## So... Do we have any Flat Earthers here?

- UncleBob
- CPS Theological Dogmatician
**Posts:**35679**Joined:**Tue Aug 03, 2004 6:00 pm**Location:**Lubbock, TX USA-
**Contact:**

### Re: So... Do we have any Flat Earthers here?

"One man's theology is another man's belly laugh." - Robert A. Heinlein

"Many of the points here, taken to their logical conclusions, don't hold up to logic; they're simply Godded-up ways of saying "I don't like that." - Skip

"Get your facts first, then you can distort them as you please." -Mark Twain

"Many of the points here, taken to their logical conclusions, don't hold up to logic; they're simply Godded-up ways of saying "I don't like that." - Skip

"Get your facts first, then you can distort them as you please." -Mark Twain

- wosbald
- Crux' Cleveland Correspondent
**Posts:**19379**Joined:**Mon Feb 25, 2008 6:00 pm**Location:**Cleveland, Ohio-
**Contact:**

### Re: So... Do we have any Flat Earthers here?

+JMJ+

Then, how does he explain this!?!UncleBob wrote: ↑Mon Nov 06, 2017 3:28 pm‘There is no real picture of Earth’: Top basketball star explains why Earth is flat

"In the end, My Immaculate Heart will triumph." - Our Lady of Fatima

- durangopipe
- Under-secretary to the Minister of Pipe Breaking
**Posts:**6056**Joined:**Wed Jan 20, 2016 3:58 pm**Location:**Southwest Colorado

### Re: So... Do we have any Flat Earthers here?

I'm torn.

I've seen the photos of the earth from space and all . . .

But I hunt in Kansas.

I've seen the photos of the earth from space and all . . .

But I hunt in Kansas.

. . . be kind to one another, tenderhearted, forgiving one another, even as God in Christ forgave you. Ephesians 4:32 (NKJV)

The most improper job of any man, even saints, is bossing other men. Not one in a million is fit for it, and least of all those who seek the opportunity.. J.R.R. Tolkien

2017 Morley - Outstanding BRATASS of the Year

The most improper job of any man, even saints, is bossing other men. Not one in a million is fit for it, and least of all those who seek the opportunity.. J.R.R. Tolkien

2017 Morley - Outstanding BRATASS of the Year

- Del
- Hacked by Kellyanne Conway
**Posts:**37654**Joined:**Mon Mar 03, 2008 6:00 pm**Location:**Madison, WI-
**Contact:**

### Re: So... Do we have any Flat Earthers here?

A small portion of the Earth has to be flat, so it doesn't roll off the Euclidian Plane of Space-Time Continuum.durangopipe wrote: ↑Mon Nov 06, 2017 6:19 pmI'm torn.

I've seen the photos of the earth from space and all . . .

But I hunt in Kansas.

Yep. The Great Plains are the bottom of the Earth.

"Utter frogshit from start to finish." - Onyx

"I shall not wear a crown of gold where my Master wore a crown of thorns." - Godfrey de Bouillon

"I shall not wear a crown of gold where my Master wore a crown of thorns." - Godfrey de Bouillon

- Sir Moose
- President Jar-Jar Binks fan club: "Meesa tink he da best!" - Perpetually in Trouble
**Posts:**3332**Joined:**Tue Mar 03, 2015 1:17 am**Location:**NW Washington (not Canada)-
**Contact:**

### Re: So... Do we have any Flat Earthers here?

The Great Plains are the bottom and Omaha is the....Del wrote: ↑Mon Nov 06, 2017 7:00 pmA small portion of the Earth has to be flat, so it doesn't roll off the Euclidian Plane of Space-Time Continuum.durangopipe wrote: ↑Mon Nov 06, 2017 6:19 pmI'm torn.

I've seen the photos of the earth from space and all . . .

But I hunt in Kansas.

Yep. The Great Plains are the bottom of the Earth.

In theory, theory and practice are the same. In practice, they are not.

- durangopipe
- Under-secretary to the Minister of Pipe Breaking
**Posts:**6056**Joined:**Wed Jan 20, 2016 3:58 pm**Location:**Southwest Colorado

### Re: So... Do we have any Flat Earthers here?

I thought The Great Sphincter was in Egypt?Sir Moose wrote: ↑Mon Nov 06, 2017 8:13 pmThe Great Plains are the bottom and Omaha is the....Del wrote: ↑Mon Nov 06, 2017 7:00 pmA small portion of the Earth has to be flat, so it doesn't roll off the Euclidian Plane of Space-Time Continuum.durangopipe wrote: ↑Mon Nov 06, 2017 6:19 pmI'm torn.

