Other Planets

(Peeps, that's John's secret - if it's non- euclidean - it's always curved.)

John himself is a non-euclidean closed flat surface getting around on a non-euclidean closed flat surface geometry being a planet, in non-euclidean space.

Isn't that right, John? 

What's the fun in saying we live on a globe, when you can rightly say we live on a non-euclidean closed flat surface?

Yes, John. The Earth is flat.

(Peeps, that's John's secret - if it's non- euclidean - it's always curved.)

John himself is a non-euclidean closed flat surface getting around on a non-euclidean closed flat surface geometry being a planet, in non-euclidean space.

Isn't that right, John? 

What's the fun in saying we live on a globe, when you can rightly say we live on a non-euclidean closed flat surface?

Yes, John. The Earth is flat.

Ah, but what you are missing is something something equivalence principle something. 

Or don’t you understand the equivalence principle either?

I have yet to see anybody here actually show that's the definition of non-euclidean. Why?

Because it's not. But if you want to rest your argument on a misunderstanding of mathematical terms fine.

I have yet to see anybody here actually show that's the definition of non-euclidean. Why?

Because it's not. But if you want to rest your argument on a misunderstanding of mathematical terms fine.

Is there some visual representation of what a non-euclidean flat earth looks like that you could share? I’m having a hard time conceptualizing it.

I have yet to see anybody here actually show that's the definition of non-euclidean. Why?

I'm yet to see you even attempt to describe this non-Euclidean geometry you claim Earth is which allows it to be flat while being non-Euclidean.

I wonder why?
Perhaps because you can't and instead cling to this non-Euclidean idea as a get-out-of-jail free card?

Especially as I have provided examples of non-Euclidean geometries which don't focus on violating the 5th postulate and explained how they wouldn't help for Earth.

Perhaps this will be easier for you:
On this "flat" earth of yours, is a line directly along the equator straight (or a geodesic)?
Is a line north-south straight (or a geodesic)?
Does a north pole exist?
Does a south pole exist?

Is there some visual representation of what a non-euclidean flat earth looks like that you could share? I’m having a hard time conceptualizing it.

That makes two of us. A picture paints a thousand words remember. I'm certain there must be a diagram of this somewhere out there?!?

I have yet to see anybody here actually show that's the definition of non-euclidean. Why?

Because it's not. But if you want to rest your argument on a misunderstanding of mathematical terms fine.

There are no mathematical terms involved. Euclidean geometry would work perfectly on a box shaped earth with six flat two dimensional surfaces, our earth being on one side.

Non-euclidean geometry studies curved rather than flat surfaces. So, naturally when you, John, refers to Earth as a non-Euclidean closed flat surface, by virtue of it being non-Euclidean, your use of the word flat translates to curved. Curved as in the closed continuous surface of a globe. The surface of a globe is not euclidean.

When you use the word non-euclidean you are actually saying, curved. You're a wordsmith.

Looking forward to your book, John! 

Quote from: Smoke Machine on October 03, 2021, 11:35:22 AM

(Peeps, that's John's secret - if it's non- euclidean - it's always curved.)

John himself is a non-euclidean closed flat surface getting around on a non-euclidean closed flat surface geometry being a planet, in non-euclidean space.

Isn't that right, John? 

What's the fun in saying we live on a globe, when you can rightly say we live on a non-euclidean closed flat surface?

Yes, John. The Earth is flat.

Ah, but what you are missing is something something equivalence principle something. 

Or don’t you understand the equivalence principle either?

I understand the equivalence principle just fine! But, what does it have to do with this discussion?

The term non-Euclidean sounds very fancy, but it really just means any type of geometry that's not Euclidean—i.e., that doesn’t exist in a flat world. A non-Euclidean geometry is a rethinking and redescription of the properties of things like points, lines, and other shapes in a non-flat world.

A Euclidean space is effectively a flat, 2 dimensional plane. Such as the classic X/Y plane that we learn about in high school maths.  A perpendicular plane is sometimes added to produce an Y/Z plane to create a 3D space.

So describing something as non-Euclidean is effectively describing something as being curved.  A finite but unbounded, non-Euclidean closed surface is basically what a sphere is.

