1

Flat Earth Debate / Re: Davis Relativity Model (Debate/discussion edition)

« on: October 25, 2017, 02:29:35 AM »

only on a flat surface could an inertial orbit work, as it works with GR.

Define "orbit" for any shape in a general space-time and prove this conjecture.

It could be described as a tangent vector remaining tangent across earth, a straight surface.

But it doesn't. Let's take a point on Earth's surface. A tangent to Earth on it is a hypothetical inertial trajectory of an object that starts in its location and velocity. This object will fall down immediately and its trajectory won't remain tangent to Earth. So no, Earth isn't flat.

I also pointed out that it was 4D space-time coordinates, with time being interconnected with 3D space.

So JackBlack was right. There are many pairs of spatial coordinates that the straight line between them isn't on Earth's trajectory. For example, Let's take an event on Earth, and an event in the sams time but at its opposite point. The straight line between them goes inside Earth and therefore isn't on Earth. So Earth isn't flat, again.

My example was in an Euclidean space-time. I can choose in which space-time my example is.

Which is why it missed the point, so it doesn't apply here.

A definition for something on non-Euclidean space-times should generalize this thing on Euclidean space-times. Anyway, forget about my parabola example. I didn't understand the definition correctly.

2

Flat Earth Debate / Re: Davis Relativity Model (Debate/discussion edition)

« on: October 24, 2017, 09:53:46 PM »

Again, AltSpace and Davis, when you look here please clarify your definition.

The Earth's flat surface?
That is when the surface is a straight surface in 4D space-time, like a geodesic in that field. It's a quite simple concept.

Nope. You didn't answer my request.
This was your definition:

Now lets look at the definition I used:

it is something based on space and how it relates to the Earth. A flat plane would be defined by the ability to traverse it in a straight line between two spatial coordinates.
...

I asked you to clarify this definition.
Maybe I wasn't specific enough (although if you read my and JackBlack's discussion you could understand it). I want you to specifically clarify what spatial coordinates are – 3D coordinates relative to Earth? 4D space-time coordinates? Something else?

Your parabola example completely misses the point, you are simply stating that it isn't straight (and therefore not flat) as applied to a Euclidean space assuming flat space.

If you warp the space-time field so a path forms a parabola relative to some more homogeneous space surrounding it, then you could describe such a path as inertial with a trajectory and straight.

My example was in an Euclidean space-time. I can choose in which space-time my example is.

3

Flat Earth Debate / Re: Whats beyond the confined dome/ice wall?

« on: October 23, 2017, 09:36:15 PM »

Extra Crispy Penguin Tenders!

Penguin McNuggets?

Peng-Fil-A?

Popeyes Penguin?

I don't know about some of the others on your list , but you can get "extra crispy" or "original recipe" at AFP.
They also serve Iced Tea.

Is the ice in the tea from the ice wall?

4

Flat Earth Debate / Re: Davis Relativity Model (Debate/discussion edition)

« on: October 23, 2017, 01:53:23 AM »

Again, AltSpace and Davis, when you look here please clarify your definition.

5

Flat Earth Debate / Re: Davis Relativity Model (Debate/discussion edition)

« on: October 23, 2017, 01:51:58 AM »

OK, but how can you translate a line in a non-Euclidean space unambiguously?

By looking at a local, Euclidean representation at each point, as I did.

OK, just make sure you did it right.

It's possible to create a hyperbolic paraboloid in many ways. One way is translating a parabola along another parabola, a different way is to translate a line along another line while rotating it in a specific way.

Yes, and that rotation means it is no longer simply translating a line along another line, and thus the surface is not flat.

OK.

I don't understand what that even mean to change its direction from its frame of reference. In its frame of reference it isn't moving so how does it have a direction?

Even though it isn't moving, it still has a direction which constitutes forwards, etc. It is still facing some direction.

I understand why "forward" stays consistent in spherical space, but you are yet to explain why it stays in GR's space-time.

Because they utilise the same principles. You have a non-Euclidean space where the object is travelling along a straight line.

Whatever.

6

Flat Earth Debate / Re: Davis Relativity Model (Debate/discussion edition)

« on: October 23, 2017, 01:32:54 AM »

Again, I think I or you didn't understand the definition correctly, so I asked AltSpace and Davis to clarify it.

And again, I do understand it and I know it only applies to Euclidean spaces.

You may know another similar definition and think it's exactly the same definition while it isn't. That's why I asked for clarification.

Yes, you asked for a curved line.

No, I asked for a straight line.
Spefically I objected to your claim:

I described how a curved line can pass through the same points as a series of straight lines which are in turn connected by a straight line in an Euclidean space.