I've seen the photos of the earth from space and all . . .

But I hunt in Kansas.

Yep. The Great Plains are the bottom of the Earth.

. . . be kind to one another, tenderhearted, forgiving one another, even as God in Christ forgave you. Ephesians 4:32 (NKJV)

The most improper job of any man, even saints, is bossing other men. Not one in a million is fit for it, and least of all those who seek the opportunity.. J.R.R. Tolkien

2017 Morley - Outstanding BRATASS of the Year

The most improper job of any man, even saints, is bossing other men. Not one in a million is fit for it, and least of all those who seek the opportunity.. J.R.R. Tolkien

2017 Morley - Outstanding BRATASS of the Year

- Sir Moose
- President Jar-Jar Binks fan club: "Meesa tink he da best!" - Perpetually in Trouble
**Posts:**3332**Joined:**Tue Mar 03, 2015 1:17 am**Location:**NW Washington (not Canada)-
**Contact:**

### Re: So... Do we have any Flat Earthers here?

I metaphorically, literally LOLed. (Or would that be LedOL?)durangopipe wrote: ↑Mon Nov 06, 2017 11:08 pmI thought The Great Sphincter was in Egypt?Sir Moose wrote: ↑Mon Nov 06, 2017 8:13 pmThe Great Plains are the bottom and Omaha is the....Del wrote: ↑Mon Nov 06, 2017 7:00 pmMon Nov 06, 2017 6:19 pmI'm torn.

I've seen the photos of the earth from space and all . . .

But I hunt in Kansas.

Yep. The Great Plains are the bottom of the Earth.

In theory, theory and practice are the same. In practice, they are not.

- UncleBob
- CPS Theological Dogmatician
**Posts:**35679**Joined:**Tue Aug 03, 2004 6:00 pm**Location:**Lubbock, TX USA-
**Contact:**

### Re: So... Do we have any Flat Earthers here?

"One man's theology is another man's belly laugh." - Robert A. Heinlein

"Many of the points here, taken to their logical conclusions, don't hold up to logic; they're simply Godded-up ways of saying "I don't like that." - Skip

"Get your facts first, then you can distort them as you please." -Mark Twain

"Many of the points here, taken to their logical conclusions, don't hold up to logic; they're simply Godded-up ways of saying "I don't like that." - Skip

"Get your facts first, then you can distort them as you please." -Mark Twain

- OldWorldSwine
- rootle round the ear 'ole
**Posts:**9525**Joined:**Sat Aug 01, 2009 6:00 pm

### Re: So... Do we have any Flat Earthers here?

He even named his theater after the Globe. So, there you are.A_Morley wrote: ↑Mon Feb 01, 2016 2:05 amI will not acknowledge the existence or legitimacy of anything not mentioned in the King James Bible, the 1662 Book of Common Prayer, the Complete Works of Charles Dickens, or the Complete Works of William Shakespeare.

Fortunately, Shakespeare alone is sufficient to convince me that the world is spherical.

Just a few examples:

For wheresoe'er thou art in this world's globe,

I'll have an Iris that shall find thee out.

Henry VI, Pt 2

act 3; sc 2

O insupportable! O heavy hour!

Methinks it should be now a huge eclipse

Of sun and moon, and that the affrighted globe

Should yawn at alteration.

Othello

act 5; sc 2

No longer from head to foot than from hip to hip:

she is spherical, like a globe; I could find out

countries in her.

Comedy of Errors

act 3; sc 2

And there you have it. The world's a globe and, thus, not flat.

"There's what's right and there's what's right and never the twain shall meet."

- OldWorldSwine
- rootle round the ear 'ole
**Posts:**9525**Joined:**Sat Aug 01, 2009 6:00 pm

### Re: So... Do we have any Flat Earthers here?

Not having read the article - because who even DOES that? - I assume it is just a new way for dimwitted neckbeards to irritate people.

"There's what's right and there's what's right and never the twain shall meet."

- Jester
- Moderator
**Posts:**1502**Joined:**Mon Sep 19, 2016 1:10 pm**Location:**Missouri

### Re: So... Do we have any Flat Earthers here?

I am fairly new here so this is my first time seeing this thread.