Quote

The term non-Euclidean sounds very fancy, but it really just means any type of geometry that's not Euclidean—i.e., that doesn’t exist in a flat world. A non-Euclidean geometry is a rethinking and redescription of the properties of things like points, lines, and other shapes in a non-flat world.

A Euclidean space is effectively a flat, 2 dimensional plane. Such as the classic X/Y plane that we learn about in high school maths.  A perpendicular plane is sometimes added to produce an Y/Z plane to create a 3D space.

So describing something as non-Euclidean is effectively describing something as being curved.  A finite but unbounded, non-Euclidean closed surface is basically what a sphere is.

Incorrect. Euclidean simply means it conforms to Euclid's axioms. A flat surface might have this property, but so might many other objects. Likewise, there are plenty of flat mathematical objects that behave different from the surface of a piece of paper and do not fit Euclid's axioms. A pacman screen would be one of them that is a flat finite non-euclidean closed space. So there you have it. Disproof of your silly idea that "non-euclidean" means round by example. There are literally infinite other examples.

Quote from: Unconvinced on October 03, 2021, 02:07:49 PM

Quote from: Smoke Machine on October 03, 2021, 11:35:22 AM

(Peeps, that's John's secret - if it's non- euclidean - it's always curved.)

John himself is a non-euclidean closed flat surface getting around on a non-euclidean closed flat surface geometry being a planet, in non-euclidean space.

Isn't that right, John? 

What's the fun in saying we live on a globe, when you can rightly say we live on a non-euclidean closed flat surface?

Yes, John. The Earth is flat.

Ah, but what you are missing is something something equivalence principle something. 

Or don’t you understand the equivalence principle either?

I understand the equivalence principle just fine! But, what does it have to do with this discussion?

I was getting to it, but the poster I was explaining it to first said it was wrong, then that they understood it, then that they didn't and then that they didn't care. You'll forgive me if I don't waste my time feeding pearls to the swine.

Quote from: John Davis on October 03, 2021, 10:54:32 PM

I have yet to see anybody here actually show that's the definition of non-euclidean. Why?

Because it's not. But if you want to rest your argument on a misunderstanding of mathematical terms fine.

Is there some visual representation of what a non-euclidean flat earth looks like that you could share? I’m having a hard time conceptualizing it.

The best way I've found to try to visualize it is through a particular thought experiment I was attempting to share before a certain poster couldn't decide whether he understood the equivalence principle or not. I have yet to abstract this visually probably partly because of the difficulties in doing so in a way that might be less confusing than understanding the though experiment.

I shall continue.

Imagine now you are on a satellite rather than the elevator we were on earlier. More than this, it is a theoretically perfect satellite - it stays at a constant height in constant free-fall above a "perfect" planet. It can be said that on this satellite - since it is in free fall - we feel no acceleration at all. This leads us to believe we are in an inertial state (by definition) and are not being acted upon by any forces. This is to say - it is not accelerating. Per the definition of acceleration this means we are clearly and definitively traversing a straight line - assuming only Newton's laws and the equivalence principle.

Do we understand this and agree with it?

Quote from: John Davis on October 03, 2021, 10:54:32 PM

I have yet to see anybody here actually show that's the definition of non-euclidean. Why?

I'm yet to see you even attempt to describe this non-Euclidean geometry you claim Earth is which allows it to be flat while being non-Euclidean.

I wonder why?
Perhaps because you can't and instead cling to this non-Euclidean idea as a get-out-of-jail free card?

Odd. I know you were in a conversation where I provided some base axioms that helped start my work down this path.

Especially as I have provided examples of non-Euclidean geometries which don't focus on violating the 5th postulate and explained how they wouldn't help for Earth.

If I say chickens exist, does it help your argument that they don't at all to show me a lion, a bear and a tiger (oh my!). No. More than this, you managed to show it breaking 1 of the five. So your supposed evidence doesn't even cover 20% of the cases assuming that only the two popular non-euclidean geometries exist (which is factually false.)

Perhaps this will be easier for you:
On this "flat" earth of yours, is a line directly along the equator straight (or a geodesic)?
Is a line north-south straight (or a geodesic)?
Does a north pole exist?
Does a south pole exist?

Yes. Yes. Yes. Yes.

Quote from: John Davis on October 03, 2021, 10:54:32 PM

I have yet to see anybody here actually show that's the definition of non-euclidean. Why?