Where you indicate you had straight lines connected by a straight line, when you did not.

You didn't say you translate the line, you said the straight lines have to be connected by a straight line.

I thought that would have been quite obvious based upon previous discussion.

The simplest example is the XY plane.
A more generic example is consider the line with vector <a1,b1,c1>.
Translate this along the line with vector <a2,b2,c2>, noting that the 2 lines are not equal.

OK, that's what I thought. My example is OK.

No it isn't.

The line you are moving along is <1,0,0>
But the lines drawn from it are not the same.
In one case you have the line <0,1,0>
In another you have <0,1,1>
In another you have <0,1,2>
These are not the same lines.
So you have not translated a line of the form <a1,b1,b1> along <a2,b2,c2>

OK, but how can you translate a line in a non-Euclidean space unambiguously?

Also note that these are yet again different to the lines you previously had.
You previously had the lines passing through the points defined by (x,x,x^2), which would make it a curved line.

No, I described straight lines that are connected by another straight line.

Not initially. Initially you described a parabola which was translated along another parabola.

It's possible to create a hyperbolic paraboloid in many ways. One way is translating a parabola along another parabola, a different way is to translate a line along another line while rotating it in a specific way.

It doesn't change direction from its frame of reference, because it doesn't move from its frame of reference.
But there is a direction from its frame of reference that is "forward" in the beginning. Why can't this direction become "up", i.e. point away from Earth, after some time?

It can't be up because it would require it to be changing direction.
So if it can't change direction from its frame of reference, how can it change direction from its frame of reference?

I don't understand what that even mean to change its direction from its frame of reference. In its frame of reference it isn't moving so how does it have a direction?

Because it's not a spherical space, but GR's space-time.

Deal with the 2D spherical space first, then move on to more complex spaces.

I understand why "forward" stays consistent in spherical space, but you are yet to explain why it stays in GR's space-time.

7

Flat Earth Debate / Re: Davis Relativity Model (Debate/discussion edition)

« on: October 22, 2017, 09:52:21 PM »

OK, I didn't understand you.
So again, one of us doesn't understand the definition correctly.
Please AltSpace/Davis, clarify what is your definition.

Again, the definition would only apply to Euclidean spaces. In non-Euclidean spaces, it gets far more complex as you can use a point and a normal and depending upon how you construct the plane would get different planes.

Again, I think I or you didn't understand the definition correctly, so I asked AltSpace and Davis to clarify it.

OK, let's take the parabola (p, p, p²). It is a curved line. It passes through one point from each line from the form (x, m, mx) – the point (x, x, x²). These lines are connected by the x axis. If it's not what you meant please provide an example for what you meant.

The parabola is not a straight line.

Yes, you asked for a curved line.

You need a straight line that is translated based upon a straight line.

You didn't say you translate the line, you said the straight lines have to be connected by a straight line.
The lines are (0, m, 0), (1, m, m), (2, m, 2m), etc. (I know it's impossible to list all of them, it's an uncountable infifnity), and they are connected by the x axis.

The simplest example is the XY plane.
Consider the line with vector<1,0,0>.
Translate this line along another line with vector <0,1,0>.
This generates a plane.

A more generic example is consider the line with vector <a1,b1,c1>.
Translate this along the line with vector <a2,b2,c2>, noting that the 2 lines are not equal.

OK, that's what I thought. My example is OK.

Instead, of doing this, you translated a curved line along a straight line (assuming you are saying to translate it along the x axis, the line x, x, x^2 is neither straight nor the x axis).

No, I described straight lines that are connected by another straight line.

I asked you why lines that go forward/backward or up/down from a line are really the same direction from it in GR's space-time

Because there is no reason for it to change direction.
From its reference frame, it is sitting there, doing nothing. Why would it change direction?

It doesn't change direction from its frame of reference, because it doesn't move from its frame of reference.
But there is a direction from its frame of reference that is "forward" in the beginning. Why can't this direction become "up", i.e. point away from Earth, after some time?

The simple 2D spherical space was an example of that.
If an object travels along a straight line around the equator, does it change direction (remember, no 3D so no up and down)? No. It continues going straight. Why should it be different in 3D (or 4D)?

Because it's not a spherical space, but GR's space-time.

8

Flat Earth Debate / Re: Davis Relativity Model (Debate/discussion edition)

« on: October 22, 2017, 05:20:14 AM »

Yes it does.
The space-time is not Euclidean and it's possible to travel between any two spatial coordinates in a straight line.

Again, the definition provided only applies to Euclidean spaces, not non-Euclidean space-time.

