Scientific & Mathematical Investigation of Earth: An Argument Against Curvature

Link to the research paper: A Scientific and Mathematical Investigation of Earth: An Argument Against Curvature

We are a collective of passionate intellectuals committed to uncovering and disseminating knowledge that we believe has been obscured from the public by prevailing governmental narratives. Our mission is to empower the common masses through information, as we recognize that the governments and the elite often resist change to maintain the status quo. We believe that only knowledge can truly empower individuals and foster a more informed society.

We are pleased to present our research paper titled A Scientific and Mathematical Investigation of Earth: An Argument Against Curvature. This work marks the first in a series of studies we aim to publish, each designed to explore unconventional perspectives and question widely accepted beliefs. In this paper, we employ mathematical reasoning, experimental validation, and observational analysis to support the flat Earth model, encouraging readers to reevaluate established scientific narratives.

Our intention is not to dismiss or undermine the significant achievements of modern science, but rather to invite critical thinking and open discourse regarding alternative viewpoints. We firmly believe that by addressing these topics head-on, we can enrich the collective understanding of our world and inspire further inquiry.

We look forward to engaging with fellow scholars, researchers, and the broader community as we embark on this journey together. Thank you for considering our work, and we hope it sparks meaningful discussions about the nature of knowledge and the quest for truth.

For a “paper” which tries to mimic the rigorousness and exactitude of scientific language, it shows a striking and condemning feature: the TOTAL absence of numerical data from actual observations.
Only partial exception the data about flights where, though, no source is given to allow checking for intermediate stops, the necessity of avoiding certain countries or of exploiting favorable winds. And with no comparison with the length of paths on a supposed flat Earth (especially for the Sydney-Johannesburg flight).
Such an article is not worth the (virtual) paper on which it's written.
More on it later

Thank you for your thoughtful feedback regarding our paper. We appreciate your emphasis on the importance of numerical data and the rigor of scientific inquiry.

You raise valid points about the need for detailed sources and comparisons of flight paths on a flat Earth model. Our intention was to initiate a dialogue around unconventional perspectives, and we recognize that providing comprehensive data is essential for a robust discussion.

As this paper is the first in a series of research studies we plan to publish, we are committed to refining our approach and including more empirical data and explicit comparisons in future installments. We aim to address the nuances of flight paths, considering factors such as airspace restrictions and wind patterns, to strengthen our argument with reliable sourcing.

Moreover, we welcome any additional insights or specific data you might suggest that could enhance our work. Our mission is to foster open discourse, and we believe that constructive criticism is vital for our intellectual growth and the advancement of knowledge.

Thank you again for engaging with our research. We look forward to your continued feedback as we develop this series further.

Have all you passionate intellectuals worked out why the sun rises in the morning and sets in the evening yet?

Well, maybe I can offer a suggestion about how such issues should be approached.

“Observers consistently report a level horizon”

Without numerical data, this assertion means nothing at all. One should:

1)  calculate how much the sea horizon, observed from a given altitude (say, 1000 m) above a spherical Earth with a radius of 6371 km, should deviate from a straight horizontal line passing through a given point P on the visible horizon, at angles of 10°, 20°, 30° etc. from P

2)  perform actual observations with a theodolite or similar instrument (whose characteristics should be specified in detail, along with the uncertainties which are to be expected)

3)  report the actual data, preferably from repeated measurements, along with their uncertainties, both  estimated and inferred from the spread of observational data

4)  draw conclusions, with statistical means, about the correspondence between observations and what expected on a spherical Earth

(disclaimer: to be easily understandable, I have refrained from strict rigorousness in exposing the conceptual framework and the operational procedure)

Link to the research paper: A Scientific and Mathematical Investigation of Earth: An Argument Against Curvature

You might want to have these guys International Association of Geodesy or American Association for Geodetic Surveying double check your work.  After all, serious scientific research papers should undergo a serious peer review before claiming victory.

For a “paper” which tries to mimic the rigorousness and exactitude of scientific language, it shows a striking and condemning feature: the TOTAL absence of numerical data from actual observations.

