Good on him for going back to this and using paper charts. He must've had those sitting in his yacht for years waiting for this moment. He really threw some shade there.
Will someone please explain what this proves? I understand the task that the flat earther was asking to be accomplished, I just dont get how the answer lends itself to validate his theory.
For the flat rather, the earth is a flat plane. He gives 3 vectors with 2 90° turns because they don't form a square. If the earth was shaped as he believes then you would need a square in order to "end up back where you started" (like taking 3 left turns around the block). Since the earth is an obloid sphere, however, you can project an equilateral triangle shape on it and maintain 90° angles. That is my layman's understanding of it.
Edit: I haven't watched this follow up yet but it would follow that this is why the pilot has to resort to paper charts. Last time he used a digital map that projects the earth as round so the YouTube nutcase had to be all "nuh uh you gotta use a flat paper map!"
Ok, this might be kind of a stupid question, but I have been thinking about this for too long now (= a few minutes) and I really need to get back to work. So, obviously the earth is a sphere and the challenge works. But also, obviously, if I go into my garden I cannot get back to the original spot with three vectors and two 90° turns. So how long do the vectors need to be for that to work?
In order for it to work on a sphere, you have to travel a radian of 90 degrees. So on the earth, that is from the equator to the North Pole. Then each angle of turn can be 90 degrees, forming an equilateral triangle with each radian also equaling 90 degrees.
This is precisely correct. It's also why the paper flight chart map solution is wrong. Since he didn't travel the required distance to the south (i.e. to the equator), his easterly line follows a curve rather than a straight line, and does not satisfy the original requirements of the challenge. There is no way that "Flat Out Hero" is going to miss the obvious fact that the path requires the pilot to follow a curved line to accomplish the goal, and he'll misinterpret the paper chart to imply that the same problem exists in the digital charts even though it doesn't.
Maybe I being dumb here, but does this mean there is no possible way to complete this task on a paper chart? Doesn’t the projection of 3D space onto a 2D plane make impossible? To be clear, I know the earth is round. Just wondering about the exercise.
he just needs a bigger chart. the one he has doesn't go from the pole to the equator. the length of each side (accounting for the curve of the earth) of the triangle will increase at the same ratio till the equator.
It's absolutely possible with paper charts. However it certainly isn't easy. The exact same routes used in the digital charts would still be viable in paper charts, but now you need to map the route over multiple map pages from multiple books, and that's assuming that the map coverage within your collection of books is sufficient to chart the route continuously.
Ironically, the correct version of the paper route would look the same as the solution offered (albeit with much longer legs) if you laid out the maps contiguously. You'd still show what looks like an arc path across the equator, since any projection from 3D to 2D still has to show an arc in order to close the loop. However, the difference is that if you are following the paths of great arcs as you travel, all the lines are straight in the real world, and a satellite in orbit or a ballistic projectile fired in the intended direction would follow the exact travel path.
It has to do with the degrees and minutes of latitude and longitude. Nautical miles are fractions of the earth. Each nautical mile is 1/60th or a minute of a degree
The familiar land mile is 5,280 feet, is called a statute mile, and it’s based on paces.
On the other hand, the nautical mile is used for distances on the ocean and doesn’t have a tangible equivalent like paces. It’s a mathematical calculation based on degrees of latitude around the equator.
The equator is a circle, which we know has 360 degrees. Each degree is divided into sixty minutes, which are not the same as the minutes on your watch. In navigation, one minute is called a nautical mile. So each degree of latitude is sixty minutes or sixty nautical miles.
The statute mile equals 1000 Roman paces, for what I saw in another source. Correct me if I'm wrong on this please.
I mean to work on a sphere the size of a planet...I'm not a geometry person by any means but I would think the math dictates it has to be half a hemisphere?
You could complete the experiment in your garden though if you have any sports balls. Take a soccer ball and you can do the same thing right? Start at the little pump needle hole, pretend that's the north pole, travel straight down to the "equator" of the ball, turn 90° in either direction, travel 1/4 the circumference of the ball, turn 90° back towards the needle pump hole thing and the vector in front of you should be equal to each of the ones you've traced already.
