I assume you are not a carpet fitter by trade. You would experience some very surprised customers.

If that sounds facetious, it isn't meant to be. Forget the complex maths (and I'm not convinced that you're not trolling), but if you can't get your head around the practicality of measuring something you are physically experiencing (be it with a straight ruler, odometer or whatever), and transferring those dimensions onto a model with which you are interacting (be that an engineering drawing, map or mental concept), I don't think you are really in a position to postulate the shape of the cosmos.

Given the time i've spent on programming the animations, i would be a very determined troll

Also i've had this work verified by at least 10 physicists by now. It is correct, i just find it very difficult to explain.

I wholeheartedly agree that this model is not practical. The only uses found so far are:

- to show it is possible to construct a flat earth model

- From this it can be deduced a flat earth is possible, but so is a globe, a pyramid or any shape universe, however it will be impossible for us to ever test, as all models will always predict all the same values for every test

- maybe there could be some value in visualization. I would love to be able to make space tangible and hold it in my hand.

Maybe i should update the title of the post to "Flat earth possible, but true shape of the universe unprovable"

As i spent a lot of time on the animations, i do tend to get bogged down into the details which i can imagine would be confusing.

Maybe I can explain better in 2D:

Imagine a cartesian coordinate grid with a line in it, terminated by points p1 and p2.

Also imagine you have some formulas that work on lines (say a length-formula)

- Now, we will express p1 and p2 in polar coordinates. Mathematically there's nothing wrong, but all our formulas break.

We can fix our formulas by reverting back to cartesian coords. so length_in_polar(polar1, polar2) = length_in_cartesian(polar_to_cart(polar1), polar_to_cart(polar2))

The details don't really matter, just that all formulas can be made to work when we switch to polar coords.

All right we now have done a coordinate transform, and everything still works.

- Now we will draw these polar coords funnily. An angle is a value between [0° and 360°].

What if we were to draw our coordinate (angle, dist) onto a orthonormal X/Y grid. Ie X ranging from [0°, 360°] and Y just the distance.

Suddenly our line, would become an arc.

It might seem crazy to draw angles linearly on an X-axis, but remember that in radians, the angle represents also the arclength of a unitcircle. It's also a length.

However this is just a representation. Mathematically nothing changed. The polar coordinates are still the same we just drew them differently.

Conclusion: We did a little magic trick whereby we changed a line into an arc, while all maths and formulas still treat it as a line.

That's what i'm doing in 3D and with all of physics:

- We take any point in x,y,z-coordinates and transform to celestial coordinates. (latitude, longitude, distance)

We must also update all formulas in physics to support this change. For example the distance formula needs to be updated as it works on cartesian instead of celestial coords.

This is not impossible, in fact physicists use celestial coords and coordinate transformation all the time.

- Now we draw our celestial coords funnily. We do the same trick as before where we draw latitude (an angle) on a straight axis instead of as an angle. This effectively creates and AE-projection like effect, and the result is the flat earth you've seen.

So we've taken the globe, and all of physics and transformed it into a flat earth, with all the physics intact.

That's it. Hope it makes more sense like this.

Philosophical implications:

The trick above generalizes to all coord transforms. You can practically turn any shape into any other shape.

And physics, well they use coord transforms all the time.

So all of physics basically works on any shape universe.

From this we can conclude that the universe can have pretty much every possible shape

As all the models always produce the same answer for every question, we'll never be able to test which model is correct and thus what shape the universe has.

Earth could be a globe, or flat or ..... Any shape is possible, none is provable. At least not from within.