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Messages - hexagon

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Flat Earth Investigations / Re: NASA Live Stream
« on: April 26, 2018, 11:12:47 AM »
If you do the same as the Economist and do bit research on Google trends, it's really quite interesting. From 2004 to roughly 2014 the interest in "flat earth" was steadily decreasing. Since then it increased by a factor of about 10. The search interest in "flat earth society" followed the trend for "flat earth" in a 1:1 fashion until 2014. But interestingly the increase since then for "flat earth society" is much lower, about a factor 1.5.

This is for general web search. If you look for searches on YouTube, "flat earth" showed also there an increase in 2014, but since last summer the interest is steadily decreasing, down to 43% from the maximum last year. It's now back on the level as around 2015/16.

For me that shows, that there is indeed an increasing curiosity in the term "flat earth", but it is not really substantial. There is no real increase in engagement into the subject. To watch a video on YouTube cost you much more time than a quick google search looking for an explanation of this term. Also the curiosity leads not in the same way to a kind of institutional interest in something like a flat earth society.

It is also interesting to see, that this mainly a US phenomenon. E.g. the interest ratio between the USA and Russia is 100:3, to the most European countries it is below 100:10. Another thing is, what triggered the interest. And there it seems, that a huge part goes back to some celebrities whose names are the most related search expression to "flat earth".     

Doesn't sound like a tide for me...

And I'm also happy to see that the big US universities outnumber the interest in "flat earth" by orders of magnitude... And even my own, comparable small University, generates at least a search interest that is in the same range as that for "flat earth". It's also nice to see, that we get every year more new physics, astronomy, geography, and so on students than people participating on flat earth meetings in the homeland of this "movement". By the way, the yearly meetings of the American Physical Society are joined by more than 10000 scientist every year. And the APS has also numbers regarding membership, it's almost 50000 people... That's a movement...   

Flat Earth Theory / Re: The Horizon is Always at Eye Level
« on: April 26, 2018, 08:39:59 AM »
On a globe the horizon is always below your eye level, because it i physically below your eye level and perspective doesn't not change physical relations between objects. Below is always below, above is always above, left is always left and right always right with respect to the optical axis defined by your eye and the point where you are looking at. Therefor, if you are looking parallel to the tangent line of the globe where you're standing, the horizon is always below.

On a flat earth there's no horizon in that sense, because the sky would be physically always above you, the ground always below you. They would only meet at infinity at the so-called vanishing point. But because no one can look that far under the atmospheric conditions of our earth, everything would be vanishing in diffusive blur far away...   

Flat Earth Theory / Re: Question from a physicist
« on: April 26, 2018, 08:29:12 AM »
And whatever is pushing the earth in this concept, feels an increasing mass and has therefor to push harder to keep the acceleration constant. And any force needs energy and an infinite force needs infinite energy.

Well, due to relativity, it's a bit more complicated.
From the perspective of an outside observer, as the speed of the Earth would approach the speed of light its acceleration would signifantly decrease. Thus the force/the energy would "only" approach infinity.
However, from our perspective, the acceleration wouldn't change and neither would the mass/the force/the energy. The FES actually got this right.

Nevertheless, UA cannot explain the non-homogeneity, such as the Eötvös effect and so on.

I think I already mentioned, that of course from the earths point of view, you would not notice the changes, but if you think about the plausibility of the whole concept of universal acceleration, you have to look from the reference frame in which you see the force acting on the earth. And an observer in that reference frame would see an almost infinite force acting on the earth. And that doesn't make any sense at all.

No one of them got it right, cause they're only looking at half of the story.

That would be like saying I don't care of the energy consumption of a big particle accelerator cause the particles don't feel their increase of mass. From the point of view of the accelerator the energy consumption is real. The same is true from the point of view of whatever is pushing the earth... 

