Distances on RE and FE consistent thanks to bendy light.

Flat earth has no curvature. RE has curvature.

By theorema egregium (Gauss), there is no isometric map (distance preserving function) between two surfaces with different gaussian curvature. Gaussian curvature is how curvature of a surface is measured independently of coordinate systems:

http://mathworld.wolfram.com/IntrinsicCurvature.html

So if distances are the same on two models, gaussian curvature is the same, and the earth is not flat.
If the earth is flat, the distances are not the same.

That's math. Accept it.

Why should also a FE map be possible only in 1:1 scale according to PlanetPizzaz?

Quote from: markjo on October 31, 2011, 06:54:26 PM

Are you saying that any of the "official" FE maps use a fixed scale?

Please, markjo, please. Try to read up on discussions you're posting in before posting in them. I've been rambling for a very long time now about how it's impossible for a FE map to use a fixed scale; and I do mean rambling. Inexcusable, tiring, repeatable, boring rambling on the same subject, to seemingly no end.

Can you do that for me? Pretty please? Just a tiny bit of paying attention before posting, for uncle PizzaPlanet.

If you're tired of rambling, then why don't you try providing some conclusive evidence?

Quote from: Nolhekh on October 31, 2011, 02:32:52 PM

I think the amount of light that reflects off is dependent on the incident angle, not necessarily the distribution... or at least the pattern of distribution.

I'm not sure why you would think so. Surely the laws of optics (with the little exception of bendy light, tee hee) still apply if the object we're reflecting light from isn't even.

Quote from: Nolhekh on October 31, 2011, 02:32:52 PM

Could this not be overcome by taking photos, one at midday, and one at night and then comparing them?

Doubtfully so. What exactly are you suggesting?
If I understand what you're getting at, I'm afraid it wouldn't work. The objects would "become bigger" and "move farther away", causing little to none observable difference on a two-dimensional picture.

Human vision is 2-dimensional just like drawings, the only difference is that the retina receives a spherical projection, while drawing/pictures usually depict a planar perspective projection, but this is corrected by the fact that the flat picture itself is subject to the spherical projection when viewed by an eye.  If objects appear to not change size due to the fact that they are getting further away and bigger, it would be so in human vision.  It would essentially be no different to just say there is no change in distortion.  An object's distance is constant, and if the bending factor of light is constant, than there is no reason for there to be any change in distortion.  I honestly don't see any reason for there to be any link between bendy light and a  fractal space.  I would expect a fractal world would be more observer oriented, and distort itself, without the aide of bendy light.

Quote from: Nolhekh on October 31, 2011, 02:32:52 PM

The distortion in maps seems to imply that distortion is consistent, but with a moving sun, this can't be so.

And it isn't so. This is part of the reason why any scaled-down map is virtually impossible. The map assumes that all of the Earth is simultaneously lit from right above the centre. I'll be perfectly honest with you - I have no idea how one would even go about mapping the whole day cycle/night, as there would be different-looking pieces overlapping each other. We'd probably end up with something in the shape of a probability cloud of sorts. That is with the exception of a 1:1-scale map, where you could just locally draw what's directly under you, and thus preserve most of sunlight's effect on the shape.

You could introduce an extra dimension into the model to help define the path of the sun.  Astronomers do this with Gravity, by adding a 4th euclidean dimension into their math, even though theoretically, you can only see 3.  From the distorted maps, you claim represent the earth, it seems your fractal earth behaves mathematically like a euclidean sphere, so why not treat the math as such?  If you spherically map such a world, you can use a measuring tape to get all the correct distance, and straighten it out, to represent the real distance in a straight line as you believe it to be.

Flat earth has no curvature. RE has curvature.

By theorema egregium (Gauss), there is no isometric map (distance preserving function) between two surfaces with different gaussian curvature. Gaussian curvature is how curvature of a surface is measured independently of coordinate systems:

http://mathworld.wolfram.com/IntrinsicCurvature.html

So if distances are the same on two models, gaussian curvature is the same, and the earth is not flat.
If the earth is flat, the distances are not the same.

