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### Messages - troolon

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1
##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: May 07, 2022, 10:00:06 AM »
I believe there are still a few nuances in the way how i see this model versus how many posters view it.

Personally i don't think there has been enough emphasis on the fact that this model can be, and in fact was originally empirically derived.
2000 years ago, the Greeks made an incompleteness error: They assumed a globe and straight light and showed it was consistent with measurements in reality.
However, what they really measured was the relationship between light and earth shape. The earth shape was an assumption.

For my approach i've started over, but this time assuming a flat earth (later to be generalized to shape-agnostic)
I've started with the observation of horizon distance: ie that the formula R/cos(phi) - R   defines the relation between earth-shape and light-ray shape (basically height difference between a laser and a lake).
From this formula (and assuming a flat earth it's possible to create an explanation for day, night, seasons, .....)
In fact i believe it's possible to rederive all of physics this way without relying on the globe, at all.

At this point we have created an alternative model to the globe model and then there are 2 possibilities:
- we find a difference between both models and derive a test to see which one is correct
- both models are equivalent

In this case the latter can be proven. In history this has happened multiple times before. Think of the ptolemaic and tychonic models for planetary motion. It can be shown both are equivalent/approximations of the globe model)
In all posts so far, there has been a lot of emphasis on the equivalence with the globe model (as it's vastly easier to explain what's happening this way than having to rederive 2000 years of gnarly mathematics
Personally i do believe it is correct to call this a "flat earth model" (tough i admit there's a a bit of semantics involved)

Diving into this i've also discovered that the flat earth debate is a lot more nuanced than i initially thought. For example a picture of globe earth from space or a ship disappearing hull first are not actually proofs of intrinsic curvature for example and this is not something i would have guessed before this post.
And then there are of course the more philosophical questions about what it means to have 2 differently shaped models.

I also see this work as a potential bridge between RE and FE. When we see a ship disappearing hull first behind the horizon, and the globies and flatiies start warring whether it's the globe, the light or the aether that's curving, we now know they're really in agreement.

2
##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: March 02, 2022, 11:01:25 PM »
Hello Rog,

First of, i don't disagree with any of the math.
I actually think we're pretty close to understanding one another and i think our disagreement might be mostly grammatical in nature.

It doesn’t matter if your model has an orthonormal basis or not. That isn’t what defines euclidean space.   Where have you posted a graphic of a parallel transport of your model?  How would it differ from the example I posted?  Nor have I seen any calculations of what the Gaussian curvature of your model is or the calculations of the Riemann tensor.  A few days ago you acknowledged that much of the math is over your head.  Now you’re an expert in differential geometry and tensor calculus?
I've made a serious effort to try learn this topic and I think i have some basic understanding of curvature now. Of course i'm not an expert.
Picture of parallel transport is in Reply #173 https://forum.tfes.org/index.php?topic=19093.msg259064#msg259064 Please enlarge the attached picture, On the small thumbnail it's not very clear i added the extra vectors.
Gauss was calculated by construction
Bee walking a circle was done in my head

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We imagine trying to draw a map of a region D ⊂ S2. The map is a smooth function  F : D → E 2
to the Euclidean plane that preserves as much information about the geometry of D as is possible.
I am not working in a euclidean plane. After coords transform my basis is not orthonormal.
One more time...it doesn’t matter if the basis isn’t orthonormal.  If it doesn’t have curvature, it is a euclidean plane.  If it has curvature it is a sphere.  Coordinate transformations don’t make any difference.
Then i misunderstood why you included the proof. Intrinsically my model is curved.

I've read the rest of your reply, and i think the basis of our disagreement lies in intrinsic versus extrinsic curvature.
I agree that intrinsically a globe has curvature. I will also agree that coordinate transformations don't change intrinsic curvature.
My model has the intrinsic curvature of a globe. (This has been shown at least 3 or 4 different ways)
However what we haven't yet discussed is extrinsic curvature, ie embedding of the surface in a higher dimension.
And in that sense my model is flat.