First off to equate young-earth creationists with flat-earthers is lazy and ignorant. Second I have yet to see a bible verse or a biblical explanation as to why people who aren't Christians claim that Christians believe in a flat earth. (stated this way because I have yet to meet a Christian who does think the earth is flat, only non-Christians trying to say that's what we believe.)

Last and certainly not least. This brave soul before you will set-out on a life threatening expedition with 24/7 live stream footage to find the edge of the earth. Millions of people, articles and dollars have been spent discussing this subject and now it's time for flat-earthers to GO-Fund-Me millions of dollars to find the edge of the beast itself. I will take a leave of work and a large sum of money (somebody has to do it) to assemble a team of experienced edge finders to end this dispute on live interwebs/tubes once and for all. The only way I preform this task is if I am funded enough to never work another day in my life (COME ON, I COULD FALL OFF THE FACE OF THE EARTH!!).

First off to equate young-earth creationists with flat-earthers is lazy and ignorant. Second I have yet to see a bible verse or a biblical explanation as to why people who aren't Christians claim that Christians believe in a flat earth. (stated this way because I have yet to meet a Christian who does think the earth is flat, only non-Christians trying to say that's what we believe.)

Last and certainly not least. This brave soul before you will set-out on a life threatening expedition with 24/7 live stream footage to find the edge of the earth. Millions of people, articles and dollars have been spent discussing this subject and now it's time for flat-earthers to GO-Fund-Me millions of dollars to find the edge of the beast itself. I will take a leave of work and a large sum of money (somebody has to do it) to assemble a team of experienced edge finders to end this dispute on live interwebs/tubes once and for all. The only way I preform this task is if I am funded enough to never work another day in my life (COME ON, I COULD FALL OFF THE FACE OF THE EARTH!!).

Pumpkin Ale is more American than apple pie! -Tuttle

"O Christmas Tree is going to be a dirge in his home this year I fear."

We almost solved the Mary issue. -FredS

"O Christmas Tree is going to be a dirge in his home this year I fear."

We almost solved the Mary issue. -FredS

- Rusty
- In Memoriam
**Posts:**25059**Joined:**Thu May 01, 2008 6:00 pm**Location:**Beelzebub's Rare Tobacco Emporium

### Re: So... Do we have any Flat Earthers here?

Am I detecting pride and worldliness?

Alright. The Flat Earthers are right. The Earth is flat. But they're not right on every scale. It's flat on a local scale. You know this too.

A Manifold in topology is a space that is Euclidean on a local level ie flat. So there exists a local scale (ours in fact) where the geometry of space (eg surface) is Euclidean. It does not have to be Euclidean on a large scale, as for example a planetary scale. You can test this in your neighbourhood. Just define three points and measure the angles between lines joining the three points and you too will see that they add to 180 degrees. It's flat. You can even choose a larger "local scale" and it is still true. But it's also true that angles of a triangle on a much larger scale (for example, lines of longitude joining the north pole with the equator) will always add up to more than 180 degrees.

Scale matters with Topological Spaces.

BTW this is the correct answer.

I now return you to your pride and worldliness.

Alright. The Flat Earthers are right. The Earth is flat. But they're not right on every scale. It's flat on a local scale. You know this too.

A Manifold in topology is a space that is Euclidean on a local level ie flat. So there exists a local scale (ours in fact) where the geometry of space (eg surface) is Euclidean. It does not have to be Euclidean on a large scale, as for example a planetary scale. You can test this in your neighbourhood. Just define three points and measure the angles between lines joining the three points and you too will see that they add to 180 degrees. It's flat. You can even choose a larger "local scale" and it is still true. But it's also true that angles of a triangle on a much larger scale (for example, lines of longitude joining the north pole with the equator) will always add up to more than 180 degrees.

Scale matters with Topological Spaces.

BTW this is the correct answer.

I now return you to your pride and worldliness.

You're out of the woods

You're out of the dark

You're out of the night

Step into the sun

Step into the light

You're out of the dark

You're out of the night

Step into the sun

Step into the light

- hugodrax
- All Around Nice Guy
**Posts:**16923**Joined:**Fri Jan 25, 2013 6:00 pm**Location:**Pittsburgh, Pennsylvania-
**Contact:**

### Re: So... Do we have any Flat Earthers here?

Right. Because you're neither arrogant nor wordly. I hope your oo-oo's freeze, Uncle Rusty.Rusty wrote: ↑Tue Nov 14, 2017 5:34 pmAm I detecting pride and worldliness?

