The Flat Earth Society
Flat Earth Discussion Boards => Flat Earth Theory => Topic started by: edby on June 07, 2018, 09:41:45 AM
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Right, but in order to convert lat/lon differences into a straight line/great circle distance, one must first agree upon the shape of the Earth (you refer to that yourself as "knowing how far apart lat/lon points are"). Using it the way you propose would reduce your argument to "the Earth is round, therefore these are the distances, therefore the Earth is round"
This is an excellent formulation of what I call the circularity objection. You hear it many times from Flatearthers: the model RE is using to prove some point itself assumes an RE model, so the proof is circular, or question begging.
Now it’s true that if I worked out a distance between two lat/lon coordinates by using spherical assumptions, then used that distance to ‘prove’ RE, that would be highly question-begging.
But what if I work out the distance in another way? The original way that (short) distances were accurately worked out was by a chains, literally a chain of links spread out on the earth’s surface like a big tape measure.
First question in this debate: do we all accept that a measurement essentially like a big tape measure, perhaps suitably adjusted (I will come on to that later) is indifferent to the shape of the earth, and distances based on this are not circular?
If not, what other measure of distance would you use? Car odometers are actually the same form of measurement – a bit like rolling up the tape measure for every turn of the wheel and reusing it.
(https://upload.wikimedia.org/wikipedia/commons/3/31/Gunter%27s_chain_at_Campus_Martius_Museum.JPG)
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In principle you only need a few short distance calibration measurements. You choose random spots around the earth, measure a fixed distance and determine the longitude/latitude coordinates of the start and end point. Then, by interpolation you can calibrate the whole longitude/latitude grid. Of course, you have to assume that the grid is regular, without discontinuities, arbitrary contractions or elongations. But beyond this, the method is independent of the supposed underlying shape.
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In principle you only need a few short distance calibration measurements. You choose random spots around the earth, measure a fixed distance and determine the longitude/latitude coordinates of the start and end point. Then, by interpolation you can calibrate the whole longitude/latitude grid. Of course, you have to assume that the grid is regular, without discontinuities, arbitrary contractions or elongations. But beyond this, the method is independent of the supposed underlying shape.
Thanks, but you are going too fast! Forget long and lat, start with versions of the 'tape measure'. Is there general agreement that this is an appropriate and independent form of distance measurement? I am working through the records of the Great Indian Survey, where there is a whole chapter on how the temperature affects the length of the chain.
It could be reasonably objected that there is no form of accurate 'tape' measurement at all. Perhaps the tape arbitrarily changes its length for no assignable reason.
So I want to proceed in very short steps of reasoning, aiming to reach agreement at each stage. Thanks.
[edit] Incidentally there was a big debate at the beginning of the India Survey between advocates of astronomical methods and geodesic methods. Colonel Lambton's arguments won the day.
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I don't appreciate you misrepresenting my position like this. I made it abundantly clear in the discussion you're referencing that I'm not making a case for or against either model, merely pointing out that that specific methodology (using GPS to determine distances) is not admissible. I also pointed out that yes, other means may exist, but that simply renders the use of GPS redundant.
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I don't appreciate you misrepresenting my position like this. I made it abundantly clear in the discussion you're referencing that I'm not making a case for or against either model, merely pointing out that that specific methodology (using GPS to determine distances) is not admissible. I also pointed out that yes, other means may exist, but that simply renders the use of GPS redundant.
I did not misrepresent your position. I quoted your exact remark, then said it was an example of 'circularity objection'. Indeed your reply here confirms that!
I agree you are not making a case for or against either model. My point is that your objection relied on the charge of circularity, and actually your objection was correct, assuming no other way of measuring distance.
And what is your reply to the "First question in this debate"? Do you accept that a measurement essentially like a big tape measure, perhaps suitably adjusted, is indifferent to the shape of the earth, and distances based on this do not depend on circularity?
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Accuracy is always relative. If you put the chain on the ground and the ground is not flat, this will give you an error if you later compare this with the coordinates.
You could use a laser and measure the direct distance between two points at a given height above the ground. But of course there is some inherent error due to the spherical shape of the earth that is more and more significant the larger the distance is.
Before you decide on the method, you should ask yourself, what level of accuracy do you need? If you want to measure the length of the equator or the distance between two cities on different continents, an error of the order of a kilometer would be acceptable. If you buy piece of land, you may want to know its size on the scale of few centimeter.
If you look at the typically discussed conceptual flat-earth earth maps, you have obvious discrepancies in the order of several hundreds up to several thousands of kilometers in some regions. E.g. in the southern hemisphere of the prototypical monoplar map. Therefor I would say, to rule out any proposed map by finding at least two points where the distance does not fit, you only need an accuracy of a kilometer or so.
Go to Australia, drive 100 km with your car, measure the coordinates and you have a more accurate calibration as you would need to show that a coordinate mapping for a monopolar map in the southern hemisphere cannot work.