Models are typically viewed from the outside. We draw them on a piece of paper and look at them as an external observer.
That is why i call this a flat model. I also believe this is how most people view it.
I do understand that intrisically my model is curved and why you wouldn't call it flat.
The correct term is probably an extrinsically flat model of an intrinsically curved surface.
And as we nearly always work on models from the outside i would abbreviate that to a "flat model" but i can see how that would be confusing to someone approaching it mathematically.

3
##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: March 02, 2022, 10:12:57 PM »
The difference is we can see the Earth. We can measure it. We can run experiments on and around it.
It's not the same as some otherworldly force or the universe being a simulation. Those are untestable and unverifiable.

Globe Earth can be disproved.  Finding a dome.  Locating the edge.  Drilling through to the underside.  Seeing it from high enough to see the entire earth as a disk. Plotting the locations of cities and finding them to align on a flat plane but not a sphere.  Exploring past the ice wall to find an infinite plane.
It's just a different representation of physics. As such there's no measurement or observation that will be predicted differently by either model.
- I'm not claiming a dome (in the model with the dome all of space is contained inside the dome, so you're never able to see or reach the dome, only an external observer could tell)
- Mathematically there's no edge in my model. Latitude goes from [0 to π] and is undefined beyond.
- You can't drill through the underside, you'll automatically curve up again
- If light curves as in my model, the disc looks like a globe from space (the light curvature was so designed it exactly counteracts the missing curvature)
- Plotting cities will work in lat/long coordinates. (they won't line up visually though, only mathematically)
...

You can't simply apply a mathematical transformation to an object and claim that the object is now transformed.
I can say latitude ' = latitude x 2 and now have an Earth twice the size.  But it doesn't mean anything, even if I render a stretched Earth, flat or round.
Still
- We can't know what the earth looks like when observed from outside the universe
- If someone needs a model of earth, there's nothing wrong if she draws a flat disc. All calculations can be done with it.

Personally i think when people are discussing shape of the earth, they're usually talking about the shape of the model.
I think I've always referred to it as FE model of FE representation and I think that term is correct.

4
##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: March 02, 2022, 09:54:49 PM »
you are here to justify FE.
I'm here to show
- It is possible to do physics with a flat representation of earth
- We can't know the true shape of the planet as observed by an external observer
- the RE/FE discussion is just as pointless as polar vs cartesian coords.

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I talked about FE with a programmer friend. He said that he had written the nav software for the Canadian Air Traffic Control system and used 3d geometry, haversines, straight out of a math textbook. Worked perfectly, airplanes in Canada today arrive exactly where they are supposed to, FE math would be different and not work. He has a degree in math.
Totally agree. I never claimed RE is wrong. FE and RE are just two representations of reality. You can write software using either one (or even switch back and forth if you iike)

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I remember when my linear algebra prof started the lecture with "Today we are going to talk about how we know the earth is not flat, Gauss' Remarkable Theorem." The normal vectors on the surface of a flat disk are parallel, so curvature is zero. The normal vectors on the surface of of a sphere are not parallel, so the curvature is not zero. Find me a math prof who will disagree with this. There aren't any. There is a reason why you are sayoing this on FE site, say it on a math web site, or astronomy, or astrophysics.
and i agree with your prof, yet i can represent all of physics on a flat plane and have it working. It's intrinsic versus extrinsic curvature.

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What you did is simple, you peeled the surface of the sphere off from the south pole and stretched it out into a disk, like popping a balloon and stretching the balloon out into a disk. All the rest is just blather. Doing this stretches out the size of everything in the southern hemisphere. In your graphics, Australia is clearly bigger than North America. Measurement is measurement, and there are many ways to know the true sizes.
And yet Brisbane and every other city has the same latitude/longitude on both the sphere and the disc.
Lat/long coordinates are invariants. Angle (or angular distance/haversine) is another invariant.
Keeping the invariants in mind, it is possible to do math/physics on a flat disc. In fact i've shown it's possible to do calculate everything physics can.

