earth's surface. This will depend on the chosen map, about which FE will internally disagree. But assuming FE likes the AE map, and RE the globe, they will compute the distances differently, radically so the further south they get.
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Doesn't the altitude of the sun at its highest point during a day depend on the time of the year ?
It does, and is known as the Declination. You can get that number from tables, but again it does not depend on any assumption about the shape of the earth. You can simply observe the declination each day at local noon (i.e. at zenith) and note it down, so you have a number for each day of the year.
Then take a sighting with the sextant to find the altitude of the sun at local noon. Latitude then given by the following formula:
LAT = 90 - ALT + DEC
Simple. Involves no assumptions about the shape of the earth, so FE and RE should agree on the latitude for any point on the earth. Likewise, if they know London (Greenwich) time, they both agree on the longitude.
Where they will profoundly disagree is on the distance implied between two points on the earth's surface. This will depend on the chosen map, about which FE will internally disagree. But assuming FE likes the AE map, and RE the globe, they will compute the distances differently, radically so the further south they get.
I think you are probably right, FE and RE should be able to agree on the latitude (and longitude) for any point on the earth. The problem is, I've never heard a FEer actually agree to that, all I've ever heard is "can't use latitude/longitude because that's based on a globe". It's a very broad statement and I've been trying to break it down into two separate issues, i) latitude/longitude for position ii) distances based on latitude/longitude. I would love to hear a FEer say, "yes, i) is OK, but ii) is not". Then at least we know where we all stand. Just can't get an opinion on this from their side unfortunately.
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I think you are probably right, FE and RE should be able to agree on the latitude (and longitude) for any point on the earth.
Not even 'probably'. For those who dislike the theory of declination, here (https://www.youtube.com/watch?v=VKjGc-VjUFk) is a neat video showing how to locate the southern celestial pole.
It’s the pure Zetetic (https://rationaltheory.fandom.com/wiki/Zetetic_Method) method, i.e. working directly from observation rather than supporting the observations, partly or wholly, on some theory.
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I think you are probably right, FE and RE should be able to agree on the latitude (and longitude) for any point on the earth.
Not even 'probably'. For those who dislike the theory of declination, here (https://www.youtube.com/watch?v=VKjGc-VjUFk) is a neat video showing how to locate the southern celestial pole.
It’s the pure Zetetic (https://rationaltheory.fandom.com/wiki/Zetetic_Method) method, i.e. working directly from observation rather than supporting the observations, partly or wholly, on some theory.
You're right we should be able to agree. The question then becomes, will we be able to agree?
Interesting video. So much easier in the northern hemisphere.
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I'll make a list of statements related to longitude and latitude. Hopefully each statement is simple enough to make it easy to find out possible disagreements.
* The elevation of the celestial pole is constant for any given location
* We can calculate the latitude of a location using the elevation of the celestial pole
* Solar noon is the time of the day when the Sun is at its highest in the sky, casting the shortest shadows
* At solar noon, the Sun appears due South or due North, except in the special case when it's directly overhead
* The difference between solar noon at a reference location (eg Greenwich) and solar noon at any given location is constant
* We can calculate the longitude from the difference between solar noon at Greenwich and local solar noon, 15 degrees of longitude being equivalent to 1 hour
* Any place on Earth is uniquely identified by a latitude and longitude
* Locations with the same longitude will see the Sun at its highest at the same time
* Locations with the same latitude will have the same variation of day length all through the year
* At the equinoxes, the elevation of the Sun at solar noon is 90 - current latitude (0 at the poles, 90 at the Equator)
* At any other time of the year, the elevation of the Sun at solar noon is 90 - current latitude + declination of the Sun
* The subsolar point at the June solstice is 23.5 degrees North, on the tropic of Cancer
* The subsolar point at the December solstice is 23.5 degrees South, on the tropic of Capricorn
* Latitude lines are east-west lines, called parallels
* Longitude lines are north-south lines, called meridians
* Meridians and parallels always cross at a right angle
* One degree of latitude along a meridian is approximately 111.3 km
* One degree of longitude along the Equator is approximately 111.3 km
* The borders of the state of Colorado were defined with meridians and parallels
* The eastern and western borders of Colorado are the same length, approximately 445 km
* The northern border of Colorado is significantly shorter than the southern border
* Meridians converge as you get further away from the Equator, either South or North
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I'll make a list of statements related to longitude and latitude. Hopefully each statement is simple enough to make it easy to find out possible disagreements.