Flat Earth Theory / Re: Question from a physicist
« on: April 25, 2018, 11:46:06 AM »
The fundamental problem with equivalence principle is, that it's only valid for homogeneous gravitational fields, which are equivalent to a constant acceleration. Real gravitational fields, i.e. fields originating in mass, are not homogeneous, and can only be replaced locally by an acceleration. The whole concept was introduced by Einstein to allow the use of special relativity at least on a local scale in a gravitational field before he invented the concept of general relativity.

Therefor inherently you have to come up with additional explanations outside the framework of general relativity if you want to use a concept like universal acceleration.

And whatever is pushing the earth in this concept, feels an increasing mass and has therefor to push harder to keep the acceleration constant. And any force needs energy and an infinite force needs infinite energy.

And, finally, it is not a god idea to use special relativity examples (constant velocity) to explain general relativity (constant acceleration) scenarios. It is misleading.             

Flat Earth Theory / Re: Question from a physicist
« on: April 25, 2018, 08:04:44 AM »
It is not the house, it is the whole earth that is moving relative to you. But in any case the example is not valid, you need the energy to accelerate against the reference system of the earth therefore the two reference frames are not equivalent. As soon as you stop to accelerate (and assuming there are no losses due to friction, and so on) there is no more energy transfer needed. The same if you stop the car.

You can also look at everything from a reference frame outside the earth, also in that case you would see, that only the car is accelerating, not the earth relative to the car.

Anyway, you cannot refer to the equivalence principle and claim because of that you can replace gravity by an acceleration without taking the other consequences of general relativity into account.       

The problem of the "debate" is inherent, you have to fail to explain something that is in contradiction to reality. From a physics point of view the only interest of discussing such an idea as the flat earth would be to take this as a gedankenexperiment and to build an alternative theoretical framework around this. This could be quite challenging and entertaining, but also for that you would need at least basic understanding of physics, which is almost never existent on the side of the flat earth believers. And I never so any kind of coherence in their explanations. In the best case they can focus on a single observation and give a kind of alternative explanation for it, but then they need a contradicting explanation for something else. Best example are maybe the maps. The monopole and the duopole models can explain very different different things, but are inherently contradicting each other. 

Flat Earth Theory / Re: Question from a physicist
« on: April 24, 2018, 03:35:24 PM »
Our perspective is not relevant, as we are inside the accelerated system. The force is acting on the entire system, you have to look at it from the inertia system where everything in embedded inside. And it goes beyond my imagination how this inertia system should look like in which something like our whole visible universe is accelerated at near light speed with a therefore almost infinite force along a straight line...   

Flat Earth Theory / Re: Question from a physicist
« on: April 24, 2018, 12:14:35 PM »
The problem is not the sufficient acceleration, it's the force that leads to this acceleration. If you take relativity theory serious, the mass of the earth would continuously increase with its speed. If the force is constant, according to F = m*a, the acceleration is inverse proportional to the mass. But if the acceleration is constant, the force has to increase in the same way as the mass. And with this the energy that is needed maintain the force is also increasing... And now think about how fast the earth would be already, how large the mass would be and therefore the force and therefore the energy...   

Flat Earth Theory / Re: Question from a physicist
« on: April 23, 2018, 12:43:54 PM »
The whole universal acceleration idea is a good example of who people come to wrong conclusion if they do not have a real understanding of the expression they using. This idea is based on the equivalence principle, that, in very simple words, says, that you cannot distinguish the effect of a gravitational field from that of a constant acceleration. But this was never supposed to be valid for the gravitational field of a whole planet. It is only valid for homogeneous gravitational field, but the field of a planet is not homogeneous it changes with the distance from the center of the planet. So you can find a certain non-inertial system for each point around the planet, but they're all different from each other depending on their distance from the center. There's no universal non-inertial system that includes the whole planet and everything above it, therefor there is no universal acceleration.       

Flat Earth Theory / Re: FET and Global Positioning System
« on: April 20, 2018, 02:52:01 PM »
You are waiting since 4 pages of discussion for an answer, because there can't be an answer. GPS is a quite straight forward, coherent concept. In the best case you can get some alternative explanations that work in some special areas, e.g. for cities and so on. But you will never be able to find a equivalent coherent explanation.

