THE EARTH IS FLAT ALRIGHT, BUT IT IS NOT A DISK!!
This was part of my conversion process to the understanding that the earth is both flat, and a concave sphere:
If the earth then is not a flat disk, and not a convex sphere why does it have distances that appear to be spherical? I then looked at possible explanations for alternate shapes. The
lambert azimuthal equal-area projection would explain the distances found in the southern hemisphere, but it does not fit the pacific ocean.
I then stumbled across
this thread on the Flat Earth forum, “Impossible geometric requirements for a flat earth.”
Levi Dettwyler
It would seem to me that there simply can't exist any model for a flat earth that would avoid the problems of not stretching the continents / oceans so much that it would be noticeable (travel times and distances would be all out of whack), significantly interfering with routes that RE people calculate based on a RE (the differing geometry and implications for angles on a sphere and a flat plane), and having airplanes regularly flying off the edge of the earth. Any map of a flat earth must avoid all three of these things, and possibly more that I haven't thought of. It's simply not possible for any such configuration to exist.
If you make Antarctica a wall of ice about the perimeter, suddenly travel times from South America to Africa increase 2-3 fold from what a RE person would expect (compare the circumferences at the south ends of a round earth and a flat earth map like the one on the wiki). If you go with this sort of map, suddenly all flights from Hawaii to China go missing, and then some. It seems quite impossible to come up with any sort of flat earth that would not run into at least one of those problems. By avoiding one of them, you exacerbate the other, and vice-versa.
In other words, in order for a flat earth to be plausible in today's society, you can't split apart continents in ways that would cause a normal RE-based flight path to go off the edge, NOR can you skew the continents such that the sizes and separation between the continents would cause significant ETA discrepancies for planes, boats, and cars (remember, the rest of the world thinks the earth is round). The map currently on the wiki and the one I linked to here both fail to meet all of these requirements, and are thus in essence complete failures and wholly implausible.
There's the slice from pole-to-pole method which creates huge problems with airplanes flying off the edge of the earth, and then there's the open up like an orange method, which creates huge problems with the distance between places and the time needed to get there. People (specifically, airlines; you know, the ones paying for every mile of commercial airplane flight?) would notice almost immediately either-way. We have not seen any such reactions on the scale we would expect to find them. Therefore, the earth should be round.
The foundation of this argument is essentially based in the fact that a sphere and a flat plane have very different geometric properties apparent to anything projected onto their surfaces. A sphere is continuous (you can never walk off the "edge"), and can't be lain flat without stretching and compressing certain areas. You can prove that a sphere has geometries incompatible with a flat plane by drawing triangles on each. On a sphere, you can draw a triangle with three 90º angles. On a flat plane, the best you can get is three 60º angles. Attempting to transfer a triangle from a sphere to a flat plane would cause substantial warping and skewing, and vice-versa.
I was actually very surprised that nothing about even something as simple as planes flying off the edge of the earth was brought up in the wiki or the FAQs.
Levi Dettwyler
Quote from: sceptimatic on April 04, 2013, 09:17:15 AM
No planes would ever get near an edge to fall off and no planes would be silly enough to be going that way anyway as they would simply freeze up and fall out of the sky.
You completely missed the point. Read the first post again (all of it; yes, that includes clicking on the link and looking at the map!).
Or, alternatively, keeping with the tradition of the flat earth society to use philosophy and logic to expose the reality of the natural world, here's a logical breakdown (a rough proof) demonstrating in two ways that the earth is not flat:
Axiom 1: Most people think the earth is a sphere.
Axiom 2: People that think the earth is a sphere plan navigation as if the earth is a sphere.
Axiom 3: A flat earth has a definite edge.
Axiom 4: A sphere has no edge or edges.
Axiom 5: Any edge that intersects the flight plan of a plane will cause that plane to not complete its flight as planned.
Axiom 6: Significant deviations from observed reality and expected reality are usually noticed and popularized.
Lemma 1: Spherical geometries and flat planar geometries are incompatible with one-another, and produce significant perturbations when projecting the surface of one onto the other. This can be proven by comparing angles of equilateral triangles.
Assume the earth is flat. Based on Axioms 1 and 2, it follows that most people plan navigation as if the earth is a sphere. Since spheres have no edges, it follows that most people plan navigation as if the earth does not have edges. Since we assume the earth is flat, the earth has a definite edge.
