[WTF_Seriously]

Though your animations are nice, they aren't much different in concept than the sunlight animation already shown on the WIKI here.

Others are discussing the distance issue.  I'm curious how your model, appearing to be north pole centric, handles full daylight in the south in winter.  Take a look at the rightmost image here:



In winter, on a flat, north monopole, disc light forms a ring around the outside like depicted.  How does your model propose light does this?

Do you mean this one? The only one i haven't encountered yet is the last wobbly one but i suppose that's because i approximated the suns orbit with a circle? If you could give me lat/long of the sun for the last one, i'll whip an image out.

Hard to tell on your image what areas are supposed to be in daylight and what are not.  Also, it appears the sun is positioned directly over the north pole which is not what happens.  As for what I was showing in the right hand image, that would be the sun at any longitude and a latitude of 23. south deg. south.  At that time, on a north pole centric disc there would be a 'spotlight' darkness surrounded by a ring of light lighting the southern regions in 24 hour daylight.

[troolon]

Yeah, perspective made the sun look wrong, I've taken a top down photo and placed the sun over Africa so you can check the latitude to be -23.
Inside the circle made by the yellow dots it's dark. Outside that circle it's day. The white lines are rays of sun, traveling from the sun to the places where it's sunset/rise.
What i believe makes my work different is that i have actual equations for all optics, and i can correctly explain anything else.
As this model is based on a coordinate transformation it is equally powerful as globe physics.
That is because this IS the globe model. Coord transformations preserve physics, and only change shape.
There is no test to differentiate between the two models.


Also it can be proven that flat is a possible shape of the earth, but the true shape of the earth can never be proven.

[SteelyBob]

The AE map has a nonorthonormal basis. We can consider two cases:
For an observer existing within the coordinate system, ie a person in austraiia, the world and distances appear as in reality.
For an observer outside of the coordinate system, you should measure distances with a flat-earth ruler. (which is curved and has non-equal distance markings)
Taking an orthogonal ruler, to a flat-earth coordinate system produces invalid results. Just like taking my bend ruler to your globe would completely invalidate it.
Mathematically: you need to use the corect flat-earth distance metric that compensates for all the distortions.
This is why I asked you about the axis of reality. Globe is the correct shape if the axis is orthonormal. Flat is the correct shape if it's a peculiar other base. As we do not know in what base we're supposed the see the universe, we also do not know what shape the earth really has.


The way this model was constructed was by applying a coordinate transform to globe physics. Coord transforms change the shape of the model, but not the physics.
So if distances work on the globe, they will also work on the flat model, by design.

Forget maps for second. Get in a car, and drive from one coast of Australia to the other. How far does the odo say you've travelled?

[stevecanuck]

Forget maps for second. Get in a car, and drive from one coast of Australia to the other. How far does the odo say you've travelled?

Or ask anyone in charge of buying materials for building such roads, laying pipe, stringing phone lines, etc. They base the amount the asphalt, pipe, and line on known mileage which just happens to comply with RE distances.

[troolon]

  You just couldn't have picked a a worse example to prove RE 
Did you know the haversine formula works on AE maps unmodified?

spherical distances are calculated using the haversine formula, which takes as input lat/long
lat/long is an invariant for the AE projection and so the globe formula will still work for the AE map unmodified.

The distance is the same number the globe physics model says it is and thus the same as my flat model says. (because the models are equivalent)

[stack]

You just couldn't have picked a a worse example to prove RE 
Did you know the haversine formula works on AE maps unmodified?

spherical distances are calculated using the haversine formula, which takes as input lat/long
lat/long is an invariant for the AE projection and so the globe formula will still work for the AE map unmodified.

The distance is the same number the globe physics model says it is and thus the same as my flat model says. (because the models are equivalent)

True, Haversine is independent of projections. But where I'm kinda hung up is still on a few things mentioned by others and maybe some not mentioned:

- Isn't it a little strange that the AE projection you're basing this all on is just that, a projection...of a globe?
- Isn't Haversine based on spherical geometry, specifically a great circle on a ball?
- In geodesy, Haversine may be used for the quick and dirty shorter calculations, but predominantly Vincenty is used because it's more accurate, based upon an ellipsoid rather than a sphere. That would seem to alter the look of the AE projection to a degree
- You mentioned something about a depiction of reality and not a map. I get that, but what's a "flat earth ruler" and where can I find one because it doesn't seem to exist in said reality

All of this gets wonky pretty fast when you start mixing projections with reality (navigation) with useable maps (navigation). For instance, the AE projection is a projection from a globe. As mentioned before, because projections are required for a globe onto a flat surface, distortions arise. For a flat earth depiction on a flat surface, no distortion is required, it's one-to-one. And it would actually resemble reality. And as I think AATW mentioned, I too have yet to see a non-distorted depiction of a flat earth on a flat surface.
Then there's the reality of navigation. How does that work exactly? Ex., QANTAS JND>SYD flight, the distance may be able to be calculated correctly on the AE, but from a reality/visual perspective, the route makes zero sense.