That's math. Accept it.

Within the same geometrical model, this is correct. Unfortunately, due to that prerequisite it's also entirely irrelevant to the matter at hand.

If you're tired of rambling, then why don't you try providing some conclusive evidence?

Since you're not willing to read the thread prior to posting, I will now proceed to question your intelligence and ignore your further posts in this thread, unless they bring something new to the thread.
I am now questioning your intelligence: You're not very intelligent.

Why should also a FE map be possible only in 1:1 scale according to PlanetPizzaz?

Because it's virtually impossible to account for the effects of EAT while scaling down a map. Scaling it down forces you to distort it in one way or another.

Human vision is 2-dimensional just like drawings, the only difference is that the retina receives a spherical projection, while drawing/pictures usually depict a planar perspective projection, but this is corrected by the fact that the flat picture itself is subject to the spherical projection when viewed by an eye.

The other difference is that we have two eyes, thus rendering us capable of depth perception. I believe the principle in action is called "parallax".

If objects appear to not change size due to the fact that they are getting further away and bigger, it would be so in human vision.

Not entirely, due to reasons stated above, but locally the change wouldn't be significant, and thus difficult to observe.

It would essentially be no different to just say there is no change in distortion.

Only locally, and only "almost" not different.

An object's distance is constant, and if the bending factor of light is constant, than there is no reason for there to be any change in distortion.

The bending of light is constant, but the distance of the sun from any given point is not.

I honestly don't see any reason for there to be any link between bendy light and a  fractal space.  I would expect a fractal world would be more observer oriented, and distort itself, without the aide of bendy light.

Any "observer-oriented" model is unlikely to be real. It would cause massive problems with mechanical distances. As you've said yourself, most distances are constant.

You could introduce an extra dimension into the model to help define the path of the sun.  Astronomers do this with Gravity, by adding a 4th euclidean dimension into their math, even though theoretically, you can only see 3.  From the distorted maps, you claim represent the earth, it seems your fractal earth behaves mathematically like a euclidean sphere, so why not treat the math as such?  If you spherically map such a world, you can use a measuring tape to get all the correct distance, and straighten it out, to represent the real distance in a straight line as you believe it to be.

I could. It would just be yet another projection of the Earth, this time introducing curvature that doesn't exist in reality. However, I doubt introducing a fourth dimension would make my world view any more understandable to the I-can't-read-lol-the-Earth-is-round type of RE'ers.

Quote from: EmperorLurk on November 01, 2011, 02:26:42 AM

Why should also a FE map be possible only in 1:1 scale according to PlanetPizzaz?

Because it's virtually impossible to account for the effects of EAT while scaling down a map. Scaling it down forces you to distort it in one way or another.

I quite understand your theory of EA, which states that the light bends, affecting our view.
But Earth has its shape, regardless of how much quantity of light it receives. Even in total darkness, the distances should be the same.
We don't want a map showing the Earth as it looks, but as it is, disregarding the question of light, because the matter of light is irrelevant in this matter.

Even in total darkness, the distances should be the same.

And they are. It's just impossible to visualise.

We don't want a map showing the Earth as it looks, but as it is, disregarding the question of light, because the matter of light is irrelevant in this matter.

How would you like to see a map that represents something that cannot be seen? Can you show me a painting of air, or, better still, a painting of partial differentiation? I don't care how it looks like. I want a painting of it as it is.
Simply, if you "quite understand" EAT, then you don't "quite understand" maps. They're pictures. I can't give you a non-visual picture that will in the meantime be visual.

I don't see any direct conection betwen light and a map.

Tell me where you se one.

I don't see any direct conection betwen light and a map.

Ironically, the answer is in your post. How do you want to see things with no light?

Quote from: EmperorZhark on November 02, 2011, 07:42:54 AM

I don't see any direct conection betwen light and a map.

Ironically, the answer is in your post. How do you want to see things with no light?

