Tessa-llated Earth - Emergent FET (Ideas or advice?)

For a while now, I've been working on a FET of my very own. I had prepared a huge document outlining the methods I had used to come about it - but I suppose that's all secondary. Here is my FET, "Tessa-llated Earth". (And yes, I am far too proud of that name)

In this model, there are three main premises.

The Earth is;
1. an infinite plane,
2. in spherical space,
3. infinitely tessellated.

Each premise plays into each other, but to keep things simple I'll be brief. I'm sure all the RErs here will grill me anyway. Essentially, the infinite Earth resolves gravity, the spherical space (I say spherical, but it's an arbitrary Reimann manifold close enough to spherical space that it makes an oblate spheroid ) resolves a lot of everything else, and the infinite tessellations facilitates travel and everything the first two don't.

Basically, you can picture it as Google Maps. If you scroll out far enough, the planet tessellates. Now imagine that is in spherical space, and you get the Tessa-llated Earth, something that looks and behaves how you would expect a Globe Earth to, but something which is not a Globe Earth.

A curious product of this setup is that it is homeomorphic to the Globe Earth, but not without self-intersection, so it is a real projective plane, fancy talk for "it is one sided". I said on a thread earlier today that there was molten metal on the other side, now I must correct myself. The Tessa-llated Earth is one sided, and so has no 'other side'.

I'd love it if you guys had questions or points so I can expand on what I've said here, and hopefully improve it too. I know I haven't exactly gone into a lot of detail, but once I get some feedback and tweak it a bit, I'll be able to do so. Thanks!

What did your therapist say?

What did your therapist say?

Am I to take it you found no flaw in the theory then, since you resort to an ad hominem?

For a while now, I've been working on a FET of my very own. I had prepared a huge document outlining the methods I had used to come about it - but I suppose that's all secondary. Here is my FET, "Tessa-llated Earth". (And yes, I am far too proud of that name)

In this model, there are three main premises.

The Earth is;
1. an infinite plane,
2. in spherical space,
3. infinitely tessellated.

Each premise plays into each other, but to keep things simple I'll be brief. I'm sure all the RErs here will grill me anyway. Essentially, the infinite Earth resolves gravity, the spherical space (I say spherical, but it's an arbitrary Reimann manifold close enough to spherical space that it makes an oblate spheroid ) resolves a lot of everything else, and the infinite tessellations facilitates travel and everything the first two don't.

Basically, you can picture it as Google Maps. If you scroll out far enough, the planet tessellates. Now imagine that is in spherical space, and you get the Tessa-llated Earth, something that looks and behaves how you would expect a Globe Earth to, but something which is not a Globe Earth.

A curious product of this setup is that it is homeomorphic to the Globe Earth, but not without self-intersection, so it is a real projective plane, fancy talk for "it is one sided". I said on a thread earlier today that there was molten metal on the other side, now I must correct myself. The Tessa-llated Earth is one sided, and so has no 'other side'.

I'd love it if you guys had questions or points so I can expand on what I've said here, and hopefully improve it too. I know I haven't exactly gone into a lot of detail, but once I get some feedback and tweak it a bit, I'll be able to do so. Thanks!

Well if it makes you happy....

Couple of points of clarification:
Is it the Earth or the space the Earth's in that's tesselated?
By infinitely tessellated, do you mean that there are infinite shapes, or that they are infinitely small?
And on spherical space, you say it's a Riemann manifold close to spherical space; is that due to the shape of the manifold, or a consequence of its inner product?

Also, what are the consequences of tessellations? Just one to begin with would be nice, it's hard to imagine what effect that could have.

Sorry for the question flurry, I love figuring things like this out. (If you ever feel like sharing the underlying document I'd be interested, by the way, though it's up to you).

Is it the Earth or the space the Earth's in that's tesselated?
By infinitely tessellated, do you mean that there are infinite shapes, or that they are infinitely small?
...
Also, what are the consequences of tessellations? Just one to begin with would be nice, it's hard to imagine what effect that could have.