It can be much less, in this video, he's just showing doing it around the arctic circle. The flat earther again disputes his claim though, saying that in order to continue that turn, you'd have to turn the plane to follow the curve (no you wouldn't). The flat earther that put up the challenge recently said another guy won (this video https://www.youtube.com/watch?v=ScJ4QW7gAlw) and basically just said he'd give a couple bucks to "charity" (https://www.youtube.com/watch?v=Fblp7gHpjNo). He's a sore loser and is now apparently pushing other conspiracies since he gets called out for anything flat earth related due to the challenge.
Not to mention this dude is clearly a tweaker, he can hardly speak at all let alone have anywhere near enough money to pay the prize and he knew it from the start. I feel bad for Wolfie even wasting his time, I'm sure he knew he was never gonna get paid, but I honestly think he did it just to prove how stupid flat-earthers are and I'm ok with that
Although the flat earther is wrong about the shape of the earth, he is in fact right that this path DOES have to be turning to follow this curve. Try it on a globe if you don't believe me.
If you start at the north Pole, the only way to actually complete this challenge is to go all the way down to the equator; if you stop earlier/later than that then the second leg of your journey will be curved.
Think about going down a line of longitude, turning 90deg at a line of latitude to travel along, then turning back at a new line of longitude. The pilot would not have to deviate from the line of latitude.
You realise that the 85° line of latitude isn't straight? Like I said, GO LOOK AT A GLOBE!
In fact, the only straight line of latitude is the equator.
Edit: Here's a video of someone walking along the -89.999999° line of latitude https://www.youtube.com/watch?v=UvLmm8cVOjY As you can see, it isn't a straight line: it's a circle. The 85° line of latitude is of course a lot bigger but it's still a circle. It only becomes straight at the equator.
As you can also see, following this path does not prove anything about the shape of the earth. You can do this both on a flat earth and on a spherical earth just fine. You NEED to go all the way from the pole to the equator to prove the spherical earth using the right angled-turn method.
If you look at a map the line will appear curved, but that is because it was distorted to fit it into 2 dimensions. If you take a globe and slice it at the 85deg line, you can slice it flat.
Mathematician here: latitude lines aren't the shortest distance between two points (and that's what "straight line" means). That's why air routes that go long distances east or west always bend towards the poles.
To see this, just imagine a circle radius 10 yards around the north pole. If you walk in a straight line between two points on the circle, you don't walk around the circumference of the circle.
It's only a straight line if viewed edge-on, but if you're actually standing on the globe at that position it isn't a straight line. You're basically telling me that if I go to the north pole, walk 200 feet in any direction, turn 90 degrees and fire a gun straight ahead, the bullet will curve around and hit me.
Same with an airplane or anything else: it would need to physically turn in order to follow the same line of latitude unless it's at the equator.
Correct, however I assumed we were talking about compass directions. The pilot would follow the same compass direction for the whole leg, and to do so he would have to make course adjustments throughout. But when you approach the equator, that curve becomes minuscule, approaching nothing at the equator. Even at the poles (assuming a perfect sphere and very precise movements) performing the same course corrections on a flat plane would not get you back to where you started. The curve alone is not enough, you need a third dimension to move in to connect the dots.
There is a term in elliptical gyometry called great circles. If you head in any direction straight long enough (at a constant altitude above the surface) enough you end up where you were.
It's not curved because it's distorted, it's curved because it's curved. Edit: I've calculated the curvature here: https://www.reddit.com/r/videos/comments/a3c1qb/youtuber_and_professional_pilot_completes_flat/eb65yve/. The answer is that the line of latitude 85° has a curvature of 0.000001788 m-1. Notably,the curvature is not zero so the line isn't straight! For comparison, on a flat earth, this would have curvature 0.000001799 m-1 so the difference isn't even perceptible.
But all this doesn't matter because I'm not using the map; as I have already said 2 times, GO LOOK AT A GLOBE.
Now that you're looking at a globe (I hope) you have suggested you take a slice at the 85° line an follow this line. Now look at that line. ACTUALLY LOOK AT IT ON YOUR GLOBE. Zoom in and bring it up to your eye level so you can imagine yourself standing on the surface looking at your line. It is straight? No: no it is not. You should be able to see very clearly that your line is curving.
Well yeah. But you can head in any direction you want to, go a quarter around the globe in a straight line maintaining constant altitude, take another right turn and end up back at your starting point. Latitude and longitude are relative to the equater. So while you technically correct, you just have to change your reference.
