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Topics - Zogg

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Flat Earth Debate / What's the Gauss curvature of the earth?
« on: November 07, 2011, 05:06:22 PM »
This question has been asked several times in other topics, but as FEers are constantly avoiding the question, I'll start a topic on its own on this. Consider the surface of the earth as 2-dimensional differentiable manifold, with metrics defined "mecanically" (think tape measure). As you might know, the Gauss curvature is an intrinsic invariant of the manifold, it can be defined without refering to any embedding space, e.g. by the formula



where C(r) is the circumference of a geodesic circle of radius r.

The question is : Is the Gauss curvature of the earth zero or non-zero?

This question is crucial for the discussion FET vs RET, because :

  • If the Gauss curvature is zero, the metrics are euclidean. So, the earth can wholly be mapped with isometric flat maps. Given the supposed disc shape of the earth*, said flat maps can be merged to a single isometric flat map. Please provide such a map.
  • If the Gauss curvature is not zero, as we REers claim, the Earth is not isometric to a plane. In other words, the earth is not flat.

FEers, it's your turn.



* A ringworld, for example, would have a collection of isometric flat maps, but not a single one.

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Flat Earth Debate / FET and space elevators
« on: November 05, 2011, 04:25:32 PM »
Although I'm still a REer, I don't feel like discussing RET vs FET tonight. So, why not discuss something else - say, whether space elevators would be technically possible under FET ?

All discussions in this topic are under the assumption that FET is true.

I invite fellow REers to join the debate, as long as FET itself isn't discussed - there are other topics for this. Also, it's not a place to discuss logistis, conspiracies or supposed NASA lies - for the sake of discussions, let's all assume that rockets, space ships etc. can do what NASA claims they can, only on a flat earth.

So, the question is : Theoretically, would a space elevator be possible in FET (with dark energy model) ? Personally I think it would : If universal acceleration increases with altitude (because it's less "shadowed" by earth) and if there is a non-negligable gravitational pull from the heavens, the sum of UA and gravitational pull on a counterweight in high altitude should exceed the UA of earth itself. So, if the counterweight is linked with earth by a strong cable (say, of carbon nanotubes), the cable should stay under tension all by itself.


What do you think?

A second question would be whether (and how) such an elevator could actually be built (under said assumption "RE spaceflight technology on a FE").

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Flat Earth Debate / FE - theory or merely hypothesis ?
« on: October 27, 2011, 04:24:56 PM »
This topic concerns a simple question : Is the so-called "Flat Earth Theory" actually a scientific theory?

Let's recall the definition of "scientific theory". I quote from Wikipedia:

A scientific theory comprises a collection of concepts, including abstractions of observable phenomena expressed as quantifiable properties, together with rules (called scientific laws) that express relationships between observations of such concepts. A scientific theory is constructed to conform to available empirical data about such observations, and is put forth as a principle or body of principles for explaining a class of phenomena. (emphasis by me)

Let's observe two variants of FEH (Flat Earth Hypothesis): The original "straight light" model, and the "bendy light" model.

(1) Straight light: As shown elsewhere, this model results in predictions which do not match with everyday's observations, such as sunrise and sunset happening 26 above the horizon. The model is hence obviously not conform to available empirical data. Hence it's not a theory.

(2) Bendy light: At first glance, the hypothesis (some might say ad-hoc hypothesis) of bendy light seems to explain away the differences between FE's predictions and the actual observations. However, it's far from being a system of scientific laws - as to date, the bendy light hypothesis is not much more than "light bends somehow upwards for unknown reasons", together with some unfounded speculation that the resulting light paths might be somewhat like y= x3/2. (Btw, if all light rays would follow similar curves, they would all come in horizontally at ground level, so the sky would be visually reduced to a luminous line at horizon level.) This is far from being a scientific law, as it doesn't allow any predictions which celestial body is seen when where. Thus, the bendy light variant is not a theory either. (Some might say "not yet", but that doesn't make it more convincing.)

To resume, FEH is actually not a scientific theory, merely a hypothesis.

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According to the FAQ, the whole FET is based on two main arguments:
  • "Looks flat to me."
  • "Samuel Birley Rowbotham said so."

I already created a topic which disproves the first argument. This topic is about the second argument.

So, some 19th century inventor claimed that earth is flat. On the other side, space agencies claim that the earth is round. Please tell me : Why should I believe Mister Rowbotham  rather than every manager, scientist, technician or astronaut who ever worked at NASA, ESA, ROSCOSMOS or any other space agency ?