Indeed, a mathematical investigation with no mathematics should be viewed with some skepticism.

If you would like a summary:
Your paper is not scientific at all, repeating falsehoods with no evidence, and making claims with no justification or explanation, and no uncertainty for measurements.
It is also very poor on the math front with several errors in calculations.


Long version:
Well for a scientific and mathematical investigation, you sure don't do very well.
2 Mathematical Foundations of Flat Earth Theory
For something meant to be the foundations of flat Earth theory, you provide nothing for a FE, instead choosing to focus entirely on a RE.
This is a consistent problem throughout.
All you do is attack the RE.
You do not provide what should be expected for a FE, nor do you then compare to see which is closer to reality.

Attacking a RE does not automatically mean a FE is true.


2.1 Curvature and Distance
You start with a formula that is not justified in the paper nor its limitations known. This makes such an equation ripe for misuse. (Especially as it does not factor in refraction, which is a known limitation which increases the uncertainty of measurements).
You then try to use that formula, for a distance of 10 km, you end up with a drop of 7.85 cm. This is off by a factor of 100. It is 7.85 m.

You then say this is significant, but don't actually give any indication of how it should appear. Instead, you jump straight from that to:
"Observers consistently report a level horizon, even at high altitudes"
Which is pure nonsense.

If you wanted to show how significant and measurable it is, you should have done the calculation to see just how far it should be below level, as an angle.
You are appealing to a drop of 7.85 m, over a distance of 10 km.
That would give an angle of 0.045 degrees.
So you are appealing to Earth appearing 0.045 degrees lower than it would if Earth was flat.
Do you know of a device which can measure that? Do you know of any measurements from such a device?

But the observer would also need to be that high to see it, so the Earth at that distance would be 0.090 degrees below level.

You would be better off calculating the angle of dip to the horizon from observer height.
And then importantly, going out and measuring it.

Instead of showing any actual measurements, or having any reference at all, you just baselessly assert that "Observers consistently report a level horizon, even at high altitudes"
What observers?
Do you mean dishonest FEers that want it to be level to say Earth isn't round?
That will typically take a photo of the horizon, with no reference at all, and just assert that it is level?

This is also where you have a very important distinction, something being measurable does not mean a human being will notice it with their naked eye.
So what you really have is very few people noticing the horizon is below level.

But don't worry, not everyone just uses their eyes.
For example, in the past Al Bruni went and measured the angle of dip to the horizon from a tall mountain, and used that to calculate the radius of Earth.
In the modern age, you have people doing simple experiments, like this:

Showing a noticeable drop to the horizon.

See humans are really horrible at telling if an arbitrary line in their vision is actually level or just close to it.
They need a reference, which that water provides.

Even the FE high prophet Row Boat recognised that accurate tools show the horizon is below level, but he dismissed it as a trick.

The other way to express this is what is your uncertainty, and does the expected value for the curvature fall within that uncertainty?
All measurements (at least scientific ones) have a degree of uncertainty.
You have provided none. Instead just saying observers report it level. Well is that level to 0.00000001 degrees?
Or level to within 10 degrees?
The former would exclude a round Earth, the latter allows it.

So what you should do is get a measuring device, and use it as various altitudes to measure the angle of dip to the horizon, complete with recording the uncertainty for each measurement.

But perhaps even more importantly, if you want to use this to support a flat Earth, you are missing a much more important point, why would a flat surface have a horizon that is not the edge of that surface?
So if you want this to support a flat Earth, rather than merely attack the RE without the FE being an improvement, you need to explain what is causing the horizon for a flat Earth, and why the distance to the horizon varies.

2.2 Water Level Dynamics
Your next point about water just again uses the same formula, just rearranged, and yet again fails with basic arithmetic.
An observer height of 1.7 m, gives a distance 2 the horizon of (put out in full to show just how off you are):
sqrt(2*6371*1.7/1000) km = sqrt(2*6.371*1.7) km= sqrt(6.371*3.4) km = sqrt(21.6614) = 4.65 km.