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My point is that your objection relied on the charge of circularity, and actually your objection was correct, assuming no other way of measuring distance.
No, my objection is correct regardless of your assumptions. You can potentially use other means to get accurate distances. You can nonetheless not use GPS for this purpose.
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My point is that your objection relied on the charge of circularity, and actually your objection was correct, assuming no other way of measuring distance.
No, my objection is correct regardless of your assumptions. You can potentially use other means to get accurate distances. You can nonetheless not use GPS for this purpose.
So I said 'your objection was correct' and you replied 'no, my objection is correct'.
Anyway, set that aside. You agree that potentially we can use other means to get accurate distances, and that is fine. Anyone else?
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So I said 'your objection was correct'
You injected an assumption into it. I implore you to retract that for the sake of honesty.
My point is that your objection relied on the charge of circularity, and actually your objection was correct, assuming no other way of measuring distance.
No, my objection is correct regardless of your assumptions. You can potentially use other means to get accurate distances. You can nonetheless not use GPS for this purpose.
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So I said 'your objection was correct'
You injected an assumption into it. I implore you to retract that for the sake of honesty.
My point is that your objection relied on the charge of circularity, and actually your objection was correct, assuming no other way of measuring distance.
No, my objection is correct regardless of your assumptions. You can potentially use other means to get accurate distances. You can nonetheless not use GPS for this purpose.
How about, the objection is correct on the assumption that the person you are objecting to is assuming an RE model. Will that do?
[edit] "such as when that person is using GPS"
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Which is the original thread that the quote in the OP was taken from?
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How about, the objection is correct on the assumption that the person you are objecting to is assuming an RE model. Will that do?
That should be "always" when the shape of the Earth is what you're trying to establish.
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Which is the original thread that the quote in the OP was taken from?
You click on the link at the top of the quote.
Right, but in order to convert lat/lon differences into a straight line/great circle distance, one must first agree upon the shape of the Earth (you refer to that yourself as "knowing how far apart lat/lon points are"). Using it the way you propose would reduce your argument to "the Earth is round, therefore these are the distances, therefore the Earth is round"
It was from 'distance from Paris to London', since consigned to the outer darkness, but mostly intact.
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How about, the objection is correct on the assumption that the person you are objecting to is assuming an RE model. Will that do?
That should be "always" when the shape of the Earth is what you're trying to establish.
That wasn't what the OP said. It referred to any 'point' that RE is trying to establish. In this case it is distance. RE says the distance is x, the objector points out (possibly correctly) that the measurement of distance has depended on RE model.
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That wasn't what the OP said.
The OP is irrelevant here. The conversation from which you picked my quote took place after the OP had been moved to AR. It was in direct response to a post by AATW, and nothing else. I also clarified the conditions under which I said what I said.
Once again, I ask you not to misrepresent me. I clarified my position. Trying to tell me that I'm wrong about my own position is unlikely to help.
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That wasn't what the OP said.
The OP is irrelevant here. The conversation from which you picked my quote took place after the OP had been moved to AR. It was in direct response to a post by AATW, and nothing else. I also clarified the conditions under which I said what I said.
Once again, I ask you not to misrepresent me. I clarified my position. Trying to tell me that I'm wrong about my own position is unlikely to help.
Would it help if I removed your quote entirely, or we trashed the thread or started again? I am substantially agreeing with you that many appeals to the RE model themselves depend on the RE model, and the circularity objection applies. So I am really really really agreeing with you. I quoted you because I thought it was an excellent formulation of a commonly made objection. So I am agreeing with you, and I am complementing you. I don't see why you have a problem.
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Would it help if I removed your quote entirely, or we trashed the thread or started again?
Perhaps. I'm not sure why this thread is titled "the circularity objection" and why it focuses on my post if all you're doing is agreeing with me. It really sounds like you're trying to start a thread on how to measure distances (of which there have already been many)
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The mapping of the world in means of distances in kilometers on one hand, and the system of longitude/latitude on the other hand was done long before GPS was even invented. It's not recently that people in Australia know how far two cities there are apart from each other. The same for any other country in the world, north and south, it doesn't matter. The same with respect to coordinates. The whole system was introduced hundreds of years ago.
Therefor it is just known, how to calibrate a degree of longitude or latitude around the world.
You know the distance in coordinates and kilometers between LA and New York, and you know the distance between Paris and Berlin in coordinates and kilometers. And you know the distances between New York and Paris in coordinates, and from the other two known distances you can now conclude what is the distance between New York and Paris in kilometers. And then you can compare this to all possible maps that came up to your mind.
The same you can do with lots of other cities that are distributed around the world. And as far as I know, up to now no one found ever any contradiction assuming a globe earth, while in any up to now presented flat-earth conceptual map the contradictions in some areas are so obvious that anyone immediately will notice them.