If (Case A) the earth is split vertically between continents, it follows that there exist many flight plans that intersect the edge of the earth. Thus, it is reasonable to conclude that modern air travel would not be possible, as a huge number of flights would not make it to their destinations as planned (plus the pilot and everyone on the plane would clearly see the edge of the earth and report it). Additionally, by Axiom 6, these deviations should be well-known and documented (in other words, it should be well-known that if you want to fly between continent A and continent B, where A and B are separated on a round earth map by the edge of the real flat earth, you will not be able to make such a flight as planned; this website shows that flights happen between continents all the time, so this is being tested every single day).
Otherwise (Case B), if the earth is split at either pole, it follows by simple geometry that land near the center of the flat earth and near the edge of the flat earth would deviate significantly from what would be expected if the earth was a sphere. Thus, since most people plan navigation as if the earth is a sphere, it is trivial to see that travel times, distances, and costs would deviate significantly from expected values for much of the earth's area. By Axiom 6, such deviations should be well-known and documented.
Since the deviations described in Case A are not well-known or documented, it follows that Case A is false. Likewise, since the deviations described in Case B are not well-known or documented, it follows that Case B is false. Thus, a flat earth cannot be split at either pole, nor can it be split vertically between the continents. Assuming there are no other sensible ways to split a sphere (along the equator doesn't work, since that would divide the continents in half!), it follows that there do not exist any way of the known arrangement of continents being represented on a flat earth. Therefore, the earth is not flat.
TL;DR: If the earth has an edge between continents, then a huge number of people would know about it, since lots of flights take place between continents. If not, then you're skewing the continents too much for it to have gone unnoticed for so long.
Another way to demonstrate that the earth is not flat is through Lemma 1. From Axioms 1 and 6, it follows that the expected arrangement of continents can be non-disruptively projected onto the surface of a sphere. From Lemma 1, it follows that the expected arrangement of continents cannot be non-disruptively projected onto the surface of a flat plane. It follows from Axiom 6 that the earth is not flat.
TL;DR: Geometry shows that it is impossible to draw a flat-earth map that does not misrepresent the observed and expected sizes of and distances between continents.
Levi Dettwyler
Note to flat-earth believers that are unfamiliar with these types of arguments: an "Axiom" is something that you assume to be true. The argument doesn't work if you can demonstrate a critical axiom to be false, but with the axioms I've chosen, that is going to be very hard to do. A "Lemma" is like a smaller argument that is easy to demonstrate the truthfulness of (slight abuse of notation here; don't kill me). In order to address my argument, you have to either demonstrate that one of my axioms is misguided OR that I made a logical jump that doesn't make sense, in which case, you have to quote the jump I made and say why A does not necessarily imply B, where A is the "if" part and B is the "then" part, e.g.:
Since A, B.
If A then B.
Because of A, it follows that B.
Note that in the above post, I gave two different arguments.
Homesick Martian
100 years ago a german mathematician developed a geometry that allows a "flat" earth. He described the surface of earth as something he called a "total plane",having no edges, no center, and yet no curvature. I recently tried to read his book. Very heavy stuff.
Levi Dettwyler
That would seem to contradict Lemma 1, unless he's using non-euclidean geometry, in which case it's irrelevant, since my argument assumes the validity of euclidean geometry for a problem like this. If you decide to reject euclidean geometry for this problem, then it doesn't really matter, since pretty much everything goes out the window at that point, and we're left floundering about with the problem of whether or not the people making these sorts of measurements are lying to us or not. If you accept the validity of euclidean geometry for this problem, then my arguments should hold, unless I made a legitimate error somewhere or was just lazy in explaining it.
Homesick Martian
The guy I'm talking about rejects Euclidian geometry, because it imples the notion of infinity, which, according to him, is self-contradictory. He tries to prove, that only Riemann's geometry is real, because it is the only geometry, where infinities do not occur. If he is right, you made a flaw by "just assuming the validity of Euclidian geometry". But that's not the view of the common flat earther. You prefer the easy prey.
Levi Dettwyler
Well, like I said, if someone's going to reject euclidean geometry, then there isn't really much I can do for them, since pretty much anything is possible at that point, so it isn't really useful. We observe that our everyday lives comply with what euclidean geometry says we should observe, so it isn't that much of a jump to induct that it should be valid for discussing the shape of the earth (or at least, less of a jump than using any other geometric framework without substantial evidence).