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But distance is not your only problem. When you stretch it, the south pole becomes the circle around the edge. If you incorporate Sigma Octantus, as directly above south pole, it becomes a circle rather than a particular point. Even if this made sense, you have to explain why observers in the southern hemisphere see it as a small dot on the part of the circle and do not see the rest of the circle. A difficult to explain combination of bent light and directional light, much like the spotlight sun problem, but worse.

Except for one thing, Sigma Octantus is not directly above the south pole, it is a little over a degree off axis. So consider the Southern Cross. It is enough south that it is seen from everywhere in the southern hemisphere as being due south. It is much like the big and little dippers in northern hemisphere. Where is the Southern Cross? It appears everywhere as outward from the disk. Where is it really? That question has no sensible answer on FE.
Mathematically it has an answer. It just does not appeal to your intuition (partly because you've been trained in orthogonal coordinate systems since elementary school)

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According to your theory, since everything is equivalent, seems like I should be able to do the same math conversion using the south pole. This gives Sigma Octantus pretty close to observed re azimuth. still requires bent light ("unknown forces with unknown equations", per the FAQ) for altitude. But now Polaris, the north star, is everywhere around the edge. Also seems pretty arbitrary to start with the poles, how about your house in the center? Start with your house and peel the surface of the sphere starting with the point directly opposite on the spherical globe. The same transform can be done choosing any point at the center. If you choose a pole, one of the pole stars makes at least some sense. Start at the equator and neither makes any sense at all.
I totally agree. You can use any point as center and when doing calculations i often translate the disc to where i'm calculating.
It seems you find the southpole makes little intuitive sense (it does work mathematically) so if you plan to do math around the southpole, I would recommend to transform using the southpole as center of the disc. The point you're making now is if globe earth should be rendered with the northpole on top or the some other point. It doesn't matter.

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You made graphics to show a transform to several different shapes. Include the pole stars in these transforms and see how much sense it makes. Let's see graphics that include the Southern Cross and the Little Dipper, visible from the places and in the direction that matches observations. You can't do it. Distances, direction, and observed location of astronomical objects are all correct in RE graphics. They are not correct in any other shape.
If you're a programmer does this help?
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def draw_as_flat(x, y, z):
lat, long, dist = convert_xyz_to_latlond(x, y, z)
render_as_disc(lat, long, dist)
This works for every possible point in space. Every point in space can be rendered with the earth being flat.
If you had your friends program, all that needed to be changed was the render function. (or you can go change all formulas to "FE-formulas" if you really want to)
If you want to understand why certain stars are visible, add lines representing rays of light to your globe model, then transform every point using the function above and you'll see the ray becomes curved.

I had this image lying around. Southern cross is in there somewhere, but i think more near the back where it's hard to make out.

5
##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: February 26, 2022, 12:17:37 AM »
A Mercator projection isn’t making the claim that the earth is actually flat. It shows a curved route because that represents the shortest distance on a globe.
There are loads of different distances. Straight through the earth, angular distance, taxicab. hamming distance if you like a weird one.
It's your responsibility to take one that makes sense: that matches observations.
Personally i find it remarkable that physics uses both spherical and euclidean distances within the same model. This alone clearly shows there's no one correct distance per model.

6
##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: February 25, 2022, 11:54:27 PM »
What do you think is the point of performing this transformation?  I've asked the OP, so what do you think is being achieved here?
1. Is it possible to make physics work on a flat model? ie can the flatties ever find a working flat earth model?
-> yes. Of course as both globe and flat representation represent the same reality, it would be very surprising if there were no correlation between the two models.
2. What's the outside shape of the universe?
-> We can't know

7
##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: February 25, 2022, 08:25:36 PM »
... we can simply use the haversine formula.

This wouldn't be the case on a flat disc, would it?

You can have infinitely many distance metrics. You have to choose one that make sense and haversine seems to match reality.
Intrinsically my model behaves like a globe. Extrinsically it's flat. When we look at a model, we look at it from the outside so extrinsically.
So i would argue it's possible to create a flat earth representation, that mathematically behaves just like a globe would.