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Would it help if I removed your quote entirely, or we trashed the thread or started again?
Perhaps. I'm not sure why this thread is titled "the circularity objection" and why it focuses on my post if all you're doing is agreeing with me. It really sounds like you're trying to start a thread on how to measure distances (of which there have already been many)
One of the core objections to FE involves the measurement of distance, which I am going to come on to. One of the core replies to that objection is that the measurement of distance (such as GPS) appeals to RE.
My purpose is to show that there are non-circular ways of establishing non-FE. Note my term 'non-FE'. Not-FE does not imply RE.
Perhaps I should have started the thread that way?
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My purpose is to show that there are non-circular ways of establishing non-FE. Note my term 'non-FE'. Not-FE does not imply RE.
Perhaps I should have started the thread that way?
Perhaps, though I don't see how that's in any way novel or controversial. I don't think anyone's denying that it's possible to argue for RET without resorting to circular logic.
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The mapping of the world in means of distances in kilometers on one hand, and the system of longitude/latitude on the other hand was done long before GPS was even invented. It's not recently that people in Australia know how far two cities there are apart from each other. The same for any other country in the world, north and south, it doesn't matter. The same with respect to coordinates. The whole system was introduced hundreds of years ago.
Therefor it is just known, how to calibrate a degree of longitude or latitude around the world.
Be careful - Pete objected before that we can't, in this forum, simply state 'it is known for 100 years that'. I hope I am not misquoting him.
Found it:
Not only are you misquoting Tom's claim in the thread's subject (and very obviously targeting him), the thread you've created consists of nothing but "You're wrong. Why are people still wrong?". As I said, you are welcome to discuss ideas in the upper, or individuals in CN/AR.
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I can sort of see where this thread might go, and what it might hope to show, but i dont want to jump ahead of the OP.
Apart from the Circularity objection, it also started out by trying to get some common ground on how to measure distances, that are distances irrespective of if the world is flat or round is that a fair comment?
However to do so we also have to get an agreement that a foot is indeed a foot, a fathom is a fathom, a metre is a metre, and so on, can we accept that they are, and they can be accepted as a unit of measure, that is not reliant upon the globular or planar nature of the world? If we cannot there is not a lot of hope for any debate going forward.
Can we agree that GPS is not required or relevant to the discussion, because of the huge volume of measurements taken place before the advent of GPS? We dont need GPS to calculate distance, so we should be able to carry on without it being a factor?
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I can sort of see where this thread might go, and what it might hope to show, but i dont want to jump ahead of the OP.
Apart from the Circularity objection, it also started out by trying to get some common ground on how to measure distances, that are distances irrespective of if the world is flat or round is that a fair comment?
However to do so we also have to get an agreement that a foot is indeed a foot, a fathom is a fathom, a metre is a metre, and so on, can we accept that they are, and they can be accepted as a unit of measure, that is not reliant upon the globular or planar nature of the world? If we cannot there is not a lot of hope for any debate going forward.
Can we agree that GPS is not required or relevant to the discussion, because of the huge volume of measurements taken place before the advent of GPS? We dont need GPS to calculate distance, so we should be able to carry on without it being a factor?
Yes to all of that. I have been researching how they actually did this long before GPS.
Pete seems to agree that there are in principle non-circular ways of establishing distance.
I would like other views from the FE side before we go any further, however.
If we cannot reach agreement, then we have what is called the 'nuclear position'. If the objection is that it is in principle impossible to measure distance at all, then that is that, end of argument.
Can we agree that GPS is not required or relevant to the discussion, because of the huge volume of measurements taken place before the advent of GPS? We dont need GPS to calculate distance, so we should be able to carry on without it being a factor?
And because those measurements relied entirely on a sophisticated version of the tape measure. More later.
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I also noted the picture at the beginning, (of a surveying chain) which is an old method of measuring distance, it was referred to in EnaG, so I would have thought there are no great objections to it, and I have seen comments on other threads where it was noted that the use of chains as a measure of distance would be acceptable, at least to some Fe proponents.
However we do need to get an agreement that an inch is reasonably well defined, as is a foot, because the chains refer to those units. Without an acceptance that they are the same unit irrespective of the shape of the earth, we will ultimately end up without any consensus or there will be a potential derailing of the thread on the definition of an inch or foot, and how it was defined.
I hope we can swiftly agree to such basic points, and get to the interesting debate.
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Inches, Feet and Yards are/were defined here, many years ago.
https://untappedcities.com/2013/02/05/london-trafalgar-square-standard-units/ (https://untappedcities.com/2013/02/05/london-trafalgar-square-standard-units/)
Is there any dispute over these as a basis of measurement?
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I also noted the picture at the beginning, (of a surveying chain) which is an old method of measuring distance, it was referred to in EnaG, so I would have thought there are no great objections to it, and I have seen comments on other threads where it was noted that the use of chains as a measure of distance would be acceptable, at least to some Fe proponents.