And of course, little things like how have people been able to circumnavigate Antarctica when it's a ring walling in the earth.

Then there's the whole bendy light rabbit hole which, well, probably needs a whole separate discussion around that.

Curious about your thoughts and thanks for pulling all this stuff together, makes for an interesting examination.

[Pete Svarrior]

Isn't it a little strange that the AE projection you're basing this all on is just that, a projection...of a globe?

This continues to be false, no matter how many times you say it. You already know this, so please stop trying to propagate this lie.

[SteelyBob]

Isn't it a little strange that the AE projection you're basing this all on is just that, a projection...of a globe?

This continues to be false, no matter how many times you say it. You already know this, so please stop trying to propagate this lie.

If it's not a projection of a globe, then what is it? Where did the shapes, sizes and positions of the various land masses come from, if not the globe? The lat/long relationship of each significant feature appears to have been preserved, unless I'm mistaken - do correct me if I'm wrong.

[SteelyBob]

You just couldn't have picked a a worse example to prove RE 
Did you know the haversine formula works on AE maps unmodified?

spherical distances are calculated using the haversine formula, which takes as input lat/long
lat/long is an invariant for the AE projection and so the globe formula will still work for the AE map unmodified.

The distance is the same number the globe physics model says it is and thus the same as my flat model says. (because the models are equivalent)

But the output of the haversine formula is the great circle distance between two points. If the earth was flat, then that wouldn't be the distance between two points, it would be some other number.

Again, if I get in a car and drive from east to west coast of Australia, what would my odo say the distance was? I would suggest it would say roughly 2500 miles or thereabouts. If the world was indeed flat, and laid out as per the AE / monopole map as shown in the wiki and your proposal, then the distances would be roughly 2.4 times greater, based on a latitude of -30 degrees, so around 6000 miles.

[Pete Svarrior]

If it's not a projection of a globe, then what is it? Where did the shapes, sizes and positions of the various land masses come from, if not the globe? The lat/long relationship of each significant feature appears to have been preserved, unless I'm mistaken - do correct me if I'm wrong.

The most commonly shared image is, if I remember correctly, a re-projection of a Mercator map, which is where the lat-lon lines were introduced. However, the map you refer to as "the AE map" predates RE by centuries.

[SteelyBob]

The most commonly shared image is, if I remember correctly, a re-projection of a Mercator map, which is where the lat-lon lines were introduced. However, the map you refer to as "the AE map" predates RE by centuries.

In response to:

Isn't it a little strange that the AE projection you're basing this all on is just that, a projection...of a globe?

you said:

This continues to be false, no matter how many times you say it

So what exactly are you saying? That the AE map isn’t a projection? That the basis of the OP’s work isn’t a projection? The existence, or not, of some vaguely referenced historic map has nothing to do with whether or not the AE map, and indeed the same map as presented in the wiki, is a projection.

[WTF_Seriously]

Yeah, perspective made the sun look wrong, I've taken a top down photo and placed the sun over Africa so you can check the latitude to be -23.
Inside the circle made by the yellow dots it's dark. Outside that circle it's day. The white lines are rays of sun, traveling from the sun to the places where it's sunset/rise.
What i believe makes my work different is that i have actual equations for all optics, and i can correctly explain anything else.
As this model is based on a coordinate transformation it is equally powerful as globe physics.
That is because this IS the globe model. Coord transformations preserve physics, and only change shape.
There is no test to differentiate between the two models.


Also it can be proven that flat is a possible shape of the earth, but the true shape of the earth can never be proven.

Interesting.  Curious.  You have equations for the optics that explain how light travels different distances and curves differently simply based off of the latitude of the sun?

Also, can you generate a similar image of what the light pattern looks like when the sun's on the equator

[WTF_Seriously]

the true shape of the earth can never be proven.

Why not?

[troolon]

Consider this thought experiment: that shows the earth can have any possible shape and we'll never be able to prove the correct one.

- coordinate transformations can turn any shape into any other shape (math cares about numbers not drawings)
- coordinate transformations don't break physics (celestial coords, cartesian, polar, ...  physics uses all of these all the time and doesn't break)
-> physics can be made to work on any shape universe
-> There is no test to differentiate between the shapes. In reality we can only observe/measure the physical properties, not the shape.
-> we can't ever test the shape of the earth. It can be flat, it can be a globe or a duck, impossible to tell from within the universe.

So have a look around you and try these two views: i'm standing on a globe and lightrays are straight,
or you could say: i'm standing on a flat plane, and light curves to exactly counteract the missing curve.
Your eyes wouldn't be able to tell the difference and there's no physical test to distinguish between the two views, it's just a matter of perception.

It's like the question: Am i moving, or is the entire universe moving around me? It's just a matter of how you look at the world.

Also this result shouldn't be very surprising. The universe could already be a sphere, a simulation, have no shape (QM), be a restored backup from 5 minutes ago ... We will simply never know the shape of the planet. It can be flat, it can be a globe or even a velociraptor.

[Pete Svarrior]

So what exactly are you saying?

