Insistence on an "Accurate" map is a rhetorical trick.

The issue with an accurate representation of a flat earth map comes up a lot. There have been some suggestions.
 
Personally, I believe it is a closed finite surface in non-euclidean space. This is a mouthful of math terms, but the end result of this is that its difficult if not impossible to create a map of the flat earth, similar to how it would be impossible to map the globe model to paper accurately without use of projections. The underlying problem is the assumption you can draw accurately a very large body in curved space on a very small flat piece of piece of paper and have it hold to scrutiny without projecting it. We already know this isn't strictly the case.

It's basically assuming Euclid's postulates are correct even though we know for a fact they aren't - ignoring what was the greatest scientific revolution of the last 2000+ years. If the earth is non-euclidean and a closed finite space he is essentially asking the impossible.

Want he wants is a map that matches the globe. Its like saying "You believe elephants are gray. I won't believe you about elephants until you produce a blue elephant for me."

Surely mapping Geographic locations from a flat earth onto a flat map should be very straight forward. It should be a case  of measuring distances and directions from a point and plotting them on a map and keep expanding outward.



The template above should work and would be a good place to start. Why not just attempted to get the land masses in their correct places relative to each other and with correct orientation to start with.

If you cant achieve it then this almost certainly proves that the Earth is in fact a globe and the FET ideas are just hyperbole.

 

Personally, I believe it is a closed finite surface in non-euclidean space.

A closed finite surface is the description of a sphere.

Quote from: John Davis on April 07, 2016, 01:20:08 PM

Personally, I believe it is a closed finite surface in non-euclidean space.

A closed finite surface is the description of a sphere.

Or any number of other things, especially considering non-euclidean space. A torus would also fit the bill. Several topological objects.  And the flat earth.

The issue with an accurate representation of a flat earth map comes up a lot. There have been some suggestions.
 
Personally, I believe it is a closed finite surface in non-euclidean space. This is a mouthful of math terms, but the end result of this is that its difficult if not impossible to create a map of the flat earth, similar to how it would be impossible to map the globe model to paper accurately without use of projections. The underlying problem is the assumption you can draw accurately a very large body in curved space on a very small flat piece of piece of paper and have it hold to scrutiny without projecting it. We already know this isn't strictly the case.

It's basically assuming Euclid's postulates are correct even though we know for a fact they aren't - ignoring what was the greatest scientific revolution of the last 2000+ years. If the earth is non-euclidean and a closed finite space he is essentially asking the impossible.

Want he wants is a map that matches the globe. Its like saying "You believe elephants are gray. I won't believe you about elephants until you produce a blue elephant for me."

"Non-euclidean" isn't a magic word. Euclidean space has a positive definition. Non-Euclidean space is simply everything else. What properties does this specific Non-Euclidean space have, exactly?

Quote from: John Davis on April 07, 2016, 01:20:08 PM

Personally, I believe it is a closed finite surface in non-euclidean space.

A closed finite surface is the description of a sphere.

Indeed, I have only just noticed this change of stance. nice!.... When did this change of stance occur?

John Davies, You now believe the earth is a sphere! well done. Have a star.

Quote from: Stanton on April 07, 2016, 02:03:56 PM

Quote from: John Davis on April 07, 2016, 01:20:08 PM

Personally, I believe it is a closed finite surface in non-euclidean space.

A closed finite surface is the description of a sphere.

Or any number of other things, especially considering non-euclidean space. A torus would also fit the bill. Several topological objects.  And the flat earth.

Then it is the non-euclidean space that allows a ball or a donut
to be described as a two dimensional shape?

Personally, I believe it is a closed finite surface in non-euclidean space.

Check me if I'm wrong, but isn't the spherical geometry used to describe a globe earth non-euclidean?

Seems like a cop-out to me.  If the earth is flat, as this society says, it should easily have a map. 

But the only way of representing shapes, directions, and areas accurately is with a globe.  Just throw in the towel already. 