Alright. The Flat Earthers are right. The Earth is flat. But they're not right on every scale. It's flat on a local scale. You know this too.

A Manifold in topology is a space that is Euclidean on a local level ie flat. So there exists a local scale (ours in fact) where the geometry of space (eg surface) is Euclidean. It does not have to be Euclidean on a large scale, as for example a planetary scale. You can test this in your neighbourhood. Just define three points and measure the angles between lines joining the three points and you too will see that they add to 180 degrees. It's flat. You can even choose a larger "local scale" and it is still true. But it's also true that angles of a triangle on a much larger scale (for example, lines of longitude joining the north pole with the equator) will always add up to more than 180 degrees.

Scale matters with Topological Spaces.

BTW this is the correct answer.

I now return you to your pride and worldliness.

Etiam mihi opinio anserem perirent.

- Rusty
- In Memoriam
**Posts:**25059**Joined:**Thu May 01, 2008 6:00 pm**Location:**Beelzebub's Rare Tobacco Emporium

### Re: So... Do we have any Flat Earthers here?

It's not about me. It's about Manifolds. Now you know the answer. And it's something that you always knew ... if you think about it. And it's correct. The ancients really did think the world is flat. And they were right on every local scale. That covers the entire world. There is no local neighbourhood anywhere on the planet where that isn't the case. The world is flat on our and their scales.hugodrax wrote: ↑Tue Nov 14, 2017 6:01 pmRight. Because you're neither arrogant nor wordly. I hope your oo-oo's freeze, Uncle Rusty.Rusty wrote: ↑Tue Nov 14, 2017 5:34 pmAm I detecting pride and worldliness?

Alright. The Flat Earthers are right. The Earth is flat. But they're not right on every scale. It's flat on a local scale. You know this too.

A Manifold in topology is a space that is Euclidean on a local level ie flat. So there exists a local scale (ours in fact) where the geometry of space (eg surface) is Euclidean. It does not have to be Euclidean on a large scale, as for example a planetary scale. You can test this in your neighbourhood. Just define three points and measure the angles between lines joining the three points and you too will see that they add to 180 degrees. It's flat. You can even choose a larger "local scale" and it is still true. But it's also true that angles of a triangle on a much larger scale (for example, lines of longitude joining the north pole with the equator) will always add up to more than 180 degrees.

Scale matters with Topological Spaces.

BTW this is the correct answer.

I now return you to your pride and worldliness.

Last edited by Rusty on Tue Nov 14, 2017 6:20 pm, edited 1 time in total.

You're out of the woods

You're out of the dark

You're out of the night

Step into the sun

Step into the light

You're out of the dark

You're out of the night

Step into the sun

Step into the light

- hugodrax
- All Around Nice Guy
**Posts:**16923**Joined:**Fri Jan 25, 2013 6:00 pm**Location:**Pittsburgh, Pennsylvania-
**Contact:**

### Re: So... Do we have any Flat Earthers here?

Of course, but it has nothing to do with whether I hope your oo-oos freeze.Rusty wrote: ↑Tue Nov 14, 2017 6:14 pmIt's not about me. It's about Manifolds. Now you know the answer. And it's something that you always knew ... if you think about it. And it's correct.hugodrax wrote: ↑Tue Nov 14, 2017 6:01 pmRight. Because you're neither arrogant nor wordly. I hope your oo-oo's freeze, Uncle Rusty.Rusty wrote: ↑Tue Nov 14, 2017 5:34 pmAm I detecting pride and worldliness?

Alright. The Flat Earthers are right. The Earth is flat. But they're not right on every scale. It's flat on a local scale. You know this too.

A Manifold in topology is a space that is Euclidean on a local level ie flat. So there exists a local scale (ours in fact) where the geometry of space (eg surface) is Euclidean. It does not have to be Euclidean on a large scale, as for example a planetary scale. You can test this in your neighbourhood. Just define three points and measure the angles between lines joining the three points and you too will see that they add to 180 degrees. It's flat. You can even choose a larger "local scale" and it is still true. But it's also true that angles of a triangle on a much larger scale (for example, lines of longitude joining the north pole with the equator) will always add up to more than 180 degrees.

Scale matters with Topological Spaces.

BTW this is the correct answer.

I now return you to your pride and worldliness.