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Flat Earth Debate / "Looks flat to me" - a valid argument?
« on: October 17, 2011, 10:31:40 PM »
According to the FAQ, the whole FET is based on two main arguments:
  • "Looks flat to me."
  • "Samuel Birley Rowbotham said so."

This topic is about the first argument. To verify if this is an argument against RET, I did a very simple thing: I modelized a hi-poly sphere in a 3D program (Softimage), with 1 unit corresponding to 1 km. Then I added some simplified houses and trees (in scale) and placed a camera in different altitudes, from 2m to 100 km, to see if you could actually see roundness of a round earth. The results:
  • Even from an altitude of 1km, the virtual round earth actually looks perfectly flat.
  • From 10km on, the horizon starts bending, just as we have seen it in those countless balloon videos FE'ers are so annoyed of.

The conclusion is that "it looks flat" isn't a valid argument against RET.

See it for yourself:


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Flat Earth Debate / FET vs. observation: The shape of the moon
« on: October 16, 2011, 03:17:05 AM »
I understand there are two rival theories in FET concerning  the shape of the moon : Spherical or discoidal. I used a 3D program (Softimage) to render images of what the moon would look like in both models.

I start from the hypothesis that the moon is 3000 miles above the earth, as claimed in your FAQ, that it's either a sphere or disc, and that its visible side or hemisphere is always pointing downwards. Let's consider an observer 3000 miles away from the point on earth below the moon. So the moon is seen from an angle of 45. Let's see what it would look like in both models:


The result is that none of the two assumptions corresponds to everynight's observation. In the spherical model, we would see a large part of the far side of the moon (coloured blue for clarity); in the discoidal model, the moon would appear as an ellipse. Logic dictates that my initial assumption must be false. Thus, the moon is actually not rotating 3000 miles above the ground, qed.   

Again, observation disproves FET.

(As a sidenote, one might argue that the moon does not actually face downwards, but somehow turns towards the observer to keep its far side hidden and its shape nice and round. But then again, given that there are about seven billions of observers scattered all over the glo... errr disc, the moon would have a hard time turning towards all of them at the same time, wouldn't it?)

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Flat Earth Debate / FET versus basic trigonometry
« on: October 15, 2011, 04:10:52 PM »
If you assume FET is true and apply basic (10th grade) trigonometry to the distance and elevation of the sun, you come to results that seem to contradict everyday's observation. My computations start from the following assumptions:

1) Earth is flat
2) The equator has a radius of about 6000 miles
3) The sun rotates at a height of 3,000 miles above sea level.
4) At equinox, the sun cycles over the equator, and the illuminated area touches the pole. (Its radius is hence about 6000 miles)
5) The sun is a sphere (sorry, McIntyre) with a radius of 16 miles

So, let's consider an observer at dusk  - the moment when he is at the border of the illuminated zone. (We RE'er call this "sunset", but I'm not sure whether the sun is supposed to set in FET.) The observer is thus 6000 miles away from the center of the illuminated disk, and the sun is 3000 miles above this center. Let's draw a picture :


1st Question: What is the (angular) elevation of the sun above the horizon ?
A simple trigonometric calculation (red triangle) tells us that the sun is actually 26 above the horizon - that's more than a quarter of all the way up to zenith ! This does not really correspond to what I'm seeing each evening.

2nd Question: What's the sun's angular size at this moment ?
Pythagoras tells us that the distance to the sun is about 6700 miles. When we apply a computation similar to the one above to the green triangle, we get a half-angle of 0.137, hence an angular size of 0.274. To compare, the thumb on a stretched arm has roughly an angular size of 2, as everybody can easily compute - that's more than seven times as much ! Again, the result does not correspond to everyday's observation.

Note that the same consideration holds for the moon which is supposed to rotate at the same altitude and is easier to observe without a blackened glass. Besides, it's easy to observe details on the moon's surface, so the size of the moon cannot be explained away with a "glow effect".

(Note also that a similar consideration holds if the sun is a disk - only that under this angle it would appear as an ellipse, which does - again- contradict observation.)


Logic dictates that if my assumptions lead to results which clearly contradict observation, the assumptions are false.
 
Now I'm really curious what couter-arguments you FE'er might find.

(Edit: Modified spelling errors ("It's" instead of "Its"; "0,137" instead of "0.137", centred image.)

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