Because it's not. But if you want to rest your argument on a misunderstanding of mathematical terms fine.

There are no mathematical terms involved.

Here's two. "Euclidean". "Geometry"

Euclidean geometry would work perfectly on a box shaped earth with six flat two dimensional surfaces, our earth being on one side.

Assuming Einstein wrong and restricting our geometry to the surface of the earth, sure.

Non-euclidean geometry studies curved rather than flat surfaces.

Incorrect. Non-euclidean geometry studies geometries that break Euclid's postulates. Hence the name.

So, naturally when you, John, refers to Earth as a non-Euclidean closed flat surface, by virtue of it being non-Euclidean, your use of the word flat translates to curved. Curved as in the closed continuous surface of a globe. The surface of a globe is not euclidean.

When you use the word non-euclidean you are actually saying, curved. You're a wordsmith.

Looking forward to your book, John! 

Ahaha. Hey rab. Thought you were dead?

I was attempting to share before a certain poster couldn't decide whether he understood the equivalence principle or not

Obviously a dig at me there John. Not sure why as I have had no problem deciding what I understand the equivalence principle to be.

Quote

I was attempting to share before a certain poster couldn't decide whether he understood the equivalence principle or not

Obviously a dig at me there John. Not sure why as I have had no problem deciding what I understand the equivalence principle to be.

As a physics student I have never been informed that gravity is a fictitious force.

Ah I'm glad you agree you don't understand it then. What exactly are you stuck on?

Basically just understanding what your non-Euclidean closed flat surface might look like.  Seems a few others are also a bit unsure about it as well. 

Must be a real chore John having to try and teach a load of silly idiots like us about the true nature of the world eh!

Basically just understanding what your non-Euclidean closed flat surface might look like.  Seems a few others are also a bit unsure about it as well. 

Great, then you can answer this simple question rather than trying to back pedal not knowing something you seem to have picked up since then:



Imagine now you are on a satellite rather than the elevator we were on earlier. More than this, it is a theoretically perfect satellite - it stays at a constant height in constant free-fall above a "perfect" planet - uniform in every way.

It can be said that on this satellite - since it is in free fall - we feel no acceleration at all. Or to put it better - since we feel no acceleration we know it is either still or not accelerating.

This leads us to believe we are in an inertial state (by definition) and are not being acted upon by any forces. This is to say - it is not accelerating and Newton's laws hold. Per the definition of acceleration this means we are definitively traversing a straight line - assuming only Newton's laws and the equivalence principle.

Do we understand this and agree with it? If not, what can I clarify or what errors did you find?

Must be a real chore John having to try and teach a load of silly idiots like us about the true nature of the world eh!

Only when someone pretends they know something they don't.

Odd. I know you were in a conversation where I provided some base axioms that helped start my work down this path.

I know in previous discussions I have pushed you to provide them, but I don't recall you ever doing so.
I also recall you providing arguments allegedly supporting your claims and then ignoring large problems with them.

If I say chickens exist, does it help your argument that they don't at all to show me a lion, a bear and a tiger (oh my!). No. More than this, you managed to show it breaking 1 of the five.

No, I have showed it breaking more than 1 of the 5. Breaking the 5th leads to non flat geometry.
Breaking the first means you can't even draw lines, which will result in breaking the 2nd and 3rd, and leaves open the possibility of the 5th.
I also gave an example of breaking the 2nd by simply having a bounded region which results in a line stopping (i.e. not being able to be extended continuously).
I also explained how breaking those postulates means you are no longer describing Earth.

The only one I haven't shown it breaking is the 4th, as I don't know how you would break right angles being congruent without resulting in a meaningless geometry where angles have no meaning.

What doesn't help YOUR argument is focusing on these abstract ideas which in no way help show that Earth's surface can be flat but non-Euclidean.
If you want a comparison with chickens, if you say chickens don't have feathers, and show that lions, bears and tigers don't have feathers, it doesn't help your argument.

You can't describe the specific non-Euclidean geometry you claim this flat Earth of yours has.
You can't even tell us just what postulates this non-Euclidean flat Earth of yours violates.
Which of the 5 do you think doesn't hold?

Quote from: JackBlack on October 04, 2021, 12:52:39 AM

Perhaps this will be easier for you:
On this "flat" earth of yours, is a line directly along the equator straight (or a geodesic)?
Is a line north-south straight (or a geodesic)?
Does a north pole exist?
Does a south pole exist?