Etiam mihi opinio anserem perirent.

- durangopipe
- Under-secretary to the Minister of Pipe Breaking
**Posts:**6056**Joined:**Wed Jan 20, 2016 3:58 pm**Location:**Southwest Colorado

### Re: So... Do we have any Flat Earthers here?

Yeah, well, no, Rusty.hugodrax wrote: ↑Tue Nov 14, 2017 6:17 pmOf course, but it has nothing to do with whether I hope your oo-oos freeze.Rusty wrote: ↑Tue Nov 14, 2017 6:14 pmIt's not about me. It's about Manifolds. Now you know the answer. And it's something that you always knew ... if you think about it. And it's correct.hugodrax wrote: ↑Tue Nov 14, 2017 6:01 pmTue Nov 14, 2017 5:34 pmAm I detecting pride and worldliness?

Alright. The Flat Earthers are right. The Earth is flat. But they're not right on every scale. It's flat on a local scale. You know this too.

A Manifold in topology is a space that is Euclidean on a local level ie flat. So there exists a local scale (ours in fact) where the geometry of space (eg surface) is Euclidean. It does not have to be Euclidean on a large scale, as for example a planetary scale. You can test this in your neighbourhood. Just define three points and measure the angles between lines joining the three points and you too will see that they add to 180 degrees. It's flat. You can even choose a larger "local scale" and it is still true. But it's also true that angles of a triangle on a much larger scale (for example, lines of longitude joining the north pole with the equator) will always add up to more than 180 degrees.

Scale matters with Topological Spaces.

BTW this is the correct answer.

I now return you to your pride and worldliness.

Depending on the "order" of the work as it's known in land surveying, or the level of accuracy required for whatever purpose the survey is being conducted, the curvature of the earth is assumed and corrected for even at the "local scale."

From your link:

"Although a manifold locally resembles Euclidean space, meaning that every point has a neighborhood homeomorphic to an open subset of Euclidean space, globally it may not: manifolds in general are not homeomorphic to Euclidean space. For example, the surface of the sphere is not homeomorphic to a Euclidean space, because (among other properties) it has the global topological property of compactness that Euclidean space lacks, but in a region it can be charted by means of map projections of the region into the Euclidean plane (in the context of manifolds they are called charts). When a region appears in two neighbouring charts, the two representations do not coincide exactly and a transformation is needed to pass from one to the other, called a transition map."

In other words, while a local space on a sphere may be represented by a flat map projection, in order for maps to be useful for the most demanding purposes multiple flat map representations/projections of local spaces on a sphere must incorporate correction for curvature.

The world ain't flat, even locally.

You can thaw your oo-oos with a hair dryer, should you so choose, but please don't do it in a public locker room.

. . . be kind to one another, tenderhearted, forgiving one another, even as God in Christ forgave you. Ephesians 4:32 (NKJV)

The most improper job of any man, even saints, is bossing other men. Not one in a million is fit for it, and least of all those who seek the opportunity.. J.R.R. Tolkien

2017 Morley - Outstanding BRATASS of the Year

The most improper job of any man, even saints, is bossing other men. Not one in a million is fit for it, and least of all those who seek the opportunity.. J.R.R. Tolkien

2017 Morley - Outstanding BRATASS of the Year

- Rusty
- In Memoriam
**Posts:**25059**Joined:**Thu May 01, 2008 6:00 pm**Location:**Beelzebub's Rare Tobacco Emporium

### Re: So... Do we have any Flat Earthers here?

Read it again. It only has to resemble a euclidean space. And it does that quite adequately.durangopipe wrote: ↑Tue Nov 14, 2017 7:16 pmYeah, well, no, Rusty.hugodrax wrote: ↑Tue Nov 14, 2017 6:17 pmOf course, but it has nothing to do with whether I hope your oo-oos freeze.Rusty wrote: ↑Tue Nov 14, 2017 6:14 pmIt's not about me. It's about Manifolds. Now you know the answer. And it's something that you always knew ... if you think about it. And it's correct.Tue Nov 14, 2017 6:01 pmTue Nov 14, 2017 5:34 pmAm I detecting pride and worldliness?

Alright. The Flat Earthers are right. The Earth is flat. But they're not right on every scale. It's flat on a local scale. You know this too.