The issue with an accurate representation of a flat earth map comes up a lot. There have been some suggestions.
 
Personally, I believe it is a closed finite surface in non-euclidean space. This is a mouthful of math terms, but the end result of this is that its difficult if not impossible to create a map of the flat earth, similar to how it would be impossible to map the globe model to paper accurately without use of projections. The underlying problem is the assumption you can draw accurately a very large body in curved space on a very small flat piece of piece of paper and have it hold to scrutiny without projecting it. We already know this isn't strictly the case.

It's basically assuming Euclid's postulates are correct even though we know for a fact they aren't - ignoring what was the greatest scientific revolution of the last 2000+ years. If the earth is non-euclidean and a closed finite space he is essentially asking the impossible.

Want he wants is a map that matches the globe. Its like saying "You believe elephants are gray. I won't believe you about elephants until you produce a blue elephant for me."

All I can say is you still seem to be trying to follow "Leo Ferrari's Theories"[1], and don't yet realise he was playing a joke in the whole notion of a "Flat Earth".

Yes, Einstein concluded that spacetime is curved, but the actual curvature in space is only significant near massive bodies. Even our Sun deflects light a minute amount, partly from the curvature of space, partly from the slowing of time. 
I know you would think it beneath your dignity to read such a thing, but this is not a bad read and keeps ones feet on the ground Gravity: from weightlessness to curvature. It is admittedly pretty low level.

But the earth is a real solid object of a well defined shape! And, I claim that shape has been clearly determined by actual measurement.

If the earth were flat then no projection would be needed. It would be a trivial matter of simply making maps of the whole or a part simply by linear scaling - no great mystery.

The problem is that no "Flat Earth Map" has yet come anywhere near fitting the measurements already made on the real earth.

And, whatever you might claim accurate maps are vital in so many areas. Luckily for those who accept GPS mapping as accurate we have quite precise digital maps to use.

If in my ignorance I have stuck my neck out too far, it will get quickly lopped off - so be it!


[1] Eric Dubay (must wash my mouth out with soapy water for mentioning the name) even accuses TFES of being a continuation of Leo Ferrari's "The Flat Earth Society of Canada", not that I put any weight on that or on anything from "dear" Eric!

The issue with an accurate representation of a flat earth map comes up a lot. There have been some suggestions.
 
Personally, I believe it is a closed finite surface in non-euclidean space. This is a mouthful of math terms, but the end result of this is that its difficult if not impossible to create a map of the flat earth, similar to how it would be impossible to map the globe model to paper accurately without use of projections. The underlying problem is the assumption you can draw accurately a very large body in curved space on a very small flat piece of piece of paper and have it hold to scrutiny without projecting it. We already know this isn't strictly the case.

It's basically assuming Euclid's postulates are correct even though we know for a fact they aren't - ignoring what was the greatest scientific revolution of the last 2000+ years. If the earth is non-euclidean and a closed finite space he is essentially asking the impossible.

Want he wants is a map that matches the globe. Its like saying "You believe elephants are gray. I won't believe you about elephants until you produce a blue elephant for me."

Well said my friend. What our friendly opponents in this debate fail to realize is that the problem you posed also exists for them. I would simply ask the Helio-centrists to produce a "map" of their non Euclidian space time that is "accurate".
I would also ask them what they mean by "Accurate". A map is simply a representation, and a poor one I might add, in two dimensions of a physical space. Whilst serving in Her Majesty's army as a young man I oft heard the saying "Do NOT confuse the map with the terrain." Sound advice then and now.

Quote from: John Davis on April 07, 2016, 01:20:08 PM

The issue with an accurate representation of a flat earth map comes up a lot. There have been some suggestions.
 
