SYD to SCL and flight range

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SYD to SCL and flight range
« on: October 14, 2017, 09:50:14 AM »
Hi all, I'm new to this forum and I'll be upfront about why I'm here. It is because someone managed to convince my long-time best friend to give some credibility to the "flat earth theory", although he hasn't completely renounced his belief in a round(ish) earth. I'm perturbed about this whole internet sensation, and here to help anyone else who is being led astray by this clearly false "theory". I understand there are psychological underpinnings to the conspiracy theory game, so I will try to stick to verifiable facts to help those who are able to understand.

I've gone through a systematic approach with my friend to help him think critically about one small topic in-depth, so as not to get bogged down with the plurality of subjects. For this, I've chosen the Sydney to Santiago non-stop route which I think is rather new (2015?). The steps are as follows:

1. The flight exists
2. The flight starts and ends at the locations specified
3. Normal everyday people take this flight: business, vacation, etc.
4. The elapsed time is as specified, about 12.5 hours
5. The flight uses the specified plane, 747-400
6. 747-400 specifications are as stated: range, takeoff weight, etc.
7. FE theory states the equator is the same length as the RE equator
8. FE and RE equator are both 24,870 miles long
9. FE and RE equator are both 7,918 miles in diameter (pi*d=dia)
10. FE shortest distance from SYD to SCL is roughly 10100 miles
11. RE shortest distance from SYD to SCL is roughly 7066 miles
12. The speed of sound is 661mph at 35,000 feet

The distance from SYD to SCL on FE can't happen for at least 2 reasons:
13. The speed would be faster than mach 1
14. The range exceeds specification

Please respond back with a specific number, or something scientific with numbers and facts. Let's leave opinions out of this discussion.

Thanks

Re: SYD to SCL and flight range
« Reply #1 on: October 14, 2017, 10:30:35 AM »
We can analyze multiple Southern Hemisphere flights which mutually connect four or more cities as well.  Displayed here on a Web Mercator Projection map are three such sets.

We begin where you did, at SCL, the “Santiago Quatro” of Santiago Chile (SCL), Auckland (AKL), Sydney (SYD), and Honolulu (HNL).  There are nonstop flights from each of these to all three of the others, in both directions (important, so we can average out the effect of the jet stream)


On the east side of the South American continent we have the “São Paulo Cinco”, interconnecting the São Paulo airports (GRU and VCP) with Johannesburg (JNB), Dakar (DKR), Dubai (DXB), and New York (JFK).  This one is not ideal due to the odd fact that there is only direct service between Dakar and São Paulo in the westbound direction, preventing us from averaging out the jet stream on that leg. 


Continuing eastward we start getting into a better-connected part of the southern hemisphere, where we find a six city set anchored to the São Paulo Cinco by virtue of sharing the JNB-DXB route: the “Indian Ocean Six”.  The other four airports in the set are Mauritius (MTU), Perth (PER), Singapore (SIN), and Hong Kong (HKG).


For the five and six city groups, the triangles that form can be shown to have geometries that are impossible on a flat surface.  Santiago, Auckland, and Sydney are too close to a straight line to give us a good non-flat argument for that set, any discrepancy there could be due to weather or approach/departure route differences, or any number of other factors.

Re: SYD to SCL and flight range
« Reply #2 on: October 14, 2017, 01:27:30 PM »
7. FE theory states the equator is the same length as the RE equator
One minor point, most FE models have the distance to the north pole be the same, not the equator. The FE equator is more like 62882 km.

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Re: SYD to SCL and flight range
« Reply #3 on: October 15, 2017, 03:36:57 AM »
Shalom and welcome to the trenches.
The Bible doesn't support a flat earth.

Scripture, facts, science, stats, and logic is how I argue.

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JerkFace

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Re: SYD to SCL and flight range
« Reply #4 on: October 15, 2017, 06:44:31 AM »
I once asked John Davis a related question,  as to whether the sum of the angles in triangles on the flat earth would add to 180 degrees,  he said that they wouldn't because the surface was non-euclidean, so the (semi) official answer is that the surface of the earth is non euclidean but flat.   ( if you can figure that out, let me know )

In my opinion all those flight times and distances are consistent with a non euclidean flat earth :)   Now cue the argument about metrics.  My money is on Minkowski.  I think the flat earthers will disagree.


Stop gilding the pickle, you demisexual aromantic homoflexible snowflake.

Re: SYD to SCL and flight range
« Reply #5 on: October 15, 2017, 10:44:43 AM »
( if you can figure that out, let me know )
I think he meant Earth's surface is a 3D hyperplane of the non-euclidian 4D space, and therefore is flat in a non-euclidean spacetime and therefore non-euclidian too. It's presented in the thread about Davis's relativity model.
BTW I don't agree with him because I think his definition of "flat" doesn't really capture flatness, but I haven't read the whole thread yet so I don't know if someone else has already pointed this out.

Re: SYD to SCL and flight range
« Reply #6 on: October 15, 2017, 02:48:24 PM »
I once asked John Davis a related question,  as to whether the sum of the angles in triangles on the flat earth would add to 180 degrees,  he said that they wouldn't because the surface was non-euclidean, so the (semi) official answer is that the surface of the earth is non euclidean but flat.   ( if you can figure that out, let me know )

In my opinion all those flight times and distances are consistent with a non euclidean flat earth :)   Now cue the argument about metrics.  My money is on Minkowski.  I think the flat earthers will disagree.
The entire basis of it is that you can orbit around Earth with Earth remaining the same distance from you, and as your orbit is by definition a straight line (or geodesic) through space-time, it must mean the surface of Earth is a straight line as well and thus Earth must be flat.

