31 Oct 15
Originally posted by twhiteheadIt is possible to be more clueless about a topic, but I think you've made a case for yourself on this one.
He was presumably referring to two places of equal distance longitudinally but at different latitudes. The further away longitudinally the points are the more deviation from an east-west path is required.
Of course you would know this if you had bothered to actually look at a globe, but instead you insist on looking at a flat map - and a specific flat ma ...[text shortened]... Truth is not relative. You are wrong and demonstrably so. You are just too dense to realise it.
My point has literally NOTHING to do with relative truth, nothing to do with subjectivity.
As is evidenced in literally EVERY post I've submitted, my focus has been on the math involved in the examples.
You cannot use a globe to prove a globe reality, any more than you can use a flat earth model to prove a flat earth reality.
Please don't present yourself so naïve by suggesting either of these scenarios are at play here.
What has been put forth is simple math: adding, multiplying, subtracting and dividing the distance between two points.
If you think you can spin it any other way, you are simply revealing the actual dense character in this exercise.
31 Oct 15
Originally posted by twhiteheadThe further away longitudinally the points are the more deviation from an east-west path is required.
He was presumably referring to two places of equal distance longitudinally but at different latitudes. The further away longitudinally the points are the more deviation from an east-west path is required.
Of course you would know this if you had bothered to actually look at a globe, but instead you insist on looking at a flat map - and a specific flat ma ...[text shortened]... Truth is not relative. You are wrong and demonstrably so. You are just too dense to realise it.
Yes, I believe googlefudge attempted to make this same claim earlier.
I'll challenge you as I challenged him on the same point (which, as we have seen up to this point, he has remained absolutely and unequivocally silent, as I suspect you will, as well).
1. Provide the formula which undergirds the claim that further distance from the equator requires a greater angle off the latitude line in order to achieve the shortest distance of travel between two longitude points.
2. Explain how the examples given (TPE to LAX and BOS to SEA) do not conform to this claim.
I suspect you will be changing the subject post haste, per your usual tack.
31 Oct 15
Originally posted by wolfgang59I've made it even more simple, but I'll humor you any way.
I'll make this as simple as I can.
In order to educate yourself do these "thought experiments".
1. Imagine you are 10 yards from the North Pole.
If you walk due East do you imagine that will look like walking in a straight line?
2. Look at two [b]different[b] projections of the world. Can you see that "straight" lines
between certain places do n ...[text shortened]... s of latitude. Are they now
the shortest distance between points on those lines?
Please try.
In that same spot (ten yards from the north pole), you are 30' from the magnetic center point.
If you want to move east by another 30' and take the shortest distance possible to get there (and remember, you're nearly 90° from the equator, so factor that into your calculations), how many steps toward the magnetic center point will you have to take to arrive 30' to the east of your starting point?
Now, since I have humored your example (which, I will point out yet again, was given AFTER the examples I submitted), will you please answer the questions put forth in the examples as well as the challenges I put to your claims regarding both the formula for the angled paths of travel in relationship to the equator as well as why the examples cited do not abide by the claims?
Originally posted by FreakyKBHHere you go:
I'll challenge you as I challenged him on the same point (which, as we have seen up to this point, he has remained absolutely and unequivocally silent, as I suspect you will, as well).
1. Provide the formula which undergirds the claim that further distance from the equator requires a greater angle off the latitude line in order to achieve the shortest distance of travel between two longitude points.
https://en.wikipedia.org/wiki/Great-circle_distance
(approximating the earth as a sphere is sufficient for the question under discussion. If you want to calculate distances accurate to metres then you need a slightly different formula that takes Earth's oblateness into account).
2. Explain how the examples given (TPE to LAX and BOS to SEA) do not conform to this claim.
They do conform. (and no, counting the syllables in my answer will not render it incorrect.).
If you think they do not conform then explain how you think they do not conform.
I suspect you will be changing the subject post haste, per your usual tack.
I suspect you will simply post the same tired old nonsense over again despite the fact that it has been answered multiple times and you just didn't like the answers.
I have not changed the subject at all in this thread since you first posted your initial thought experiment. Pretending that I have is dishonest of you.
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Originally posted by FreakyKBH
[b]The further away longitudinally the points are the more deviation from an east-west path is required.
Yes, I believe googlefudge attempted to make this same claim earlier.
I'll challenge you as I challenged him on the same point (which, as we have seen up to this point, he has remained absolutely and unequivocally silent, as I suspect you will, as ...[text shortened]... rm to this claim.