I think the entire dialog can be split into 3 questions:
- What does the earth look like in an orthonormal reference frame/euclidian geometry
-> a sphere / obloid spheroid.
- Can we model physics on a flat earth?
-> yes, my model does that.
- What is the real shape of the planet / what is the correct coordinate system?
-> coordinate system is a choice not a given especially for the universe that we can't observe externally.

I believe when flatties and globies are debating shape, they're just discussing coordinate systems. (unless they make additional claims)

8
##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: February 21, 2022, 10:37:44 PM »
Also, this is wrong. As it has been mentioned, curvature is invariant over a change of coordinates. If it's non-zero, there is no possible change of coordinates that can turn it to zero globally.
Doesn't matter the axis or coordinate basis. If your model has non-zero intrinsic curvature, it isn't flat
You're quite right the intrinsic curvature is indeed curved. Mathematically it's a curved space.
But i believe extrinsic curvature to be zero (i'm sure Rog will have a 70 page proof or something about this

When you look at a model of the world, you look at the model from the outside. So i believe it's correct to say it's a flat representation of physics.

For me personally i can even look at the world and experience it as the flat representation.
For example when i see a picture of a ship with a missing keel, i can very often imagine it's the light that's curving.
Or when i see a globe from space, i can superimpose the model and tell myself: ah yes, that's a flat disc distorted by curvy light.

Some people seem to feel more comfortable looking at the world as flat, and now science can explain the world in their view if they want to...

9
##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: February 18, 2022, 10:45:01 PM »
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Straight is the shortest distance between two points, regardless of the coordinate system.  Straight is a curve on a sphere.  What would be the shortest distance between NY and Moscow on your model?

If I understand the model, and Troolon, correct me if I'm wrong, I think it's pretty simple. It's a great circle, identical in both the RE and Troolon models. Same route, same distance. Just depicted, portrayed, visually different. Just like how the route would show as curved on a Mercator projection though it appears "straight" on a globe.
Thumbs up, you've got it

10
##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: February 18, 2022, 10:42:54 PM »
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Straight is only defined the way you think it is in an orthonormal basis.
Straight is the shortest distance between two points, regardless of the coordinate system.  Straight is a curve on a sphere.  What would be the shortest distance between NY and Moscow on your model?
[/quote]
After coord transform we're working in (lat,long) based coordinates. So haversine gives the shortest distance for 2 points on earth.

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Not all transformations are isometric, which just means a transformation that it doesn’t distort angles or distances.
Here is the mathematical proof. (starts around slide 20) I can’t help you much working through it, but I suggest that unless you can contradict the math, you really don’t have any basis to say that your model doesn’t have any distortions.
The problem in the mathematical proof is on slide 5:
We imagine trying to draw a map of a region D ⊂ S2. The map is a smooth function  F : D → E 2
to the Euclidean plane that preserves as much information about the geometry of D as is possible.
I am not working in a euclidean plane. After coords transform my basis is not orthonormal.

I've told you this before: you're drawing an orthonormal basis next to mine and then start measuring things according to your base. That's now how coord transforms, maths or physics work.

Also i found this definition for isometry: https://en.wikipedia.org/wiki/Isometry.
It's basically any transformation that preserves distances. And my transform preserves distances. It is isometric.
What you're doing is taking a coord transformed base, putting an orthonormal basis next to it, and then start measuring. That's not the definition of isometric. You have to use the distance metric of your coord transfromed metric space.

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Since the curvature of the sphere does not vanish, it CANNOT BE LOCALLY ISOMETRICALLY MAPPED TO THE EUCLIDEAN PLANE
except my "disc" is not an euclidean plane. It does not have an orthnormal base.
- You've had me calculate curvature of my space using gauss and it came out indistinguishable from a sphere.
- You then had me do parallel transports, which were indistinguishable from a sphere.
- I've given you the calculation for riemann tensor and ricci scalar, and it was comparable with a sphere.
You never found fault in any of the math, and yet you now call it a euclidean plane which violates all of the above.