But there are a few massive problems with this.
The first, and most important, is that this reasoning only works in Euclidean spaces, not non-Euclidean spaces like space-time.
Another is that not all geodesics through space-time remain the same distance from Earth, not even all those which have some point travelling perpendicular to a line connecting Earth to the trajectory (which by definition would include all lines except those going directly through the centre of Earth).
Some will be hyperbolic trajectories, where Earth gets closer and closer, and then starts moving further away, which would indicate that Earth is convex. Others are sub-orbital elliptical trajectories, colliding with the surface of Earth which would indicate Earth is concave. Others are elliptical orbits where the distance to Earth varies periodically, which would indicate an undulating Earth.
Another issue is that it is ignoring all the other points on Earth's surface. Similar to being able to measure the distance to the point below, you can also measure the distance to other points on the surface of Earth, and that indicates Earth is a sphere.

But the simplest analysis is with the equivalence principle which standing on Earth in the presence of gravity is indistinguishable from being on an object accelerating upwards at g. This shows that Earth's surface is not a space-time geodesic (or flat), and instead is constantly curving up (or out), constantly "expanding" as the time axis tries to crush it.


The other option is a completely different route where Earth is merely in non-Euclidean space (without trying to appeal to space-time).
The problem with this is how you measure the curvature of space and why light bends.
Unless you can make it distinguishable from a RE and light going straight (at least through space-time), then it is just a RE in disguise to pretend it is flat.
It also creates the issue of all the FE claims of missing curvature would work equally well against this model (i.e. not at all).

Without light bending, the simplest way to measure if space is Euclidean or not is with light, and there are several ways.
One is to shine 2 beams of light parallel to one another (preferably in a vacuum), and see how the distance between them changes (and as a bonus, the distance from the starting point to them, which is not necessarily measured along the line the light traveled but can be along another straight line)), doing so in multiple directions.
In Euclidean space, they remain the same distance apart.
In spherical space, they first converge (get closer together), then cross, then diverge (get further apart), reaching a maximum (which should be the initial separation distance) before starting to converge again, crossing and diverging and reaching a maximum at the starting point.
In hyperbolic space, they diverge, with the rate of the change in rate of divergence continually decreasing until eventually they reach a point where they act like 2 lines which started at an angle in Euclidean space.
In other spaces you can have some combination of the above.
In cylindrical spaces they remain the same distances apart, yet can loop around, with beams fired at an angle crossing one another multiple times (depending on the starting directions).

But if Earth's surface is going to be flat, then a beam of light fired parallel to Earth's surface should remain the same distance above.

Another option is to measure the apparent intensity of a light source with changing distance.
The 1/r^2 law is based upon Euclidean geometry where as the light propagates outwards, the same energy is spread over the surface of a sphere.
In hyperbolic geometry, due to the divergence stated above, the surface area of the sphere grows faster than r^2, and thus the apparent intensity decreases faster.
In spherical geometry, due to the convergence/divergence above, the intensity becomes periodic. It start decreasing as you move away from the source, but with a decrease slower than 1/r^2, reaching a minimum and then starts increasing, reaching a maximum (which is the initial intensity), and then starts decreasing again, reaching a minimum, then growing in intensity to original maximum at the starting point.

This can also be done in 2D with a 1/r law to compare with, but requires a 2D light source.

Re: SYD to SCL and flight range
« Reply #7 on: October 15, 2017, 02:57:03 PM »
( if you can figure that out, let me know )
I think he meant Earth's surface is a 3D hyperplane of the non-euclidian 4D space, and therefore is flat in a non-euclidean spacetime and therefore non-euclidian too. It's presented in the thread about Davis's relativity model.
BTW I don't agree with him because I think his definition of "flat" doesn't really capture flatness, but I haven't read the whole thread yet so I don't know if someone else has already pointed this out.
The idea of flatness does cover it in non-Euclidean spaces, at least to some extent.
The issue is how he tries to compare an unknown line with a flat line to determine if the unknown line is flat. He is using a method that only works in Euclidean spaces.

Re: SYD to SCL and flight range
« Reply #8 on: October 15, 2017, 10:03:50 PM »
( if you can figure that out, let me know )
I think he meant Earth's surface is a 3D hyperplane of the non-euclidian 4D space, and therefore is flat in a non-euclidean spacetime and therefore non-euclidian too. It's presented in the thread about Davis's relativity model.
BTW I don't agree with him because I think his definition of "flat" doesn't really capture flatness, but I haven't read the whole thread yet so I don't know if someone else has already pointed this out.
The idea of flatness does cover it in non-Euclidean spaces, at least to some extent.
The issue is how he tries to compare an unknown line with a flat line to determine if the unknown line is flat. He is using a method that only works in Euclidean spaces.
Please read my message there:
https://www.theflatearthsociety.org/forum/index.php?topic=72129.msg1970276#msg1970276
(TL;DR – he requires a straight line through space-time between every spatial coordinates and thus also allowing non-flat surfaces like the hyperbolic paraboloid)

Re: SYD to SCL and flight range
« Reply #9 on: October 16, 2017, 01:25:58 AM »
Please read my message there:
https://www.theflatearthsociety.org/forum/index.php?topic=72129.msg1970276#msg1970276
(TL;DR – he requires a straight line through space-time between every spatial coordinates and thus also allowing non-flat surfaces like the hyperbolic paraboloid)
I had been meaning to respond to that but ran out of time.
That isn't what he is suggesting at all.
He is using the fact that space-time is non-Euclidean and thus a "straight" line through space-time will appear curved, such as an orbit.

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rabinoz

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Re: SYD to SCL and flight range
« Reply #10 on: October 16, 2017, 02:03:40 AM »
Please read my message there:
https://www.theflatearthsociety.org/forum/index.php?topic=72129.msg1970276#msg1970276
(TL;DR – he requires a straight line through space-time between every spatial coordinates and thus also allowing non-flat surfaces like the hyperbolic paraboloid)
I had been meaning to respond to that but ran out of time.
That isn't what he is suggesting at all.
He is using the fact that space-time is non-Euclidean and thus a "straight" line through space-time will appear curved, such as an orbit.
The trouble with all this Davis non-Euclidean Flat Earth Hypothesis is that it has absolutely no theoretical or physical basis.