General definitions also make no special sense of time. As such, when it says "spatial coordinates" that would include the time coordinate.

OK, I didn't understand you.
So again, one of us doesn't understand the definition correctly.
Please AltSpace/Davis, clarify what is your definition.

I described how a curved line can pass through the same points as a series of straight lines which are in turn connected by a straight line in an Euclidean space.

No you didn't.
You described a surface which has numerous straight lines on it and numerous curves on it.
You did not show that these straight lines were connected. Instead you showed that the curved lines were connected by another curved line.
And you couldn't go between 2 points in a straight line.

OK, let's take the parabola (p, p, p²). It is a curved line. It passes through one point from each line from the form (x, m, mx) – the point (x, x, x²). These lines are connected by the x axis. If it's not what you meant please provide an example for what you meant.

Because if you stand on Earth you can see its direction changes.

So?
You are standing on Earth, not the object.
Again, this is an issue with non-Euclidean spaces.

Of course it's an issue with non-Euclidean spaces. In Euclidean spaces lines in the same direction from a line are just lines with the same vector. I asked you why lines that go forward/backward or up/down from a line are really the same direction from it in GR's space-time

9

Flat Earth Debate / Re: Davis Relativity Model (Debate/discussion edition)

« on: October 22, 2017, 03:32:17 AM »

I know it isn't flat, but AltSpace's/Davis's definition says it is.

No it doesn't.

Yes it does.
The space-time is not Euclidean and it's possible to travel between any two spatial coordinates in a straight line.

It can also happen in an Euclidean space.
For example, the lines (x, m, xm) for every x where m is the parameter are all connected by the x axis but form a hyperbolic paraboloid, on which there are many curved lines.

In Euclidean spaces you loose the specialness of the time axis that you have in curved space time.
You can't just ignore one of the part of the coordinates. You need to consider all three. You cannot get from any generic coordinate to another.
Also note that there are many curved lines on Euclidean planes.

I described how a curved line can pass through the same points as a series of straight lines which are in turn connected by a straight line in an Euclidean space.

From its perspective it's not going, from Earth's perspective it clearly changes direction.

Yes, from its perspective it can be considered stationary. Regardless, why should it change direction?

Because if you stand on Earth you can see its direction changes.

10

Flat Earth Debate / Re: Danang says pi=3

« on: October 22, 2017, 01:28:11 AM »

If you define it as three, I have found out it is interesting, but not relevant

Like your relativity model.

11

Flat Earth Debate / Re: Davis Relativity Model (Debate/discussion edition)

« on: October 22, 2017, 01:27:16 AM »

No, the surface is still a paraboloid.
The space-time is an Euclidean space-time with a little distortion, like a hill.

Again, if the surface is basically Euclidean with a little distortion, where that distortion is not at the paraboloid, then it isn't flat.
You can't go between any 2 points in a straight line remaining on the surface.

I know, but in my example I took a surface that was not flat in an Euclidean space-time, and changed a zone in space-time that doesn't intersect with the surfasce, what keeps the surface not flat.

The fact that the surface doesn't follow straight lines in this space which have any relation like a normal plane would (e.g. all straight lines pass through a point where they are all normal to the same vector, or they start in the same direction relative to another straight line.

I know it isn't flat, but AltSpace's/Davis's definition says it is.

Why are you adding speed to the discussion? It doesn't matter.
There are the same points on Earth and on the hyperplane (which is a hyperplane if we assume that forward really doesn't change).
Therefore Earth's surface is the hyperplane.

Again, the connectivity of points matters. The speed determines this connectivity.
It is only Euclidean spaces where the connectivity doesn't matter.
In non Euclidean spaces you can have a curved line pass through the same points as a series of straight lines which are in turn connected by a straight line.

It can also happen in an Euclidean space.
For example, the lines (x, m, xm) for every x where m is the parameter are all connected by the x axis but form a hyperbolic paraboloid, on which there are many curved lines.

South remains south (if you travel along the equator).
I suggest forward becomes up, up becomes back, back becomes down and down becomes forward. It's a very simple rotation in respect to Earth. Why isn't it the right way to decide which straight lines are in the same plane?

Because in the non-Euclidean space, it is simply going forwards. Why would its direction change? Why would it suddenly start going up or down?

From its perspective it's not going, from Earth's perspective it clearly changes direction.

Also, the path around the equator I made into a 2D problem. There was only forwards/backwards and left/right.

But the object that is orbiting Earth isn't walking on its surface, but going on a straight line in space-time.

12

Technical Support / Re: Why does The Flat Earth Society acronym become "google"?