But here's a very simple visual example: Take a compass and draw a circle anywhere on the AE map.
Circles represent all points at the same distance from the center. Does this circle represent all points at equal distance?
Obviously not, you said yourself there's distortion.
So my "disc" is demonstrably not an euclidean geometry.

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At what point have i tried to "flatten" the sphere?
-> By trying to project a sphere onto a flat surface without any distortion.
Not treating it as a euclidean geometry.

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If it has intrinsic curvature, it doesn't matter how you view it.  It will always have intrinsic curvature and you can always detect it with some simple tests.
Agreed. Mathematically it behaves like a euclidean globe. But i can represent it whatever way i like.
I can represent it in an orthonormal base and say i live on a sphere with straight light.
Or i can represent it in my way, and look at reality as a flat earth with curvy light.
I'm able to construct a consistent world view either way and i'm able to make the same predictions of reality in either representation.
However when i switch to FE representation, i should be aware not to use any properties exclusive to euclidean geometries.

11
##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: February 18, 2022, 12:11:21 AM »
If I had to guess, OP is studying some things like mapping and/or coordinate transformations presently and found an interesting way to take a deeper dive into the topic than just reading stale textbook material. And that's a perfectly valid reason to want to work through a problem like this as well.
Actually, 4 weeks ago i was puzzled that there had been so little improvement in the flat earth model over the years that i decided to investigate myself. At this point my take was that flat earth is obviously wrong, but there must be something better than the fully illuminated flat disc that's shown in all the media.
So I started very easy by adding disappearing keels to the flat map and discovered the flat earth horizon formula. When you then realize you can't see below the horizon in reality and that the horizon on a flat map is a cone you can't see outside of, then all of optics suddenly starts to work (ie day/night/seasons/....)
But i started running into mathematical difficulties modeling this and so I stumbled upon the coord transform learning that flat-earth and globe-earth physics are really the same thing.

I then went through a brief period of: "have i finally gone totally bonkers, or just the regular nutty with a hint of inspiration"
So that's when I had my results double-checked and entered a bit of a moral dilemma whether to make this public or not.
In the end i chose to because:
- someone else is bound to find it (bendy light theory came sooo close)
- the science community might be briefly surprised, but science adapts and so i doubt it would do any long-term damage
- I find the insults and dogma on both sides of the debate very irritating. I'm hoping this will tone both sides down and hopefully bring them together.

I don't get any enjoyment of riling people up, quite the contrary.
The biggest sentiment i get from this is frustration with myself at not being able to communicate this more clearly.

Though i must say i'm extremely thankful everyone has remained polite and some of the discussions have been very interesting.
And if some bozo came to me claiming we couldn't ever know the shape of the planet, i would be equally incredulous and eager to prove him wrong
So thank you everyone for the exchanges so far.

12
##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: February 17, 2022, 10:42:20 PM »
If it is impossible for us to 'step outside' to see the true shape of things then there is no way of knowing if your theory is true or not.
If something is impossible to observe then there is no way to prove it exists one way or another.  If you can't disprove a theory, it's not a theory.
Very correct.
The only problem is that everything you've posited above is also true for orthonormal bases and globe earth.
So globe shape is also an unfalsifiable theory.
One minor detail i would like to clarify is that it's impossible to see a difference between the flat and globe representation of physics.
We can of course make measurements in reality and check that they align with what physics predicts in both models.
It's just the shape we can't differentiate.
Orthornormal bases have some nice properties, and we're so very used to them that we sometimes forget it's just a convention.

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We can only know what we can see and measure. In my experience, my measurements and observations show the Earth to be a globe. If it's another shape in a hypothetical greater universe that I can't see or touch or examine in any way, then that's the realm of religion, belief and faith.
I've just created a second model, that also explains all your experiences, measurements and observations equally well on a universe with a flat earth.
It's the same physics, just a different shape. Like bar charts and pie charts.... Math can't see shape, only numbers and relations between them.
So globe shape is indeed in the realm of speculation.
That's indeed the point i was making.
Do note it also works the other way around. If someone ever makes a flat-earth model, i'll use the same trick to turn it into a globe.

