Quantitative evaluation & comparison of world-maps

[RogerOwens]

I didn't say that G&G invented or promoted RMS or weighted-aggregation of different metrics (or any particular such weighting). I said they used those things. And they did use those things.

Michael Ossipoff
42 M
October 7th
2241 UTC

[daan]

The claim:

I didn't say that G&G invented or promoted RMS or weighted-aggregation of different metrics (or any particular such weighting). I said they used those things. And they did use those things.

The reality:

I've heard of Gott & whatever, but their comparison-scheme is a weighted aggregation of several comparison-quantities (which, it seems to me, were largely RMS global-aggregations of various -point-metrics).

“Their comparison scheme”, as singular and unqualified in any way by the context, does not admit the existence of two other comparison schemes: the ones that actually are theirs. “Their comparison scheme” does not equate to “they merely used it” and does equate to “they own it” and, if they are known for a comparison scheme, then this is it. But it’s not.

Nobody falls for your sophistry, Ossipoff. You never get away with any of this, but you keep shoveling it out as if you expect to. It’s not going to change.

— daan

[RogerOwens]

"Their comparison-scheme" meant "the comparison-scheme by which they rated world map-projections". I neither spoke of nor claimed to know that scheme's history, ownership or origin.

"My town is Tulsa" doesn't meant that I own Tulsa. "My ruler is Idi Amin" doesn't mean that I own Idi Amin. "Fido's owner is George" doesn't mean that Fido owns George.

You're reading into "their" what you want to see in it.

Michael Ossipoff

[daan]

"Their comparison-scheme" meant "the comparison-scheme by which they rated world map-projections". I neither spoke of nor claimed to know that scheme's history, ownership or origin.

"My town is Tulsa" doesn't meant that I own Tulsa. "My ruler is Idi Amin" doesn't mean that I own Idi Amin. "Fido's owner is George" doesn't mean that Fido owns George.

You're reading into "their" what you want to see in it.

Michael Ossipoff

“My town is Tulsa” means “My town is neither Boston, nor Seattle, nor anywhere else; it is Tulsa.” Therefore, “My comparison scheme is an extension of Laskowski’s” means, “My comparison scheme is neither the integral of skew nor the integral of flexion; it is an extension of Laskowski’s”. Your statement about Goldberg & Gott’s comparison scheme is the equivalent to “Goldberg & Gott’s comparison scheme is an extension of Laskowski’s”. Therefore, your statement implies, “Goldberg & Gott’s scheme is neither the integral of skew nor the integral of flexion.” The problem with that statement is that Goldberg & Gott’s schemes are the integral of skew and the integral of flexion. That makes your statement wrong.

If you intended your statement in some broader context, such as on-going conversation about “the comparison scheme that they noted at the end of their paper as augmenting Laskowski’s scheme with their own schemes”, then, within that context, “their comparison scheme” could be taken to refer to that. The onus is on you to qualify statements you make out of nowhere so as to make them not-wrong to the listener. Your statement came with no such context; it was a proclamation, out of nowhere, that Goldberg & Gott’s comparison “scheme” was blahdy blahdy blah, as if they had no other and that is the one they are known for, and because that is the one they are known for, then we all know what you’re talking about. But we didn’t, because you provided no such context.

I do not know why I have to spell out such elementary logic. You are wrong, over and over and over, and if you cannot see that, then you are a fool. I will delete any more of this nonsense if you post it. This board is not for you to abuse with fallacies and pride-driven blindness. I have no idea if you knew what you meant when you wrote what you wrote. I simply do not care. If it becomes clear to you that your audience misunderstood you, then a simple, “I should have been more clear,” would suffice, rather than these tedious, fallacy-laden rationalizations.

— daan

[RogerOwens]

No, it was about schemes for comparing or rating map-projections. G&G did so as I described. Skewness and flexion were only part of the method by which G&G rated map-projections. (...even if they didn't invent or own all of the map-rating technique that they used.)

Michael Ossipoff
42 Tu
October 8th
2107UTC

[daan]

Nobody cares what Ossipoff (or I) meant. I am going to explain what Goldberg-Gott did.

The Goldberg-Gott paper is 45 pages. It is broken down as follows:

• Pages 1–24 develop the theory behind flexion and skew.
• Pages 25–26 discuss considerations for assessing global measures for a suite of metrics, each independently (that is, without aggregating them). In addition to the global integrals of flexion and skew, they state: using RMS of flation; RMS of angular error; RMS of log of quotient of map distance and globe distance; and the average number of map boundary cuts crossed by the shortest geodesic connecting a random pair of points.
• Page 26–27, roughly 1½ pages, notes that flexion and skew could be added into Laskowski’s scheme. They give an “example” of how that could be done with results in the text (no table) for how six projection would fare, given the caveats that the weightings are arbitrary as well as the parameters.
• Page 28 is the Conclusions sections, with no mention of the Laskowski aggregation. In full:

  We have developed two new measures of curvature distortions found in maps of the earth. The Skewness and the Flexion can be used to identify particularly warped sections of a map, or to identify features (such as the U.S. Canada border), which appear as a straight line on some map projections but do not, in fact, follow geodesics. We have developed a new graphical tool, called the Goldberg-Gott indicatrices, which can be used to show these distortions, along with those in area and shape, at many points in a map, and have produced indicatrix maps for a number of popular projections. Finally, we have used these measures to produce global distortion measures for different projections. We have found that the Winkel-Tripel produces low distortion on most measures, and, in particular, has the lowest skewness of all projections in our sample with a 180◦ boundary cut.