* The elevation of the celestial pole is constant for any given location
Location? Did you mean latitude?
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I'll make a list of statements related to longitude and latitude. Hopefully each statement is simple enough to make it easy to find out possible disagreements.
* The elevation of the celestial pole is constant for any given location
Location? Did you mean latitude?
There probably was a better way to phrase that. I do mean location. At a given location, the elevation of the celestial pole is constant, it doesn't change over time. This is required if you want to determine a unique, constant latitude from that measurement.
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I do mean location. At a given location, the elevation of the celestial pole is constant, it doesn't change over time.
That makes sense. Some comments. The statements can be divided into those which are simply definitions, and those which would have to be verified empirically. Of the latter, these could be divided into those which have no implication for the shape of the earth, and those (if any) which do.
Some of the definitions are covert. You say “At solar noon, the Sun appears due South or due North”, but you haven’t defined ‘North’ or ‘South’. Clearly magnetic poles are not meant. Perhaps you might define N and S in terms of the axis of apparent celestial rotation. As for ‘Latitude’, you could define it by the elevation of Polaris, or the Southern pole star.
Do any of these imply the shape of the earth? We have “Locations with the same longitude will see the Sun at its highest at the same time”. That implies (there is a geometrical proof) that a line of longitude is the shortest distance between any two points on that line, meaning that if the earth is flat, they must be straight. But then there is a problem with “Meridians converge as you get further away from the Equator, either South or North”.
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I do mean location. At a given location, the elevation of the celestial pole is constant, it doesn't change over time.
That makes sense. Some comments. The statements can be divided into those which are simply definitions, and those which would have to be verified empirically. Of the latter, these could be divided into those which have no implication for the shape of the earth, and those (if any) which do.
Some of the definitions are covert. You say “At solar noon, the Sun appears due South or due North”, but you haven’t defined ‘North’ or ‘South’. Clearly magnetic poles are not meant. Perhaps you might define N and S in terms of the axis of apparent celestial rotation.
Actually, it can also be used as a definition of North and South. South is were the Sun is at solar noon if you're north of the tropic of Capricorn. North is the opposite direction, West is due left if you face North. Most common definitions of North and South imply a round Earth, so I prefer not to include them. Maybe someone will come up with a different definition. The point is to see if any of these statements could be refuted.
As for ‘Latitude’, you could define it by the elevation of Polaris, or the Southern pole star.
As there is no southern equivalent of Polaris, I prefer the term "celestial pole": the point in the sky around which the stars seem to be spinning. The direction you have to point an equatorial mount at to cancel out the apparent movement of the stars. Also, Polaris is not exactly at the celestial pole, but it's probably close enough for our purpose.
Do any of these imply the shape of the earth? We have “Locations with the same longitude will see the Sun at its highest at the same time”. That implies (there is a geometrical proof) that a line of longitude is the shortest distance between any two points on that line, meaning that if the earth is flat, they must be straight. But then there is a problem with “Meridians converge as you get further away from the Equator, either South or North”.
That's part of the point, none of these statements alone directly implies a shape of the Earth. But all of them should be verifiable without requiring space travel or anything out of reach. And all together, I guess they're hard to fit in a flat Earth model.
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That's part of the point, none of these statements alone directly implies a shape of the Earth. But all of them should be verifiable without requiring space travel or anything out of reach. And all together, I guess they're hard to fit in a flat Earth model.
Convergence of longitude lines does imply a shape of the Earth, if longitude lines are the shortest distance between two points, i.e. straight. Then two straight lines enclose a space, right?
See Euclid postulate I (https://mathcs.clarku.edu/~djoyce/java/elements/bookI/post1.html).
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Convergence of longitude lines does imply a shape of the Earth, if longitude lines are the shortest distance between two points, i.e. straight. Then two straight lines enclose a space, right?
The shortest distance over the surface of any globe is the arc (S). The shortest distance between the points is the chord (C), but that cannot be travelled without mining into the globe.
Arc S will appear straight only if you view it from directly above. Else it will appear curved. But it's never physically straight
(https://upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Circularsegment.svg/257px-Circularsegment.svg.png)
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Convergence of longitude lines does imply a shape of the Earth, if longitude lines are the shortest distance between two points, i.e. straight. Then two straight lines enclose a space, right?
The shortest distance over the surface of any globe is the arc (S). The shortest distance between the points is the chord (C), but that cannot be travelled without mining into the globe.