« on: October 20, 2017, 07:37:02 AM »

Thank you.

13

Flat Earth Debate / Re: Davis Relativity Model (Debate/discussion edition)

« on: October 20, 2017, 07:13:54 AM »

What key parts and what properties? I didn't say that a line equidistant from another straight line is straight in a general non-Euclidean space-time. I started with a curved surface in an Euclidean space-time and then added some curvature to the space-time in a place that has nothing to do with the surface.

Then how does it fit the definition?
If the surface is a hill in the region where the space is flat, then it isn't flat.

No, the surface is still a paraboloid.
The space-time is an Euclidean space-time with a little distortion, like a hill.

Yes oops, I got confused.
The time curves downwards too and the orbits are the lines where the curvature of Earth in the spatial directions matches the curvature of time, making them straight.

And this works in other non-Euclidean spaces as well, were lines which appear curved in Euclidean representations are actually straight.
This makes it hard to say if a surface is flat or not.

I know, but in my example I took a surface that was not flat in an Euclidean space-time, and changed a zone in space-time that doesn't intersect with the surfasce, what keeps the surface not flat.

Of course it is straight there.

And is the surface flat?
If you translate the line along the x axis, you are just using straight lines.

Yes, I meant to say "flat"

I know all of that, but I showed a way to construct a huperplane that equals to Earth's surface (assuming back and left don't change):

But it doesn't actually match. It is turned with respect to Earth's surface. Unlike Euclidean geometry where that wouldn't matter because straight lines all curve the same (not at all), in Euclidean space it does matter. But in non-Euclidean spaces they don't all curve the same.

Why are you adding speed to the discussion? It doesn't matter.
There are the same points on Earth and on the hyperplane (which is a hyperplane if we assume that forward really doesn't change).
Therefore Earth's surface is the hyperplane.

Because the directions, relative to Earth, that look like the "forward" and the "upward" of the object change.

Relative to our Euclidean representation.
For the object moving along Earth, it appears the same, unless you are suggesting forward becomes south.

South remains south (if you travel along the equator).
I suggest forward becomes up, up becomes back, back becomes down and down becomes forward. It's a very simple rotation in respect to Earth. Why isn't it the right way to decide which straight lines are in the same plane?

14

Flat Earth Debate / Re: Davis Relativity Model (Debate/discussion edition)

« on: October 20, 2017, 04:06:10 AM »

But AltSpace's/Davis's definition says it is.

As I said, it lacks a key part for non-Euclidean spaces.
That has been his problem all along. He has been trying to use properties of lines/planes which only exist in Euclidean spaces. In non-Euclidean spaces it becomes more complex.

What key parts and what properties? I didn't say that a line equidistant from another straight line is straight in a general non-Euclidean space-time. I started with a curved surface in an Euclidean space-time and then added some curvature to the space-time in a place that has nothing to do with the surface.

On Earth, Earth curves downwards and the time curves upwards, resulting that some paths (circular orbits) remain the same. I still don't think it makes Earth flat.

It's more the other way around. Time curves objects downwards. The pressure inside Earth forces it up. These are 2 forces are balanced resulting in the surface of Earth remaining the same, but these pressure is not part of space-time, so in space-time Earth's surface is continually curving outwards, cancelling the curvature of time curving inwards.
But for orbits, there is no extra force. They just follow a path in space-time.
Do you accept that these orbits are straight lines?

Yes oops, I got confused.
The time curves downwards too and the orbits are the lines where the curvature of Earth in the spatial directions matches the curvature of time, making them straight.

If you had a surface which was a "parabolic cylinder", of the form z=-t^2, would you accept that that is flat?
This is a plane of translation, where you have parabolas due to curvature due to the t axis, which is then translated along the x axis.

In my space-time? Let me think about it. In one hand, it is flat in every point in time, but in the other, it curves in the time axis. Also, from other frames of reference it is clearly not flat even in frozen points in time. So no.

No, as this hypothetical space time, where a straight path is curved at a rate of -t^2, akin to parabolic arcs due to gravity.

Of course it is straight there.

Why? There is a collection of events. Why should the way I connect them matter?

Because the way that connects them dictates how time would curve the line.
The simplest example is looking at different orbits/trajectories.
A circular orbit around Earth is a straight line. But if you tried to go faster or slower, the straight line would become an elliptical orbit or a parabolic/hyperbolic trajectory.
So if you go at the speed of an elliptical orbit, but follow the circular orbit, that circular path is no longer a straight line.