A Manifold in topology is a space that is Euclidean on a local level ie flat. So there exists a local scale (ours in fact) where the geometry of space (eg surface) is Euclidean. It does not have to be Euclidean on a large scale, as for example a planetary scale. You can test this in your neighbourhood. Just define three points and measure the angles between lines joining the three points and you too will see that they add to 180 degrees. It's flat. You can even choose a larger "local scale" and it is still true. But it's also true that angles of a triangle on a much larger scale (for example, lines of longitude joining the north pole with the equator) will always add up to more than 180 degrees.

Scale matters with Topological Spaces.

BTW this is the correct answer.

I now return you to your pride and worldliness.

Depending on the "order" of the work as it's known in land surveying, or the level of accuracy required for whatever purpose the survey is being conducted, the curvature of the earth is assumed and corrected for even at the "local scale."

From your link:

"Although a manifold locally resembles Euclidean space, meaning that every point has a neighborhood homeomorphic to an open subset of Euclidean space, globally it may not: manifolds in general are not homeomorphic to Euclidean space. For example, the surface of the sphere is not homeomorphic to a Euclidean space, because (among other properties) it has the global topological property of compactness that Euclidean space lacks, but in a region it can be charted by means of map projections of the region into the Euclidean plane (in the context of manifolds they are called charts). When a region appears in two neighbouring charts, the two representations do not coincide exactly and a transformation is needed to pass from one to the other, called a transition map."

In other words, while a local space on a sphere may be represented by a flat map projection, in order for maps to be useful for the most demanding purposes multiple flat map representations/projections of local spaces on a sphere must incorporate correction for curvature.

The world ain't flat, even locally.

You can thaw your oo-oos with a hair dryer, should you so choose, but please don't do it in a public locker room.

Here's another reference that actually uses this example to illustrate a manifold.

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

Last edited by Rusty on Tue Nov 14, 2017 8:48 pm, edited 1 time in total.

You're out of the woods

You're out of the dark

You're out of the night

Step into the sun

Step into the light

You're out of the dark

You're out of the night

Step into the sun

Step into the light

- durangopipe
- Under-secretary to the Minister of Pipe Breaking
**Posts:**6056**Joined:**Wed Jan 20, 2016 3:58 pm**Location:**Southwest Colorado

### Re: So... Do we have any Flat Earthers here?

I'll let the comment stand. The earth is not flat, even locally. In this case the manifold is a heuristic, not a physical reality.

From Mathworld:

"Possibly what's confusing you is that the statement refers to the surface of the sphere, not the space the sphere is sitting in. If we ignore relativistic effects (and the fact that the Earth isn't quite a sphere), yes the sphere is in a Euclidean 3-dimensional space. In that space all the convenient Euclidean things apply. But the statement didn't refer to the sphere, or the space it's sitting in: it referred to the surface of the sphere. The surface of the sphere is a 2-dimensional space, not a 3-dimensional one, and points on it only need 2 coordinates (latitude and longitude, for example).

To help see the difference, consider a straight line between London and New York. In the 3-dimensional Euclidean space in which the Earth is embedded, that straight line goes through the Earth. But if we're only considering the surface of the Earth, that line doesn't exist. The straight line (shortest distance between the two points) on the surface lies along the great circle. Now consider drawing the lines from both New York and London to, say, Capetown, to make a triangle. Yes, if you draw the lines through the Earth you will get a nice Euclidean triangle with angles that add up to 180 degrees. But those lines don't exist in the space you are considering: you can only draw lines on the surface of the Earth. The angles of the triangle drawn on the surface of the Earth add up to more than 180 degrees, so the space must be non-Euclidean.

Edit: The bit after the "but" just seems to be saying that for most purposes you can treat a smallish bit of the Earth as if it were flat. You probably don't need to worry about the curvature of the Earth when looking at a street-map of your town."

From Mathworld:

"Possibly what's confusing you is that the statement refers to the surface of the sphere, not the space the sphere is sitting in. If we ignore relativistic effects (and the fact that the Earth isn't quite a sphere), yes the sphere is in a Euclidean 3-dimensional space. In that space all the convenient Euclidean things apply. But the statement didn't refer to the sphere, or the space it's sitting in: it referred to the surface of the sphere. The surface of the sphere is a 2-dimensional space, not a 3-dimensional one, and points on it only need 2 coordinates (latitude and longitude, for example).

