objections to the roundness of Earth

[bilby]

https://sites.math.washington.edu/~conroy/m120-general/horizon.pdf

Sets out the simple case in an easy to understand format.

 

[Loren Pechtel]

And the point is?

The point is that the earth doesn't really look flat. It is only the irregularities, the unsmoothness, plus our closeness to the ground, that hides the curvature.

Consider the mountain picture earlier. That shows what's really going on--our ability to actually see far enough to see the curvature is limited.

A while back I found a site that you click a point, it shows you what you should be able to see. Somewhat mistaken, a point put on top of the highest point in the area was wildly wrong but a point nearby was pretty close to accurate except for not understanding that some land to the south is shadowed. But there's a major difference between what it showed and what I could see--all of the more distant lands were completely blanked by the atmosphere. Supposedly I have line of sight to some points ~300 miles away--but the best I have actually been able to do is perhaps 100.

 

[Loren Pechtel]

Flat earth is the stupidest conspiracy theory I’ve ever seen as it is nearly trivially debunked by almost anyone anywhere.

What portion of Flat-Earthers actually believe the Earth is flat? Aren't many just having fun?

I'm guessing that VERY few people agree that Birds aren't real.

Just like God. Real unless defined integer. Just ask any Fortran programmer.

 

[lpetrich]

By the well known Quasi Conformal Mapping Jackson-Jones-Smith-Rodriguez theorem spherical is a special case of flat.

Source?

One can do a coordinate projection from a spherical surface to a planar one, but that projection will inevitably cause some distortion. One can do a projection that preserves some property, but it will be at the expense of sacrificing other properties.

Spherical coordinates: radius r, colatitude (90d-latitude) or polar angle ap, longitude or azimuthal angle az:
r*sin(ap)*cos(az), r*sin(ap)*sin(az), r*cos(ap)

Rectangular coordinates: x, y, polar coordinates: r, a:
x = r*cos(a), y = r*sin(a)
r = sqrt(x^2+y^2), a = arctan(y/x)

Kinds of projections:

• Rectangular: x = az, y = Y(ap)
• Polar: r = R(ap), a = az
• Quasi-rectangular: x = X(ap)*az, y = Y(ap)
• Various others

 

[lpetrich]

Examples:

Polar:

• Distance-preserving for some point: R(ap) = ap (the UN-flag projection)
• Orthographic (view from a distance): R(ap) = sin(ap)
• Equal-area: R(ap) = 2*sin(ap/2)
• Stereographic (conformal): R(ap) = 2*tan(ap/2)
• Modified stereeographic: r = rsg^p, a = p*asg for some parameter p
• Gnomonic (geodesic-preserving): R(ap) = tan(ap)

Will use al = pi/2 - ap for these ones:

Rectangular:

• Same-latitude: Y(ap) = al
• Equal-area: Y(ap) = sin(al)
• Mercator (conformal): Y(ap) = log(tan(pi/4 + al/2))

Quasi-rectangular:

• Same-latitude equal area: X(ap) = cos(al), Y(ap) = al
• Mollweide (elliptical boundary): X(ap) = cos(ax), Y(ap) = (pi/2)*sin(ax) where ax - sin(ax)*cos(ax) = (pi/2)*sin(al)

 

[steve_bank]

Source? A joke.

Science and math are definitions. There is no real debate in my option. Somehow fits a definition or it does not. If no existing definition fist create a new definition.

Roundness is more metaphysics than math or science. In Geometric Dimensioning and Tolerancing used in mechanical engineering to specify shoes of parts, roundness has a definition, as does flatness.

We went through this before. There are models for the Earth. Spherical as a simple model accurate enough for mnay misapplications.

Geometric dimensioning and tolerancing - Wikipedia

en.wikipedia.org

If I were to be technical using a mathematically perfect sphere as a model I would say something like the Earth is spherical to +- xx meters referenced from the center of mass of the Earth.

A 3d topological model would have distance from center to surface vs latitude and longitude.

There are flat 2d maps that show distance and relative position. There are topological maps with altitude contours.

As to the OP question, as humans do not have appeared to have changed much I word think the ancient arguments for and against a spherical Earth would have been no different than debates today.

Creationism vs evolution. Natural vs human caused climate change.

I read a short book on topology and conformal mapping years ago for general background information. It has practical uses.

 

[bilby]

An historical note. Watched a documentary on them,Hmong trivesman who word with s in the VN war.

It turned out when they flew over on planes they had no idea of the Earth as a globe. It was traumatic for some.