It is somewhat akin to longitudes and latitudes on Earth or more accurately in spherical geometry.
At the equator, if you go along a path around the longitudes while keeping the same latitude (e.g. east to west), you are travelling in a straight line.
However, if you try the same north or south of the equator, you will be curving. At these locations to follow a straight line you need to change your latitude as well.
So all the points in spherical geometry can be connected by straight lines, but not all the lines connecting points are straight.

I know all of that, but I showed a way to construct a huperplane that equals to Earth's surface (assuming back and left don't change):

But I think it matches the 2nd way of making a flat surface – get a circular orbit as the 1st line and a circular orbit in the opposite direction as the 2nd one. In your 3D sketch you're done, but if you are in 4D space-time you'll get the equator and will need a 3rd line, such as a orbits along longitudes.

I thought about this again and I think it doesn't, Because I don't understand why front-up-back-down don't switch places (front means sending the line with more speed in your direction, back with less, and the others mean sending it in some speed in other directions too).

Why would it? It is going forward at a constant speed, along a straight line, not curving.

Again, appealing to spherical geometry, consider these maps:


Say you start out at (0E, 0N), heading East. The straight path in this geometry follows 0E, so in the first map it appears as a circle, in the second, as a straight line.
Now you start with left being due north.
After 90 degrees, which way is left?
Is it still due north (which would be fully supported by the second map), or would it now be due east with you facing due south (which the first map would have as parallel in our Euclidean representation)?
It gets more complicated in 3D as you can rotate around a straight line without noticing it, switching around left/up/down/right.
It gets even more complicated with large objects in orbit which don't rotate to follow the orbit.

Because the directions, relative to Earth, that look like the "forward" and the "upward" of the object change.

15

Flat Earth Debate / Re: Davis Relativity Model (Debate/discussion edition)

« on: October 20, 2017, 02:34:56 AM »

Because it's exactly the same surface on exactly the same space-time, except for some distortion somewhere that doesn't have anything to do with that surface.

Does it have nothing to do with the surface?

Yes, it does.

If so, then it likely isn't flat.

But AltSpace's/Davis's definition says it is.

But that isn't the case here. Here we are dealing with paths that are curved due to the curvature of space-time.

On Earth, Earth curves downwards and the time curves upwards, resulting that some paths (circular orbits) remain the same. I still don't think it makes Earth flat.

If you had a surface which was a "parabolic cylinder", of the form z=-t^2, would you accept that that is flat?
This is a plane of translation, where you have parabolas due to curvature due to the t axis, which is then translated along the x axis.

In my space-time? Let me think about it. In one hand, it is flat in every point in time, but in the other, it curves in the time axis. Also, from other frames of reference it is clearly not flat even in frozen points in time. So no.
BTW, it also fits their definition, just to see how weak it is.

I meant to ask if you think Earth's surface, as a 3D collection of points in 4D space-time is a hyperplane.

That is dependent upon the connectivity of the points.

Why? There is a collection of events. Why should the way I connect them matter?

But what does left/up mean in your space-time and why are they the same direction from the line (like lines with the same vectors are the same direction from a line in Euclidean space)?

A hypothetical object starts out with a up being the direction of the normal to the plane. Forward is the direction along its trajectory.
It starts out with another straight line off to its left at some angle. It moves along its path, and keeps projecting the line along that angle.
But as it moves forward, the space itself (space-time) curves down, yet it continues moving forward, meaning the local up/down and left/right need to curve with it.

Does that make sense?

I thought about this again and I think it doesn't, Because I don't understand why front-up-back-down don't switch places (front means sending the line with more speed in your direction, back with less, and the others mean sending it in some speed in other directions too).

16

Flat Earth Debate / Re: SYD to SCL and flight range

« on: October 19, 2017, 07:03:01 AM »

This is more of another map problem if anything.

So provide a map that solve this problem – an FE map that can explain every flight.

17

Flat Earth Debate / Re: Soyuz fakery caught on camera

« on: October 19, 2017, 06:52:42 AM »

Parts or all of it? It is not burning, clearly moving.

First, how can you see if it's burning or not? If something is burning that far away you'll just see a little dot on the sky. If it looks greater you'll see the fire as a circle because it's in free falling.
Second, of course it is moving. Things that fall from an orbit or from a rocket fall in a speed that is close to the orbit/rocket speed.

Do you understand why you don't see it's burning and why it's moving?

Yes I do. But you seem don't understand.

I'll sharpen the question.
Do you understand why you can't know if its burning, and why the fact that it's moving doesn't have anything to do with it being a rocket or space junk?