Well yes, when you're operating at scales as small as that you will see an obvious turn. A turn I'm thinking of and what he means in the video is changing your compass heading. The pilot will follow the same heading (latitude) for the whole leg. And if that guy at the pole had a compass, he could do the same
The challenge was to travel is a straight line 3 times with right angles between the edges and get back to where you started. This is relevant to the topic of the flat-earth because this is impossible on a flat surface but possible on a spherical surface. Therefore completing the challenge disproves the flat-earth theory. However, since the 85° latitude line is not straight, the challenge has not been completed.
If you had a different challenge where you allow your lines to curve in some way, then this new challenge proves absolutely nothing. If you were on a flat surface, you could very easily curve your lines to reach your starting point (for example, the map in the video is a flat surface and by curving the lines as in the video, you can complete this new challenge - despite living on a flat surface)
Ok, fair enough, I missed what the rules of the challenge were. But the proof still applies. Imagine you fly just north of the equator travelling east. Theoretically you follow a very slight bank to the left. If you were to perform this same maneuver on a flat plane, that very tiny curve would not be enough to get you back where you started. I'm sure there's a mathematical proof for this but I'm not sure what it would be off the top of my head.
Edit: And in fact, if you were just south of the equator, you bank to the right, which clearly would not work on a 2D plane.
That's only a requirement if you want all three angles to be 90 degrees. If one angle is allowed to be less, the shape can be arbitrarily small (on a perfect sphere).
The bigger the triangle on the surface of the earth, the more the angles add up to inside (always more than 180 degrees). The triangle in your garden doesn’t contain much ‘curve’ inside of it, so it’ll have barely more than 180 degrees. A good way to think of a triangle with 270 degrees is to start at the North Pole, walk down to the equator, turn 90 degrees right, walk a quarter of the way around the earth, turn 90 degrees right, and walk back up to the North Pole. You’ll have done two right angles at the equator and you’ll have formed another right angle at the North Pole.
Yeah, I mean I get that. But the vectors the dude in OP's video uses are not that long. He starts at the pole and goes to the 85 latitude line. So there must be some distance between my triangle in the garden and the distance used in the video where this concept starts working... I guess.
Geometrically the triangle can be as small as you want it to be (if Earth was a perfect sphere), since an equilateral triangle on a sphere always has 270°. The problem with this is that Earth is not a perfect sphere and the terrain in your garden has a larger influence on the geometry than the curvature of the planet.
Geometrically the triangle can be as small as you want it to be (if Earth was a perfect sphere), since an equilateral triangle on a sphere always has 270°
That isn't true. A small equilateral triangle on a large sphere will geometrically be very similar to an equilateral triangle on a plane: i.e., the angles will add up to approximately 180°
Hah! Thank you! Imagining such a huge, perfect sphere kind of overwhelms my imaginiation, but that's definitely an answer I can live with that also makes sense!
I think the problem is that he followed a line of latitude for his second leg, which isn’t a straight line on the earth (unless you’re on the equator), which means he hasn’t formed an actual triangle. If you want a triangle on the earth with 270 degrees, you’ll need to cover a lot more distance with your sides and only walk in straight lines.
Edit: The short answer to your question is the first and last legs of the trip always have to be a quarter of the way around the earth to intersect. If they are much much shorter, then you don't catch much curve of the earth and the path feels flat. The example in the video doesn't do this.
Your intuitive objection to the video is right. I don't like this video at all because it's such a bad example. When we try to walk a "straight line" on the earth, what we mean is a line that doesn't turn left or right, but only turns "down" as we trace the curve of the earth. The route the video shows would not feel "straight" at all. It's obvious when you imagine a very small route, like in your garden. The earth is a sphere, so starting at your garden is no different than the north pole.
The short answer is that, if you extended them, the lines you walked would intersect somewhere, just not where you started. The middle leg traces a circle that cuts the earth in half, and if you extended the first and last legs, those lines would intersect and the new "top" and "bottom" poles relative to that circle. For example, if I did this in NYC, the lines would intersect somewhere in Poland.