I suspect you will be changing the subject post haste, per your usual tack.[/b]
2. Explain how the examples given (TPE to LAX and BOS to SEA) do not conform to this claim.
Well for starters they are not two points at the same latitude.
Also they are are not an equal distance apart nor are they an equal angle apart.
Also, as Twhitehead says, they do conform. The great circle linking TPE and LAX meets the equator at a larger
angle than the great circle linking BOS and SEA, and the great circle linking TPE and LAX goes farther north
than the great circle linking BOS and SEA. while those two points are farther north, they are also much closer together,
putting them near the 'top' of their great circle, as opposed to TPE and LAX which are farther down.
1. Provide the formula which undergirds the claim that further distance from the equator requires a greater
angle off the latitude line in order to achieve the shortest distance of travel between two longitude points.
Why?
You don't understand plain english, I see no reason to suppose you would understand maths any better.
Also it's completely unnecessary, it's blindingly obvious just by looking at [or imagining] a sphere.
A mathematical formula wouldn't prove anything, because maths is just a way of describing what is going on.
It doesn't dictate what is going on.
I could write all kinds of formula's which would give the right answer and have no relationship to what is actually
going on.
This is a problem MUCH better suited to exploring via the methods we have already proposed.
Ie, just look at a frickin' globe.
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31 Oct 15
Originally posted by FreakyKBH
I've made it even more simple, but I'll humor you any way.
In that same spot (ten yards from the north pole), you are 30' from the magnetic center point.
If you want to move east by another 30' and take the shortest distance possible to get there (and remember, you're nearly 90° from the equator, so factor that into your calculations), how many steps t ...[text shortened]... vel in relationship to the equator as well as why the examples cited do not abide by the claims?
In that same spot (ten yards from the north pole), you are 30' from the magnetic center point.
WTF?
Are you really that stupid?
You are 10 meters from the north pole.
You walk east.
You walk in a circle with a radius of 10m around the north pole.
It's that frickin' simple.
31 Oct 15
Originally posted by twhiteheadThey do conform. (and no, counting the syllables in my answer will not render it incorrect.).
Here you go:
https://en.wikipedia.org/wiki/Great-circle_distance
(approximating the earth as a sphere is sufficient for the question under discussion. If you want to calculate distances accurate to metres then you need a slightly different formula that takes Earth's oblateness into account).
[b]2. Explain how the examples given (TPE to LAX and BOS to ...[text shortened]... ce you first posted your initial thought experiment. Pretending that I have is dishonest of you.
If you think they do not conform then explain how you think they do not conform.
As has been stated enough times to be sufficient as consistent testimony, I will only assume you accept the proof offered as sufficient to change your claims.
Oh: what's that?
You don't accept what has been offered?
That leaves it to you to discredit what has been offered instead of asking me to repeat the same material again.
If they conformed, we would see TPE to LAX take a much more shallow angle of trajectory than BOS to SEA, as the former scenario has a beginning point 25° closer to the equator than the latter.
Instead, TPE to LAX takes much deeper angle of trajectory than BOS to SEA.
Please stop playing silly little games and play the ball where it actually sits.
I suspect you will simply post the same tired old nonsense over again despite the fact that it has been answered multiple times and you just didn't like the answers.
Again: how one feels about the answers is inconsequential.
The answers either line up with reality, or the do not.
What precious little you have offered (none of it supported, of course) has been without support and baseless, with a little bit of anecdotal thrown in, just for fun.
Answer the questions or admit defeat.
Two things I'm certain you'll never do!
31 Oct 15
Originally posted by googlefudgeWell for starters they are not two points at the same latitude.2. Explain how the examples given (TPE to LAX and BOS to SEA) do not conform to this claim.
Well for starters they are not two points at the same latitude.
Also they are are not an equal distance apart nor are they an equal angle apart.
[quote]1. Provide the formula which undergirds the claim that further distance from the equator ...[text shortened]... ted to exploring via the methods we have already proposed.
Ie, just look at a frickin' globe.
Check.
That's been established.
TPE to LAX has a difference of 8° from one to the other.
BOS to SEA has a difference of 5° from start to finish.
TPE sits at 22° above the equator.
BOS sits at 47° above the equator.
That's a difference of 25° between start points.
LAX sits 33° above the equator.
SEA sits 42° above the equator.
That's a difference of 9° between end points.
Also, as Twhitehead says, they do conform... putting them near the 'top' of their great circle, as opposed to TPE and LAX which are farther down.
Um, huh?
How does any of that either make sense or agree with your earlier contention of trajectory being dependent upon proximity to the equator?