If you make a map that preserves physical distances rather than optical distances it would be a start. Ignoring any acrobatics that light may or may not be doing, it should still be possible to create a scale model (or map???) that preserves the physical distances between points in the model. For example, if you took the distances between several major cities around the world and tries to create a physical model where the distances were to scale, the shape you get is a sphere.

As already mentioned, a Euclidean sphere is an acceptable projection, yes. Please be sure to read the thread prior to responding to it. I tire of saying the same things over and over just because people come up with the same "new ideas" multiple times.

As already mentioned, a Euclidean sphere is an acceptable projection, yes. Please be sure to read the thread prior to responding to it. I tire of saying the same things over and over just because people come up with the same "new ideas" multiple times.

PP₁, although I generally agree with the sentiment of your post, the thread is over 30 pages long, and that's a lot of material to digest (although, a lot of it is excellent reading for toilet-times).

PP₁, although I generally agree with the sentiment of your post, the thread is over 30 pages long, and that's a lot of material to digest (although, a lot of it is excellent reading for toilet-times).

Do you suggest that expecting people to read the thread is more demanding than them expecting me to answer the same question over and over in the same thread? The effort to understand each other should be split.
At least read the last few pages. This especially goes to markjo, who butts into a conversation whose context can be understood for reading just a few posts back and yet manages to show he has no lime clue what we're talking about here, and jraffield1, who manages to bring up the topic of a sphere map within five posts of me agreeing that a sphere would be an acceptable projection, with its good and bad sides.

As already mentioned, a Euclidean sphere is an acceptable projection, yes. Please be sure to read the thread prior to responding to it. I tire of saying the same things over and over just because people come up with the same "new ideas" multiple times.

So you're saying that the Earth is round but looks... round?

So you're saying that the Earth is round but looks... round?

No, I'm not. I am saying that the Earth can be successfully projected onto a sphere, and that such a projection will have its pros and cons.

Quote from: jraffield1 on November 02, 2011, 05:49:52 PM

So you're saying that the Earth is round but looks... round?

No, I'm not. I am saying that the Earth can be successfully projected onto a sphere, and that such a projection will have its pros and cons.

What would be a downside to having a model that preserves distance, area, and position?

What would be a downside to having a model that preserves distance, area, and position?

Oh, there would be none at all. Of course, we're not talking about models, but maps, and your question doesn't even apply to the subject, but hey; here's your answer.

...sigh... all right, all right.

Following El Cid's suggestion, I will try to be a bit nicer and just correct the mistake in your question. But only this once. From now on you're supposed to pay attention.

"What would be a downside to having a spherical map?"

Ah, that's a good question! If you read the post I originally directed you to, you'd know. But here it is for you once again: Well, it doesn't preserve position if we consider more than two dimensions (aka we assume that we're actually talking about reality), requires the introduction of a redundant "fourth" dimension, and distorts the shape of everything devilishly by curling it into a ball, and makes it entirely impossible to travel in a straight line. If we do extend it to a model, it also introduces the necessity of gravitation, which is a broken theory, easily disproved by observable data.

Gosh, haw eager are you not to produce a FE map!
Gibberish about projection, about light, no answer about scales...

Everyone is turning again your ludicrous theories, and you carry on, not paying attention to any single argument.

Ypu've totally lost your marbles on this one!

Quote from: jraffield1 on November 02, 2011, 10:28:30 PM

What would be a downside to having a model that preserves distance, area, and position?

Oh, there would be none at all. Of course, we're not talking about models, but maps, and your question doesn't even apply to the subject, but hey; here's your answer.

...sigh... all right, all right.

Following El Cid's suggestion, I will try to be a bit nicer and just correct the mistake in your question. But only this once. From now on you're supposed to pay attention.

"What would be a downside to having a spherical map?"