Yes. Yes. Yes. Yes.

Good, next question, is the line along the equator at 90 degrees to lines going north-south?
Do two N-S lines, along different longitudes (which for simplicity also will not be 180 degrees apart), meet with a non-0 angle at the north and south pole?

A pacman screen would be one of them that is a flat finite non-euclidean closed space.

I consider a flat torus to follow Euclidean geometry.
You can pick 2 points and draw a line between them.
You can extend that line continuously (yes it will overlap onto itself, but Euclid is unclear on if that is allowed)
You can describe a circle with a point and radius.
All right angles are equal to each other.
And the parallel postulate holds.

But regardless, this doesn't describe the geometry of Earth.
Again, can you give an example which could potentially be Earth?

Imagine now you are on a satellite rather than the elevator we were on earlier. More than this, it is a theoretically perfect satellite - it stays at a constant height in constant free-fall above a "perfect" planet. It can be said that on this satellite - since it is in free fall - we feel no acceleration at all. This leads us to believe we are in an inertial state (by definition) and are not being acted upon by any forces. This is to say - it is not accelerating. Per the definition of acceleration this means we are clearly and definitively traversing a straight line - assuming only Newton's laws and the equivalence principle.

Or, instead of imagining you are on a satellite, lets accept we are on the surface of Earth, and even walking around on it.
We notice that we are not in free fall.
Instead we feel a force pushing us upwards.
This leads us to conclude we are not in an inertial state and thus are not traversing a straight line.
Can we agree on that?

You cannot use a product of Euclidean geometry when you claim it is non-Euclidean.
In non-Euclidean geometry it is not certain that a line equidistant to a "straight" line is straight.
So a circular orbit remaining the same height above Earth doesn't prove that line on Earth is straight.

Quote from: John Davis on October 04, 2021, 09:07:42 AM

Odd. I know you were in a conversation where I provided some base axioms that helped start my work down this path.

I know in previous discussions I have pushed you to provide them, but I don't recall you ever doing so.
I also recall you providing arguments allegedly supporting your claims and then ignoring large problems with them.

I have yet to see a large problem with my model, but would happily dismiss (as I have other models I have suggested) once it has been shown to be incorrect.

I will attempt to find my early starts of a new set of postulates which I shared here. They have changed since then, but should provide enough to make you realize your mistakes in this constant line of argument.

Quote from: John Davis on October 04, 2021, 09:07:42 AM

If I say chickens exist, does it help your argument that they don't at all to show me a lion, a bear and a tiger (oh my!). No. More than this, you managed to show it breaking 1 of the five.

No, I have showed it breaking more than 1 of the 5. Breaking the 5th leads to non flat geometry.
Breaking the first means you can't even draw lines, which will result in breaking the 2nd and 3rd, and leaves open the possibility of the 5th.
I also gave an example of breaking the 2nd by simply having a bounded region which results in a line stopping (i.e. not being able to be extended continuously).
I also explained how breaking those postulates means you are no longer describing Earth.

The only one I haven't shown it breaking is the 4th, as I don't know how you would break right angles being congruent without resulting in a meaningless geometry where angles have no meaning.

What doesn't help YOUR argument is focusing on these abstract ideas which in no way help show that Earth's surface can be flat but non-Euclidean.
If you want a comparison with chickens, if you say chickens don't have feathers, and show that lions, bears and tigers don't have feathers, it doesn't help your argument.

You can't describe the specific non-Euclidean geometry you claim this flat Earth of yours has.
You can't even tell us just what postulates this non-Euclidean flat Earth of yours violates.
Which of the 5 do you think doesn't hold?

At least four of them. A new geometry is necessary if we wish to describe the universe as it is.

Of course they all hold in a euclidean space.

Quote from: John Davis on October 04, 2021, 09:07:42 AM

Quote from: JackBlack on October 04, 2021, 12:52:39 AM

Perhaps this will be easier for you:
On this "flat" earth of yours, is a line directly along the equator straight (or a geodesic)?
Is a line north-south straight (or a geodesic)?
Does a north pole exist?
Does a south pole exist?

Yes. Yes. Yes. Yes.