The Earth itself is tessellated across the infinite plane. So, if you walk far enough, you'll end up where you started, because the Earth repeats infinitely. You can picture it like this:

If you walk all the way around the Globe Earth back to where you started, you will have passed through an entire tessellation on the Flat Earth. You can keep doing this forever and you will never get to the end of the tessellations.

And on spherical space, you say it's a Riemann manifold close to spherical space; is that due to the shape of the manifold, or a consequence of its inner product?

Similarly to how the Globe Earth is so close to a sphere that a sphere can be used in its place for a number of calculations, so too is this manifold close to spherical space.

Have I explained that right?

So, there are an infinite number of copies of Earth in an infinite plane?

Like, if I start at London traveling west, I end in a copy of our Earth? And a copy of me from an Earth East from my original one ends up in my Earth? Everytime I travel around the planet I end up in an Earth exactly like mine, where my copy just went to another Earth the same moment I crossed the division? Are my loved ones all just copies from another planet?

That's scary and depressing as hell. XD

I'm glad the Earth is round. 

So, there are an infinite number of copies of Earth in an infinite plane?

Like, if I start at London traveling west, I end in a copy of our Earth? And a copy of me from an Earth East from my original one ends up in my Earth? Everytime I travel around the planet I end up in an Earth exactly like mine, where my copy just went to another Earth the same moment I crossed the division? Are my loved ones all just copies from another planet?

That's scary and depressing as hell. XD

I'm glad the Earth is round.

Oh, nonono! That would be truly terrifying! I'm saying the surface of the Earth tessellates, not all of reality. You can picture it as walking around a sphere, eventually you'll arrive at the same location. Nothing else is copied!

Don't think I'm getting it.

Say, me and a friend of mine start in London. I go West, and he goes East. In a round Earth, we'd just fly around the planet and meet at the same place.

By your theory though, I should end in the London at the Earth west from ours, while he ends in the Earth at the east. We both wouldn't meet there, unless copies of us from other Earths also entered that Earth at the same time, while other copies also entered our copies' original Earths, and that would have to happen at infinite Earths.

How could us end up in the same place by going to opposite directions in a flat plane? Don't get how that could happen. 

The Earth itself is tessellated across the infinite plane. So, if you walk far enough, you'll end up where you started, because the Earth repeats infinitely. You can picture it like this:

If you walk all the way around the Globe Earth back to where you started, you will have passed through an entire tessellation on the Flat Earth. You can keep doing this forever and you will never get to the end of the tessellations.

Ah, right, thanks, sorry I was approaching it from completely the wrong direction.
Are all the Earths the same one, or are there an infinite number of deterministic worlds where the same events are occurring? (Which probably sounds like a stupid question, just checking, tessellation may be a misleading term as it implies the latter).
Or we're getting solipsistic and only one Earth exists, and which one changes depending on where you are 
I love any theory that ends up with pondering philosophy so this is definitely a good start.

How could us end up in the same place by going to opposite directions in a flat plane? Don't get how that could happen.

Are all the Earths the same one, or are there an infinite number of deterministic worlds where the same events are occurring? (Which probably sounds like a stupid question, just checking, tessellation may be a misleading term as it implies the latter).

I haven't really done this part of the theory justice. I'll try to explain. Essentially, in spherical space, travelling in a straight line for long enough will take you back to where you began (like walking around a sphere would, but in 2D space). The 'tessellations' are more a representation of this property on an infinite plane, so if you were to travel in a curved line, then you would never be able to reach any 'edge' or boundary to the Earth.

Mathematically, it's like a Mobius Strip, there is one side, so no matter how far or where you walk, you'll always be at a definite location on Earth. Nothing can 'fall off'. So tessellation perhaps isn't the correct term, but it is a helpful illustration, and I like the pun a lot.