Einstein, quite intentionally, designed his GR to reduce to Newton's Laws of Motion and Gravitation as velocities and masses reduce to zero.
He did this, of course, because he was quite certain of the correctness of Newton's theories under these limit conditions.
As was Nikola Tesla, as far as I can determine, even though Tesla did agree with Einstein at all.

John Davis's non-Euclidean Flat Earth Hypothesis seems to have no such constraint.

On a cosmic scale the masses of the objects in the solar are very small and apart from a few exceptional cases velocities are far less than c.
As a result the curvature of spacetime in our vicinity is absolutely minute.
For example the effect of the curvature of the spacelike component of spacetime is
       an increase in the earth's diameter by about 4 mm and
       an increase in the sun's diameter by about 1.4 m - an absulutely minute effect!
For all practical purposes we live in a 3D Euclidean space.

From my point of view this apparently serious discussion of the Davis non-Euclidean Flat Earth Hypothesis is nothing more than an interesting "academic exercise".

But the big problem that seems to give an air of respectibility  to a completely baseless and ridiculous hypothesis.
And has no place in a discussion on "SYD to SCL and flight range".

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JerkFace

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Re: SYD to SCL and flight range
« Reply #11 on: October 16, 2017, 02:49:19 AM »
Please read my message there:
https://www.theflatearthsociety.org/forum/index.php?topic=72129.msg1970276#msg1970276
(TL;DR – he requires a straight line through space-time between every spatial coordinates and thus also allowing non-flat surfaces like the hyperbolic paraboloid)
I had been meaning to respond to that but ran out of time.
That isn't what he is suggesting at all.
He is using the fact that space-time is non-Euclidean and thus a "straight" line through space-time will appear curved, such as an orbit.
The trouble with all this Davis non-Euclidean Flat Earth Hypothesis is that it has absolutely no theoretical or physical basis.

Einstein, quite intentionally, designed his GR to reduce to Newton's Laws of Motion and Gravitation as velocities and masses reduce to zero.
He did this, of course, because he was quite certain of the correctness of Newton's theories under these limit conditions.
As was Nikola Tesla, as far as I can determine, even though Tesla did agree with Einstein at all.

John Davis's non-Euclidean Flat Earth Hypothesis seems to have no such constraint.

On a cosmic scale the masses of the objects in the solar are very small and apart from a few exceptional cases velocities are far less than c.
As a result the curvature of spacetime in our vicinity is absolutely minute.
For example the effect of the curvature of the spacelike component of spacetime is
       an increase in the earth's diameter by about 4 mm and
       an increase in the sun's diameter by about 1.4 m - an absulutely minute effect!
For all practical purposes we live in a 3D Euclidean space.

From my point of view this apparently serious discussion of the Davis non-Euclidean Flat Earth Hypothesis is nothing more than an interesting "academic exercise".

But the big problem that seems to give an air of respectibility  to a completely baseless and ridiculous hypothesis.
And has no place in a discussion on "SYD to SCL and flight range".

To understand it, you need to take a step back and realise it's a layer of obfustication.  if I can claim the surface of a globe is flat, in some sense or other,  then the distances and times in the southern hemisphere can be perfectly explained.   ( It's a globe ),  but JD can claim he thinks of it as flat in some sense. 

I deliberately avoided discussion the distortion of space-time that would be required to make it match reality,  that's not important when the objective is obfustication and diversion.

For the record Non Euclidean is not flat in any practical sense.
Stop gilding the pickle, you demisexual aromantic homoflexible snowflake.

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rabinoz

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Re: SYD to SCL and flight range
« Reply #12 on: October 16, 2017, 03:56:09 AM »
I deliberately avoided discussion the distortion of space-time that would be required to make it match reality,  that's not important when the objective is obfustication and diversion.
I'll leave you to your :D obfustication :D.

Quote from: Rayzor
For the record Non Euclidean is not flat in any practical sense.
My point there is that Einstein's GR does not curve space in our vicinity enough to even measure.
Hence we live in a 3-D Euclidean space.
The effects of GR, in our vicinity, are mostly due to the curving of the timelike component of spacetime - see JackBlack's diagrams, where orbital motion is (almost) periodic in space, but not in time.

If, however, you consider our movement confined to the surface of a sphere (an approximation to the earth) then you can look on our being confined to a 2-D non-Euclidean space.

But we are not actually confined to the surface of the earth. We can go under the surface (though not far) and above the surface as far "as we like".
Hence the "2-D non-Euclidean space" is just an artifice that is helpful for travel limited to the surface.

None of this, of course, bears any relation to John Davis''s Ferrari Effect.

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th3rm0m3t3r0

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Re: SYD to SCL and flight range
« Reply #13 on: October 16, 2017, 06:05:30 PM »
I once asked John Davis a related question,  as to whether the sum of the angles in triangles on the flat earth would add to 180 degrees,  he said that they wouldn't because the surface was non-euclidean, so the (semi) official answer is that the surface of the earth is non euclidean but flat.   ( if you can figure that out, let me know )

In my opinion all those flight times and distances are consistent with a non euclidean flat earth :)   Now cue the argument about metrics.  My money is on Minkowski.  I think the flat earthers will disagree.

No one is claiming that the Earth is completely level. That's ridiculous. The surface of the Earth, no matter its shape, lies in 3D space, and is therefore non-euclidean.

The flight times are what they are. I still don't understand the problem with this.


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JerkFace

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Re: SYD to SCL and flight range
« Reply #14 on: October 16, 2017, 06:19:59 PM »
I once asked John Davis a related question,  as to whether the sum of the angles in triangles on the flat earth would add to 180 degrees,  he said that they wouldn't because the surface was non-euclidean, so the (semi) official answer is that the surface of the earth is non euclidean but flat.   ( if you can figure that out, let me know )

In my opinion all those flight times and distances are consistent with a non euclidean flat earth :)   Now cue the argument about metrics.  My money is on Minkowski.  I think the flat earthers will disagree.