To help see the difference, consider a straight line between London and New York. In the 3-dimensional Euclidean space in which the Earth is embedded, that straight line goes through the Earth. But if we're only considering the surface of the Earth, that line doesn't exist. The straight line (shortest distance between the two points) on the surface lies along the great circle. Now consider drawing the lines from both New York and London to, say, Capetown, to make a triangle. Yes, if you draw the lines through the Earth you will get a nice Euclidean triangle with angles that add up to 180 degrees. But those lines don't exist in the space you are considering: you can only draw lines on the surface of the Earth. The angles of the triangle drawn on the surface of the Earth add up to more than 180 degrees, so the space must be non-Euclidean.

Edit: The bit after the "but" just seems to be saying that for most purposes you can treat a smallish bit of the Earth as if it were flat. You probably don't need to worry about the curvature of the Earth when looking at a street-map of your town."

Last edited by durangopipe on Tue Nov 14, 2017 9:08 pm, edited 1 time in total.

The most improper job of any man, even saints, is bossing other men. Not one in a million is fit for it, and least of all those who seek the opportunity.. J.R.R. Tolkien

2017 Morley - Outstanding BRATASS of the Year

- hugodrax
- All Around Nice Guy
**Posts:**16923**Joined:**Fri Jan 25, 2013 6:00 pm**Location:**Pittsburgh, Pennsylvania-
**Contact:**

### Re: So... Do we have any Flat Earthers here?

Nomine exhaustim, manifoldi, ooh-oohs frigidariiae.Rusty wrote: ↑Tue Nov 14, 2017 8:38 pmRead it again. It only has to resemble a euclidean space. And it does that quite adequately.durangopipe wrote: ↑Tue Nov 14, 2017 7:16 pmYeah, well, no, Rusty.hugodrax wrote: ↑Tue Nov 14, 2017 6:17 pmTue Nov 14, 2017 6:14 pmTue Nov 14, 2017 6:01 pmTue Nov 14, 2017 5:34 pmAm I detecting pride and worldliness?

Alright. The Flat Earthers are right. The Earth is flat. But they're not right on every scale. It's flat on a local scale. You know this too.

A Manifold in topology is a space that is Euclidean on a local level ie flat. So there exists a local scale (ours in fact) where the geometry of space (eg surface) is Euclidean. It does not have to be Euclidean on a large scale, as for example a planetary scale. You can test this in your neighbourhood. Just define three points and measure the angles between lines joining the three points and you too will see that they add to 180 degrees. It's flat. You can even choose a larger "local scale" and it is still true. But it's also true that angles of a triangle on a much larger scale (for example, lines of longitude joining the north pole with the equator) will always add up to more than 180 degrees.

Scale matters with Topological Spaces.

BTW this is the correct answer.

I now return you to your pride and worldliness.

Depending on the "order" of the work as it's known in land surveying, or the level of accuracy required for whatever purpose the survey is being conducted, the curvature of the earth is assumed and corrected for even at the "local scale."

From your link:

"Although a manifold locally resembles Euclidean space, meaning that every point has a neighborhood homeomorphic to an open subset of Euclidean space, globally it may not: manifolds in general are not homeomorphic to Euclidean space. For example, the surface of the sphere is not homeomorphic to a Euclidean space, because (among other properties) it has the global topological property of compactness that Euclidean space lacks, but in a region it can be charted by means of map projections of the region into the Euclidean plane (in the context of manifolds they are called charts). When a region appears in two neighbouring charts, the two representations do not coincide exactly and a transformation is needed to pass from one to the other, called a transition map."

In other words, while a local space on a sphere may be represented by a flat map projection, in order for maps to be useful for the most demanding purposes multiple flat map representations/projections of local spaces on a sphere must incorporate correction for curvature.

The world ain't flat, even locally.

You can thaw your oo-oos with a hair dryer, should you so choose, but please don't do it in a public locker room.

Here's another reference that actually uses this example to illustrate a manifold.

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

Etiam mihi opinio anserem perirent.

- Goose55
- Brother of the Briar
**Posts:**7620**Joined:**Thu Feb 11, 2016 6:44 pm**Location:**Southern Arizona, U.S.A.

### Re: So... Do we have any Flat Earthers here?

The earth is not flat, and it's also infinitesimally small compared to the now known universe. Lots of real estate out there. The Real Estate agent that told you "they don't make it any more" was lying.

"At present we're on the wrong side of the door. But all the pages of the New Testament are rustling with the rumor that it will not always be so." ~ C.S. Lewis