13
##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: February 17, 2022, 10:16:56 PM »
Not treating it as any coordinates.  Treating it as simply distance between two points.  Distance can be measured and distances must equate if the two models are indeed similar.

In the RE model we can call distance 'Rounds'  In yours we can call them 'Troolons'.  Regardless the coordinate system, the distance from A to B is X and the distance from A to C is Y. The value of Rounds and Troolons need not equate but the distance in both models must still be the same.  In addition, there must be a conversion factor that is constant between the two models for converting one distance to another.
- a straight ruler as you know it, is only translation-, rotation-, reflection-invariant in an orthonormal base. It also only scales linearly as long as you stay in a orthonormal base.
- If you really want to measure distances in the flat-world representation you should use rather special curvy rulers and be aware that they're not translation or rotation invariant.
However if i were to take by bendy flat-earth ruler to your globe all distances would also be totally "broken".
- there are multiple possible distance metrics. You already mentioned two: spherical distance and euclidean distance, but there are infinitely many more distance metrics and most of them are not measurable with a ruler.

I will agree that rulers behaving well is a very handy property of orthonormal bases.
But what you're really doing here is picking one very specific shaped ruler, and one very specific base that accidentally work nice together, and therefore declare this the only valid way to measure. Or actually worse, you take your "straight" ruler to my non-orthonormal base and just declare it broken.

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Looking at your map, if Sydney to LAX is 1 troolon, it appears that Sydney to Santiago is on the order of 1.5 troolons.  For the two models to be identical it should be .94 troolons.  Admittedly, I may be misunderstanding how things are measured in your system but your flat disc map seems pretty easy to interpret with respect to relative distances.
My coordinates are in (lat, long). So my distances are calculated with haversine, and will thus give the same result as on your globe.
You're taking a straight ruler, to a non-orthonormal base and then applying the linear scaling property of straight-rulers in orthonormal bases.
Math says no

Or if you like a less mathy analogy: You can measure bar-charts with a ruler, linearly scale it and find the value it represents.
You can't do this with a pie-chart. That doesn't mean pie-charts are wrong or broken.
They're just a different way to view the same data.

14
##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: February 17, 2022, 09:44:06 PM »
I suspect there's a pesky singularity if you go below the surface far enough, though
I haven't encountered a pasky singularity yet: no divisions by zero.
But you're right there's some unintuitive behavior at the center of the earth, but nothing worse than expressing cartesian (0,0) in polar coordinates

15
##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: February 17, 2022, 09:32:59 PM »
The map is exactly as accurate as it's the same physics.
Take a logarithmic X and Y axis and draw a circle around (1000,1000) with diameter 1000. I will not longer look like circle.
Are logarithmic scales therefore "wrong" and need to be "reexamined"?

How do you measure a distance on a globe scale-model?
- You take ruler and measure the distance. (Incidentally note rulers don't fit to globes very well. Ideally you'd need a curvy ruler)
- You calculate the distance using math (multiplying by the scale factor)

You measure distances on the flat-earth representation of physics exactly the same way. (Do note that distances are not scale and rotation invariant so you might find this more akin to finding distances on a logarithmic scale)
- you find start and end point
- you calculate the distance using math. (eg haversine)
Do note, in practice i very seldomly see people calculating distances using globes. Most people just use coordinates and maths.

Okay, so what does your map report as the distances from New York to San Francisco then San Francisco to Brisbane then Brisbane to Perth?
My model is in celestial coordinates (latitude, longitude, distance from the center of the earth)
And as all cities have a fixed distance of 6000km we can simply use the haversine formula.
So to know the distance between cities:
- First, convert all cities to (latitude, longitude).
- Then use haversine to find the distances.
It's exactly the same formula as on a globe, so the result will also be identical.
(lat, lon) are invariant to AE transformation and so the formula is also invariant.

Or in general distance_in_celestial(p1, p2) = distance_in_cartesian(celest_to_cart(p1), celest_to_cart(p2))
So by definition, it will always produce the same distance result as on a globe.
It's just a different representation. Same physics...