No one is claiming that the Earth is completely level. That's ridiculous. The surface of the Earth, no matter its shape, lies in 3D space, and is therefore non-euclidean.

The flight times are what they are. I still don't understand the problem with this.

I thought you were a flat earther?  Have you changed sides?
Stop gilding the pickle, you demisexual aromantic homoflexible snowflake.

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th3rm0m3t3r0

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Re: SYD to SCL and flight range
« Reply #15 on: October 16, 2017, 06:35:32 PM »
I once asked John Davis a related question,  as to whether the sum of the angles in triangles on the flat earth would add to 180 degrees,  he said that they wouldn't because the surface was non-euclidean, so the (semi) official answer is that the surface of the earth is non euclidean but flat.   ( if you can figure that out, let me know )

In my opinion all those flight times and distances are consistent with a non euclidean flat earth :)   Now cue the argument about metrics.  My money is on Minkowski.  I think the flat earthers will disagree.

No one is claiming that the Earth is completely level. That's ridiculous. The surface of the Earth, no matter its shape, lies in 3D space, and is therefore non-euclidean.

The flight times are what they are. I still don't understand the problem with this.

I thought you were a flat earther?  Have you changed sides?

Uh, no?


I don't profess to be correct.
Quote from: sceptimatic
I am correct.

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JerkFace

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Re: SYD to SCL and flight range
« Reply #16 on: October 16, 2017, 06:38:57 PM »
I once asked John Davis a related question,  as to whether the sum of the angles in triangles on the flat earth would add to 180 degrees,  he said that they wouldn't because the surface was non-euclidean, so the (semi) official answer is that the surface of the earth is non euclidean but flat.   ( if you can figure that out, let me know )

In my opinion all those flight times and distances are consistent with a non euclidean flat earth :)   Now cue the argument about metrics.  My money is on Minkowski.  I think the flat earthers will disagree.

No one is claiming that the Earth is completely level. That's ridiculous. The surface of the Earth, no matter its shape, lies in 3D space, and is therefore non-euclidean.

The flight times are what they are. I still don't understand the problem with this.

I thought you were a flat earther?  Have you changed sides?

Uh, no?

So you know the definition of non euclidean means not flat?
Stop gilding the pickle, you demisexual aromantic homoflexible snowflake.

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th3rm0m3t3r0

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Re: SYD to SCL and flight range
« Reply #17 on: October 16, 2017, 06:52:05 PM »
I once asked John Davis a related question,  as to whether the sum of the angles in triangles on the flat earth would add to 180 degrees,  he said that they wouldn't because the surface was non-euclidean, so the (semi) official answer is that the surface of the earth is non euclidean but flat.   ( if you can figure that out, let me know )

In my opinion all those flight times and distances are consistent with a non euclidean flat earth :)   Now cue the argument about metrics.  My money is on Minkowski.  I think the flat earthers will disagree.

No one is claiming that the Earth is completely level. That's ridiculous. The surface of the Earth, no matter its shape, lies in 3D space, and is therefore non-euclidean.

The flight times are what they are. I still don't understand the problem with this.

I thought you were a flat earther?  Have you changed sides?

Uh, no?

So you know the definition of non euclidean means not flat?

Mountains and valleys exist. It's much rarer on Earth to find a level surface than not. (Excluding oceans, for that point.)

Nobody is debating this.


I don't profess to be correct.
Quote from: sceptimatic
I am correct.

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JerkFace

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Re: SYD to SCL and flight range
« Reply #18 on: October 16, 2017, 07:12:47 PM »
I once asked John Davis a related question,  as to whether the sum of the angles in triangles on the flat earth would add to 180 degrees,  he said that they wouldn't because the surface was non-euclidean, so the (semi) official answer is that the surface of the earth is non euclidean but flat.   ( if you can figure that out, let me know )

In my opinion all those flight times and distances are consistent with a non euclidean flat earth :)   Now cue the argument about metrics.  My money is on Minkowski.  I think the flat earthers will disagree.

No one is claiming that the Earth is completely level. That's ridiculous. The surface of the Earth, no matter its shape, lies in 3D space, and is therefore non-euclidean.

The flight times are what they are. I still don't understand the problem with this.

I thought you were a flat earther?  Have you changed sides?

Uh, no?

So you know the definition of non euclidean means not flat?

Mountains and valleys exist. It's much rarer on Earth to find a level surface than not. (Excluding oceans, for that point.)

Nobody is debating this.

LOL.  thanks for confirming your ignorance. 


Stop gilding the pickle, you demisexual aromantic homoflexible snowflake.

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th3rm0m3t3r0

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Re: SYD to SCL and flight range
« Reply #19 on: October 16, 2017, 07:53:26 PM »
I once asked John Davis a related question,  as to whether the sum of the angles in triangles on the flat earth would add to 180 degrees,  he said that they wouldn't because the surface was non-euclidean, so the (semi) official answer is that the surface of the earth is non euclidean but flat.   ( if you can figure that out, let me know )

In my opinion all those flight times and distances are consistent with a non euclidean flat earth :)   Now cue the argument about metrics.  My money is on Minkowski.  I think the flat earthers will disagree.

No one is claiming that the Earth is completely level. That's ridiculous. The surface of the Earth, no matter its shape, lies in 3D space, and is therefore non-euclidean.

The flight times are what they are. I still don't understand the problem with this.

I thought you were a flat earther?  Have you changed sides?

Uh, no?

So you know the definition of non euclidean means not flat?

Mountains and valleys exist. It's much rarer on Earth to find a level surface than not. (Excluding oceans, for that point.)

Nobody is debating this.

LOL.  thanks for confirming your ignorance.