However we do need to get an agreement that an inch is reasonably well defined, as is a foot, because the chains refer to those units. Without an acceptance that they are the same unit irrespective of the shape of the earth, we will ultimately end up without any consensus or there will be a potential derailing of the thread on the definition of an inch or foot, and how it was defined.
I hope we can swiftly agree to such basic points, and get to the interesting debate.
This https://en.wikipedia.org/wiki/History_of_the_metre gives a history of how the metre was defined. But we should be able to agree in principle that if we take any rigid object, such as a platinum bar, at a certain temperature, and call its length 1 XXX, then whatever has the same length as it, has length of 1 XXX.
But people might still disagree with this. Suppose we calibrate a ruler to the 1 XXX rod, and go round measuring things. Perhaps the length of the ruler is constantly changing? How would we know?
(Actually, we would know if the lengths of the things we were measuring remained the same length. We could compare them with each other, and thus find out that the length of the ruler was changing relative to them. But a more sophisticated objection is that the lengths of all things are constantly changing, in proportion.)
Inches, Feet and Yards are/were defined here, many years ago.
https://untappedcities.com/2013/02/05/london-trafalgar-square-standard-units/ (https://untappedcities.com/2013/02/05/london-trafalgar-square-standard-units/)
Is there any dispute over these as a basis of measurement?
Yep, that kind of stuff. I still would like to see if FE supporters are agreed on that type of unsophisticated (but still accurate) method of measurement.
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You're getting too bogged down with units.
The units don't matter.
What matters is can we determine the distance in whatever unit been some far flung cities in a way that we can all agree that those are the true distances.
If you can do that you can then look at whether there is any way of arranging those cities on a flat map so that those distances are accurately represented.
If you can then it means the earth could be flat, if you can't then it's because your arrangement is a projection and the earth is actually another shape.
You might be able to work out what that shape is from the distances.
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You're getting too bogged down with units.
The units don't matter.
What matters is can we determine the distance in whatever unit been some far flung cities in a way that we can all agree that those are the true distances.
If you can do that you can then look at whether there is any way of arranging those cities on a flat map so that those distances are accurately represented.
If you can then it means the earth could be flat, if you can't then it's because your arrangement is a projection and the earth is actually another shape.
You might be able to work out what that shape is from the distances.
Not about units essentially, but measurement. You need a way to measure the length of something, right? So you need to express it in some unit. How else would you do it?
If you can do that you can then look at whether there is any way of arranging those cities on a flat map so that those distances are accurately represented.
You are jumping too far forward. I want to see if FE agrees
1. we can measure short distances (say 100m) accurately, and without circularity
2. we can measure much longer distances (say 5,000km) accurately, and without circularity
3. What this implies for shape of earth.
We have not reached (1) yet.
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If you can do that you can then look at whether there is any way of arranging those cities on a flat map so that those distances are accurately represented.
You are jumping too far forward. I want to see if FE agrees
1. we can measure short distances (say 100m) accurately, and without circularity
2. we can measure much longer distances (say 5,000km) accurately, and without circularity
3. What this implies for shape of earth.
We have not reached (1) yet.
I think, first you have to find out how accurate you can measure longitude and latitude coordinates. Then you know the minimum distance over which you would have to do a length measurement with equivalent accuracy.
Then you have to look for the systematic error, comparing a flat surface and spherical surface on that length scale. Then you know how significant your results are.
Let's say you can measure 100m with an accuracy of 1m. That's one percentage of error. And on the same distance you can measure the degrees latitude/longitude with 1% accuracy. 10000km you can then measure with an accuracy of 10km if you know the corresponding coordinates. Discrepancies for flat-earth maps can reach errors in the order of 50%. That's far beyond your accuracy...
And I guess no one can deny that we can measure 100m with an accuracy of 1m. But I have no feeling about how accurate you can measure degrees of longitude/latitude.
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If you can do that you can then look at whether there is any way of arranging those cities on a flat map so that those distances are accurately represented.
You are jumping too far forward. I want to see if FE agrees
1. we can measure short distances (say 100m) accurately, and without circularity
2. we can measure much longer distances (say 5,000km) accurately, and without circularity
3. What this implies for shape of earth.
We have not reached (1) yet.
I think, first you have to find out how accurate you can measure longitude and latitude coordinates. Then you know the minimum distance over which you would have to do a length measurement with equivalent accuracy.
Then you have to look for the systematic error, comparing a flat surface and spherical surface on that length scale. Then you know how significant your results are.
Let's say you can measure 100m with an accuracy of 1m. That's one percentage of error. And on the same distance you can measure the degrees latitude/longitude with 1% accuracy. 10000km you can then measure with an accuracy of 10km if you know the corresponding coordinates. Discrepancies for flat-earth maps can reach errors in the order of 50%. That's far beyond your accuracy...