16
##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: February 17, 2022, 09:24:20 PM »
Why are you doing this? You said you've run it past graduate physicists or similar, and they pronounced it "practically useless", so what's your purpose?
i believe it's very relevant for the flat-earth "debate".
I find that people are unreasonably attached to shape.
It basically makes the entire debate as moot as polar vs cartesian coordinates.
The simple truth is you can't know the shape of the earth. One person can claim it's flat with bendy light, the next may claim it's a globe.
It's just a different view. It's like 2 colorblind people both insisting their color is the right one....

17
##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: February 16, 2022, 09:07:37 PM »
I would like to know which physicists agree with your ideas. I doubt any would say the earth could be any shape, or that changing coordinate systems changes shapes yet they are still equivalent, or that measurement varies.
Unfortunately I have no references to share. These people don't fancy half the internet mailing them for explanations.

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You are doing the equivalent of looking at a funhouse mirror and seeing your legs looking a foot long and deciding you just don't know how long your legs are, any mirror could be right. Graph a ruler on cartessian, then logarithmic. The graph on cartessin will be isometric, linear, a multiple of the straight line. The graph on some coordinate system might be curved, but the ruler is still straight. It is not "could be any shape, no one knows". Please enroll in geometry class.
For a funhouse mirror it's quite easy for an outside observer to see the shapes don't match with the owner.
Problem is we can't step outside of the universe to check. We have no absolute references.
If the universe were a simulation, how would you tell it's simulating a flat earth or a globe?
For someone inside the simulation, Australia will have the same size regardless. And you just can't know what the computer is calculating.

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Gps <snipped> depends on radio waves going straight and the speed of light being constant. If this is true Under your theories, we can't be sure of either. gps would be impossible.
Yet it works amazingly well.
Of course it works in a flat representation of physics. It's just a representation, all predictions are the same. Can't be distinguished remember?

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Do radio waves travel straight and is the speed of light constant? If not, how does gps work?
Speed of light is constant, in the flat-earth representation radio waves travel in curves. It's distance that's not what you think it is.

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If I buy a lidar measuring gadget at Home Depot and take it to Australia, will it still work correctly? I think it will.
Same physics in both models. Indistinguishable.

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Bear in mind that you can buy a usb gps receiver and download open source gps software. You can examine the algorithms and look at raw data. There are web sites where you can look at the current locations of gps satellites and see their transmissions. If you know where satellite is and you can map the locations on the surface of the earth, the result will be a sphere.
never said the globe representation was wrong, quite the contrary.

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The question boils down to: Australia too big on FE, just right on RE. Is the earth round, or is measurement impossible or somehow variable in ways that no one noticed, detectable only by the observing that straight light doesn't work on FE and completely unexplained?
Let's play a little game....
I'm going to design a universe. It's either going to be a globe with straight light, a flat earth with bendy light, or a rectangle earth with different bendy light.
I will place you in my little universe.
How will you and your ruler tell in what universe you are?
Remember for an inside observer all universes measure the same...

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Do you acknowledge that gps and lkidar devices work and match RE theory, while FE is not consistent with observed results without "fudge factors", as the FAQ says, "unknown forces with unknown equations"?
I agree physics works remarkably well. You're quoting comments on a different model I don't believe are applicable. It's the same physics. It's just a different representation. Bendy light stopped just before realizing this.

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Where is Sigma Octantus?
I'll try to make an updated graph
But you seem to be missing the point: this flat earth is just a different representation of physics.
You're trying to debunk globe physics...