Why were so many Hmong refugee men in central California dying in their sleep in the early 1980s? They were experiencing fear-induced heart failure as a result of Nightmare/ sleep paralysis experiences.

To conclude that nightmares and sleep paralysis so severe as to be fatal, amongst people who had to flee for their lives from a warzone, is down to their inability to cope with long distance travel, or to understand the shape of the Earth, strikes me as both idiotic and slightly racist.

Many US servicemen who returned from Vietnam suffered similar mental issues. Are we to conclude that they too were devotees of a flat Earth? Perhaps the levels of PTSD were higher amongst servicemen from the Bible Belt?

Or is it more plausible that a war offers plenty of opportunity for trauma that can result in nightmares?

 

[steve_bank]

Some people are just plain irrational.

 

[Jokodo]

Hi.

I know the Greeks and Egyptians were the first to mathematically prove the Earth was round, even coming very close to determining its size.

If you're thinking of Eratosthenes, his experiment doesn't show the earth is round. It showed the size of the earth *assuming* it is round, and *assuming* the sun is, for all intents and purposes, infinitely far away. With these assumptions, when you put two pills in the ground at 1000km apart and wait for one of them to be directly under the sun so it casts no shade, you can determine when you measure the second one to be 9° off that the Earth's circumference, all 360 degrees of it, must be roundabout 40,000km. But under the assumption of a flat earth and a sun at a limited distance, those same 9° can be used to infer that the sun is approximately 6300-something km above the first pole. It's only when you third pole at a third location that there starts to be a noticeable difference. With a third pole at another 2000km from the second one, the round earth predicts the sub should be 27° (3×9°) off center, while for a flat earth, the formula is a bit more complex (atan(3×tan(9)) and come out as ~25.4°. At another 9000km (10,000km), the flat earth model predicts the sun to be still over 30° up, but with a significantly smaller apparent size, while a round earth predicts it to be bang on the horizon but the same size it was at noon.

So everytime you watch the sunset, you're doing a modified Eratosthenes.

 

[DBT]

Take a flight at sunset, you get a sunset then a sunrise as you gain altitude.

 

[Jokodo]

Take a flight at sunset, you get a sunset then a sunrise as you gain altitude.

No need for fancy stuff like planes. Watch scattered high-altitude clouds at sunset. U you'll see them still in sunlight when the the sun has already set on you. They'll be discernibly illuminated from below, too!

 

[DBT]

Take a flight at sunset, you get a sunset then a sunrise as you gain altitude.

No need for fancy stuff like planes. Watch scattered high-altitude clouds at sunset. U you'll see them still in sunlight when the the sun has already set on you. They'll be discernibly illuminated from below, too!

And satellites before the shadow of the earth obscures them (or sunrise in the mornings).

 

[Loren Pechtel]

Take a flight at sunset, you get a sunset then a sunrise as you gain altitude.

No need for fancy stuff like planes. Watch scattered high-altitude clouds at sunset. U you'll see them still in sunlight when the the sun has already set on you. They'll be discernibly illuminated from below, too!

I've seen it many times in the mountains. Basically all access to our local mountain is on the east side, the west is pretty much impassible. Those of us who do long hikes out there often see local "sunset" long before the sky goes dark.

 

[Shadowy Man]

Take a flight at sunset, you get a sunset then a sunrise as you gain altitude.

No need for fancy stuff like planes. Watch scattered high-altitude clouds at sunset. U you'll see them still in sunlight when the the sun has already set on you. They'll be discernibly illuminated from below, too!

This happens with some rocket launches too:



The trail down low is in shadow while higher up it enters the direct sunlight

 

[bilby]

Take a flight at sunset, you get a sunset then a sunrise as you gain altitude.

No need for fancy stuff like planes. Watch scattered high-altitude clouds at sunset. U you'll see them still in sunlight when the the sun has already set on you. They'll be discernibly illuminated from below, too!

This happens with some rocket launches too:

View attachment 47900

The trail down low is in shadow while higher up it enters the direct sunlight

That would be expected once the Sun is below the edge of the Earth's disk.

 

[Shadowy Man]

Take a flight at sunset, you get a sunset then a sunrise as you gain altitude.

No need for fancy stuff like planes. Watch scattered high-altitude clouds at sunset. U you'll see them still in sunlight when the the sun has already set on you. They'll be discernibly illuminated from below, too!

This happens with some rocket launches too:

View attachment 47900

The trail down low is in shadow while higher up it enters the direct sunlight

That would be expected once the Sun is below the edge of the Earth's disk.

If only their ideas were that coherent.