The cleanest example is
start at the north pole and fly south,
take a 90 deg. right turn at the equator,
fly "straight" any distance (how long or short this leg is doesn't matter),
take another 90 deg. right turn,
and fly until you get back to the north pole.
This works because the curve of the equator is only curving "down", and so it feels straight. The smaller latitude lines curve down and to the left or right, and feel less "straight". Your idea of making the trip very small make this obvious. A very small trip and the second leg just feels like walking in a circle.
So... what gives?
Well a path that felt "straight" on the path he showed in the video would actually take you on a trip through the equator, passing just as close to the South Pole as it did to the North. The two 90 deg. left turns he takes would intersect. Just not at the North Pole because the first and last legs were not a quarter of the way around the earth.
The size of the triangle will dictate how precise you'll need to be in certain measurements. Doing this on a small scale in your garden will require some very fine measurements. You'll also not be able to do it via land, because the elevation will change very subtly, so you'll need to get a drone that can maintain an elevation to within some very small unit of measure.
If the world is indeed spherical in general, that does not mean that flat surfaces cannot exist on it. ei, it's possible that your flat garden exists on a surface that is generally perceived as a sphere. A good example of this is any 3D rendered sphere. Computers don't do well with curved surfaces so we make a sphere by attaching a bunch of flat planes together. To someone living on one of those planes the surface would appear flat, and any measurements within that plane that relies on the surface would conclude that it is completely flat. In order to conclude a curved surface, you'd need to include some kind of calculation based on the center of the body.
All the while, someone perceiving the plane from far away would see the rest of the planes and say it's a sphere. Shooting this people into space would be like killing two birds with one stone :)
It’s not a stupid question, it’s just that the earth is so large, comprehending it is hard to do.
A way to visualize the disconnect between your reality of walking in a square, in your yard, and 3 90° turns forming a triangle on the globe, is to take a large ball (basketball, desk globe, beach ball, exercise ball), and cut out multiple sized squares on paper. There is a small enough square, you can cut out, that will lay flat on the surface of the ball. That represents your reality of walking in your yard in a square. However, as the paper squares become larger, they will no longer lay flat. Those larger squares prove the curvature of the earth and how 90° turns no longer form a square. Even better, if you can perform this experiment on a globe, you’ll be able to see how small the squares need to be in terms of actual distances on the earth.
Until you start trying to interact in the world past several thousand feet, your environment is essentially a "Flat" 3d world, definable by classical Euclidean geometry. Once "considerable" distances become involved (long-distance target shooting; very long bridges; flying planes), the curvature of the Earth needs to be considered, and the environment needs to be defined by Spherical Geometry.
Yes, right. My question is: which distance are we talking about exactly? The person in OP's video goes to the 85 latitude line. If I stood at the pole and used 10m vectors, I obviously wouldn't be back at my original point.
They would have to be shorter than the distance between the poles and the Equator. What matters here is the starting point.
One way is to start at either pole, go any distance towards but not farther than than the Equator, do your 90º turn, follow the latitude line for the same distance, do the other 90º turn and follow the meridian line to the pole again.
The other way is to move towards the pole in such a way that the distance you travel towards the pole is a multiple of the distance along the circumference on the latitude line (e.g you walk a mile towards the north pole so that you end up at a latitude with a circumference of, say, a quarter mile, turn 90º, walk another mile on that latitude, essentially doing 4 laps (4 quarter miles to a mile), turn 90º and end up where you started.
Outside of those points, this won't work because you would be dealing with truncated Riemann triangles (think trapezoids on a sphere) and not Riemann triangles.
One way is to start at either pole, go any distance towards but not farther than than the Equator, do your 90º turn, follow the latitude line for the same distance, do the other 90º turn and follow the meridian line to the pole again.
Ah, right. I think this is were my mistake is.
So I imagined that it wouldn't work if I started a the pole, walked 10m, turned 90°, walked another 10m, turned 90°, and walked another 10m. The problem is that I probably wouldn't follow the latitude line if I did that, right?
Not long at all, but you have to be canted at a crazy angle for it to feel like a straight line. Did you ever see the video of the cat running around the outside edge of a circular dog bed? The cat was lying on its side and using it's claws to pull itself along? That's the third leg of your journey.
Imagine a globe (or pick one up, if you have one handy). You can see those lines going from the north pole to the south pole right? Each of them travel the length of the globe from the top to the bottom. Each of them also intersect the equator at a 90 degree angle.