Levi Dettwyler
Wait, I'm a moron. It doesn't matter whether or not they "accept" euclidean geometry, because they can just prove it to themselves. Take a ball, and have it represent the earth. Draw a line from the north pole straight down to the equator, then another one 1/4th of the way along the equator, and then straight back up to the north pole. It's a triangle with three 90º angles! Next they realize that this simply can't be drawn on a flat piece of paper. Now just scale everything up by about 100 million, and the same principle applies to the earth.
Homesick Martian
I should remind you here, that I'm not talking about a view anyone holds on this forum, but about a book I'm currently reading written by a German mathematician in the 20s, and I myself haven't made my mind up how much of a crank he was (is this good English?). It is, anyway, the most interesting flat earth theory I've encountered so far.
Ernst Barthel?
Yep.
Homesick Martian
All these problems disappear at once, if you would realize 3 things.
1. Earth is flat.
2. You're allways in the center.
3. You can never reach the edge.
If it's not the kind of answer, you are comfortable to discuss, it is (historically) the answer you have got. And those flat earth maps, everything has been said, that could be said about it.
Levi Dettwyler
Actually, that still leaves both problems, with the first one just being in a slightly different form. For one, it would imply that there is a direction that you can fly in that would result in you effectively leaving the known world. Like I said earlier, this would still cause a huge number of planes to vanish, even if they aren't going off the edge. They would either have to turn around in utter confusion (since they would have thought they were just flying around the earth), or they would have gone far enough to not be able to make it back with the fuel they have, so they would be lost.
In addition to not solving the commercial airline problem, it doesn't address the fact that the expected spherical geometries of continents would not match the geometries of the continents on this flat world. Everyone THINKS the earth is round, so they expect to be able to do things like make triangles with three 90º angles. If the earth is indeed flat, then it would force the continents to be warped from their expectations. You can't project the surface of a sphere onto a flat plane without distorting its proportions.
Homesick Martian
You still view "flat" and "round" in an Euclidian way. I have not yet reached the part where Barthel proves that earth is a "Total Plane" and therefore haven't yet understood what that even means. I'm still struggling with his proof that Euclidian geometry is contradictory. But obviously earth is something like the middle plane of the universe. Since it follows a Riemann geometry it can be a closed surface and yet be without curvature, so he assertains. The same maps, that apply to RE model also apply to Barthel's model.
The way I present that here makes the thing look quite trivial, for RG is a well known thing. But I speak about a book of some hundreds highly abstract pages, most of which I haven't read yet. In fact his reasoning is rather deep and more challenging than I [ex]pected.
Levi Dettwyler
Actually, I'm not anymore. I'm viewing it from the perspective of you can prove this to yourself by drawing a triangle on a ball. You don't need Euclidean geometry to tell you that it's impossible. You can prove that it's impossible right in front of your own eyes. Find a ball, draw a line from the north pole down to the equator, then another one around 1/4th of the equator, then back up to the north pole again. A triangle containing 3 90º angles. It is impossible to draw this shape on a flat piece of paper. Thus, you can't project the surface of a sphere onto a flat plane without severely distorting it, because there are certain shapes that can exist on the surface of the ball in your hand that cannot exist on the flat piece of paper in front of you. Apply this concept to the earth, and boom. The flat earth is impossible, lest we would have noticed the severe deviations in continent arrangement and shape from our expectations of a round earth.
========
This then led me to
Lactantius and the work of Ernst Barthel on the Flat Earth forum:
Lactantius is probably Rolf Keppler (descendant of Johannes Kepler) from Germany. His website is
www.rolf-keppler.de/ and you will probably want to use the Google translation tool to translate his many pages it if you don’t know German. His research is based on German thinker and philosopher, Ernst Barthel, which is based on non-Euclidean space – an incredible concept. However, given Occam’s Razor theory, it does explain all the evidence! That is why the moderators of the flat earth forum left and started another website. As Lactantius correctly observed, they were paid trolls trying to expound the incorrect flat earth model.
So the universe is self contained within the confines of a concave spherical non-Euclidean geometry which is flat, just not a disk, and like a mobius strip curves back into itself !! Who’d of thought? No wonder there has been confusion down through the ages. This explains how eclipses work. Why there is a seeming dark body in the sky which has been called Nibiru. It explains the sometimes retrograde motion of the planets. And it also is a killer explanation on why there are no extra-terrestrials! ! I can finally rest on knowing the truth. Now I just have to translate Ernest Barthel’s works…
This just shows the level of indoctrination that we have all experienced. The earth doesn't spin, has never spun, and will never spin. Like I said earlier, your/our ignorance / indoctrination into the ball earth is just so deep, we unconsciously keep thinking that way.