  The potentially ambiguous phrase “used these measures to produce global distortion measures for different projections” becomes unambiguous with “We have found that the Winkel-Tripel produces low distortion on most measures”, where it becomes clear they refer to the table of 6 unaggregated measures for 27 projections on Page 31.
• Pages 29–30 are citations.
• Page 31 is a table of six independent (no aggregation) global metrics for 27 projections, as explained on pp. 25–26.
• Pages 32–33 are illustrations of flexion and skew ‘indicatrices’.
• Pages 34–45are illustrations of their local skew and flexion metrics on various projections.

This is the objective situation. Any further posting that Ossipoff does to make claims or representations about what he meant in previous postings is irrelevant to the purpose of this board, and will be deleted.

— daan

[RogerOwens]

If it doesn't matter what Ossipoff said or meant, then daan should have thought of that before he said that what Ossipoff said was wrong. .

No, skewness and flexion are NOT G&G's comparison-scheme.

That's because a single metric, or a pair of them, is not someone's comparison-scheme unless that someone has offered it as the the way to compare or rate map-projections.

G&G have never offered skewness &/or flexion as sole basis for a comparison of map-projections.

None of my comparison-quantities is a comparison-scheme, because I do not offer any one of them as sole basis for a comparison of map-projections.

Yes I value min-scale, and it it's my favorite. But even I don't use it by itself to rate map-projections. As I've said, an equal-area map's min/max-scale (or another kind of map's min point min-scale) must not be too high.

For example, as much as I like Behrmann, its low min/max scale at high-lat is a big drawback for it.

And though Optimal-CEA-Stack has high min-scale, its min/max scale is too low for my taste. (But hopefully there's a parameters-combination that will give CEA-Stack a good min-scale and an acceptable min/max scale).

I don't advocate or offer any one of my comparison-quantities as a comparison-scheme as defined above. G&G have never offered scewness &/or flexion as a comparison scheme by that definition.

So no, skewness and flexion are NOT G&G's comparison-scheme.

Michael Ossipoff
42 Tu
October 8th
2333 UTC

[daan]

If it doesn't matter what Ossipoff said or meant, then daan should have thought of that before he said that what Ossipoff said was wrong.

That’s right. And I should have started deleting your postings a lot sooner than I did.

No, skewness and flexion are NOT G&G's comparison-scheme.

Nobody made any such claim. This is looking a lot like a straw man. Flexion and skew are local metrics. Local metrics are not comparison schemes.

The global integral of each is, however, a comparison scheme.

That's because a single metric, or a pair of them, is not someone's comparison-scheme unless that someone has offered it as the the way to compare or rate map-projections.

“The way” is wrong. This is looking a lot like a straw man. “A way” would be correct.

And the “offer” business is an opinion that you have that intent must be present in order to categorize a metric or combinations of metrics as a comparison scheme. My opinion, which I clarify some below, differs. But, as opinions, there is no way to argue correctness. If you attempt to argue that your opinion is correct or preferable, or if you even elaborate on the opinion, then I will delete the posting. The question of intent in comparison schemes isn’t germane to this forum.

G&G have never offered skewness &/or flexion as sole basis for a comparison of map-projections.

Nobody made any such claim as “sole”. This is looking a lot like a straw man.

None of my comparison-quantities is a comparison-scheme, because I do not offer any one of them as sole basis for a comparison of map-projections.

Your offering is irrelevant, in my opinion. I doubt anyone would accept anyway, but if someone used any of the global measures you proposed to compare map projections, those measures would be comparison schemes. Sorry man. Your own babies, not even yours anymore.

G&G have never offered scewness &/or flexion as a comparison scheme by that definition.

When you quantify things and tabulate them, you set them up to be compared. Goldberg & Gott tabulate them, right there in their paper. 27 easy comparisons in a table. If you devise a way to compare things, you’ve got a comparison scheme. That’s my opinion. Full stop.

So no, skewness and flexion are NOT G&G's comparison-scheme.

I agree. But if you drop the dash, and if you take the global integral of skew and flexion separately, rather than using local skew and flexion, then yup. Comparison schemes. Two of them. And they compare. Right there in the table of 27 projections.

Warning, Ossipoff: Given the straw-mannish and opinion-based assertions, your posting looks a lot like you’re trying to pick an argument over a nuance of semantics that isn’t relevant to the purpose of this board. If anyone at all cares about what you just proposed, you’ve stated your piece and I’ve stated mine, and they are free to decide however they like. Full stop.

— daan

[quadibloc]

When I clicked that link some years ago, the link led directly to their paper. This time it led to a payment-screen.

I don't blame you, but that paywall wasn't where a Google search led me.

[RogerOwens]

that paywall wasn't where a Google search led me.

Then I'll try more Google searches.

Michael Ossipoff
42 W
October 9th
1426 UTC