Arc S will appear straight only if you view it from directly above. Else it will appear curved. But it's never physically straight
(https://upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Circularsegment.svg/257px-Circularsegment.svg.png)
If the earth is a globe, yes. But the question is whether any of GreatATuin's statements above imply something about the shape of the earth. If they imply that two apparently straight lines enclose a space, then the earth cannot be flat. For FE to be true, either (1) lines of longitude are not straight or (2) lines of longitude do not converge at the Poles.
Note that (1) is true under the bipolar model, where lines of longitude converge, but for that reason are not straight. And (2) is true of the AE model, where the lines are straight but do not converge at the South Pole.
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My statements don't actually mention "straight lines", just North-South and East-West lines. On a globe Earth, meridians are great circles that converge at the poles, parallels are rhumb lines perpendicular to the meridians. Parallels are not great circles, except in the special case of the Equator. Being circles at the surface of a sphere, they obviously are not "straight" in a 3D sense like a laser beam.
On a flat Earth, what parallels and meridians look like highly depends on the model. None of the flat Earth models I've seen are compatible with my list of statements.
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For FE to be true, either (1) lines of longitude are not straight or (2) lines of longitude do not converge at the Poles.
Lines of lat or long are bisected by angles, the difference between such lines being expressed in degrees of angle.
By definition, this has no meaning on FE. Where would you draw the angle? Where do the lines or vectors forming the angle meet?
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Take it as a thought experiment: for one moment, forget the geometrical definitions of latitude and longitude, just consider them as coordinates of a location on Earth.
The point is that we can determine latitude and longitude through observation of celestial objects and measurements of time. And conversely, knowing latitude and longitude allows us to know for example at what time the Sun rises and sets on a given date.
Of course, the mere fact that we can use angles as coordinates should tell us something about the shape of the Earth. But let's start with the basics, and let's see if someone denies the reality of the concept of latitude and longitude.
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My statements don't actually mention "straight lines",
I agree, I was just wondering if one could add a further statement that longitude lines are the shortest distance between two points, to see if that is a point of disagreement.
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I've read a number of posts where latitude and longitude are dismissed by FErs because they are based on a globe earth.
Robin,
I've researched this and I'm also confused about the claim because we have been able to navigate using the stars without using the words "Longitude" and "Latitude"
In terms of Latitude it does not appear to me to be based on a spherical coordinate system. It appears to be based on where you are, in relation to the North star. This was made clear to me when I learned about the Kamal.
https://en.wikipedia.org/wiki/Kamal_(navigation)
The video below discusses the Kamal around 2 minutes.
https://www.youtube.com/watch?v=2Bv8dc19HQ0&t=384s
So is it only the longitude part of the system which is based on a spherical earth?
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I've read a number of posts where latitude and longitude are dismissed by FErs because they are based on a globe earth.
Robin,
I've researched this and I'm also confused about the claim because we have been able to navigate using the stars without using the words "Longitude" and "Latitude"
In terms of Latitude it does not appear to me to be based on a spherical coordinate system. It appears to be based on where you are, in relation to the North star. This was made clear to me when I learned about the Kamal.
https://en.wikipedia.org/wiki/Kamal_(navigation)
The video below discusses the Kamal around 2 minutes.
https://www.youtube.com/watch?v=2Bv8dc19HQ0&t=384s
So is it only the longitude part of the system which is based on a spherical earth?
I agree, you don't need to be on a spherical earth for latitude to have a meaning and it's undoubtedly useful for navigation. I would really like to hear from a range of FErs whether they would accept this and if not, why not?
I'd go further and say I don't believe there is an issue with longitude either. In principle, finding your longitude is easy. Find the exact time when the sun was due south at Greenwich UK. Find the exact time when the sun is due south at your current location. Work out the time difference. If it's 1 hour, then you are 15° away from Greenwich. This can work on a flat earth just as well as a spherical one, it's simply making use of the fact that the sun appears to travel across the sky at 15° per hour, nothing more. The sun certainly does this, it's easily observed, so if the earth is flat, then it's doing this on a flat earth, so the method still works.
In practice it's not quite as simple as that because the 15° per hour is only an average, it does speed up and slow down a bit throughout the year, but there are known ways to correct for this (see equation of time https://en.wikipedia.org/wiki/Equation_of_time (https://en.wikipedia.org/wiki/Equation_of_time)).
Very informative video by the way.