Personally, I believe it is a closed finite surface in non-euclidean space. This is a mouthful of math terms, but the end result of this is that its difficult if not impossible to create a map of the flat earth, similar to how it would be impossible to map the globe model to paper accurately without use of projections. The underlying problem is the assumption you can draw accurately a very large body in curved space on a very small flat piece of piece of paper and have it hold to scrutiny without projecting it. We already know this isn't strictly the case.

It's basically assuming Euclid's postulates are correct even though we know for a fact they aren't - ignoring what was the greatest scientific revolution of the last 2000+ years. If the earth is non-euclidean and a closed finite space he is essentially asking the impossible.

Want he wants is a map that matches the globe. Its like saying "You believe elephants are gray. I won't believe you about elephants until you produce a blue elephant for me."

Well said my friend. What our friendly opponents in this debate fail to realize is that the problem you posed also exists for them. I would simply ask the Helio-centrists to produce a "map" of their non Euclidian space time that is "accurate".
I would also ask them what they mean by "Accurate". A map is simply a representation, and a poor one I might add, in two dimensions of a physical space. Whilst serving in Her Majesty's army as a young man I oft heard the saying "Do NOT confuse the map with the terrain." Sound advice then and now.

Yes but, if as I stated before, the earth were flat no projection would be necessary and all maps could be as accurate as required.

Of course, "Do NOT confuse the map with the terrain", would still be sound advice. The map would still be a flat representation of a 3-dimensional surface. Even a flat earth would have mountains, valleys, rivers and oceans.

Insistence on an "Accurate" map is a rhetorical trick.

It sure is a trick. 
I would be happy if the astronoughtical folks (with or without lab coats) showed the world a camera's bird's eye view hanging from a rising weather balloon. 

1 camera + 1 balloon = case closed

Quote from: John Davis on April 07, 2016, 01:20:08 PM

Insistence on an "Accurate" map is a rhetorical trick.

It sure is a trick. 
I would be happy if the astronoughtical folks (with or without lab coats) showed the world a camera's bird's eye view hanging from a rising weather balloon. 

1 camera + 1 balloon = case closed

" class="bbc_link" target="_blank" rel="noopener noreferrer">Here's the faster, better version.  2 cameras + 1 Black Brant IX sounding rocket.  That wasn't so hard. 

That wasn't so hard.

That was garbage.  Your video shows nothing. 

Please stop cluttering the forum with nonsense.  Is it too much to ask NASA-liars to produce a live-stream of the ENTIRE "globe" or is Hubble just a bullshit Hollyweird stunt?




EDITED TO ADD:  Thanks for the video anyways.  I like the camera-effect at the 2minute mark.  It shows the world that the appearance of rings around planetary "objects" can be illusions. 

Please stop cluttering the forum with nonsense.  Is it too much to ask NASA-liars to produce a live-stream of the ENTIRE "globe" or is Hubble just a bullshit Hollyweird stunt?

Huh?  What does Hubble have to do with showing a live stream of the earth?  Granted, there are lots of satellites (allegedly) pointed at the earth, but Hubble isn't one of them.  Maybe you should check out some of the ones that are:
https://en.wikipedia.org/wiki/List_of_Earth_observation_satellites

Quote from: Blue_Moon on April 08, 2016, 06:02:42 AM

That wasn't so hard.

That was garbage.  Your video shows nothing. 

Please stop cluttering the forum with nonsense.  Is it too much to ask NASA-liars to produce a live-stream of the ENTIRE "globe" or is Hubble just a bullshit Hollyweird stunt?

EDITED TO ADD:  Thanks for the video anyways.  I like the camera-effect at the 2minute mark.  It shows the world that the appearance of rings around planetary "objects" can be illusions.

I don't see what the problem was.  That video got a better view of the curvature of the earth than a balloon ever could.  Yet when you're shown an even better video than you asked for, you just retreat behind more petty insults, demands for evidence that you could easily have found yourself, and downright idiotic assumptions based on insignificant details.  You really are committed to ignorance, aren't you. 