18

Flat Earth Debate / Re: Davis Relativity Model (Debate/discussion edition)

« on: October 19, 2017, 05:31:08 AM »

IDK how to define "flat" in this space-time or in non-Euclidean space-times in general. My whole point was that the definition used by AltSpace/Davis was problematic because things such as this paraboloid fit it while they clearly aren't flat

Except this statement makes no sense.
If you can't define flat how can you say they clearly aren't flat?

Some people would say similar things about straight lines in non-euclidean geometry and say they clearly aren't straight, but in that space, they are.
The issue is our Euclidean representation of it.

But when it goes to a plane, it becomes more complex due to the different ways to make a plane and them no longer agreeing.

Because it's exactly the same surface on exactly the same space-time, except for some distortion somewhere that doesn't have anything to do with that surface.

But what does left/up mean in your space-time and why are they the same direction from the line (like lines with the same vectors are the same direction from a line in Euclidean space)?

A hypothetical object starts out with a up being the direction of the normal to the plane. Forward is the direction along its trajectory.
It starts out with another straight line off to its left at some angle. It moves along its path, and keeps projecting the line along that angle.
But as it moves forward, the space itself (space-time) curves down, yet it continues moving forward, meaning the local up/down and left/right need to curve with it.

Does that make sense?

Yes, thank you.

I thought we are talking about space-time which consists of events, not space-time-speed which consists of some kind of states or something.

The events are points. The connections between points are trajectories We weren't discussing points, we were discussing trajectories:

BTW, do you think that Earth's trajectory is flat in space-time?

An event in space-time would only correspond to a single point on Earth's surface at a single time. Asking if that is flat makes as much sense as asking if a point is straight/flat.

I meant to ask if you think Earth's surface, as a 3D collection of points in 4D space-time is a hyperplane.

19

Technical Support / Why does The Flat Earth Society acronym become "google"?

« on: October 19, 2017, 05:19:09 AM »

Sometimes I want to write here the society's name in short, so I write the acronym, but it becomes google.
Why is that?

20

Flat Earth Debate / Re: Soyuz fakery caught on camera

« on: October 19, 2017, 05:09:38 AM »

Parts or all of it? It is not burning, clearly moving.

First, how can you see if it's burning or not? If something is burning that far away you'll just see a little dot on the sky. If it looks greater you'll see the fire as a circle because it's in free falling.
Second, of course it is moving. Things that fall from an orbit or from a rocket fall in a speed that is close to the orbit/rocket speed.

Do you understand why you don't see it's burning and why it's moving?

21

Flat Earth Debate / Re: Davis Relativity Model (Debate/discussion edition)

« on: October 19, 2017, 01:44:22 AM »

So is the paraboloid flat then?

Again, the definition is harder. I'm not sure. I would need to know more about the space, and how to define a "flat" surface in this space.

IDK how to define "flat" in this space-time or in non-Euclidean space-times in general. My whole point was that the definition used by AltSpace/Davis was problematic because things such as this paraboloid fit it while they clearly aren't flat

The orientation would be covered by the angle.

What?

The angle between the lines can be considered as just a single angle, or you can consider how you change the path between the 2 lines. For example, you can have the circular orbit, and keep the line at an angle of 45 degrees left, instead of 45 degrees up.

But what does left/up mean in your space-time and why are they the same direction from the line (like lines with the same vectors are the same direction from a line in Euclidean space)?

But Earth isn't spinning fast enough to follow that path in space-time.
And, that only works on the equator. Away from the equator it would fall towards the equator.
So at the very least, even if Earth was spinning fast enough, the "flat" trajectory would have the surface collapse to a disk and pop back out.

But I showed you a way to create Earth's surface, as a collection of events, as a flat plane defined by lines. Why does it matter if we don't follow these lines?

Because this surface is a trajectory through space time. As such, to be on this surface you need to be following that trajectory.

I thought we are talking about space-time which consists of events, not space-time-speed which consists of some kind of states or something.

22

Flat Earth Debate / Re: If the earth is flat, what shape is it?

« on: October 19, 2017, 01:07:13 AM »

Interesting. We are seeing good evidence that it is not remotely likely to be a disc. Yet dogma-fuelled flattists such as Jora and his ilk seem to insist it's a disc. While also screeching that the zetetic method is the only way to know things.

If you have a trianglular or rectangular (or every cyclic polygon shaped) map, you can just expand it to its circumscribed circle and get a disc.

23

Flat Earth Debate / Re: Davis Relativity Model (Debate/discussion edition)

« on: October 18, 2017, 09:31:16 PM »

If it really matters that much for you, just add a little distortion somewhere not on the paraboloid (like a little hill on a flat surface).