It behaves exactly how you would expect a sphere to, only on a flat plane.

Does that clear it up a little? To be honest, I've never really had to explain it off-script before, so let me know if I'm being confusing.

Ah, interesting. What you're describing might be typical non-Euclidean FET, or an interesting variation where it isn't the metric that leads to you going back on yourself but rather a certain area of space itself being duplicated on and on by whatever means.
What is there that sets the tessellations apart from the effects of spherical space?

Ah, interesting. What you're describing might be typical non-Euclidean FET, or an interesting variation where it isn't the metric that leads to you going back on yourself but rather a certain area of space itself being duplicated on and on by whatever means.
What is there that sets the tessellations apart from the effects of spherical space?

Well, usually the size of the plane determines how far you must travel before you loop back in on yourself, but since the plane is infinite, there has to be another factor which determines size. Or, another way of putting it, an infinite sheet of paper can be wrapped around any size ball you choose, an infinite number of times. So the size of the tessellations determines the size of the 'ball'. Is that what you mean by "a certain area of space itself being duplicated on and on"?

I don't know how close that is to typical non-Euclidean FET, if it is the same hopefully I've been able to more strictly mathematically define what that would look like, as a real projective plane set in spherical space.

Nothing else is copied!

So I think we're still left with the question:  are the circumstances in each of the "tiles" in the tesselation independent?  In other words, if I take off in a plane from my city, fly "around the world" and land back where I started, I'm on a different version of the earth right?  Would there now be two of me in this tile, while everyone back on the first one thinks I vanished?

Secondly where would the boundary between tiles be...or am I thinking about this too simplistically?

Quote from: Tessa Yuri on August 06, 2017, 02:58:21 PM

Nothing else is copied!

So I think we're still left with the question:  are the circumstances in each of the "tiles" in the tesselation independent?  In other words, if I take off in a plane from my city, fly "around the world" and land back where I started, I'm on a different version of the earth right?  Would there now be two of me in this tile, while everyone back on the first one thinks I vanished?

Secondly where would the boundary between tiles be...or am I thinking about this too simplistically?

They aren't tiles so much as a loop back in on the same location, like a 2D Möbius strip. So in your hypothetical circumstance, you're on the same Earth, in the same place, just that each location on Earth has an infinite number of coordinates assigned to it, depending on how many tiles or revolutions you have passed through.

Well, usually the size of the plane determines how far you must travel before you loop back in on yourself, but since the plane is infinite, there has to be another factor which determines size. Or, another way of putting it, an infinite sheet of paper can be wrapped around any size ball you choose, an infinite number of times. So the size of the tessellations determines the size of the 'ball'. Is that what you mean by "a certain area of space itself being duplicated on and on"?

I don't know how close that is to typical non-Euclidean FET, if it is the same hopefully I've been able to more strictly mathematically define what that would look like, as a real projective plane set in spherical space.

If instead of wrapping a sheet of paper around a ball mutliple times, a sheet of paper was wrapped once around it and the edges taped together, to potentially stretch the analogy too far, would there be any difference between that situation and your tessellations?
If so, in practise, what?

Sorry for labouring this point, I think it's where most of the misunderstanding seems to be.

Quote from: Tessa Yuri on August 07, 2017, 04:45:03 AM

Well, usually the size of the plane determines how far you must travel before you loop back in on yourself, but since the plane is infinite, there has to be another factor which determines size. Or, another way of putting it, an infinite sheet of paper can be wrapped around any size ball you choose, an infinite number of times. So the size of the tessellations determines the size of the 'ball'. Is that what you mean by "a certain area of space itself being duplicated on and on"?

I don't know how close that is to typical non-Euclidean FET, if it is the same hopefully I've been able to more strictly mathematically define what that would look like, as a real projective plane set in spherical space.

If instead of wrapping a sheet of paper around a ball mutliple times, a sheet of paper was wrapped once around it and the edges taped together, to potentially stretch the analogy too far, would there be any difference between that situation and your tessellations?
If so, in practise, what?