Exactly what I said already, nothing more, nothing less. If you're trying to find a second meaning in it, you're doing it wrong.

That the AE map isn’t a projection?

I object to the naming of "the AE map" - that implies that it was originally produced through the azimuthal equidistant projection, which it wasn't.

That the basis of the OP’s work isn’t a projection?

Indeed.

The existence, or not, of some vaguely referenced historic map has nothing to do with whether or not the AE map, and indeed the same map as presented in the wiki, is a projection.

This is incorrect. While you can recreate reasonably good images that closely resemble the FE map through the use of the AE projection, it is not how the map came to be. This is essential basic knowledge without which you should not be posting here. Stack does have this knowledge, and is deliberately spreading misinformation - there was no need for me to go into much detail in order to plainly point out to him that he'll be stopping immediately.

[WTF_Seriously]

Consider this thought experiment: that shows the earth can have any possible shape and we'll never be able to prove the correct one.

- coordinate transformations can turn any shape into any other shape (math cares about numbers not drawings)
- coordinate transformations don't break physics (celestial coords, cartesian, polar, ...  physics uses all of these all the time and doesn't break)
-> physics can be made to work on any shape universe
-> There is no test to differentiate between the shapes. In reality we can only observe/measure the physical properties, not the shape.
-> we can't ever test the shape of the earth. It can be flat, it can be a globe or a duck, impossible to tell from within the universe.

So have a look around you and try these two views: i'm standing on a globe and lightrays are straight,
or you could say: i'm standing on a flat plane, and light curves to exactly counteract the missing curve.
Your eyes wouldn't be able to tell the difference and there's no physical test to distinguish between the two views, it's just a matter of perception.

It's like the question: Am i moving, or is the entire universe moving around me? It's just a matter of how you look at the world.

Also this result shouldn't be very surprising. The universe could already be a sphere, a simulation, have no shape (QM), be a restored backup from 5 minutes ago ... We will simply never know the shape of the planet. It can be flat, it can be a globe or even a velociraptor.

Consider this thought experiment.  I'm in the ISS and I circle the planet every 90-ish minutes.

[troolon]

Dear Sirs,

My model IS globe physics expressed in celestial coordinates (lat, long, distance).

- The ISS works in the model because it works in globe physics
- distances work in the model because they work in globe physics
- Vincenti works in the model because it works in globe physics
- light rays work in the model because it works in globe physics
- ...
You are trying to debunk globe physics in celestial coordinates.

It is very surprising, but physics works regardless of shape. Math doesn't care how it's drawn!
And there is perhaps an important detail to highlight: You are looking at the model from outside the universe like a God. Gods can see the true shape of the universe. For an observer inside the universe, they all behave the same. From inside the universe it's impossible to tell them apart as all these models physics ARE THE SAME.






The implications of this is that flat earth has been proven possible. As has any other shape universe. We will never be able to tell.

[SteelyBob]

That the basis of the OP’s work isn’t a projection?

Indeed.

So the OP is wrong about his/her own work? From the linked site:

There exists a coordinate transformation that transforms 3D cartesian space into an infinitely high cylinder, whereby spheres around the origin are transformed into their azimuthal equidistant projection.

The entire concept is based around an AE projection.

While you can recreate reasonably good images that closely resemble the FE map through the use of the AE projection, it is not how the map came to be. This is essential basic knowledge without which you should not be posting here. Stack does have this knowledge, and is deliberately spreading misinformation - there was no need for me to go into much detail in order to plainly point out to him that he'll be stopping immediately.

Leaving aside the OP and his work, could you enlighten me and tell me how the FE map came to be then? The wiki appears to be lacking in this department, unless I'm missing something? https://wiki.tfes.org/Flat_Earth_Maps

What process, if not AE projection, was used to create this map?

[AATW]

The implications of this is that flat earth has been proven possible. As has any other shape universe. We will never be able to tell.

This continues to be untrue no matter how many times you say it.
Distance is not a mathematical concept, it's a physical thing. You can travel between places and measure the physical distance between them.
If you do that with enough pairs of places you can then determine whether it is possible to plot those places and the known distances between them on a flat plane. If you can't then the earth cannot be flat.

[SteelyBob]

Dear Sirs,

My model IS globe physics expressed in celestial coordinates (lat, long, distance).

- The ISS works in the model because it works in globe physics
- distances work in the model because they work in globe physics
- Vincenti works in the model because it works in globe physics
- light rays work in the model because it works in globe physics
- ...
You are trying to debunk globe physics in celestial coordinates.

It is very surprising, but physics works regardless of shape. Math doesn't care how it's drawn!
And there is perhaps an important detail to highlight: You are looking at the model from outside the universe like a God. Gods can see the true shape of the universe. For an observer inside the universe, they all behave the same. From inside the universe it's impossible to tell them apart as all these models physics ARE THE SAME.

The implications of this is that flat earth has been proven possible. As has any other shape universe. We will never be able to tell.

I note you seem to be evading my point about actual distances experienced. You can't just wave it away.