Good, next question, is the line along the equator at 90 degrees to lines going north-south?
Do two N-S lines, along different longitudes (which for simplicity also will not be 180 degrees apart), meet with a non-0 angle at the north and south pole?

Quote from: John Davis on October 04, 2021, 08:56:42 AM

A pacman screen would be one of them that is a flat finite non-euclidean closed space.

I consider a flat torus to follow Euclidean geometry.

You can pick 2 points and draw a line between them.
You can extend that line continuously (yes it will overlap onto itself, but Euclid is unclear on if that is allowed)
You can describe a circle with a point and radius.
All right angles are equal to each other.
And the parallel postulate holds.

You are right the Clifford torus is a bad example in that it is euclidean. You are wrong in that you think you have shown all five broken.

But regardless, this doesn't describe the geometry of Earth.

Which need not be done to throw out your ridiculous and repeated claims that non-euclidean means non-flat. However as pointed out I'll have to throw another one of the infinite examples.

A non-euclidean flat geometry:
1: A straight line segment may be drawn from any given point to any other.
2: A straight line may be extended to any finite length.
3: Right Angles are not congruent

You are trying as hard as you might to win by the definition of "flat", however it is the geometry that defines what flat is, not you in some circular argument around flat is euclidean and non-flat is non-euclidean.

Again, can you give an example which could potentially be Earth?

Quote from: John Davis on October 04, 2021, 09:04:57 AM

Imagine now you are on a satellite rather than the elevator we were on earlier. More than this, it is a theoretically perfect satellite - it stays at a constant height in constant free-fall above a "perfect" planet. It can be said that on this satellite - since it is in free fall - we feel no acceleration at all. This leads us to believe we are in an inertial state (by definition) and are not being acted upon by any forces. This is to say - it is not accelerating. Per the definition of acceleration this means we are clearly and definitively traversing a straight line - assuming only Newton's laws and the equivalence principle.

Or, instead of imagining you are on a satellite, lets accept we are on the surface of Earth, and even walking around on it.
We notice that we are not in free fall.
Instead we feel a force pushing us upwards.
This leads us to conclude we are not in an inertial state and thus are not traversing a straight line.
Can we agree on that?

You cannot use a product of Euclidean geometry when you claim it is non-Euclidean.
In non-Euclidean geometry it is not certain that a line equidistant to a "straight" line is straight.
So a circular orbit remaining the same height above Earth doesn't prove that line on Earth is straight.

It is sufficient when we talk of a flat earth to talk of the bounding space of earth being flat. As before, we are not worried whether there are hills and valleys and what not, physical or as the shape of space itself. More than this we can show this is the case pretty easily by examining the iteration of such orbits as they approach the earth as well as with non-orbiting bodies near the surface.

I will attempt to find my posts on the subject.

For those who wish to skip ahead, someone did write up their take on this some time ago:
https://www.theflatearthsociety.org/forum/index.php?topic=72129.0

I have yet to see a large problem with my model

We are yet to see your model.
Instead we just have vague claims of a non-Euclidean flat Earth.

At least four of them. A new geometry is necessary if we wish to describe the universe as it is.

So by that you are saying that none of the first 4 postulates hold?
That you can't draw lines between 2 points, even though arguments you provide rely upon drawing lines between 2 points?
With contradictions like that, is it really surprising people don't take it seriously?

And you seemed to have skipped the questions:
Is the line along the equator at 90 degrees to lines going north-south?
Do two N-S lines, along different longitudes (which for simplicity also will not be 180 degrees apart), meet with a non-0 angle at the north and south pole?

You are right the Clifford torus is a bad example in that it is euclidean. You are wrong in that you think you have shown all five broken.

No, I'm not wrong as I never claimed that.

Quote

But regardless, this doesn't describe the geometry of Earth.

Which need not be done to throw out your ridiculous and repeated claims that non-euclidean means non-flat.

Which does need to be done if you want to try claiming it is a non-Euclidean flat Earth.
If you want to have a generic idea which has no connection to Earth, then that is a different issue.

But as we know the first 4 postulates hold on Earth, then that leaves only the 5th to be violated, which would lead to a non-flat surface.
So for the surface of Earth, non-Euclidean means non-flat.