And is that distortion making the space non-Euclidean?

Yes, like a flat surface with a hill.

Is so, then it comes back to being a non-Euclidean space making the definition much harder.

So is the paraboloid flat then?

But in 3D it's not only the angle that matters, but also the orientation. If you check my example, you'll see that the translated line always remain perpendicular to the y axis, that it's being translated along.

The orientation would be covered by the angle.

What?

In non-Euclidean spaces there is a question of how you translate the lines.

Yes, that was what I meant.

I kept it such that for a Euclidean approximation for the point the lines would be restricted to a plane, where the normal points towards the centre of Earth/the centre of the orbit.

OK, sounds good.

When considered as a point (i.e. all of Earth moving together), yes.
When considered as a collection of points/a surface, no. If it did it would follow a path like this:

and we would constantly be in free fall.

But I think it matches the 2nd way of making a flat surface – get a circular orbit as the 1st line and a circular orbit in the opposite direction as the 2nd one. In your 3D sketch you're done, but if you are in 4D space-time you'll get the equator and will need a 3rd line, such as a orbits along longitudes.

But Earth isn't spinning fast enough to follow that path in space-time.
And, that only works on the equator. Away from the equator it would fall towards the equator.
So at the very least, even if Earth was spinning fast enough, the "flat" trajectory would have the surface collapse to a disk and pop back out.

But I showed you a way to create Earth's surface, as a collection of events, as a flat plane defined by lines. Why does it matter if we don't follow these lines?

24

Flat Earth Debate / Re: Soyuz fakery caught on camera

« on: October 18, 2017, 08:19:54 AM »

Parts or all of it? It is not burning, clearly moving.

First, how can you see if it's burning or not? If something is burning that far away you'll just see a little dot on the sky. If it looks greater you'll see the fire as a circle because it's in free falling.
Second, of course it is moving. Things that fall from an orbit or from a rocket fall in a speed that is close to the orbit/rocket speed.

25

Flat Earth Debate / Re: Davis Relativity Model (Debate/discussion edition)

« on: October 18, 2017, 08:01:55 AM »

But I moved my parabola an a parabola for the sake of my claim.

And with your space being euclidean, your surface is not flat, as time is no longer special and would no longer be treated separately to the spatial dimensions and thus spatial coordinates would include time.

If it really matters that much for you, just add a little distortion somewhere not on the paraboloid (like a little hill on a flat surface).

Are you sure that there are two (space-time) points on this surface that the line that connects them isn't on the surface? (maybe most of them are and it's sure that there will be, but I'm not familiar enough with non-Euclidean spaces)

Yes.
A straight line through this non-Euclidean space-time will either remain at the same temporal component, or only go forward or only go backwards in time. There are none which start going forward and then go backwards.
The only part which introduces curvature is the temporal component, i.e. if you have a line with a constant temporal component, then not only will it be straight for this non-Euclidean space-time, it will be straight for this representation of this space-time in Euclidean space.
Now then, with that start at the point where all these lines cross.
Pick 2 lines going in opposite directions, such as the 2 parabolic trajectories (pretty much any work, they don't even need to be matched, it will just limit the exact time's you can use).
Now proceed along these until you get to some time value. If you chose a circular orbit, make sure this isn't a half integer multiple (which includes full integer multiples) of the orbital period.
You now have 2 different points in space, at the same time.
As they are at the same time, the path connecting them can have no temporal difference. That is the path connecting them must be a vector purely through space, not through time. This means it can be found by a simple straight line between the 2 points.
But a straight line between these 2 points goes off the surface.
For example:

The cyan (or whatever) line is a straight line through space time, the only one connecting those 2 points (4 actually) on the surface, yet does not remain on the surface.

OK.

Are you sure that you rotated the line correctly?

Yes. I'm sure.
The angle between the straight line it is translated along (the helix path of the orbit), and the line which is being translated, remains the same.
If you translated it differently you would get similar issues.

But in 3D it's not only the angle that matters, but also the orientation. If you check my example, you'll see that the translated line always remain perpendicular to the y axis, that it's being translated along.

BTW, do you think that Earth's trajectory is flat in space-time?

When considered as a point (i.e. all of Earth moving together), yes.
When considered as a collection of points/a surface, no. If it did it would follow a path like this:

and we would constantly be in free fall.

But I think it matches the 2nd way of making a flat surface – get a circular orbit as the 1st line and a circular orbit in the opposite direction as the 2nd one. In your 3D sketch you're done, but if you are in 4D space-time you'll get the equator and will need a 3rd line, such as a orbits along longitudes.