Does it feel a little bit like you're trying to talk yourself out of the position?
It sure sounds like it...
This is a problem MUCH better suited to exploring via the methods we have already proposed.
Ie, just look at a frickin' globe.
We can, but it is misleading.
Every globe we have it perfectly spherical, a literal round ball.
Every great circle formula is dependent upon a literal round ball.
Even your experiment with a string fails on a literal round ball--- and is rendered nonsensical on an irregularly shaped ellipsoid.
These paths of flight or navigational routes by ships do make sense on a flat earth map, for some reason.
31 Oct 15
Originally posted by FreakyKBHNo proof was offered. If you believe it was, please direct me to the post in which you believe it was offered. I certainly did not see you offer a proof and say "here is the proof" or anything of that nature.
Oh: what's that?
You don't accept what has been offered?
That leaves it to you to discredit what has been offered instead of asking me to repeat the same material again.
I can hardly ask you to repeat material you haven't provided.
If they conformed, we would see TPE to LAX take a much more shallow angle of trajectory than BOS to SEA, as the former scenario has a beginning point 25° closer to the equator than the latter.
No, that is not the case. I explained to you that the further away points are from each other longitudinally the larger the angle. You then claimed that TPE to LAX and BOS to SEA did not conform to that. Now you state that they do exactly what I said, and then say they do not conform to what I said. Huh?
Again: how one feels about the answers is inconsequential.
Then why did you start counting the syllables and try to use that as your sole argument against them? Clearly your only real objection was you didn't like them.
Answer the questions or admit defeat.
Which question do you now claim I have not answered? The ones where I gave one syllable answers? How many syllables were you looking for before you count it as an answer?
31 Oct 15
Originally posted by FreakyKBHThe earth is only slightly different from a sphere. For the distances you have been quoting spherical calculations are more than sufficient. If you quoted distances to the nearest centimetre then you might need a slightly more accurate model, but then we would also want to ask what way the wind was blowing so we know which direction the plane took off. (which makes several kilometres difference).
Even your experiment with a string fails on a literal round ball--- and is rendered nonsensical on an irregularly shaped ellipsoid.
These paths of flight or navigational routes by ships do make sense on a flat earth map, for some reason.
No, they do not make sense on a flat earth map. Can you provide a flat earth map on which they make sense? I thought not.
31 Oct 15
Originally posted by twhiteheadNo proof was offered. If you believe it was, please direct me to the post in which you believe it was offered. I certainly did not see you offer a proof and say "here is the proof" or anything of that nature.
No proof was offered. If you believe it was, please direct me to the post in which you believe it was offered. I certainly did not see you offer a proof and say "here is the proof" or anything of that nature.
[b]That leaves it to you to discredit what has been offered instead of asking me to repeat the same material again.
I can hardly ask you to ...[text shortened]... one syllable answers? How many syllables were you looking for before you count it as an answer?[/b]
All that is required is to look back at all of the posts prior to these.
Shouldn't be too hard to prove or disprove, one way or another.
No, that is not the case. I explained to you that the further away points are from each other longitudinally the larger the angle. You then claimed that TPE to LAX and BOS to SEA did not conform to that. Now you state that they do exactly what I said, and then say they do not conform to what I said. Huh?
Ah, I see your chicanery reveals itself again.
You are, in a word, pathetic.
The emboldened text immediately above my two previous sentences is an exact quote of your response to me.
You wish the reader to think I've challenged you while agreeing with you, thereby rendering my position untenable.
Let's disabuse the reader of such notion with a small trip to reality, shall we?
"If they conform..." began my original statement.
Who or what was the "they" in that statement?
To what was the conforming referring?
Ah, yes.
The original statement was a challenge to googlefudge's claim that a position's proximity to the equator would determine the trajectory a path must follow, i.e., the closer to the equator, the more shallow the angle; the further from the equator, the more dramatic the angle.
In this scenario, TPE to LAX has both beginning point and ending points closer to the equator than BOS to SEA.
The only other significant factor is the difference in longitude travel, which we will get to in due time.
The trajectory for the BOS to SEA is ~1° to the north of the final destination's latitude.
The trajectory for the BOS to SEA is ~6° to the north of the beginning destination's latitude.
The trajectory for the TPE to LAX is ~17° to the north of the final destination's latitude.
The trajectory for the TPE to LAX is ~25° to the north of the beginning destination's latitude.
CLEARLY, the trajectory for the TPE to LAX is significantly greater from both beginning and ending positions than the trajectory for the BOS to SEA, despite googlefudge's claim that points closer to the equator will have more shallow angles than those further from the equator.