But that's the fundamental problem of the whole flat earth idea. Of course you can always find alternative explanations for certain aspects, but they soon start to contradict each other and then you have to introduce more and more assumptions. In the end the whole idea is based on a single observation, that the earth looks flat if you are looking out of your window. That's all. But already if you look out of your window and you try to imagine how a hypothetical flat earth would look, you would notice that it would be quite different from what you actually see.

The core challenge for a flat earth believer is to find explanations why a flat earth looks like a round earth, and everything that exist on this flat earth behaves like the earth would be round. You have to twist and bend everything so that it fits, but can't. If you solve one problem, another appears. It's for the same reason you have so many different types of maps, you cannot transform a 3D object into a 2D one without distortions. You can find a suitable solution for a map, that represents a certain aspect quite well and another that fits better to something else.

And that's not only true for maps. Everything works different, looks different and is experienced differently on a 3D world compared to a (functional) 2D world.       

Flat Earth Theory / Re: On a globe Earth the horizon should not curve
« on: April 20, 2018, 07:27:37 AM »
Our visual perception is the result of a one-point projection of a 3D environment onto a 2D plane. In the same way as photography works.

If you look on a picture with lots of virtual lines going straight away from parallel to the optical axis of the camera, you will notice that all this line below the optical axis (which is at the center of your image) will point upwards, all lines below will point downwards, all lines left will point right and all lines right will point left.

And all lines close to the optical axis will finally seem to meet at one point, the so-called vanishing point. Mathematically this point lies in infinite distance from the observer, but that's not what you observe. Lines too far away from the optical axis will not meet at the vanishing point. But all of this lines and their symmetric counterparts below and above the optical axis will meet on one horizontal line. That's the horizon of your image.

If you are sea level this image horizon and the horizon of the earth with the sky are practically identical. You can't resolve the difference. If you climb up, your perception will be more or less the same. Both, the horizon of your image and the real horizon will seem to go up with you. But, with the help of some reference tools or carefully analyzing your picture, you will notice that the real horizon is falling more and more below the image horizon (which is defined by your eye level). And it will become more apparent the higher you climb up.

The real horizon would only stay at eye level if it would be located at infinity, but it's not. And all horizontal in a one-point projection stay below optical axis. But nevertheless, horizontal lines further away appear higher than horizontal lines close to you in a picture. And because the real horizon is already quite far away from you, he appears quite close to the image horizon. And if you climb up the real horizon is even pushed away from you, so in the projection the real horizon also seems to go up. But not as fast as the image horizon.       

Flat Earth Theory / Re: On a globe Earth the horizon should not curve
« on: April 19, 2018, 10:58:47 AM »
Hm, it's not that simple. Take for example the vanishing point. Of course, if you take the geometric definition this point is at infinity. But it this also always a practical definition? If you want to do a landscape painting or a CGI graphics where would you put the vanishing point? You would put it at a finite distance. The same if you take a photograph, let's say of a long and narrow street. Parallel lines would meet at one point at finite distance at the horizon, which is at your eye height. And so on...

The observations in EnaG are not that wrong and the models proposed are valid to describe this observations up to a certain degree. The question is more where is the limit? And from which point on you have to introduce more and more assumptions that are in contradiction to other aspects of your model.

To explain the sinking ship effect, he introduced the effect of waves. And yes, a tiny boat in a stormy sea can vanish behind waves. So far, this observation is not wrong. And of course, how strong this effect is, has something to do with distances and perspective. But it has it's limitations. You can not explain that a huge ship on calm sea is sinking behind the horizon, that simply does not work. Therefor, waves don't give you a consistent explanation for all observations in all situations. That's a problem.

And if you want to explain sunset/sunrise, you have to make even more assumptions like discontinuities in Euclidean geometry and so on.   

You have to be aware of the limits of your model, if you want to be taken serious. But if you stay inside this limitations any model is fine.   