And I guess no one can deny that we can measure 100m with an accuracy of 1m. But I have no feeling about how accurate you can measure degrees of longitude/latitude.
You don't in fact have to appeal to long and lat in order to map very large areas of the earth's surface. Then you can of course calibrate one against the other, as you rightly mention.
However we are still waiting for the views of FE supporters on whether we can measure short distances by 'tape measure' type methods.
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The advantage of that method is, that you have not to measure every single distance, especially across large areas of water like oceans. And I'm not aware of severe objections by flat earth believers on the longitude/latitude system as such. I have the impression they usually accept that coordinates of places like London or Sydney, etc. are indeed known or which places are on the equator and so on.
The grid of coordinates seems to be a common starting point. The disagreement is on the metric of this grid. To get this metric, its easier to go for short distances, because then the influence of the assumed shape is much smaller.
It doesn't matter if you measure 100m on a sphere as big as the earth or on a flat surface. On this length scale such a sphere can be seen as locally flat.
And you can do this in a direct measurement, with a ruler, with a laser, with a car whatever you have. But if you want to make a direct measurement on a scale of thousands of kilometers, it's getting more and more difficult. Already the definition of a straight line as shortest distance is not equivalent on a sphere and on a plane on this scale.
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While we are waiting, and that may be for some time, let’s move on to the next part of the argument.
See below for part of the Great Indian Survey, this part performed about 1834, therefore well before GPS. The method was as follows. Establish two ‘baselines’, one at Dehra Doon (now Dehradun), the other at Sironj. The baseline is measured using the chain type tape measure, but with sophisticated and then state of the art compensation for thermal expansion. Drive a pillar into the ground, mark an arrow on it, then roll out the chain to full length and construct a second pillar, with an arrow marking the end point of the chain. There was all sorts of stuff they did to ensure the measurement was accurate.
Once the baseline is established between points A and B, find a third point C, measure the two angles BAC and ABC using a theodolite. From this it follows from Euclidean geometry (which is the geometry of a flat plane) that we can calculate the distances AC and BC.
Perhaps FE supporters might disagree with Euclid at this point, but that doesn’t matter. It least we know where they disagree.
Knowing all three distances we can then find a fourth point, find the two relevant angles, then work out two new distances and so on. The point is to avoid the laborious tape measure method and extensive labour.
You note from the picture that they worked their way down from Dehradun to Sironj by this method, distance about 500 miles. Two of the final triangulation points were the Sironj baseline, so they could compare the tape measure method with the triangulation method, including any accumulated errors. Supposedly the error was 7 inches in 500 miles, or 0.011%. That’s not bad, in my view.
Furthermore you can see they had another three sets of triangulation systems. In this way, over about 60 years, they covered the whole of India.
We still haven’t mentioned latitude and longitude (Hexagon please take note), nor the shape of the earth. Nothing but painstaking tape measure and angular measurement, with unbelievable accuracy for the time, in my view.
(http://www.logicmuseum.com/w/images/6/63/Dehradun_sironj.jpg)
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The advantage of that method is, that you have not to measure every single distance, especially across large areas of water like oceans. And I'm not aware of severe objections by flat earth believers on the longitude/latitude system as such. I have the impression they usually accept that coordinates of places like London or Sydney, etc. are indeed known or which places are on the equator and so on.
They don't disagree with longitude/latitude as far as it measures positions. They object to inferring a distance from those positions, o/a of the circularity.
That is the whole point of my describing in detail how they measured distance in 1835 without using long/lat.
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The advantage of that method is, that you have not to measure every single distance, especially across large areas of water like oceans. And I'm not aware of severe objections by flat earth believers on the longitude/latitude system as such. I have the impression they usually accept that coordinates of places like London or Sydney, etc. are indeed known or which places are on the equator and so on.
They don't disagree with longitude/latitude as far as it measures positions. They object to inferring a distance from those positions, o/a of the circularity.
That is the whole point of my describing in detail how they measured distance in 1835 without using long/lat.
Yes, that's what I meant with metric. It gives you coordinates, but no distances. To get distances you have to assign a metric.
In the map you showed, I assume, the terrain was not flat. Is the apparent length of the edges of the triangles a measure of that? Or in other words, they always used chains of constant length but the effective distance on the map varied due to hills and valleys?
And how did they placed the cities outside the area covered by the triangles in to relation with each other? How did they defined the starting point? I assume that they did this with the help of longitude and latitude coordinates?
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And how did they placed the cities outside the area covered by the triangles in to relation with each other? How did they defined the starting point? I assume that they did this with the help of longitude and latitude coordinates?
The purpose was to establish an accurate 'skeleton', on which flesh could later be covered. This was the principle of all surveying and map making until very recently.
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And how did they placed the cities outside the area covered by the triangles in to relation with each other? How did they defined the starting point? I assume that they did this with the help of longitude and latitude coordinates?