Ah, that's a good question! If you read the post I originally directed you to, you'd know. But here it is for you once again: Well, it doesn't preserve position if we consider more than two dimensions (aka we assume that we're actually talking about reality), requires the introduction of a redundant "fourth" dimension, and distorts the shape of everything devilishly by curling it into a ball, and makes it entirely impossible to travel in a straight line. If we do extend it to a model, it also introduces the necessity of gravitation, which is a broken theory, easily disproved by observable data.

I'm afraid you are mistaken about gravity. While it is currently incomplete, it is extremely accurate, with 99.9% of all observations in line with its predictions.

From my own experiments regarding pendulums and comparing my results to those of others, I have concluded that the Earth must be rotating, and from comparing the distances between different cities around the world I have concluded that the Earth must be spherical. I have done the experiments, done the research, and I have found the truth. I think this represents a win for zetetic globularism.

I'm afraid you are mistaken about gravity. While it is currently incomplete, it is extremely accurate, with 99.9% of all observations in line with its predictions.

I am merely repeating what RE scientists say; they say that the current model of gravitation comes with a bunch of anomalies and discrepancies.

From my own experiments regarding pendulums and comparing my results to those of others, I have concluded that the Earth must be rotating, and from comparing the distances between different cities around the world I have concluded that the Earth must be spherical. I have done the experiments, done the research, and I have found the truth. I think this represents a win for zetetic globularism.

About the pendula: Comparing the results to those of others is a nice way to jump into confirmation bias. Feel free to provide your logbooks for review, though.

About rotundity: I have provided a distance-consistent model that is not spherical. You have made an assumption that distance-consistency implies rotundity. Confirmation bias proven.

About rotundity: I have provided a distance-consistent model that is not spherical. You have made an assumption that distance-consistency implies rotundity. Confirmation bias proven.

"Mathematically speaking, a sphere and a plane are not isometric, even locally."
http://en.wikipedia.org/wiki/Theorema_Egregium

I know it's from wikipedia, but it is a valid result that follows from theorema egregium.

Two spaces are isometric iff there is an isometry between the two spaces.

An isometry is
"A bijective map between two metric spaces that preserves distances"
http://mathworld.wolfram.com/Isometry.html

This means if distances are consistent, the earth is not flat.

Within the same geometry, yes.
This is not the case.

in the ambient 3-dimensional Euclidean space.

Within the same geometry, yes.
This is not the case.

Could you expand?

Could you expand?

Why are you asking me to expand the same thing over and over again?
The principle you've posted applies to a three-dimensional Euclidean geometry.
I have already explained that the geometry of this model is not Euclidean.

The 2D SURFACE is non-euclidean, but is embedded in a higher dimensional Euclidean space. The surface itself has curvature independent of its embedding. The SURFACES are not isometric. You can't change that.

"A curvature such as Gaussian curvature which is detectable to the "inhabitants" of a surface and not just outside observers. An extrinsic curvature, on the other hand, is not detectable to someone who can't study the three-dimensional space surrounding the surface on which he resides."

http://mathworld.wolfram.com/IntrinsicCurvature.html

Gaussian curvature does NOT rely on the embedding in a higher dimension.

Why are you asking me to expand the same thing over and over again?

Seriously though, that's what she said? Eh?

Sorry, carry on.

The 2D SURFACE is non-euclidean, but is embedded in a higher dimensional Euclidean space.

Perhaps according to you. Certainly not according to me.

Gaussian curvature does NOT rely on the embedding in a higher dimension.

That's great, because we're not "embedding" anything in a "higher" dimension. We're applying a non-Euclidean geometry.

Perhaps you should get a better understanding of non-euclidean geometries and manifolds in general (particularly Riemannian manifolds since these are smooth and have the notion of distance).

Perhaps, or perhaps not. However, your theorem only applies to Euclidean geometries, thus rendering it irrelevant.

I'll say it in a different way. If you take two crossing lines (geodesics) in non-Euclidean 3-space (let's make the lines perpendicular for ease of imagination), they will define a surface. You are claiming that said surface will have no curvature since the two lines defining it are "straight" in the given space. But that surface will actually have intrinsic curvature that comes from the space itself.