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I'd go further and say I don't believe there is an issue with longitude either. In principle, finding your longitude is easy. Find the exact time when the sun was due south at Greenwich UK. Find the exact time when the sun is due south at your current location. Work out the time difference. If it's 1 hour, then you are 15° away from Greenwich. This can work on a flat earth just as well as a spherical one, it's simply making use of the fact that the sun appears to travel across the sky at 15° per hour, nothing more. The sun certainly does this, it's easily observed, so if the earth is flat, then it's doing this on a flat earth, so the method still works.
The main issue that I have with longitude being shape agnostic is that it a lot more complicated to calculate and was not really done by ancient navigators when the FE concept was much more mainstream than it is now. It's more modern. It's not something you can calculate with sometime as simple as some rope and a board. Claims that it is based on a spherical coordinate system, from my perspective, are much more challenging for me to understand or offer an alternate theory to.
With latitude it seems to me that there is strong evidence that a navigator who calculated latitude and thought the earth was flat would do so in a similar way to a navigator who thought the earth was round.
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I'd go further and say I don't believe there is an issue with longitude either. In principle, finding your longitude is easy. Find the exact time when the sun was due south at Greenwich UK. Find the exact time when the sun is due south at your current location. Work out the time difference. If it's 1 hour, then you are 15° away from Greenwich. This can work on a flat earth just as well as a spherical one, it's simply making use of the fact that the sun appears to travel across the sky at 15° per hour, nothing more. The sun certainly does this, it's easily observed, so if the earth is flat, then it's doing this on a flat earth, so the method still works.
The main issue that I have with longitude being shape agnostic is that it a lot more complicated to calculate and was not really done by ancient navigators when the FE concept was much more mainstream than it is now. It's more modern. It's not something you can calculate with sometime as simple as some rope and a board. Claims that it is based on a spherical coordinate system, from my perspective, are much more challenging for me to understand or offer an alternate theory to.
With latitude it seems to me that there is strong evidence that a navigator who calculated latitude and thought the earth was flat would do so in a similar way to a navigator who thought the earth was round.
I agree that latitude is simpler and has been an integral part of navigation for much longer. Again it would be a good starting point to at least establish if latitude on its own is or isn't a contentious issue for FErs.
The central difficulty with longitude is that it's all about time and until the 18th C there wasn't a reliable way of keeping time accurately, by which time of course, a belief in a globe earth was pretty much universal. Having said that, unless time is somehow a concept which doesn't work on a flat earth, everything else about the method is observation of the heavens and observations are observations, the shape of the earth doesn't really affect the results.
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I agree that latitude is simpler and has been an integral part of navigation for much longer. Again it would be a good starting point to at least establish if latitude on its own is or isn't a contentious issue for FErs.
The central difficulty with longitude is that it's all about time and until the 18th C there wasn't a reliable way of keeping time accurately, by which time of course, a belief in a globe earth was pretty much universal. Having said that, unless time is somehow a concept which doesn't work on a flat earth, everything else about the method is observation of the heavens and observations are observations, the shape of the earth doesn't really affect the results.
The question I have is how can we determine if your position in relation to the north star is based on a flat earth and refraction or a globe earth and refraction to determine if the claims that it's based entirely on a globe earth are supported or refuted by the evidence. As of now I don't know.
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The central difficulty with longitude is that it's all about time and until the 18th C there wasn't a reliable way of keeping time accurately, by which time of course, a belief in a globe earth was pretty much universal. Having said that, unless time is somehow a concept which doesn't work on a flat earth, everything else about the method is observation of the heavens and observations are observations, the shape of the earth doesn't really affect the results.
Conceptually longitude is simple. Find the point at which the sun is highest, then look up the time at Greenwich. These days, simple. 200 years ago, not simple.
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The question I have is how can we determine if your position in relation to the north star is based on a flat earth and refraction or a globe earth and refraction to determine if the claims that it's based entirely on a globe earth are supported or refuted by the evidence. As of now I don't know.
The fact that the North star has a certain altitude is merely an observation. You measure it in angles. How would that tell you anything about the shape of the earth?
But add the fact that its angle changes by 1 degree for every 111km you travel towards it or away from it, may tell you something. Nothing is certain of course, but the very simplest theory to explain that observation is that the earth is (approximately) spherical. Doesn't mean that it is spherical, and absolutely nothing can prove it for certain. But that hypothesis is one very simple explanation.
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but the very simplest theory to explain that observation is that the earth is (approximately) spherical.