...What?


I don't profess to be correct.
Quote from: sceptimatic
I am correct.

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rabinoz

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Re: SYD to SCL and flight range
« Reply #20 on: October 16, 2017, 08:34:24 PM »
So you know the definition of non euclidean means not flat?
As far as I am concerned your definition of non-Euclidean is incomplete.

There can be non-flat things in Euclidean geometry. It is not limited to plane geometry.
Quote
Euclid's Elements
The Elements is mainly a systematization of earlier knowledge of geometry. Its improvement over earlier treatments was rapidly recognized, with the result that there was little interest in preserving the earlier ones, and they are now nearly all lost.
There are 13 total books in the Elements:
  • Books I–IV and VI discuss plane geometry. Many results about plane figures are proved, for example "In any triangle two angles taken together in any manner are less than two right angles." (Book 1 proposition 17 ) and the Pythagorean theorem "In right angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle." (Book I, proposition 47)

  • Books V and VII–X deal with number theory, with numbers treated geometrically via their representation as line segments with various lengths. Notions such as prime numbers and rational and irrational numbers are introduced. The infinitude of prime numbers is proved.

  • Books XI–XIII concern solid geometry. A typical result is the 1:3 ratio between the volume of a cone and a cylinder with the same height and base.

From: Wikipedia, Euclidean geometry
Euclidean geometry is not restricted to two dimensions.

Non-Euclidean Geometry includes:
Quote
1.3 Spherical Geometry:
Spherical geometry is a plane geometry on the surface of a sphere. In a plane geometry, the basic concepts are points and lines. In spherical geometry, points are defined in the usual way, but lines are defined such that the shortest distance between two points lies along them. Therefore, lines in spherical geometry are great circles. A great circle is the largest circle that can be drawn on a sphere. The longitude lines and the equator are great circles of the Earth. Latitude lines, except for the equator, are not great circles. Great circles are lines that divide a sphere into two equal hemispheres.

From: 3: What is Non-Euclidean Geometry



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th3rm0m3t3r0

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Re: SYD to SCL and flight range
« Reply #21 on: October 16, 2017, 10:25:36 PM »
So you know the definition of non euclidean means not flat?
As far as I am concerned your definition of non-Euclidean is incomplete.

There can be non-flat things in Euclidean geometry. It is not limited to plane geometry.
Quote
Euclid's Elements
The Elements is mainly a systematization of earlier knowledge of geometry. Its improvement over earlier treatments was rapidly recognized, with the result that there was little interest in preserving the earlier ones, and they are now nearly all lost.
There are 13 total books in the Elements:
  • Books I–IV and VI discuss plane geometry. Many results about plane figures are proved, for example "In any triangle two angles taken together in any manner are less than two right angles." (Book 1 proposition 17 ) and the Pythagorean theorem "In right angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle." (Book I, proposition 47)

  • Books V and VII–X deal with number theory, with numbers treated geometrically via their representation as line segments with various lengths. Notions such as prime numbers and rational and irrational numbers are introduced. The infinitude of prime numbers is proved.

  • Books XI–XIII concern solid geometry. A typical result is the 1:3 ratio between the volume of a cone and a cylinder with the same height and base.

From: Wikipedia, Euclidean geometry
Euclidean geometry is not restricted to two dimensions.

Non-Euclidean Geometry includes:
Quote
1.3 Spherical Geometry:
Spherical geometry is a plane geometry on the surface of a sphere. In a plane geometry, the basic concepts are points and lines. In spherical geometry, points are defined in the usual way, but lines are defined such that the shortest distance between two points lies along them. Therefore, lines in spherical geometry are great circles. A great circle is the largest circle that can be drawn on a sphere. The longitude lines and the equator are great circles of the Earth. Latitude lines, except for the equator, are not great circles. Great circles are lines that divide a sphere into two equal hemispheres.

From: 3: What is Non-Euclidean Geometry

Thanks.

Rayzor just thinks he's better than everyone else and can't be wrong.


I don't profess to be correct.
Quote from: sceptimatic
I am correct.

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JerkFace

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Re: SYD to SCL and flight range
« Reply #22 on: October 16, 2017, 10:51:42 PM »
So you know the definition of non euclidean means not flat?
As far as I am concerned your definition of non-Euclidean is incomplete.

There can be non-flat things in Euclidean geometry. It is not limited to plane geometry.
Quote
Euclid's Elements
The Elements is mainly a systematization of earlier knowledge of geometry. Its improvement over earlier treatments was rapidly recognized, with the result that there was little interest in preserving the earlier ones, and they are now nearly all lost.
There are 13 total books in the Elements:
  • Books I–IV and VI discuss plane geometry. Many results about plane figures are proved, for example "In any triangle two angles taken together in any manner are less than two right angles." (Book 1 proposition 17 ) and the Pythagorean theorem "In right angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle." (Book I, proposition 47)

  • Books V and VII–X deal with number theory, with numbers treated geometrically via their representation as line segments with various lengths. Notions such as prime numbers and rational and irrational numbers are introduced. The infinitude of prime numbers is proved.

  • Books XI–XIII concern solid geometry. A typical result is the 1:3 ratio between the volume of a cone and a cylinder with the same height and base.

From: Wikipedia, Euclidean geometry
Euclidean geometry is not restricted to two dimensions.

Non-Euclidean Geometry includes:
Quote
1.3 Spherical Geometry:
Spherical geometry is a plane geometry on the surface of a sphere. In a plane geometry, the basic concepts are points and lines. In spherical geometry, points are defined in the usual way, but lines are defined such that the shortest distance between two points lies along them. Therefore, lines in spherical geometry are great circles. A great circle is the largest circle that can be drawn on a sphere. The longitude lines and the equator are great circles of the Earth. Latitude lines, except for the equator, are not great circles. Great circles are lines that divide a sphere into two equal hemispheres.