Quote from: John Davis on April 07, 2016, 01:20:08 PM

Personally, I believe it is a closed finite surface in non-euclidean space.

Check me if I'm wrong, but isn't the spherical geometry used to describe a globe earth non-euclidean?

I'm not sure what you mean specifically. We had globes far before non-euclidean geometry was recognized as useful.

Seems like a cop-out to me.  If the earth is flat, as this society says, it should easily have a map. 

But the only way of representing shapes, directions, and areas accurately is with a globe.  Just throw in the towel already.

You don't understand the complexities at hand. You need to show us the only way of representing shapes,directions and areas accurately is a globe - you can't just state it as a matter of fact. Simply having a globe that represents space somewhat correctly is not enough to say there are no additional solutions.

If you want an accurate map of the flat earth look at a globe. That is a projection of the non-euclidean flat earth on a round surface.

Quote from: Stanton on April 07, 2016, 02:03:56 PM

Quote from: John Davis on April 07, 2016, 01:20:08 PM

Personally, I believe it is a closed finite surface in non-euclidean space.

A closed finite surface is the description of a sphere.

Indeed, I have only just noticed this change of stance. nice!.... When did this change of stance occur?

John Davies, You now believe the earth is a sphere! well done. Have a star.

I most certainly do not. Round logic never fails to amaze me.

Compare:
Self: "The Flat Earth is a CFS"
Other: "CFS describes a sphere."
Other: "Thus the Flat Earth is A Sphere!"

Self: "A dog is an animal"
Other: " Animal describes a cat."
Other: "Dogs are Cats!"

Surely mapping Geographic locations from a flat earth onto a flat map should be very straight forward. It should be a case  of measuring distances and directions from a point and plotting them on a map and keep expanding outward.



The template above should work and would be a good place to start. Why not just attempted to get the land masses in their correct places relative to each other and with correct orientation to start with.

If you cant achieve it then this almost certainly proves that the Earth is in fact a globe and the FET ideas are just hyperbole.

It does not work. At best I can do a projection. In which case, why is the UN logo not good enough for you?

It does not work. At best I can do a projection. In which case, why is the UN logo not good enough for you?

It would help if we knew what you are projecting. By your own admission, closed finite surface can refer to any number of shapes. Non-euclidean space can refer to any number of spaces. So far, your theory doesn't actually exclude the current scholary opinion, aka "round earth", or does it?

Quote from: getrealzommb on April 07, 2016, 01:38:35 PM

Surely mapping Geographic locations from a flat earth onto a flat map should be very straight forward. It should be a case  of measuring distances and directions from a point and plotting them on a map and keep expanding outward.



The template above should work and would be a good place to start. Why not just attempted to get the land masses in their correct places relative to each other and with correct orientation to start with.

If you cant achieve it then this almost certainly proves that the Earth is in fact a globe and the FET ideas are just hyperbole.

It does not work. At best I can do a projection. In which case, why is the UN logo not good enough for you?

The UN flag is an azimuthal equidistant projection that only extends 60 degrees south.  It doesn't show Antarctica.  It was chosen to not focus on any one nation.  Plus, the circular shape serves it quite well aesthetically.  It doesn't prove there's a conspiracy, and it doesn't have any advantage over other AEP maps. 

Quote from: Blue_Moon on April 07, 2016, 09:02:23 PM

Seems like a cop-out to me.  If the earth is flat, as this society says, it should easily have a map. 

But the only way of representing shapes, directions, and areas accurately is with a globe.  Just throw in the towel already.

You don't understand the complexities at hand. You need to show us the only way of representing shapes,directions and areas accurately is a globe - you can't just state it as a matter of fact. Simply having a globe that represents space somewhat correctly is not enough to say there are no additional solutions.

If you want an accurate map of the flat earth look at a globe. That is a projection of the non-euclidean flat earth on a round surface.