The difference in longitude between BOS and SEA is ~51° from east to west.
The difference in longitude between TPE and LAX is ~121° from west to east.
TPE to LAX is roughly 2.4 times the longitude distance of BOS to SEA.
Somehow, the numbers just don't add up, do they...
Then why did you start counting the syllables and try to use that as your sole argument against them? Clearly your only real objection was you didn't like them.
No.
31 Oct 15
Originally posted by twhiteheadNo, they do not make sense on a flat earth map.
The earth is only slightly different from a sphere. For the distances you have been quoting spherical calculations are more than sufficient. If you quoted distances to the nearest centimetre then you might need a slightly more accurate model, but then we would also want to ask what way the wind was blowing so we know which direction the plane took off. (w ...[text shortened]... e on a flat earth map. Can you provide a flat earth map on which they make sense? I thought not.
Of course they don't make sense: you haven't even considered them in juxtaposition!
Can you provide a flat earth map on which they make sense? I thought not.
Just because you are unwilling doesn't mean others are unable.
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02 Nov 15
1 edit
Originally posted by FreakyKBH
Quoted in main text.
Well for starters they are not two points at the same latitude.
Check.
That's been established.
TPE to LAX has a difference of 8° from one to the other.
BOS to SEA has a difference of 5° from start to finish.
TPE sits at 22° above the equator.
BOS sits at 47° above the equator.
That's a difference of 25° between start points.
LAX sits 33° above the equator.
SEA sits 42° above the equator.
That's a difference of 9° between end points.
My point was that you were not comparing like with like. My simplified example had points on
exactly the same latitude, and all sets of points were an equal angle apart.
However your examples are not at equal latitude, and not anywhere close to either the same distance
apart, or the same angular separation.
The angle of the great circle as measured with respect to the equator will depend on where the 'top'
or highest latitude of the great circle reaches. To completely define any great circle you simply need
two points on that circle that are less than 180 degrees apart.
The two great circles corresponding to your two sets of two points have differing points of highest latitude.
The high point on the route from BOS to SEA is appx N48 35' 42" [W107 19' 30"]
The high point on the route from LAX to TPE is appx N48 58' 08" [W172 16' 12"]
This means that both great circles are very similar, with their greatest difference being that their highest points are
at very different longitudes.
So they will have roughly the same [actually very very similar] angles as they intersect the equator.
However the longer route does go farther north and thus will intersect at a higher angle.
The reason that the route with the highest start and end points doesn't have the highest peak is because those
start and end points are much much closer together and thus sit nearer the top of their great circle.
All this I obvious if you plot it out on Google Earth with the ruler feature as I keep recommending.
Actual flight paths deviate strongly from these shortest routes for all kinds of reasons [such as avoiding restricted
airspace, avoiding or taking advantage of favourable winds [jet stream] or routing to spend as little time as possible
over water away from emergency landing sites etc] and will seldom if ever actually track the shortest possible route
from a mathematical standpoint. Although future improvements in air-traffic-control might reduce the discrepancy.
Also, as Twhitehead says, they do conform... putting them near the 'top' of their great circle, as opposed to TPE and LAX which are farther down.
Um, huh?
How does any of that either make sense or agree with your earlier contention of trajectory being dependent upon proximity to the equator?
Does it feel a little bit like you're trying to talk yourself out of the position?
It sure sounds like it...
The angle is dependent upon the proximity of the top of the circle to the equator.
In the simplified example I gave, the lower latitude points had corresponding lower latitude peaks to go with them.
This was because all my sets of points were at equal angle separation from each other.
A similar effect would have been achieved by having the points at an equal distance separation.
I chose angular separation as you can follow lines of Longitude when creating these points on Google Earth.
In your unnecessarily complex examples the points are at difference angles of separation and at different distances of
separation as WELL as at different latitudes. Funnily enough this resulted in great circles that were nearly identical in
terms of angle with respect to the Equator, with near identical peaks.
As the farther apart, [and farther south] points are farther from the high point on their great circle the angle at which the
great circle meets these points is greater than for the BOS to SEA route.
However as the important angle is the angle of intersection with the equator [a fixed reference point] this doesn't undermine
what I said, or have been saying. Or contradict what the others have been saying on this topic.
This is a problem MUCH better suited to exploring via the methods we have already proposed.
Ie, just look at a frickin' globe.
We can, but it is misleading.
Every globe we have it perfectly spherical, a literal round ball.
Every great circle formula is dependent upon a literal round ball.