From: 3: What is Non-Euclidean Geometry

Thanks.

Rayzor just thinks he's better than everyone else and can't be wrong.

Nope,  just more than you.

You seem to think that the existence of mountains and valleys somehow proves something about the shape of the earth.

Rabinoz is wrong about what the definition of euclidean is,  if the angles of a triangle add up to 180 degrees then the surface is euclidean.  if more than 180 the curvature is convex,  less than 180 the curvature is concave.

The sum of the angles of triangles on the surface of the earth add to more than 180 degrees, so it's non euclidean.   

Non euclidean means not flat.

You can use other rules of euclidean geometry as well, like parallel lines. 

Rabinoz misunderstood the concept of a surface.  I'm sure he'll be along any minute to explain about 3d objects in Minkowski space..



Stop gilding the pickle, you demisexual aromantic homoflexible snowflake.

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th3rm0m3t3r0

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Re: SYD to SCL and flight range
« Reply #23 on: October 17, 2017, 12:25:45 AM »
So you know the definition of non euclidean means not flat?
As far as I am concerned your definition of non-Euclidean is incomplete.

There can be non-flat things in Euclidean geometry. It is not limited to plane geometry.
Quote
Euclid's Elements
The Elements is mainly a systematization of earlier knowledge of geometry. Its improvement over earlier treatments was rapidly recognized, with the result that there was little interest in preserving the earlier ones, and they are now nearly all lost.
There are 13 total books in the Elements:
  • Books I–IV and VI discuss plane geometry. Many results about plane figures are proved, for example "In any triangle two angles taken together in any manner are less than two right angles." (Book 1 proposition 17 ) and the Pythagorean theorem "In right angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle." (Book I, proposition 47)

  • Books V and VII–X deal with number theory, with numbers treated geometrically via their representation as line segments with various lengths. Notions such as prime numbers and rational and irrational numbers are introduced. The infinitude of prime numbers is proved.

  • Books XI–XIII concern solid geometry. A typical result is the 1:3 ratio between the volume of a cone and a cylinder with the same height and base.

From: Wikipedia, Euclidean geometry
Euclidean geometry is not restricted to two dimensions.

Non-Euclidean Geometry includes:
Quote
1.3 Spherical Geometry:
Spherical geometry is a plane geometry on the surface of a sphere. In a plane geometry, the basic concepts are points and lines. In spherical geometry, points are defined in the usual way, but lines are defined such that the shortest distance between two points lies along them. Therefore, lines in spherical geometry are great circles. A great circle is the largest circle that can be drawn on a sphere. The longitude lines and the equator are great circles of the Earth. Latitude lines, except for the equator, are not great circles. Great circles are lines that divide a sphere into two equal hemispheres.

From: 3: What is Non-Euclidean Geometry

Thanks.

Rayzor just thinks he's better than everyone else and can't be wrong.

Nope,  just more than you.

You seem to think that the existence of mountains and valleys somehow proves something about the shape of the earth.

Rabinoz is wrong about what the definition of euclidean is,  if the angles of a triangle add up to 180 degrees then the surface is euclidean.  if more than 180 the curvature is convex,  less than 180 the curvature is concave.

The sum of the angles of triangles on the surface of the earth add to more than 180 degrees, so it's non euclidean.   

Non euclidean means not flat.

You can use other rules of euclidean geometry as well, like parallel lines. 

Rabinoz misunderstood the concept of a surface.  I'm sure he'll be along any minute to explain about 3d objects in Minkowski space..

I don't at all. If you'd look back and read what I said, I was just pointing out that whether the Earth is flat or round, the land is uneven in the majority of places. This would result in portions being concave and convex regardless of the shape, and thus a triangle would probably not be a perfect 180 degrees in many places.


I don't profess to be correct.
Quote from: sceptimatic
I am correct.

*

rabinoz

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Re: SYD to SCL and flight range
« Reply #24 on: October 17, 2017, 12:31:21 AM »
So you know the definition of non euclidean means not flat?
<< rab
As far as I am concerned your definition of non-Euclidean is incomplete.

There can be non-flat things in Euclidean geometry. It is not limited to plane geometry.
Quote
Euclid's Elements
The Elements is mainly a systematization of earlier knowledge of geometry. Its improvement over earlier treatments was rapidly recognized, with the result that there was little interest in preserving the earlier ones, and they are now nearly all lost.
There are 13 total books in the Elements:
  • Books XI–XIII concern solid geometry. A typical result is the 1:3 ratio between the volume of a cone and a cylinder with the same height and base.

From: Wikipedia, Euclidean geometry
Euclidean geometry is not restricted to two dimensions.

Non-Euclidean Geometry includes:
Quote
1.3 Spherical Geometry:
Spherical geometry is a plane geometry on the surface of a sphere. In a plane geometry, the basic concepts are points and lines. In spherical geometry, points are defined in the usual way, but lines are defined such that the shortest distance between two points lies along them. Therefore, lines in spherical geometry are great circles. A great circle is the largest circle that can be drawn on a sphere. The longitude lines and the equator are great circles of the Earth. Latitude lines, except for the equator, are not great circles. Great circles are lines that divide a sphere into two equal hemispheres.

From: 3: What is Non-Euclidean Geometry

Rabinoz is wrong about what the definition of euclidean is, 
Nope. You might note that I thought of that.
Euclidean geometry is not restricted to two dimensions and includes solid geometry.
Quote
Books XI–XIII concern solid geometry. A typical result is the 1:3 ratio between the volume of a cone and a cylinder with the same height and base.

Quote from: Rayzor
if the angles of a triangle add up to 180 degrees then the surface is euclidean.  if more than 180 the curvature is convex,  less than 180 the curvature is concave.
The sum of the angles of triangles on the surface of the earth add to more than 180 degrees, so it's non euclidean.   
The earth is in is 3-D Euclidean space, which as we saw above includes solid figures, including spheres.
A situation where non-Euclidean space comes in is when motion is confined to the surface of a sphere and this covered by Spherical Geometry, which I specifically included.