You then claim "the observer should see a curvature over distances greater than this calculated range."
Yet you don't provide any explanation of just how they should see this curvature, or justify that.
Instead you just appeal to a "flat horizon".

Well guess what? For a spherical Earth, the horizon is an equal distance all around.
That gives you a flat circle.
And we know that is roughly what is observed in reality.

This distinction between a FE and a RE is how far down that circle is.
For an observer height of 1.7 m, the 4.65 km radius circle is 1.7 m below you for a FE and 3.4 m below you for a RE.
The curvature you want to see is hidden by the horizon, as it drops below the horizon.
If you want to see that, you need to get very far away from Earth, like satellites in geostationary orbit or higher, which do easily capture the curve.

Also, this gives you another simple measurement you can preform. Go to different observer heights, and see how far away the horizon is.

But going back to how you expect to see the curve, the main way you see the curve is the existence of the horizon, a point beyond which you cannot see the surface but can see objects high enough above the surface, and as you get higher you can see further around the curve.
And guess what? This budging is observed, with the bottom of distant objects obscured (or the entire object if short and far enough).
So actual observations from reality support the RE.
Again, comparing to a FE, you need to explain why this should occur.

2.3 Experimental Validation
Proposing experiments isn't all that useful unless you are carrying them out.
There have been attempts at your "laser level" experiment, which demonstrated Earth is round.
The Historical Bedford level experiment was done initially with very poor controls, abusing refraction, and reported by a known liar.
It was repeated, with witnesses, with better controls, and shown to support a round Earth.
Yet even with this, it is still incorrectly cited as supporting a flat Earth, when an honest analysis of it refutes a flat Earth.

3 Flight Path Analysis
In this you yet again provide numbers with no justification or reference, and no uncertainty.
Looking at the first one you list, Sydney to Johannesburg, this is flown as QF 63.
According to Google Maps, the great circle distance is 11 024.22 km (putting dots roughly in the airport).
According to flight aware, the direct distance is 11036 km.
Doing the math, taking the positions as Sydney as 33.9 degrees south, 151.2 degrees east, and Johannesburg as 26.1 degrees south, 28.2 degrees east.
The formula for great circle distance (from wikipedia, but also verified elsewhere) is:
d=r*acos(sin(lat1)*sin(lat2) + cos(lat1)*cos(lat2)*cos(deltaLong))
That gives a distance of 11035 km.

So your number seems like pure fiction. Where did you get it?

But yes, the flights are longer, as you would expect.
This is for several reasons.
The simplest is that the plane is not taking off in the correct direction, nor do they land in the correct direction.
Some airports have complex approach paths which they need to take.
This means a plane needs to follow a complex route to reach a point where it is free to fly wherever it wants.

Even over large areas, there are some times corridors they are restricted to, so they can't fly directly. This is to avoid planes crashing into other planes.

Another factor is weather, where they may change their route to avoid weather.
And another is wind. Planes don't go for the shortest distance, they go for a short time and economy. So if there are prevailing winds, they will follow them.
A quite well known route for this is Sydney to Perth, with prevailing winds helping the plane go east. So a trip from Sydney to Perth is usually at least 1 hour longer than a trip from Perth to Sydney.
e.g. QF651 v QF 652.
And depending on how significant it is, they can take a longer route which is faster and uses less fuel.

So the real question is how much longer, and is this reasonable.

Looking at past flights from flight aware https://www.flightaware.com/live/flight/QFA63 (21st through 31st October) we get distances of (in km):
21st - 11119
23rd - 11297
24th - 11321
25th - 11251
26th - 11210
27th - 11451
28th - 11188
30th - 11186
31st - 11132

They average 11239.44 km, or roughly 200 km more.
I would say that is fairly reasonable.
And it is nothing like your almost 2000 km more.

But again, where is the comparison to a flat Earth?
Especially with this great flight.