The purpose was to establish an accurate 'skeleton', on which flesh could later be covered. This was the principle of all surveying and map making until very recently.
Which is why most hills and high points in the uk have “trig” points on the top. They can be seen from other trig points and the distance worked out between them. This distance between them is based on the chains and the solid measuring tape and the shape of the earth has no influence on the distances.
Can we hope that this method might be accepted and agreed upon by all to be independant of the shape of the earth?
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Can we hope that this method might be accepted and agreed upon by all to be independant of the shape of the earth?
Not entirely. If you take this chains of equal length and like in the map above build hexagons consisting of equilateral triangles out of them, this will work only on a perfectly flat surface. On a sphere this will not fit together. How do you distinguish now a shallow hill on a flat-earth from a "flat" part of a spherical earth? Or take a shallow valley on spherical earth. In this case the chains would fit together as a perfectly regular hexagon. Same for a flat area on a flat earth.
In end the spherical shape gives a slit offset for all the measurements, that you have to take into account depending on the accuracy you want to achieve.
Edit: See also the Wikipedia article about the great trigonometrical survey of India. It's not explained in detail, but the problem is obvious:
https://en.wikipedia.org/wiki/Great_Trigonometrical_Survey#Correcting_deviations
Same for the Principal Triangulation of Great Britain:
https://en.wikipedia.org/wiki/Principal_Triangulation_of_Great_Britain#Corrections
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On a sphere this will not fit together.
So the Flat Earth objection would be that this method is inherently flawed, because of distortions produced by the round shape of the earth? Sounds OK.
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On a sphere this will not fit together.
So the Flat Earth objection would be that this method is inherently flawed, because of distortions produced by the round shape of the earth? Sounds OK.
Yes, because at some point you have to take the spherical shape into account.
But, as I explained above, this are tiny corrections compared to the distortions you have in any imaginable flat-earth map. E.g. look at the prototypical monopolar map and check the size of Australia. The width is two to three times too large. You can't explain this with systematic measurement errors that would be orders of magnitude smaller.
In the end, both things, the corrections surveyors have to take into account and the impossibility of a correctly scaled flat-earth map, have the same origin, the incompatibility of Euclidean and spherical geometry.
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If you can quantify those corrections, say to a percentage, 0.1% for example, then it might be reasonable to suggest that the distances obtained were within that accuracy if they were on a flat earth, or a globe earth yes?
It would be helpful if there was an agreement from both sides of the debate, trying to find some common ground.
If not the subject is not going to progress, and there is not debate.
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I will repeat. So the killer objection from the Flat Earth side is: the method is flawed on account of the earth being a spheroid??
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I will repeat. So the killer objection from the Flat Earth side is: the method is flawed on account of the earth being a spheroid??
I wouldn’t like to assume what objections the Re supporters might put up, but that is one of the objections that i have seen used a number of times.
If the method/results that you are trying to show are dependent on the world being spherical, then the results must be flawed, and therefore are suspect, and not admissible.
However i may be wrong, and as we have not seen many RE supporters on this thread for a while, it is hard to guess what the objection might be. But I would suggest that in order to get any agreement then it would be important to show that the outcome in not reliant upon the earth being a globe in the first place.
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I will repeat. So the killer objection from the Flat Earth side is: the method is flawed on account of the earth being a spheroid??
I wouldn’t like to assume what objections the Re supporters might put up, but that is one of the objections that i have seen used a number of times.
If the method/results that you are trying to show are dependent on the world being spherical, then the results must be flawed, and therefore are suspect, and not admissible.
However i may be wrong, and as we have not seen many RE supporters on this thread for a while, it is hard to guess what the objection might be. But I would suggest that in order to get any agreement then it would be important to show that the outcome in not reliant upon the earth being a globe in the first place.
I think this confuses two things. (1) The result depends or is reliant on the assumption that the earth is spheroid (2) The results are what they are because the earth is spheroid.
Suppose I take a large beach ball, and mark an ‘equator’ and a ‘north pole’ on it. Then I draw two ‘lines of longitude’ from the pole to the equator line. I measure the angle at the pole, and it is 15 degrees. Then I measure the angles at the equator and find that they are both 90 degrees. So to my astonishment the three angles add up to more than 180 degrees! Shock!
The ‘flat beach ball’ supporter beside me leaps up and down with joy. This proves that my measurement was incorrect or contained an error etc because it ‘was reliant upon’ the assumption that the beach ball was a ball. So I have proved nothing!
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If the method of measuring distance on the earth requires that the earth be a globe, then that method will be rejected as being flawed, as the earth is not a globe (as shown by EnaG)
It’s hard to find any method which does not have an element of the globe nature of the earth as part of its method, or an adjustment due to the earths shape.
However i think quantifying the adjustment, and therefore the final differences might help
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The problem is not to measure a given distance between two points, the problem is to give this measurement a meaning in terms mapping.