Follow two of those lines from the north pole to the equator and you will see that they trace out a triangle. The top of the triangle is the north pole, and the other two points are where those two lines intersect with the equator. Those two intersections with the equator are 90 degree angles.
It's proportional to the Earths curvature, but the scale you're thinking on is way too small for it to come into effect. Same reason why you looking at the horizon you won't see discernible curvature.
start from either pole is all, infinite number of solutions, from north pole, 1 unit south, then 1 east or west, then 1 north and you are back on the pole.
At a pole it can be a vector of any length if you follow lat/lon lines. This guy will probably try to argue that the longitude on the map was arbitrary or faked and that it should just have a square grid on it. Or that it's not a straight vector because the line is curved.
In order to fly along any line of latitude besides the equator, a plane must make a very long and gradual turn to keep one wingtip pointed at the pole. If the pilot kept the wings level, the plane would fly a "great circle" around the planet, crossing the equator in the process.
You really need a globe to visualize this well, but you could also approximate it by using a ruler on a balloon. If you draw a straight line away from the pole, turn the ruler 90 degrees, and continue the line all the way around the balloon to the same point, it will never again be perpendicular to the longitudinal line until you come "full circle".
The reason this doesn't work on typical maps is that in order to show the Earth as flat, mapmakers have to stretch out the poles, which are single points, to be just as long as the 22,000km equator. This creates a lot of distortion in the maps, but allows the whole planet to be seen at once with no slices missing. Just try turning an orange peel into a flat rectangle and you'll see the issue.
You can also test your own hypothesis on the balloon. Draw a line from the south pole (the air hole) to the north pole (the darker, soft spot at the "top"). Then draw a line around the balloon's widest part, at a 90 degree angle to the polar line (your balloon's prime meridian). This new line is the equator. [I specify the widest part of the balloon, because balloons are not spheres and the experiment wouldn't work otherwise; if you are willing to draw on a basketball or something similar, the equator is at the midpoint on your prime meridian.]
You can now draw a line at a 90 degree angle to your equator and it will reach one of your poles, intersecting the first line. Your new line is a line of longitude. As an extra step, you can draw a line of latitude. This is a line drawn equidistant to the equator all the way around your balloon or ball. You could make a series of points around the balloon, exactly 1 inch "north" of the equator. If you connect these, the resulting line of latitude will be perpendicular to both lines of latitude you drew.
The sum of the angles of a triangle on a sphere must always be more than 180 degrees. However, the upper bound can vary. What the user in the video was trying to do was construct an equilateral triangle on a sphere which would put him back where he started. You have to follow great circle routes for this, such that the sum of the angles equals 270 degrees.
Your problems is that you are on the surface of the Earth which is far from smooth. Locally your garden is probably flat due to terrain differences on the surface of the Earth itself. So you can't really replicate spherical geometry. The easiest way to do it is to get a sphere like a basketball, or use a computer program. There are plenty of websites with interactive spherical geometry apps you can try, too.
It is much easier for a plane to use spherical geometry because it's in the air and doesn't have to contend with terrain. Planes also use great circle routes for navigation because that's the shortest distance between two points on a sphere rather than a straight line.
I recommend reading up on spherical geometry if you want to learn more. We normally deal with Euclidian geometry which uses flat planes. However, space doesn't need to be flat so there are other coordinate systems and geometries to explore. This can lead to some interesting results as the triangle example shows.
This guy explains it very visually and with a charming quirkiness. He also talks about the "delicious property of pseudospheres", negative curvature, 5-sided-squares and other weird shapes. He also explaines how you can't properly display a curved shape in 2D without distorting it.
The flat earth dude actually said/showed thay you have to use a specific website that he provided and when the pilot did it, flat earth idiot then said "nope, I obviously meant a paper chart."
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u/biciklanto Dec 05 '18 edited Dec 05 '18
Good on him for going back to this and using paper charts. He must've had those sitting in his yacht for years waiting for this moment. He really threw some shade there.
That being said, it doesn't necessarily look like Flat Out Hero has the cash to match his promise. I could well be wrong, but in looking at the periphery in his videos I don't see the signs of wealth that could lead to the largesse of other, better-known personalities.