Quote from: Rayzor
Non euclidean means not flat.
You can use other rules of euclidean geometry as well, like parallel lines. 
Rabinoz misunderstood the concept of a surface.
So no, I did not mis-understand anything.
It is true to say that non-Euclidean means that the space is not flat, but Euclidean space can certainly include mountains and valleys, etc.

It is only if we consider our geometry as confined to a spherical surface that we are in a 2-D non-Euclidean space.
This class of non-Euclidean space is called Spherical Geometry and you can use the triangle and parallel line rules.

But in reality, we are not confined to a spherical surface. That is just an approximation that allows the use of Spherical Geometry and Spherical Trigonometry to calculate distances (say using the Haversine Formula) between locations specified by lat/long.

The approximation arises because
  • the earth's surface in not perfectly spherical. 
    For example the distance from Sydney Airport (at -33.94735° 151.17943°) to Heathrow (at 51.47002° -0.45430°)
    is 17,020 km based on a spherical earth and 17,016 km using more accurate calculations.
    The spherical approximation is very good, but not perfect.
  • Our movement is not confined to the surface of the earth, spherical or not, We dig into it (a minute distance), fly to 20 km above it and send spacecraft an almost unlimited distance above it.
    The altitude an aircraft flies above the earth does affect the length of the flight, but again only by a few tens of km.
Quote from: Rayzor
I'm sure he'll be along any minute to explain about 3d objects in Minkowski space.
;D ;D If you insist, after we have dealt with hyperbolic space it's only a little step to Minkowski space;D ;D

I know I've been pedantic and laboured the point,
but I want to distance the real earth as for as possible from the John Davis's non-Euclidean Flat Earth Hypothesis.

The space we live might be curved by Einstein's GR, but that curvature
          at the surface of Earth is immeasurably small - about 1 part in 3.2 x 109 and even
          at the surface of the Sun is still extremely small - about 1 part in 109.
So for all practical purposes, we live in a 3-D Euclidean space and the non-Euclidean only comes in if you consider movement confined to a 2-D spherical surface.

Einstein's GR reduces almost exactly to Newton's Laws of Motion and Gravitation anywhere in the solar system and
that was quite intentional on Einstein's part as he recognised that in the low mass low-speed limit Newton was correct.



Re: SYD to SCL and flight range
« Reply #25 on: October 17, 2017, 12:49:30 AM »
No one is claiming that the Earth is completely level. That's ridiculous. The surface of the Earth, no matter its shape, lies in 3D space, and is therefore non-euclidean.
Just because it isn't flat doesn't mean it is non-Euclidean.

The flight times are what they are. I still don't understand the problem with this.
Only because you choose not to.
It is impossible for these flights to exist. It requires the planes to fly much faster than they are capable of doing, and there is no reason for the airlines to fly these routes like they do if Earth was flat.

Rayzor just thinks he's better than everyone else and can't be wrong.
No, that would be you.
I don't at all. If you'd look back and read what I said, I was just pointing out that whether the Earth is flat or round, the land is uneven in the majority of places. This would result in portions being concave and convex regardless of the shape, and thus a triangle would probably not be a perfect 180 degrees in many places.
No. Triangles would be 180 degrees. What wouldn't is curved lines or many sided shapes moving around in 3D.

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JerkFace

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Re: SYD to SCL and flight range
« Reply #26 on: October 17, 2017, 01:06:03 AM »
So you know the definition of non euclidean means not flat?
<< rab
As far as I am concerned your definition of non-Euclidean is incomplete.

There can be non-flat things in Euclidean geometry. It is not limited to plane geometry.
Quote
Euclid's Elements
The Elements is mainly a systematization of earlier knowledge of geometry. Its improvement over earlier treatments was rapidly recognized, with the result that there was little interest in preserving the earlier ones, and they are now nearly all lost.
There are 13 total books in the Elements:
  • Books XI–XIII concern solid geometry. A typical result is the 1:3 ratio between the volume of a cone and a cylinder with the same height and base.

From: Wikipedia, Euclidean geometry
Euclidean geometry is not restricted to two dimensions.

Non-Euclidean Geometry includes:
Quote
1.3 Spherical Geometry:
Spherical geometry is a plane geometry on the surface of a sphere. In a plane geometry, the basic concepts are points and lines. In spherical geometry, points are defined in the usual way, but lines are defined such that the shortest distance between two points lies along them. Therefore, lines in spherical geometry are great circles. A great circle is the largest circle that can be drawn on a sphere. The longitude lines and the equator are great circles of the Earth. Latitude lines, except for the equator, are not great circles. Great circles are lines that divide a sphere into two equal hemispheres.

From: 3: What is Non-Euclidean Geometry

Rabinoz is wrong about what the definition of euclidean is, 
Nope. You might note that I thought of that.
Euclidean geometry is not restricted to two dimensions and includes solid geometry.
Quote
Books XI–XIII concern solid geometry. A typical result is the 1:3 ratio between the volume of a cone and a cylinder with the same height and base.

Quote from: Rayzor
if the angles of a triangle add up to 180 degrees then the surface is euclidean.  if more than 180 the curvature is convex,  less than 180 the curvature is concave.
The sum of the angles of triangles on the surface of the earth add to more than 180 degrees, so it's non euclidean.   
The earth is in is 3-D Euclidean space, which as we saw above includes solid figures, including spheres.
A situation where non-Euclidean space comes in is when motion is confined to the surface of a sphere and this covered by Spherical Geometry, which I specifically included.

Quote from: Rayzor
Non euclidean means not flat.
You can use other rules of euclidean geometry as well, like parallel lines. 
Rabinoz misunderstood the concept of a surface.
So no, I did not mis-understand anything.
It is true to say that non-Euclidean means that the space is not flat, but Euclidean space can certainly include mountains and valleys, etc.