Take this example. You measure the distance between two points A and B with a chain. The area between the two points is flat, in the sense that every part of the chain is always perpendicular to a plumb bop.
Now you take a laser at point A at height h above the ground. And you measure the distance to a correspondent point at height h above the ground at B.
On a flat earth both measurements would give the same result. On a spherical earth not. And the discrepancy increases with distance and height.
Now assume you go with your chain to another place, that is equally flat, but about h higher than the first area. Now you will get again a different result on globe earth but not on flat-earth.
You see, on a flat-earth surveying is quite simple, because a flat-earth follows Euclidean geometry and all our measurement methods are Euclidean. They measure straight lines or assume to measure straight lines.
But a globe follows spherical geometry, therefor you have to correct your measurements to account for that.
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If the method of measuring distance on the earth requires that the earth be a globe, then that method will be rejected as being flawed, as the earth is not a globe (as shown by EnaG)
..but if more than one method is used, and the results from each tally with each other, within reasonable limits of error, and they are all based on globe mechanics .....
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If the method of measuring distance on the earth requires that the earth be a globe, then that method will be rejected as being flawed, as the earth is not a globe (as shown by EnaG)
It’s hard to find any method which does not have an element of the globe nature of the earth as part of its method, or an adjustment due to the earths shape.
However i think quantifying the adjustment, and therefore the final differences might help
But the flaw is in the end not a flaw, it's the solution. All surveys took the shape of the earth into account, the result is a perfectly working map of the world. If they would have taken a flat-earth into account (meaning no spherical corrections), the resulting map would be full of inconsistency and contradictions.
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I know all that, and i agree with all you say, i am only playing devils advocate a bit here, and trying to think of the objections that may be raised.
As they will.
If there has to be an adjustment made to account for the spherical earth, I agree with it. It will make the spherical earth map more accurate, and confirm our knowledge of the round earth, but I am not the one you need to convince!
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But a globe follows spherical geometry, therefor you have to correct your measurements to account for that.
No you don't have to correct your measurements in any way.
I agree that if we want to represent these measurements on a flat surface, we will have to 'correct' them. But the measurements in themselves are perfectly correct.
There seems to be a logical confusion here between
(A) We get result y on the assumption that x is true, therefore x is true
(B) We get result y because x is true, therefore x is true
(A) is clearly invalid, (B) is not.
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But the flaw is in the end not a flaw, it's the solution. All surveys took the shape of the earth into account, the result is a perfectly working map of the world. If they would have taken a flat-earth into account (meaning no spherical corrections), the resulting map would be full of inconsistency and contradictions.
Agree, although it wasn't a flaw in the first place. The measurements were correct all along.
If there has to be an adjustment made to account for the spherical earth, I agree with it. It will make the spherical earth map more accurate, and confirm our knowledge of the round earth, but I am not the one you need to convince!
No adjustment required. The measurements are what they are. They have to be 'adjusted' in order to represent them on a flat map, of course.
But a globe follows spherical geometry, therefor you have to correct your measurements to account for that.
Again, no 'correction' needed, unless the results need to be interpreted on a flat surface.
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But the flaw is in the end not a flaw, it's the solution. All surveys took the shape of the earth into account, the result is a perfectly working map of the world. If they would have taken a flat-earth into account (meaning no spherical corrections), the resulting map would be full of inconsistency and contradictions.
Agree, although it wasn't a flaw in the first place. The measurements were correct all along.
If there has to be an adjustment made to account for the spherical earth, I agree with it. It will make the spherical earth map more accurate, and confirm our knowledge of the round earth, but I am not the one you need to convince!
No adjustment required. The measurements are what they are. They have to be 'adjusted' in order to represent them on a flat map, of course.
But a globe follows spherical geometry, therefor you have to correct your measurements to account for that.
Again, no 'correction' needed, unless the results need to be interpreted on a flat surface.
I partly disagree. But maybe only, because for me some words have a slightly different meaning.
For me the single measurements as such are obviously correct. If I measure 100m, then this are 100m within the accuracy of the method applied. There is no doubt.
But as soon as you try to combine all your single measurements to a map, you need corrections, if the earth is spherical. It's triangulation, and the angles of triangles only sum up to 180° if the earth is flat.
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But as soon as you try to combine all your single measurements to a map, you need corrections, if the earth is spherical. It's triangulation, and the angles of triangles only sum up to 180° if the earth is flat.
If you combine them onto a spherical map, what's the problem? A map doesn't have to be flat.
My point is that there is no substantive inaccuracy in the measurements. They will fit perfectly on a spheroid.
Btw the debate from the 18th century onwards was not whether the earth was spherical, that had been known for a long time. The question was whether a line drawn around the poles would be 'longer' than a line drawn around the equator.
The Indian surveyors understood this well, and part of their work was to understand how far the earth differed from a perfect sphere.