Sorry for labouring this point, I think it's where most of the misunderstanding seems to be.

They would be identical, but because this is actually a 2D plane, both would be an infinite plane, or else you couldn't "tape the edges together", if that makes sense.

They would be identical, but because this is actually a 2D plane, both would be an infinite plane, or else you couldn't "tape the edges together", if that makes sense.

Ok, that sounds fairly like the non-Euclidean model.
You're left with the main weakness of the non-Euclidean model; being able to explain why things work. Promising start though.

So there aren't multiple Earths, and more like a single Earth that exist in infinite different places in space at the same time? Are they like reflections of the same Earth?

So there aren't multiple Earths, and more like a single Earth that exist in infinite different places in space at the same time?

Yes. Imagine you could measure the distance as you walked around a Globe Earth. With each rotation, the distance you've walked increases. On a Globe Earth though, you still start and finish at the same coordinates. On this model of the Earth, your coordinates instead reflect how far you've walked, even though you still start and finish at the same place. Non-Euclidean space is tricky like that.

Ok, that sounds fairly like the non-Euclidean model.
You're left with the main weakness of the non-Euclidean model; being able to explain why things work. Promising start though.

What do you mean by "why things work"? Do you mean why it exists and how it formed?

Quote from: Jane on August 07, 2017, 10:47:50 AM

Ok, that sounds fairly like the non-Euclidean model.
You're left with the main weakness of the non-Euclidean model; being able to explain why things work. Promising start though.

What do you mean by "why things work"? Do you mean why it exists and how it formed?

Questions like why the Sun appears to move across the sky, what makes the stars move, etc. You seem to be using gravity, but I don't think you can borrow RE explanations etc for the other topics quite so easily.
Plus if from a distance the world can appear like a globe, the infinite plane/gravity trick you're using could potentially have some weird effects, depending on how the tessellations work. You'd have an infinite plane occupying what would seem like a finite space, which is mathematically possible but the gravity calculations you can use for an infinite plane only come out nicely when it's flat. Have the infinite plane be modelled as a ball... Because you can't just have a lone Earth work like that because the tessellations don't stand alone; one tile doesn't have the infinite-plane-gravity explanation, it's affected by the adjacent tiles on and on...  At lower altitudes the infinite plane could give us this gravity, but the less planar it is the more mass is centred beneath you.
Might be wrong, but it seems to check out, so this isn't a model you can slip into the RE model or anything. There are other FE explanations, but not all would line up with the infinite plane, and regardless I'm not sure which you use.

For a while now, I've been working on a FET of my very own. I had prepared a huge document outlining the methods I had used to come about it - but I suppose that's all secondary. Here is my FET, "Tessa-llated Earth". (And yes, I am far too proud of that name)

In this model, there are three main premises.

The Earth is;
1. an infinite plane,
2. in spherical space,
3. infinitely tessellated.

Each premise plays into each other, but to keep things simple I'll be brief. I'm sure all the RErs here will grill me anyway. Essentially, the infinite Earth resolves gravity, the spherical space (I say spherical, but it's an arbitrary Reimann manifold close enough to spherical space that it makes an oblate spheroid ) resolves a lot of everything else, and the infinite tessellations facilitates travel and everything the first two don't.

Basically, you can picture it as Google Maps. If you scroll out far enough, the planet tessellates. Now imagine that is in spherical space, and you get the Tessa-llated Earth, something that looks and behaves how you would expect a Globe Earth to, but something which is not a Globe Earth.

A curious product of this setup is that it is homeomorphic to the Globe Earth, but not without self-intersection, so it is a real projective plane, fancy talk for "it is one sided". I said on a thread earlier today that there was molten metal on the other side, now I must correct myself. The Tessa-llated Earth is one sided, and so has no 'other side'.