I agree. And generally speaking since the simplest is also likely to be the most obvious, then best go with that as an explanation until someone comes up with something better (or more simple) wouldn't you say?
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I agree that latitude is simpler and has been an integral part of navigation for much longer. Again it would be a good starting point to at least establish if latitude on its own is or isn't a contentious issue for FErs.
The central difficulty with longitude is that it's all about time and until the 18th C there wasn't a reliable way of keeping time accurately, by which time of course, a belief in a globe earth was pretty much universal. Having said that, unless time is somehow a concept which doesn't work on a flat earth, everything else about the method is observation of the heavens and observations are observations, the shape of the earth doesn't really affect the results.
The question I have is how can we determine if your position in relation to the north star is based on a flat earth and refraction or a globe earth and refraction to determine if the claims that it's based entirely on a globe earth are supported or refuted by the evidence. As of now I don't know.
I'm not sure if refraction is a significant factor for mid-latitudes because the north star will be quite high above the horizon (or however you are determining level). Near the equator, when polaris is very low, sure.
I don't really see how measuring the angular height of something could be connected to the shape of the earth. Clearly we can measure the angular height and almost by definition if we measure this height/angle from two different locations and find it to be the same, then we say these are at the same latitude. We know that ancient mariners used things like kamals and this enabled them to find their way back to the correct port when they needed to, so the system clearly works, whether the earth is flat or some other shape.
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The question I have is how can we determine if your position in relation to the north star is based on a flat earth and refraction or a globe earth and refraction to determine if the claims that it's based entirely on a globe earth are supported or refuted by the evidence. As of now I don't know.
The fact that the North star has a certain altitude is merely an observation. You measure it in angles. How would that tell you anything about the shape of the earth?
I tend to agree after seeing the videos about it but it's a common belief that latitude is based on the earth being a sphere instead of based on how far you are away from the north star. What test could we devise to determine if this is true or not.
But add the fact that its angle changes by 1 degree for every 111km you travel towards it or away from it, may tell you something. Nothing is certain of course, but the very simplest theory to explain that observation is that the earth is (approximately) spherical. Doesn't mean that it is spherical, and absolutely nothing can prove it for certain. But that hypothesis is one very simple explanation.
couldn't that also mean that the earth is not a sphere with the light from the north star propagating outward in a circle?
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The question I have is how can we determine if your position in relation to the north star is based on a flat earth and refraction or a globe earth and refraction to determine if the claims that it's based entirely on a globe earth are supported or refuted by the evidence. As of now I don't know.
The fact that the North star has a certain altitude is merely an observation. You measure it in angles. How would that tell you anything about the shape of the earth?
I tend to agree after seeing the videos about it but it's a common belief that latitude is based on the earth being a sphere instead of based on how far you are away from the north star. What test could we devise to determine if this is true or not.
What test could we devise to determine whether the apparent angle of Polaris to the horizon is in fact the apparent angle of Polaris to the horizon? Question makes no sense. Latitude by definition is the angle we observe, whether correct or not.
But add the fact that its angle changes by 1 degree for every 111km you travel towards it or away from it, may tell you something. Nothing is certain of course, but the very simplest theory to explain that observation is that the earth is (approximately) spherical. Doesn't mean that it is spherical, and absolutely nothing can prove it for certain. But that hypothesis is one very simple explanation.
couldn't that also mean that the earth is not a sphere with the light from the north star propagating outward in a circle?
It could mean that. If you allow enough curvature of light, anything is possible.
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The question I have is how can we determine if your position in relation to the north star is based on a flat earth and refraction or a globe earth and refraction to determine if the claims that it's based entirely on a globe earth are supported or refuted by the evidence. As of now I don't know.
The fact that the North star has a certain altitude is merely an observation. You measure it in angles. How would that tell you anything about the shape of the earth?
I tend to agree after seeing the videos about it but it's a common belief that latitude is based on the earth being a sphere instead of based on how far you are away from the north star. What test could we devise to determine if this is true or not.
I can stand at a certain point in my garden and measure the angular height of a tree at the other end of the garden. If I stand closer to the tree, the angle gets larger, further away and the angle gets smaller. What if anything I can deduce about the shape of the earth from this I really don't know and I don't know what additional test I could make to my tree measurement to determine the shape of the earth either.
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The question I have is how can we determine if your position in relation to the north star is based on a flat earth and refraction or a globe earth and refraction to determine if the claims that it's based entirely on a globe earth are supported or refuted by the evidence. As of now I don't know.