Globes are the sources of projections; they aren't projections themselves.  Are you saying that the earth is flat, but functions topographically like a globe?  I mean, you're halfway to admitting that the earth is a globe.  You just have to move past your ideas of aether and universal acceleration or whatever. 
So I'm bringing back my go-to argument:
How can satellites follow the paths that they do if the earth is not a globe, and how can we track them as if they were following elliptical orbits?  How is it that we can define the motions of other planets and moons the same way?  Why do rockets need to accelerate horizontally so much?  If universal acceleration is pushing them down, what's holding them up?  Aether is off-limits, because it can't account for all the things we can observe satellites doing.  Dark matter is also off limits, because it is beyond what you are prepared to understand. 

Quote from: John Davis on April 07, 2016, 01:20:08 PM

The issue with an accurate representation of a flat earth map comes up a lot. There have been some suggestions.
 
Personally, I believe it is a closed finite surface in non-euclidean space. This is a mouthful of math terms, but the end result of this is that its difficult if not impossible to create a map of the flat earth, similar to how it would be impossible to map the globe model to paper accurately without use of projections. The underlying problem is the assumption you can draw accurately a very large body in curved space on a very small flat piece of piece of paper and have it hold to scrutiny without projecting it. We already know this isn't strictly the case.

It's basically assuming Euclid's postulates are correct even though we know for a fact they aren't - ignoring what was the greatest scientific revolution of the last 2000+ years. If the earth is non-euclidean and a closed finite space he is essentially asking the impossible.

Want he wants is a map that matches the globe. Its like saying "You believe elephants are gray. I won't believe you about elephants until you produce a blue elephant for me."

"Non-euclidean" isn't a magic word. Euclidean space has a positive definition. Non-Euclidean space is simply everything else. What properties does this specific Non-Euclidean space have, exactly?

Very true. I still laugh at when Neil DeGrasse Tyson tried to claim that you can't see curvature at sea level because its a basic postulate of non-euclidean geometry, despite the definition of a circle being one of Euclid's postulates. What a fool he is, hiding behind words he knows the populace can't understand.

Our Postulates:

• A segment AB can be drawn joining any two points A and B.
• Given segment AB and segment BC:
  A straight line AB can be drawn by extending line segment AB indefinitely
  such that each point D on line AB is on a line segment CD that is congruent and normal to CB and CA.
• The line AB will intersect each of its points at length of its period
• ...

These postulates follow directly from the Satellite Thought Experiment. I am still attempting to reduce the total postulates to 4 by combining postulate 3. It seems very realizable.

Relevent Definitions:
Point: A is a point if it is indivisble
Period: The length for AB to intersect A
Line: A line is breadthless period.
Straight Line: A straight line is a line which lies evenly with the points on itself
Congruent: Segment AB is congruent to CA if they share length
Normal:  AB is normal to CD if they intersect at right angles

I'm still attempting to combine 2 and 3 to bring my total axiom count down to 4.

So, could we continue or discussion from that other thread, were we discussed this very thing?

Quote from: John Davis on March 24, 2016, 01:31:31 PM

One where newton's laws hold. For example, if you were in orbit around a body you would be in an inertial frame of reference as you would experience weightlessness.

Actually, the weightlessness is the exact reason we can't define it as an inertial frame of reference. There is acceleration, without any forces acting. Newton's laws doesn't hold, because gravity is not a newtonian force. Gravity is an effect of curved space-time, and the effect is acceleration without forces. But we can turn acceleration into a force using F=ma. It's not actually a force, but there is acceleration, so a pseudo-force can be created to describe the acceleration.

Quote from: John Davis on March 24, 2016, 01:31:31 PM

Quote from: Master_Evar on March 24, 2016, 09:52:02 AM

Quote from: John Davis on March 24, 2016, 06:42:55 AM

Well can measure the curvature by assuming gravity is a pseudo-force and that Newton's 3 Laws of Motion hold. If acceleration is felt we know space is being curved. So we take inertial Frames of Reference as something akin (but not exactly like) an absolute coordinate system. This is how we know it would be flat in curved space and not curved in flat space or curved in curved space.