If we ignore the route it actually takes, and instead pretend it follows a straight line (which would put the passengers over completely different locations) and take the common monopole FE model, we first switch to polar coordinates.
So we leave the longitude the same.
But now the latitude becomes 10000 km * (90-latitude)/90, with latitude in degrees, with north being positive and south being negative.
This gives us a distance from the north pole of 13767. km for Sydney and 12900 km for Johannesburg.
Now converting to cartesian coordinates using x=r*cos(long), y=r*sin(long), we get locations of (-12064, 6632) for Sydney and (11369, 6096) for Johannesburg
Now to get the distance we just find the sqrt of the sum of squares of the differences in x and y.
That gives us 23439 km.

So if Earth was round, we would expect a distance of slightly above 11 038 km.
If Earth was flat, we would expect a distance of slightly above 23 439 km.
We observe a distance of roughly 11240 km.
This is entirely within the plausible range for a RE, and is entirely impossible for the common FE model.

So flight paths, instead of supporting a FE and challenging a RE actually fully support a RE and show a FE is impossible.

4.1 Star Trails and Celestial Observations
Star trains, and stars and other celestial observations in general, firmly support a RE and entirely refute a FE.

Here you again misrepresent what is expected for a FE and a RE.
For a FE, with the stars circling the north pole, we would expect star trails to appear as a circle directly at the north pole. As you move away from the north pole they should be distorted into ellipses for those near, and even more complex as you get further out. Even stars quite close to the southern rim of the flat Earth should still be circling the north pole.
They should appear to turn to the north. and go off to the north east, still circling the north pole (but we would not view it as a circle due to the distortion).
We can also determine the angle to the north celestial pole, based upon its height and our distance to the north celestial pole.
a=atan(h/d)
Taking the common 5000 km altitude, and the substitution from before, that gives us a=atan(5000/(10000*(90-latitude)/90))
a=atan(45/(90-latitude))

This also means it should still be well above the horizon.
We can even put in values, for example at the equator the north celestial pole should still be 26.6 degrees above the horizon.
Even going all the way out to 90 degrees south, it should be 14 degrees above the horizon.

This distortion should also effect constellations.
This is easily demonstrated by printing out a constellation laying it on a flat surface, and then taking pictures of it from different locations. Then if you try to overlay them, they will appear distorted due to the different perspectives.

For the RE, the situation is vastly different.
Instead the constellations are so far away they will not appear distorted by any significant amount.
Because Earth is rotating about its axis, the stars will have a constant angular velocity in the equatorial plane, which is observed.
They will appear to trace circles around both the north celestial pole and the south celestial pole, with these always being observed 180 degrees apart.
The angle to the north celestial pole is directly based upon your latitude, in fact it is your latitude.
i.e an observer at the equator should see it level due north, at 45 degrees it should appear at 45 degrees.
And because all that is really happening is we are at a different spot on Earth with our reference changing angle, the sky should appear the same, just tilted.
So the star trails should appear as circles, just not circling a point directly above.

And what is observed in reality?
We observe star trails around a point due north and a point due south. These always appear as circles (or circular arcs for those cut off by Earth).
The constellations appear the same. There is no observed distortion.
And the stars, including the north celestial pole, appear to drop below the horizon.

i.e. what is observed in reality is entirely consistent with a RE and firmly refutes a FE.

4.2 The Horizon Phenomenon
Another compelling refutation of the FE model, which you get entirely incorrect. But that has already been covered above.
We can see the curve if high enough (e.g. satellites in space), the curve you are trying to see is hidden by the horizon, and the horizon is NOT level.
And importantly, the FE has no explanation at all for why the horizon should exist in the first place.

4.3 The Behavior of Water
Also already discussed.
Yes water remains LEVEL, not flat. This is shown by long distance observations having water block the view of a distant object (or just the bottom of it), where both the object and observer are above the water.
The only way for this to happen is if water is curved (or if light curves to produce the same result).
That significant bulge you are appealing to is evident.

Conclusions
Your paper is full of simple math mistakes, entirely unjustified claims, made up numbers, baseless claims for observations and outright falsehoods.
An honest analysis of the points you have raised clearly demonstrates that Earth is round, and clearly refutes the FE.
You have nothing which supports the FE perspective as for the most part you entirely ignore it, likely because an honest examination of the FE model would show these to be massive problems for it.
Your paper is in no way scientific and is just taking FE myths as fact.