The fact that the North star has a certain altitude is merely an observation. You measure it in angles. How would that tell you anything about the shape of the earth?
I tend to agree after seeing the videos about it but it's a common belief that latitude is based on the earth being a sphere instead of based on how far you are away from the north star. What test could we devise to determine if this is true or not.
I can stand at a certain point in my garden and measure the angular height of a tree at the other end of the garden. If I stand closer to the tree, the angle gets larger, further away and the angle gets smaller. What if anything I can deduce about the shape of the earth from this I really don't know and I don't know what additional test I could make to my tree measurement to determine the shape of the earth either.
If the tree was 323 light-years tall, then you could determine the shape by plotting the angles easily enough, just like we do with the North Star.
For a normal sized tree, if you get far enough away from it then the angle is going to behave differently if you are on a plane or a sphere. It will get lower faster on a sphere and eventually vanish. On a flat plane the angle will change rapidly when close, but far away it will slow down until it hardly changes at all.
Either way, if you plot the angle and distance measurements, they are only going to fit one shape.
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The question I have is how can we determine if your position in relation to the north star is based on a flat earth and refraction or a globe earth and refraction to determine if the claims that it's based entirely on a globe earth are supported or refuted by the evidence. As of now I don't know.
The fact that the North star has a certain altitude is merely an observation. You measure it in angles. How would that tell you anything about the shape of the earth?
I tend to agree after seeing the videos about it but it's a common belief that latitude is based on the earth being a sphere instead of based on how far you are away from the north star. What test could we devise to determine if this is true or not.
I can stand at a certain point in my garden and measure the angular height of a tree at the other end of the garden. If I stand closer to the tree, the angle gets larger, further away and the angle gets smaller. What if anything I can deduce about the shape of the earth from this I really don't know and I don't know what additional test I could make to my tree measurement to determine the shape of the earth either.
If the tree was 323 light-years tall, then you could determine the shape by plotting the angles easily enough, just like we do with the North Star.
For a normal sized tree, if you get far enough away from it then the angle is going to behave differently if you are on a plane or a sphere. It will get lower faster on a sphere and eventually vanish. On a flat plane the angle will change rapidly when close, but far away it will slow down until it hardly changes at all.
Either way, if you plot the angle and distance measurements, they are only going to fit one shape.
The tree is quite tall, it's a Scots pine. I'm trying to imagine it 323 light-years tall, that would be something to behold!
Just to take a step back here and explain the thinking behind my original post, I've been trying to separate measuring the angle from measuring distances, because the minute we introduce distance, we get into shape and then bendy light/refraction, general relativity, non-euclidean geometries, interactive scale maps and all that stuff which goes around and around and gets nowhere with no agreement at all. The discussions become polarised.
Since you can measure an angle and/or measure a span of time, without measuring any distances at all, I'm saying let's just do that. We end up with two angles, a latitude and a longitude. We know that these are useful for navigation on the earth, because they've been used for centuries (especially latitude which goes back much much further).
9th century Arab sailors were using a kamal to determine latitude for navigation even before compasses were available.
What I want to know from flat earthers then is why they think measuring latitude with a kamal back in the 9th century can be dismissed as irrelevant because it's based on a spherical earth. It isn't, it's just measuring an angle, why can't you measure an angle on a flat earth?
I'd have liked to include longitude as well, but because that's more complicated and wasn't reliably used until the 17th C, then I'm happy to leave that out of the discussion too.
Honestly I'm just trying to backtrack to find some common ground we can all agree on. Haven't really got anywhere so far though.
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9th century Arab sailors were using a kamal to determine latitude for navigation even before compasses were available.
What I want to know from flat earthers then is why they think measuring latitude with a kamal back in the 9th century can be dismissed as irrelevant because it's based on a spherical earth. It isn't, it's just measuring an angle, why can't you measure an angle on a flat earth?
I think it's more the modern longitude and latitude system which is considered based on a spherical earth vs ancient latitude only systems but i'm not sure. Once I saw the kamal video I was confused about what made the ancient latitude measurements were based on the spherical earth. Back then I was under the impression that most of the people thought the earth was flat.
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Why can we only balance eggs on their ends when it is a solstice? I need answers.
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Help, can any provide me with an answer to my friend who said " I left NY on a cruise ship and noticed as we sailed away the high rise buildings were disappearing gradually from the bottom and could only see the top floors. that proves the earth is round." I told him I would explain that the next time we meet. Would someone be kind enough to help. kind Regards, paul