How? Sorry, but this is exactly what I talked about in my post. Yes, we know space (-time) is curved. And if you "unwrapped" it, we could define an inertial frame of reference, and from that a "true" coordinate system. But how do you know that earth would be flat, when there is no way to measure how much space is bent? Yes, we can measure acceleration between bodies, but that is space-time, time is also bent. How do we separate space from time?

We can define an inertial frame of reference by simply finding one in which all pseudo-forces cancel out and you are essentially weightless. A perfectly stable orbiting body accomplishes this. We know its inertial because we know Newton's 3 Laws hold.

I think you misunderstand the concept of "pseudo-forces". The thing with pseudo-forces is that they can't be felt, because they don't exist. Acceleration caused by pseudo-forces are non-inertial, hence objects subjected to pseudo-forces are truly non-inertial frames. We can create pseudo-inertial frames by saying that objects are subjected to these pseudo-forces, but of course there are no real forces, so this pseudo-inertial frame won't be a true inertial frame.


Then there's also another thing - general relativity is currently just the most used and accepted model for gravity. In the standard model, it has been discovered that there hypothetically could exist a particle they call the graviton, which would carry the force of gravity. This field would be mostly indistinguishable from general relativity. This would mean that space doesn't actually bend (as described by general relativity, at least), and that gravity is indeed a force (according to the standard model's definition of a force). The graviton is really hard to detect, so this can't be confirmed yet.

Quote from: John Davis on April 08, 2016, 08:49:42 AM

Quote from: Blue_Moon on April 07, 2016, 09:02:23 PM

Seems like a cop-out to me.  If the earth is flat, as this society says, it should easily have a map. 

But the only way of representing shapes, directions, and areas accurately is with a globe.  Just throw in the towel already.

You don't understand the complexities at hand. You need to show us the only way of representing shapes,directions and areas accurately is a globe - you can't just state it as a matter of fact. Simply having a globe that represents space somewhat correctly is not enough to say there are no additional solutions.

If you want an accurate map of the flat earth look at a globe. That is a projection of the non-euclidean flat earth on a round surface.

Globes are the sources of projections; they aren't projections themselves.  Are you saying that the earth is flat, but functions topographically like a globe?

Yes. The globe is an close enough projection of a non-euclidean flat earth.

  I mean, you're halfway to admitting that the earth is a globe.  You just have to move past your ideas of aether and universal acceleration or whatever. 

UA? I don't hold in UA. The fact still stands - water is level. This explains why.

So I'm bringing back my go-to argument:
How can satellites follow the paths that they do if the earth is not a globe, and how can we track them as if they were following elliptical orbits?  How is it that we can define the motions of other planets and moons the same way?  Why do rockets need to accelerate horizontally so much?

Satellites follow newtons laws and travel in a straight line through curved space.

  If universal acceleration is pushing them down, what's holding them up?  Aether is off-limits, because it can't account for all the things we can observe satellites doing.  Dark matter is also off limits, because it is beyond what you are prepared to understand.

In the future, I'd thank you kindly to not assume what I believe or what is "off limits." What ridiculous metrics you try to hold us to to avoid thinking! However, I'm all for a fair playing field. I won't mention dark matter if you don't mention anything involving motion or gravity until we know you are prepared to understand it.

If you can provide a projection, do so: being able to visualize a model is always handy. There are a number of tricks you can use in a drawing to simulate atypical behaviour: the lines you see on a lot of maps, for example.

Some definition of the non-Euclidean space would also be handy: whatever properties you know it possesses. It doesn't need to be an exhaustive list, just possible explanations how how a flat object can have distances etc only possible on a sphere (in Euclidean space).

So, could we continue or discussion from that other thread, were we discussed this very thing?