A non-euclidean flat geometry:
1: A straight line segment may be drawn from any given point to any other.
2: A straight line may be extended to any finite length.
3: Right Angles are not congruent

And how do you have a coherent geometry without right angles being congruent?
Just what would right angles not being congruent mean?
Just what is a right angle in this geometry?

This also raises the question of how you can use such right angles in your attempt to "prove" Earth is flat, with lines at right angles to a satellite's trajectory and Earth surface?

It is sufficient when we talk of a flat earth to talk of the bounding space of earth being flat.

No, it isn't. Showing some bounding region to be flat, doesn't mean Earth itself is flat.
While we aren't focusing on mountains and valleys, we are also not focusing a satellite off in orbit.

So no, we don't need to bother focusing on the orbit of a satellite at all.
Instead we can just focus on the surface of Earth and people standing on it, which clearly experience a force showing it is not following a geodesic through spacetime.
That should be enough to show that appeals to GR wont help you.

For those who wish to skip ahead, someone did write up their take on this some time ago:
https://www.theflatearthsociety.org/forum/index.php?topic=72129.0

And that post also contains some of the main objections, like how you are using orbits through spacetime to try to declare Earth is flat, even though those paths are only for specific paths through spacetime, not just any path through space, and don't match up to the actual surface of Earth.

And what is the main response to that? To just ignore any path which shows Earth isn't flat and instead only accept those which can be used to pretend Earth is flat.
Quite dishonest, and quite circular. Accepting that Earth's surface does have a temporal component as it is moving through space (and even appealing to that), while completely ignoring that temporal component and pretending you can use a path that traverses the same space, but with a massively different temporal component.
And of course, all while ignoring the fact that it is trying to use something from Euclidean geometry in a non-Euclidean space.

It also raises the question of just how would you define a "flat" surface in non-Euclidean geometry, with some examples of several different ideas to make up such a "flat" surface, specifically in a 3D non-Euclidean space representing 2D space + time; showing that different ways to make a "flat" surface, lead to different surfaces.

And this wonderful gem:

I'm sorry Alt, but basically all of this boils down to a round Earth, but using a lot of needless complexity that has no observational support to ultimately describe it as flat.

It would just be easier to admit that the round Earth is the correct functional model rather than jumping through all these hoops hoping to "win" on a technicality.

Quote from: Smoke Machine on October 04, 2021, 04:51:17 AM

Quote from: John Davis on October 03, 2021, 10:54:32 PM

I have yet to see anybody here actually show that's the definition of non-euclidean. Why?

Because it's not. But if you want to rest your argument on a misunderstanding of mathematical terms fine.

There are no mathematical terms involved.

Here's two. "Euclidean". "Geometry"

Quote

Euclidean geometry would work perfectly on a box shaped earth with six flat two dimensional surfaces, our earth being on one side.

Assuming Einstein wrong and restricting our geometry to the surface of the earth, sure.

Quote

Non-euclidean geometry studies curved rather than flat surfaces.

Incorrect. Non-euclidean geometry studies geometries that break Euclid's postulates. Hence the name.

Quote

So, naturally when you, John, refers to Earth as a non-Euclidean closed flat surface, by virtue of it being non-Euclidean, your use of the word flat translates to curved. Curved as in the closed continuous surface of a globe. The surface of a globe is not euclidean.

When you use the word non-euclidean you are actually saying, curved. You're a wordsmith.

Looking forward to your book, John! 

Ahaha. Hey rab. Thought you were dead?

Rab would be peering down through the clouds and chuckling to himself, "The huckster, John Davis is at it again and still teasing his book he hasn't even written the first word for."

I'm not assuming Einstein wrong at all, and I am restricting earth's geometry to the earth's physicality. 

Non-euclidean geometry includes a very large globe with bumps referred to as hills and mountains, and valleys and depressions filled with water, all that break euclid's postulates. Curves - Non-Euclidean through and through. 

John, make it easier for everybody and show us all a 3d model of your non-euclidean flat earth model, that isn't a sphere?

I simply can't visualize what you're talking about in practical terms in 3 dimensional space. You do know what three dimensional space is, right? 

Surely there is more to being a theoretical scientist than shaving a bald spot on the top of your head and putting on a pair of spectacles and a bow tie?

A photographer who takes 2 dimensional photos of the 3 dimensional world, is arguably capturing flat 2 dimensional images from a reference point. Is this where you're going with this?