I'd love it if you guys had questions or points so I can expand on what I've said here, and hopefully improve it too. I know I haven't exactly gone into a lot of detail, but once I get some feedback and tweak it a bit, I'll be able to do so. Thanks!

Occams Razor was made for moments like this. There is all the guff above or... the earth is spherical. So which one is simpler (and less insane)?

Hmmm... That's certainly some food for thought Jane. I'll try and pick through what you've said and see what I can or can't explain.

Questions like why the Sun appears to move across the sky, what makes the stars move, etc.

That would be an effect of the properties of spherical space, but I think this is brought up in a bit so I'll see what I can say then.

You'd have an infinite plane occupying what would seem like a finite space, which is mathematically possible but the gravity calculations you can use for an infinite plane only come out nicely when it's flat.

But it is flat. If I had an infinite ball it would be different, but this is an infinite flat plane that possesses all the properties of a sphere. The tessellations, spherical space, all of it could be condensed down into: "A flat plane that mathematically behaves identically to a sphere." I'm confused by how it would behave differently just because it is in spherical space. Could you elaborate?

Because you can't just have a lone Earth work like that because the tessellations don't stand alone; one tile doesn't have the infinite-plane-gravity explanation, it's affected by the adjacent tiles on and on.

Naturally, it only works if the plane is infinite. But the tessellations are necessitated as a direct result of the infinite nature and spherical space.

Might be wrong, but it seems to check out, so this isn't a model you can slip into the RE model or anything.

I don't really see why not; if it behaves exactly like a sphere.

How does sunset work taking into account what we can observe: The sun moves across the sky at a constant angular velocity, and does not change shape or size as it approaches and then goes below the horizon. If your answer uses perspective, it is as weak as all the other FE theories.

How does sunset work taking into account what we can observe: The sun moves across the sky at a constant angular velocity, and does not change shape or size as it approaches and then goes below the horizon. If your answer uses perspective, it is as weak as all the other FE theories.

My answer does not use perspective; I think I've covered this above when talking about spherical space.

For a while now, I've been working on a FET of my very own. I had prepared a huge document outlining the methods I had used to come about it - but I suppose that's all secondary. Here is my FET, "Tessa-llated Earth". (And yes, I am far too proud of that name)

In this model, there are three main premises.

The Earth is;
1. an infinite plane,
2. in spherical space,
3. infinitely tessellated.

Each premise plays into each other, but to keep things simple I'll be brief. I'm sure all the RErs here will grill me anyway. Essentially, the infinite Earth resolves gravity, the spherical space (I say spherical, but it's an arbitrary Reimann manifold close enough to spherical space that it makes an oblate spheroid ) resolves a lot of everything else, and the infinite tessellations facilitates travel and everything the first two don't.

Basically, you can picture it as Google Maps. If you scroll out far enough, the planet tessellates. Now imagine that is in spherical space, and you get the Tessa-llated Earth, something that looks and behaves how you would expect a Globe Earth to, but something which is not a Globe Earth.

A curious product of this setup is that it is homeomorphic to the Globe Earth, but not without self-intersection, so it is a real projective plane, fancy talk for "it is one sided". I said on a thread earlier today that there was molten metal on the other side, now I must correct myself. The Tessa-llated Earth is one sided, and so has no 'other side'.

I'd love it if you guys had questions or points so I can expand on what I've said here, and hopefully improve it too. I know I haven't exactly gone into a lot of detail, but once I get some feedback and tweak it a bit, I'll be able to do so. Thanks!

It's all very well having grandiose ideas about things, but sooner or later one needs to be practical. So here's a few questions you can answer, or not.
How did your infinite tesilated planet thing form?
What were the physical laws that caused it to happen?
Why did those laws that caused the infinite planet thing to form not do the same to the moon, sun and all the other observed planets and stars that have been observed?
For an infinite plane you require an infinite amount of matter, where did that infinite amount of matter come from?
Can you post images that show the infinite plane? ....as I can post images that show it not to be infinite.
As someone once said extraordinary claims require extraordinary evidence.
I look forward to seeing all your extraordinary evidence, othwise what you are saying is no more than tepid air.