Quote from: Master_Evar on March 25, 2016, 09:13:14 AM

Quote from: John Davis on March 24, 2016, 01:31:31 PM

One where newton's laws hold. For example, if you were in orbit around a body you would be in an inertial frame of reference as you would experience weightlessness.

Actually, the weightlessness is the exact reason we can't define it as an inertial frame of reference. There is acceleration, without any forces acting. Newton's laws doesn't hold, because gravity is not a newtonian force. Gravity is an effect of curved space-time, and the effect is acceleration without forces. But we can turn acceleration into a force using F=ma. It's not actually a force, but there is acceleration, so a pseudo-force can be created to describe the acceleration.

Quote from: John Davis on March 24, 2016, 01:31:31 PM

Quote from: Master_Evar on March 24, 2016, 09:52:02 AM

Quote from: John Davis on March 24, 2016, 06:42:55 AM

Well can measure the curvature by assuming gravity is a pseudo-force and that Newton's 3 Laws of Motion hold. If acceleration is felt we know space is being curved. So we take inertial Frames of Reference as something akin (but not exactly like) an absolute coordinate system. This is how we know it would be flat in curved space and not curved in flat space or curved in curved space.

How? Sorry, but this is exactly what I talked about in my post. Yes, we know space (-time) is curved. And if you "unwrapped" it, we could define an inertial frame of reference, and from that a "true" coordinate system. But how do you know that earth would be flat, when there is no way to measure how much space is bent? Yes, we can measure acceleration between bodies, but that is space-time, time is also bent. How do we separate space from time?

We can define an inertial frame of reference by simply finding one in which all pseudo-forces cancel out and you are essentially weightless. A perfectly stable orbiting body accomplishes this. We know its inertial because we know Newton's 3 Laws hold.

I think you misunderstand the concept of "pseudo-forces". The thing with pseudo-forces is that they can't be felt, because they don't exist. Acceleration caused by pseudo-forces are non-inertial, hence objects subjected to pseudo-forces are truly non-inertial frames. We can create pseudo-inertial frames by saying that objects are subjected to these pseudo-forces, but of course there are no real forces, so this pseudo-inertial frame won't be a true inertial frame.

If you wish. 

Actually you misunderstand the concept of pseudo-forces. They can be felt. You are essentially saying you can't feel the pull backwards when you speed up your car or to the left when you turn it. This is ludicrous.

And yes, they arise from taking an inertial frame of reference as an inertial one.

Quote

Then there's also another thing - general relativity is currently just the most used and accepted model for gravity. In the standard model, it has been discovered that there hypothetically could exist a particle they call the graviton, which would carry the force of gravity. This field would be mostly indistinguishable from general relativity. This would mean that space doesn't actually bend (as described by general relativity, at least), and that gravity is indeed a force (according to the standard model's definition of a force). The graviton is really hard to detect, so this can't be confirmed yet.

Its been discovered that there hypothetically could be? That's some kind of discovery there. I discovered a French Man on Mars just the other day then.

The standard model is fiction piled on top of fiction piled on top of fiction. Unless the standard model can reconcile a preferred coordinate space and a relative one it is ridiculously distinguishable from relativity. You've been reading too much Smolin, perhaps?

Furthermore, its not hard to detect, its virtually impossible. ^{Can Gravitons Be Detected? Tony Rothman, Stephen Boughn. Accessed 4/8/2016 http://arxiv.org/abs/gr-qc/0601043}

If you can provide a projection, do so: being able to visualize a model is always handy. There are a number of tricks you can use in a drawing to simulate atypical behaviour: the lines you see on a lot of maps, for example.

A globe is reasonable projection. The UN logo is another.

Some definition of the non-Euclidean space would also be handy: whatever properties you know it possesses. It doesn't need to be an exhaustive list, just possible explanations how how a flat object can have distances etc only possible on a sphere (in Euclidean space).

Provided before you posted.