26

Flat Earth Debate / Re: If the earth is flat, what shape is it?

« on: October 17, 2017, 10:58:59 PM »

Peirce quincuncial projection

And belong to the The INTERNATIONAL SQUARE EARTH SOCIETY, By Roger M. Wilcox
Who cares if the Americas are a bit bent?

Maybe a triangular Earth can fix that?

Or even better than a butterfly, might be a "bat-wing" earth:

The Cahill-Keyes "Real-World" Map

But how do you travel so shortly from US to Japan? Is there a portal in the edge of Earth?

27

Flat Earth Debate / Re: Danang says pi=3

« on: October 17, 2017, 10:49:58 PM »

C=4(1+¾²)r

Why?
I don't think anyone understood your post where you explained that. Can you clarify what you wrote there?

28

Flat Earth Debate / Re: Davis Relativity Model (Debate/discussion edition)

« on: October 17, 2017, 10:40:56 PM »

My space-time was indeed Euclidean. A definition for sonething on non-Euclidean space-times should generalize the definition for Euclidean ones.

No it wasn't.
If your space-time was Euclidean, objects travelling along the time axis would travel in a straight line. It would not travel in a parabola.

But I moved my parabola an a parabola for the sake of my claim.

In Euclidean space time, it isn't just spatial coordinates. it is any coordinates. You need to be able to go from any point (x,y,z) or (x,y,t) on the "plane" to any other point on the "plane", while travelling in a "straight" line, without leaving the "plane".

If your space-time is Euclidean, time is not special.

So it's a minkowski space where straight lines are still straight. It doesn't really matter.

What key part?

In Euclidean space, a plane is defined by a point and a normal.
There are 2 main ways (that I can think of) to construct a plane, one is by taking this point, and drawing every line through this point which is normal to the normal vector.
Another way is to take 2 vectors which are normal to the normal, and translate one of these vectors along the direction of the other.
With Euclidean spaces (which would include Euclidean space-time, these produce the same planes, and you can go between any 2 points on this plane while travelling in a straight line, remaining on the plane.

For non-Euclidean spaces, it isn't that simple, you can get a multitude of different planes by following the above methods.
For example, by taking all the vectors through a point which are normal to another vector, you get something like this:

Are you sure that there are two (space-time) points on this surface that the line that connects them isn't on the surface? (maybe most of them are and it's sure that there will be, but I'm not familiar enough with non-Euclidean spaces)

If however you take a line and translate it along another line you can get something like theses 2 surfaces:

Are you sure that you rotated the line correctly? Because you can get the hyperbolic paraboloid by translatg a line along another line and rotate it in a specific way. (for example, the paraboloid z = xy can be produced by taking the x axis, and translate it along the y axis while keeping its slope in the xz plane your y value)
Of course it's a very stupid example, but in non-Euclidean spaces it's not always so sure to which direction you should orient the line.

So the different methods no longer produce the same lines.
More importantly, you are no longer able to go from one point on the plane to another point on the plane while travelling in a straight line which remains on the plane (note: these need to be straight lines in non-Euclidean space-time).

But sometimes it's possible, for example, if your space-time is spherical, the great spheres are planes and every two points on them can be connected by a straight line.

If you try and make a 2D plane from 4D space-time, you can get a sphere, and I think you can do that in a way where both methods of making the plane agree, but I need to think about it some more to make sure.

OK, think about it.
BTW, do you think that Earth's trajectory is flat in space-time?

29

Flat Earth Debate / Re: This is all a bit absurd.

« on: October 17, 2017, 12:28:49 PM »

It's a key issue that defines denpressure and wipes out nonsense gravity.

The problem with your denpressure is that

pressure doesn't have a preferred direction – the same air pressure is pressing the floor, the walls and the ceiling.
Also, in a vaccum chamber on Earth objects still fall down in 9.8 m/s/s

That video is absolute nonsense.

OK, maybe you don't accept that things fall in vaccum, but what about the fact that pressure presses in all directions and not just downwards?
You can see it when you blow a balloon – the pressure inside pushes it to expand in every direction, but if you put there a weight that falls downwards (without blowing the balloon) you can see that the balloon only expands downwards.

30

Flat Earth Debate / Re: This is all a bit absurd.

« on: October 17, 2017, 10:07:47 AM »

It's a key issue that defines denpressure and wipes out nonsense gravity.

The problem with your denpressure is that

pressure doesn't have a preferred direction – the same air pressure is pressing the floor, the walls and the ceiling.
Also, in a vaccum chamber on Earth objects still fall down in 9.8 m/s/s