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Still waiting for your graphics to show sunset in Denver and how Salt Lake City sees daylight over the entire dome while St Louis sees night sky over the entire dome. Please show how someone at night looks up and see stars over the entire dome, including where the sun is. See right through the sun to the stars (beyond?) without seeing the light of the sun. Can you make a model that shows where sun and stars are, but from the point of view of someone on the surface?
Theoretically yes. Practically that's not how the software is currently written, nor do i have immediate plans. If you desperately want to see it, make it yourself, i've explained the transformation, it's not hard:
- convert to celestial coordinates relative to the center of the earth
- draw latitude on a straight axis

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Like this: https://stellarium-web.org/
My latest model with the planet of the solar system is verifiable with stellarium. The positions of the planets match the time.
I've actually been thinking about doing earth based views in software and it's just pointless. The way i would write it would be a bunch a coord transforms back and forth between celestial and cartesian coords, and they'd all cancel out. I'd rather save myself the trouble.
You still don't seem to be grasp my model is regular physics. It's just a different representation.
You're asking me to make drawings of regular physics.

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But show how everything works when you move around the simulation on the surface. There's your homework.
I'm not taking homework from you.
Also i've deleted various paragraphs i deemed offensive.
I believe i've been very accommodating and polite with my replies to you. If you keep up the hostilities i will stop replying.

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##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: February 16, 2022, 07:23:23 PM »
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What is meant is the intrinsic curvature of the space, meaning it is independent of the choice of coordinates. There are clever methods of determining whether and to what extend your space deviates from flat euclidean space, namely Gaussian curvature, and, more importantly, the Riemann tensor.
You are correct that transforming from Cartesian to Geo graphic coordinates doesn’t change the intrinsic curvature, but just drawing latitude on a straight axis doesn’t change it either.
Would have loved if you told me that before all the hours or trying to understand differential geometry
Actually i learned something new... thanks.

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The problem comes when you try and “flatten” the sphere...without any distortion.
At what point have i tried to "flatten" the sphere?

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You keep contradicting yourself by stating that your model has intrinsic curvature and also stating that we can’t know the shape of the earth.  The very definition of intrinsic curvature is that “the inhabitants” can know.  So which is it?  Does your model have intrinsic curvature or is it impossible to know the shape of the earth?
The model has intrinsic curvature but noone says an orthonormal axis is the only way it can be viewed.
There are infinitely many more representations, and the only way to truly know the correct axis, if it even exists, is to look at the universe from the outside.
I think it all depends on how i want to look at reality.
I can see a ship disappearing over the horizon keel first and see it as evidence of curvature of the globe, or i can think of it as a flat earth with light curving upwards.
Neither is wrong, they're just different views on the same reality.

Personally I think people are way too attached to a preferred shape.

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##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: February 16, 2022, 06:42:42 PM »
I'm not calculating anything.  I'm looking at your picture.  When you look at the disc, straight line path from Syndney to Santiago goes right past LA and continues for a significant distance.  It's a simple observation.  No math involved.
My axis are the equator (circular) and the Greenwich greatcircle. What 'straight' path are you taking?
Straight is only defined the way you think it is in an orthonormal basis.
This drawing is in celestial coordinates (lat, lon, distances). Please don't treat it as (x,y,z) cartesian coords because that will indeed break everything.

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##### Flat Earth Theory / Re: Found a fully working flat earth model?
« on: February 16, 2022, 06:38:34 PM »
When a theory in physics doesn't predict the tangible, measurable reality of the world, it's wrong and has to be reexamined. Your map is simply wrong about the relative sizes, shapes and position of the Earth's major continents.

It would be different if your map produced more accurate measurements then a round Earth map but it doesn't. Are you saying it's impossible for us to measure any distances?
The map is exactly as accurate as it's the same physics.
Take a logarithmic X and Y axis and draw a circle around (1000,1000) with diameter 1000. I will not longer look like circle.
Are logarithmic scales therefore "wrong" and need to be "reexamined"?

How do you measure a distance on a globe scale-model?
- You take ruler and measure the distance. (Incidentally note rulers don't fit to globes very well. Ideally you'd need a curvy ruler)
- You calculate the distance using math (multiplying by the scale factor)

You measure distances on the flat-earth representation of physics exactly the same way. (Do note that distances are not scale and rotation invariant so you might find this more akin to finding distances on a logarithmic scale)
- you find start and end point
- you calculate the distance using math. (eg haversine)
Do note, in practice i very seldomly see people calculating distances using globes. Most people just use coordinates and maths.

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