It is only if we consider our geometry as confined to a spherical surface that we are in a 2-D non-Euclidean space.
This class of non-Euclidean space is called Spherical Geometry and you can use the triangle and parallel line rules.

But in reality, we are not confined to a spherical surface. That is just an approximation that allows the use of Spherical Geometry and Spherical Trigonometry to calculate distances (say using the Haversine Formula) between locations specified by lat/long.

The approximation arises because
  • the earth's surface in not perfectly spherical. 
    For example the distance from Sydney Airport (at -33.94735° 151.17943°) to Heathrow (at 51.47002° -0.45430°)
    is 17,020 km based on a spherical earth and 17,016 km using more accurate calculations.
    The spherical approximation is very good, but not perfect.
  • Our movement is not confined to the surface of the earth, spherical or not, We dig into it (a minute distance), fly to 20 km above it and send spacecraft an almost unlimited distance above it.
    The altitude an aircraft flies above the earth does affect the length of the flight, but again only by a few tens of km.
Quote from: Rayzor
I'm sure he'll be along any minute to explain about 3d objects in Minkowski space.
;D ;D If you insist, after we have dealt with hyperbolic space it's only a little step to Minkowski space;D ;D

I know I've been pedantic and laboured the point,
but I want to distance the real earth as for as possible from the John Davis's non-Euclidean Flat Earth Hypothesis.

The space we live might be curved by Einstein's GR, but that curvature
          at the surface of Earth is immeasurably small - about 1 part in 3.2 x 109 and even
          at the surface of the Sun is still extremely small - about 1 part in 109.
So for all practical purposes, we live in a 3-D Euclidean space and the non-Euclidean only comes in if you consider movement confined to a 2-D spherical surface.

Einstein's GR reduces almost exactly to Newton's Laws of Motion and Gravitation anywhere in the solar system and
that was quite intentional on Einstein's part as he recognised that in the low mass low-speed limit Newton was correct.

Nothing wrong with what you are saying, it's just that we are discussing the geometry of flight times and distances,  the geometry proves the surface of the earth is non euclidean.
Stop gilding the pickle, you demisexual aromantic homoflexible snowflake.

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rabinoz

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Re: SYD to SCL and flight range
« Reply #27 on: October 17, 2017, 02:44:43 AM »
Nothing wrong with what you are saying, it's just that we are discussing the geometry of flight times and distances,  the geometry proves the surface of the earth is non euclidean.
That would be nice, but :D someone,:D who shall remain nameless,  let the genie out of the bottle with:
In my opinion all those flight times and distances are consistent with a non euclidean flat earth :)   
Now cue the argument about metrics.  My money is on Minkowski.  I think the flat earthers will disagree.
;D No names, no pack drill. ;D

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JerkFace

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Re: SYD to SCL and flight range
« Reply #28 on: October 17, 2017, 03:03:41 AM »
Nothing wrong with what you are saying, it's just that we are discussing the geometry of flight times and distances,  the geometry proves the surface of the earth is non euclidean.
That would be nice, but :D someone,:D who shall remain nameless,  let the genie out of the bottle with:
In my opinion all those flight times and distances are consistent with a non euclidean flat earth :)   
Now cue the argument about metrics.  My money is on Minkowski.  I think the flat earthers will disagree.
;D No names, no pack drill. ;D

I should be more careful, I was having a shot at the Davis idea of non-euclidean flatness.  ( I did actually say that I'd like someone to explain that meant )

Not surprisingly no-one did.  ( in the context of flight times and distances, which implies I was talking about the surface of the earth )

Thermoman,  obligingly noted that mountains aren't flat,   very astute.
« Last Edit: October 17, 2017, 03:05:52 AM by Rayzor »
Stop gilding the pickle, you demisexual aromantic homoflexible snowflake.

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rabinoz

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Re: SYD to SCL and flight range
« Reply #29 on: October 17, 2017, 03:35:52 AM »
Nothing wrong with what you are saying, it's just that we are discussing the geometry of flight times and distances,  the geometry proves the surface of the earth is non euclidean.
That would be nice, but :D someone,:D who shall remain nameless,  let the genie out of the bottle with:
In my opinion all those flight times and distances are consistent with a non euclidean flat earth :)   
Now cue the argument about metrics.  My money is on Minkowski.  I think the flat earthers will disagree.
;D No names, no pack drill. ;D

I should be more careful, I was having a shot at the Davis idea of non-euclidean flatness.  ( I did actually say that I'd like someone to explain that meant )

Not surprisingly no-one did.  ( in the context of flight times and distances, which implies I was talking about the surface of the earth )

Thermoman,  obligingly noted that mountains aren't flat,   very astute.
Now, if we can only get Mr Can't Spell Thermometer to tell us what his flat earth looks like we might get somewhere.
I guess all we have is the FAQ, where Jack says
Quote
What does the earth look like?
As seen in the diagrams above, the earth is in the form of a disk with the North Pole in the center and Antarctica as a wall around the edge. This is the generally accepted model among members of the society. In this model, circumnavigation is performed by moving in a great circle around the North Pole.

The earth is surrounded on all sides by an ice wall that holds the oceans back. This ice wall is what explorers have named Antarctica. Beyond the ice wall is a topic of great interest to the Flat Earth Society. To our knowledge, no one has been very far past the ice wall and returned to tell of their journey. What we do know is that it encircles the earth and serves to hold in our oceans and helps protect us from whatever lies beyond.

Here is picture of a proposed, but certainly not definitive, flat earth:
Note that the map is "certainly not definitive", but there seem no doubt about "As seen in the diagrams above, the earth is in the form of a disk with the North Pole in the center and Antarctica as a wall around the edge".

Surely Jack's knowledge of the FE transcends that of th3rm0m3t3r0?

So unless something better comes along, I guess we use the "Ice-Wall" map.