How did your infinite tesilated planet thing form?

Same way science says it did. I wouldn't claim to have researched enough to be able to contradict them on that.

Why did those laws that caused the infinite planet thing to form not do the same to the moon, sun and all the other observed planets and stars that have been observed?

They did. Who said the Sun and other planetary bodies weren't the same as the Earth?

For an infinite plane you require an infinite amount of matter, where did that infinite amount of matter come from?

Why do you say it needs an infinite amount of matter? Or, to put it another way, where did the space-time continuum come from? I'm a little confused why you say there needs to be an infinite amount of matter, could you elaborate on why? I can sortof see the point you're trying to make, but I'm not really getting the specifics of what you're asking.

Can you post images that show the infinite plane? ....as I can post images that show it not to be infinite.

https://www.google.com.au/search?rlz=1C1CYCH_enAU527AU528&tbm=isch&q=images+of+earth+from+space&chips=q:images+of+earth+from+space,g_1:real&sa=X&ved=0ahUKEwiF5YiMrcfVAhWJxLwKHXttCuQQ4lYIKSgA&biw=1440&bih=794&dpr=1#imgrc=-vscieVwP9w93M:

I'd love it if you guys had questions or points so I can expand on what I've said here, and hopefully improve it too. I know I haven't exactly gone into a lot of detail, but once I get some feedback and tweak it a bit, I'll be able to do so. Thanks!

Why does light bend?

How can you distinguish this from a round Earth in flat space?

How do you explain gravity?

Also, you can simply leave out the tessellations and just have the spherical space.

Spherical space allows you to walk around it and come back to the same point.

In order for it to be infinite with tessellation it would appear identical to flat space.

That would be an effect of the properties of spherical space, but I think this is brought up in a bit so I'll see what I can say then.

Fair enough, just consider it a note for the future. That's the hardest part of, essentially, coordinate shifts between RET and FET. You can get it all to work mathematically but there are a lot of explanations that need to be different.

But it is flat. If I had an infinite ball it would be different, but this is an infinite flat plane that possesses all the properties of a sphere. The tessellations, spherical space, all of it could be condensed down into: "A flat plane that mathematically behaves identically to a sphere." I'm confused by how it would behave differently just because it is in spherical space. Could you elaborate?

It might mathematically behave identically to a sphere, but you still need to be able to demonstrate a way where that's possible. Certainly you can make it appear like a sphere from a distance, but for us to stay on its surface and for it to stay flat you need an infinite plane. From a distance, all the tessellations are overlaid. Take the following hypothetical:
You're on the infinite plane. You're pulled down, but not crushed because the plane is finite. You're pulled to the sides, but because the plane is infinite in each direction there's a balance between the forces.
Now, purely hypothetically, make it an infinite arc. Just by a couple of degrees, but now there's far more mass underneath you, off to either side. The infinite lengths on each side of you are now also that little bit below you. The downwards force from your sides is greater; horizontally still balanced, but there's more vertical.
Increase the arc, and the downwards force in turn increases.
Now imagine the curvature's complete, and all that infinite plane is rolled up into a ball. It still has the same mass, but now it's in a finite area. If you were standing there, the force would be a fair bit bigger.

That's the problem. You've used photos from space, but with an infinite plane in finite space all of that mass would be beneath the person. if you want to use tessellations as some way to excuse them, that works, but you'd need to explain how it is they don't have a similar effect on the Earth's surface and thus negate the infinite plane.

You can get a flat plane to behave like a sphere if you want, but that doesn't mean it'll behave like a sphere of equal mass to a round Earth.

Super cool!

A flat Earth "theory" that uses NASA (and other space agencies) Earth-from-space photographs as evidence!