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I know all that, and i agree with all you say, i am only playing devils advocate a bit here, and trying to think of the objections that may be raised.
As they will.
If there has to be an adjustment made to account for the spherical earth, I agree with it. It will make the spherical earth map more accurate, and confirm our knowledge of the round earth, but I am not the one you need to convince!
I know, the usual objection is, that you take a round earth into account and therefor you get nice globe. But this objection is wrong, you only get a nice globe, because your measurements were done on a globe. If the earth would be flat and you would assume a globe you would end up with a completely distorted globe.
Its the inverse problem the flat-earth believers have if they try to construct a flat map...
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But as soon as you try to combine all your single measurements to a map, you need corrections, if the earth is spherical. It's triangulation, and the angles of triangles only sum up to 180° if the earth is flat.
If you combine them onto a spherical map, what's the problem? A map doesn't have to be flat.
Yes, if you directly project the measurements onto a model of the globe earth, then it will directly fit. But flat-earthers are right if they say, no one is carrying around globes for navigation, everyone uses flat maps.
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Yes, if you directly project the measurements onto a model of the globe earth, then it will directly fit. But flat-earthers are right if they say, no one is carrying around globes for navigation, everyone uses flat maps.
But they would have to concede the flat maps have errors! But the Flat earthers deny there are errors.
If the earth would be flat and you would assume a globe you would end up with a completely distorted globe.
The ‘tape measurement’ system does not assume a globe.
If we started with Lat/Lon coordinates and inferred a distance from that, assuming a spherical surface, then that would be ‘assuming a globe’.
I don’t know if you are confused yourself, or whether you are trying to represent the arguments of a person who is deeply confused!
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But this objection is wrong [according to FE], you only get a nice globe, because your measurements were done on a globe.
But if it’s ‘because’ rather than ‘assuming that’, then FE position collapses.
[edit]Put it another way:
FE: You are wrong because you have assumed that the earth is a globe.
FE: You are wrong because the earth is a globe.
See the difference?
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Yes, if you directly project the measurements onto a model of the globe earth, then it will directly fit. But flat-earthers are right if they say, no one is carrying around globes for navigation, everyone uses flat maps.
But they would have to concede the flat maps have errors! But the Flat earthers deny there are errors.
If the earth would be flat and you would assume a globe you would end up with a completely distorted globe.
The ‘tape measurement’ system does not assume a globe.
If we started with Lat/Lon coordinates and inferred a distance from that, assuming a spherical surface, then that would be ‘assuming a globe’.
I don’t know if you are confused yourself, or whether you are trying to represent the arguments of a person who is deeply confused!
It assumes a globe earth in the moment you transfer your data on a map.
It's easy to see. Let's assume two groups of surveyors are starting at the same point. And they do their triangulation measurements along two different directions. And the angle between the two directions is 60°. Now the proceed like this for 1000km. After that both change their directions by 60°. On a flat earth they would now meet after 500km under an angle of 0° degree. And all the points they measured would fit together to a nice triangle each side 1000km long, all angles 60°.
And on a globe?
They would first proceed along two great circles that intersect at the starting point under an angle of 60°. After 1000km they would change their direction again by 60° to approach each other. But are they now following the same great circle? No, at a distance unequal to 500km they would meet under an angle unequal to 0°, because they are following two different great circles. To meet in a straight line on the same great circle, they would have to turn by a bit more than 60°. But anyway, they would not meet after 500 km, because also the initial 60° angle was wrong.
You see, in the whole procedure of large scale mapping you have to take into account, what is the shape of the underlying surface. Only on small scales you can neglect it.
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But this objection is wrong [according to FE], you only get a nice globe, because your measurements were done on a globe.
But if it’s ‘because’ rather than ‘assuming that’, then FE position collapses.
[edit]Put it another way:
FE: You are wrong because you have assumed that the earth is a globe.
FE: You are wrong because the earth is a globe.
See the difference?
Yes, that's my point. The objection they have, is a pseudo argument.
if you're dealing with sphere, its not a problem to take this into account, it's a must. While on a flat-earth, it would be a must to take a plane into account.
The geometry you use, must be the one of the space you're dealing with.
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It assumes a globe earth in the moment you transfer your data on a map.
I wonder if this is an English language problem. Do you mean that it implies a globe earth in the moment you transfer your data on a map?
English 'assumes' and 'implies' have radically different meanings.
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It assumes a globe earth in the moment you transfer your data on a map.
I wonder if this is an English language problem. Do you mean that it implies a globe earth in the moment you transfer your data on a map?
English 'assumes' and 'implies' have radically different meanings.
Possible, I'm not a native speaker...
I wanted to say, that it will not fit together to a nice map if just take your raw data and you try to draw a 2D map out of them. You have to do a projection like any cartographer has to do. You have to adjust the measured angles and/or distances.