Even your experiment with a string fails on a literal round ball--- and is rendered nonsensical on an irregularly shaped ellipsoid.
These paths of flight or navigational routes by ships do make sense on a flat earth map, for some reason.
As has been repeatedly pointed out, the Earth deviates from a perfect sphere by a very small amount.
For our purposes here the differences are irrelevant.
Certainly if you are playing with a physical globe and a piece of string the errors in your measurements with string are vastly
larger than the errors from the globe being a 'perfect' sphere.
It's also possible [I don't know] that the 'globe' in google Earth is NOT in fact a perfect sphere. It might actually be more accurate
and reflect [at the least] the fact that the Earth is oblate... Regardless, it's not a problem relevant to our discussion.
The Relativity of Wrong
By Isaac Asimov
The Skeptical Inquirer, Fall 1989, Vol. 14, No. 1, Pp. 35-44
http://chem.tufts.edu/answersinscience/relativityofwrong.htm
.............
Another way of looking at it is to ask what is the "curvature" of the earth's surface Over a considerable length, how much does the surface deviate (on the average) from perfect flatness. The flat-earth theory would make it seem that the surface doesn't deviate from flatness at all, that its curvature is 0 to the mile.
Nowadays, of course, we are taught that the flat-earth theory is wrong; that it is all wrong, terribly wrong, absolutely. But it isn't. The curvature of the earth is nearly 0 per mile, so that although the flat-earth theory is wrong, it happens to be nearly right. That's why the theory lasted so long.
......
About a century after Aristotle, the Greek philosopher Eratosthenes noted that the sun cast a shadow of different lengths at different latitudes (all the shadows would be the same length if the earth's surface were flat). From the difference in shadow length, he calculated the size of the earthly sphere and it turned out to be 25,000 miles in circumference.
The curvature of such a sphere is about 0.000126 per mile, a quantity very close to 0 per mile, as you can see, and one not easily measured by the techniques at the disposal of the ancients. The tiny difference between 0 and 0.000126 accounts for the fact that it took so long to pass from the flat earth to the spherical earth.
............
And yet is the earth a sphere?
No, it is not a sphere; not in the strict mathematical sense. A sphere has certain mathematical properties - for instance, all diameters (that is, all straight lines that pass from one point on its surface, through the center, to another point on its surface) have the same length.
That, however, is not true of the earth. Various diameters of the earth differ in length.
..............
The earth has an equatorial bulge, in other words. It is flattened at the poles. It is an "oblate spheroid" rather than a sphere. This means that the various diameters of the earth differ in length. The longest diameters are any of those that stretch from one point on the equator to an opposite point on the equator. This "equatorial diameter" is 12,755 kilometers (7,927 miles). The shortest diameter is from the North Pole to the South Pole and this "polar diameter" is 12,711 kilometers (7,900 miles).
The difference between the longest and shortest diameters is 44 kilometers (27 miles), and that means that the "oblateness" of the earth (its departure from true sphericity) is 44/12755, or 0.0034. This amounts to l/3 of 1 percent.
To put it another way, on a flat surface, curvature is 0 per mile everywhere. On the earth's spherical surface, curvature is 0.000126 per mile everywhere (or 8 inches per mile). On the earth's oblate spheroidal surface, the curvature varies from 7.973 inches to the mile to 8.027 inches to the mile.
The correction in going from spherical to oblate spheroidal is much smaller than going from flat to spherical. Therefore, although the notion of the earth as a sphere is wrong, strictly speaking, it is not as wrong as the notion of the earth as flat.
02 Nov 15
1 edit
Originally posted by googlefudgeGoogle Earth is displayed as a perfect sphere. Display of latitude / longitude, measurements etc all use the WSG84 datum which approximates the Earth as an oblate spheroid. It is the same datum used by GPS. From what I can tell, if altitude is not specified, it assumes an altitude of 80m (don't ask me why). It is however capable of calculating distances with altitude taken into account, but I have not analysed what formula is used in that case.
It's also possible [I don't know] that the 'globe' in google Earth is NOT in fact a perfect sphere. It might actually be more accurate and reflect [at the least] the fact that the Earth is oblate... Regardless, it's not a problem relevant to our discussion.
Interestingly China uses a different datam (for security reasons) and all Chinese maps do not line up with GPS measurements. (this includes road maps such as Google Maps.)
Not mentioned in your post is the inaccuracies due to approximating the earth as a sphere can often be less important than inaccuracies from not taking altitude into account. An aircraft travelling at 40,000 feet must travel a longer distance than a ship travelling at sea level.