Science is not about truth, that's something for philosophers. Science is about finding the best explanation for a certain observation that is consistent with all the other explanations already found for past observations and that allows you to predict the outcome of observations not yet done.

And this explanation is given in form of a model written down in the language of mathematics. And this process of modeling the observations is not static, it undergoes an infinite process of refinement based on new, more precise observations, better tools, both, experimental and mathematical, and an overall progress in understanding. And this process of refinement is not linear, sometimes you have to go back a part of the way and change your direction. That's what science is all about.       

Flat Earth Theory / Re: On a globe Earth the horizon should not curve
« on: April 19, 2018, 08:06:46 AM »
Resolution without contrast is not possible. The image of a single point is given by the so-called point spread function of the optical system, which is basically a 2D Bessel function. The central peak of the Bessel function defines the size of the Airy disc.

Two points of equal brightness and color can be resolved if the centers of their Airy discs are about one diameter of the Airy disc apart. Which means there is a dip in intensity in between the centers of the Airy discs of about 50%.

Without this contrast you can't resolve anything. Of course, you also need a certain amount of intensity. That's the reason why a light source on a black background can be seen from further away than a black point on a bright background. 

The consequences of this effect on the human perception are more or less described in a correct way in EnaG, but the author draws the completely wrong conclusions out of this regarding perspective and vanishing point. As mentioned above, everything else is just a consequence of this false interpretation.

It seems that at some point the author went to the see and observed that the reconstruction of an object with a telescope as it worked on the street did not work for a ship at the sea much further away and to save his false interpretation he introduced the effect of waves, which he vastly exaggerated.

In the end it is quit easy to understand EnaG and the ideas presented in that book. The bare observations are more or less correct, but because of a lack of background knowledge he draws completely wrong conclusions.       

Flat Earth Theory / Re: On a globe Earth the horizon should not curve
« on: April 18, 2018, 03:23:27 PM »
The core problem in EnaG regarding everything related to perspective, vanishing point, horizon and so on, is that the author did not understood the problem of optical resolution. He describes at some point in the book the effect, that he could no longer see the black boots of some soldiers in the distance, but he could recover them by using a telescope. Form him this is the key to the sinking ship effect. But in reality he suffered from the limited optical resolution of his eyes, at a certain distance he could simply not distinguish the boots from the dark street, while the brighter clothes of the soldiers were still visible. And of course a telescope increases the optical resolution and recovered the boots. 

From the distance between the soldiers to him and his eye height he calculated an angle, which, no wonder, is roughly the angle of optical resolution. But he uses this angle now to calculate the distance to the vanishing point. And from this false conclusion everything else followed. The restoring effect of the telescope, the shift of the vanishing point depending on the height of the observer, the behavior of the so-called perspective lines, the increasing horizon and so on...

All explanations are twisted to fit to this false initial conclusion of a very simple observation.

Flat Earth Theory / Re: On a globe Earth the horizon should not curve
« on: April 18, 2018, 07:26:48 AM »
May I asked what "round earth theory" is? Even after doing science for over 20 year now, I never met someone studying "round earth theory", never been at a university or institute offering this as a course, lecture or seminar, not even seen a book about this...

Flat Earth Theory / Re: On a globe Earth the horizon should not curve
« on: April 12, 2018, 10:43:57 AM »
Of course the horizon could curve on a globe. This follows directly from the full rotational symmetry of a sphere. If I turn around by 360° while staying perpendicular to the surface any line at a fixed distance describes a circle centered around me with its normal parallel to my rotation axis. So I'm looking down onto a circle with my in the center.

Flat Earth Theory / Re: Radii of Certain Circles of Latitude
« on: April 11, 2018, 09:20:53 AM »
Indeed, the perception of the horizon on a flat earth would be very different from what we observe on our earth. Maybe not so much regarding the surface, cause we're quite close to the surface and the perspective uplift of the surface approach eye level roughly at the same distance where the optical resolution limits our ability to distinguish anything close the surface. But regarding anything up in the sky it be very different. All this sinking behind the horizon effects of clouds, the sun, the moon or airplanes would not be possible. They would just fade out due to light scattering, limited optical resolution and so on, but still staying high in the sky until they vanish.       