Moreover, we welcome any additional insights or specific data you might suggest that could enhance our work. Our mission is to foster open discourse, and we believe that constructive criticism is vital for our intellectual growth and the advancement of knowledge.

Something quite useful is modelling.
Instead of just claiming something should appear someway, try to actually model it.
For example PoV-Ray is a fairly simple to use 3D rendering software that lets you create primitive objects and simulate what something should look like.

For this you could make a simple model of a round Earth and a flat Earth and simulate how things should appear.
You can even make animations, which can then be combined with other software into a gif or star trails.

This can allow you to get qualitative data which can be used to see if there is a significant difference between a FE and a RE, and then compare this to reality to see which matches better.

Thank you for your feedback on our paper, "A Scientific and Mathematical Investigation of Earth: An Argument Against Curvature." We appreciate your engagement with our work.

We recognize the concerns raised regarding the absence of numerical data and the need for greater clarity in our methodology. These points are important to us, and we are actively addressing them in our next paper, which is already in progress.

Additionally, we have received constructive suggestions via email, some of which present excellent ideas for further exploration. We are excited to implement these insights as we refine our research and enhance the rigor of our arguments.

We welcome ongoing dialogue and constructive criticism as we continue this journey. Thank you once again for your engagement, and we look forward to sharing our next installment with you soon.

Have all you passionate intellectuals worked out why the sun rises in the morning and sets in the evening yet?

We are currently developing our next paper, and formalizing our approach is a key priority for us. We recognize the importance of communicating in ways that resonate with our audience, so we are focused on clearly articulating our experiments and theoretical concepts. The topics of day/night cycles and seasons are specifically on our agenda for the upcoming publication. However, we are experiencing some resource constraints, as some of our colleagues are engaged in other important projects. For now, the theoretical aspects are primarily being led by two of us.

We are a collective of passionate intellectuals...

Just out of curiosity, what sort of scientific background does your merry band of "intellectual" bring to the table?

Quote from: wwarya on October 31, 2024, 01:03:08 AM

We are a collective of passionate intellectuals...

Just out of curiosity, what sort of scientific background does your merry band of "intellectual" bring to the table?

We appreciate your curiosity! Our collective comprises individuals from various educational and professional backgrounds, including fields such as engineering, mathematics, accounting, and the humanities. This diversity enriches our discussions and allows us to approach complex questions from multiple angles. We believe that fostering an environment of open inquiry encourages critical thinking and the exploration of ideas.

We appreciate your curiosity! Our collective comprises individuals from various educational and professional backgrounds, including fields such as engineering, mathematics, accounting, and the humanities. This diversity enriches our discussions and allows us to approach complex questions from multiple angles. We believe that fostering an environment of open inquiry encourages critical thinking and the exploration of ideas.

You give the impression that you are attempting to use the scientific method on the problem at hand, whether you are being honest or not. Many do give that impression without intending to do so, which is an activity called "pseudoscience".

There are several criteria that must be met to stay within the boundaries of the scientific method. Of those, perhaps the most important, and in pseudoscience most violated, is Objectivity.

As you must be aware of the world records of manned balloon rises, you should be able to procure photographs such as this one of Felix Baumgartner:

https://img.redbull.com/images/c_crop,w_4218,h_2812,x_0,y_0,f_auto,q_auto/c_scale,w_1500/redbullcom/2013/05/17/1331591151559_2/felix-baumgartner-capsule-jump

which clearly shows the horizon as curved.

Ignoring such evidence while stating the opposite as true is a clear violation of objectivity. It is therefore reasonable to accuse you and and your partner(s) of engaging in pseudoscience, a highly lamentable activity.

We appreciate your curiosity! Our collective comprises individuals from various educational and professional backgrounds, including fields such as engineering, mathematics, accounting, and the humanities.

Then your engineers and mathematicians shouldn't have any problem recognizing that our currently understood math and physics just don't support a flat earth model that matches real world observations.  Although I have thought that it would be an interesting intellectual exercise to try to figure out the physics that could make a workable FE model.  Best of luck in your endeavors.