Flat Earth Theory / Re: Radii of Certain Circles of Latitude
« on: April 10, 2018, 03:40:34 PM »
The problem is the selective perception of reality. Of course, if you look along a straight line of railway tracks they seem to merge in a single point at the horizon. For lots off people that would be an sufficient proof that perspective lines meet in a vanishing point at the horizon. And then they start sharing pictures of this as proof.

If they would look at reference lines further apart from each other, the perception would be very different, they just would not merge. But such examples are not so easy to find. A picture of merging railway tracks almost everyone has seen in his live. It's quite convincing on the first glance... 

And regarding the drop of the horizon below eye level. It's almost impossible to observe with bare eyes due to effect of perspective. Again, what you observe with out any tools, just with your bare eyes, is that the horizon is elevating if you go up. If you take pictures of the horizon and show them around almost everyone will say the horizon is at the center of the picture independent of the height it was taken from. It's not easy to convince someone, that the horizon is really not rising. The drop of the horizon is nothing you experience every day, the common experience is more that it stays fixed.

Flat Earth Theory / Re: Radii of Certain Circles of Latitude
« on: April 10, 2018, 01:46:05 PM »
All the confusion in discussions about the horizon is the result of different definitions of what the horizon actually is.

On a globe, the horizon is the result of the limited sight due to the spherical shape of the globe. It's defined by that tangent to the sphere that goes to the observers eyes. At the same time this is the optical axis of the imaging system of your eyes if we are looking down to the horizon. And of course everything below this optical axis belongs to the globe and everything above belongs to the sky. This is independent of the elevation of the observer, the only thing that changes is the distance between the observer and the horizon. The horizon is further away if the observer goes up.

On the other hand, if we align the optical axis horizontally (now it's a tangent to the sphere at the position of the observer), the horizon is slightly below the optical axis and therefor also a tiny bit of the sky. And if the observer is going up, the horizon will drop more and more.

On a flat earth everything is very different. First of all, there is no horizon in the above sense on a flat earth. The surface of the earth and the sky stay parallel until infinity. So you have to come up with a new definition of the horizon, to explain what you actually see that the sky is apparently touching the surface of the earth.

And the solution is indeed perspective. Perspective is a consequence of our eyes optical imaging system. We have constant field of view where everything is projected on the fixed size of our retina. Therefore the further something is away the more it is apparently squeezed together on the retina. Or in other words, the apparent distance between a certain point and the optical axis will shrink with distance to the observer even though the actual distance to the optical axis does not change. Everyone knows this from looking along a street or into a tunnel. Everything is straight and parallel and nevertheless the walls of the tunnel seem to come closer and closer to each other.

Regarding the  flat earth, perspective would therefor lead to the effect that the surface of the earth and the sky would apparently approach each other. But that does not entirely solve the problem of the observed horizon, because earth and sky would only touch each other in infinity, at the so called vanishing point.

Therefor you need some trick to bring the vanishing point closer to the observer. And if you read EnaG, then the solution is the effect of optical resolution. Of course, beyond a certain distance two points are apparently merging with each other. This limits how far you can see. And you move the vanishing point from infinity to this point and you get your horizon.

And this horizon is indeed moving up if the observer is moving up and looking horizontally. Just because the optical axis is moving up together with the observer.

This can be easily seen if you are look along a tunnel while going down on your knees or standing up. The vanishing point will always follow you. The same if you move left and right, it always follows.     

That is the reason why the question of the 'eye-level horizon' is so important for the flat-earth believers. The rising horizon only works on a flat earth, while the dropping horizon only works on a globe.

Unfortunately, the two are almost not distinguishable with your bare eyes again cause of the effect of perspective... It's a nice topic therefor to generate confusion if you are not fully aware of the mechanisms behind it.           

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