Gilbert two-world perspective doesn't make sense

[quadibloc]

Also, your opinion is intolerant, a non sequitur, and ignores the projection’s better qualities.

I realize that it is trying to communicate with someone who asks for a source, and then, when given one, asks what you mean by it. Not recognizing "I" as a typo for "It" can, I suppose, be put down to not having English as one's first language.

But in this case, one can indeed confidently assert that the Gilbert two-world perspective projection is not suitable for an atlas map of any kind whatsoever. It really is of no use or value for general-purpose mapping. So Piotr is "right" in having doubts about the value of the projection.

And his complaint about the perspective not being adjustable does have some merit. The projection is misnamed. It should be called Gilbert's two-world orthographic projection, of course. However, that is also Gilbert's fault and not yours.

When I said that Piotr was right, why did I put right in quotation marks?

Well, the Gilbert two-world perspective projection is not meant for providing atlases with another map projection which better optimizes distortion properties. Of course, I had the good fortune to first encounter the projection in the famous Mathematical Games article by Martin Gardner on unusual map projections, which discussed the globe in Gilbert's office.

While most map projections are created to optimize distortion characteristics, sometimes a map projection is instead meant to illustrate a point. And Gilbert's two-world perspective projection was intended to illustrate how pervasive use of the Mercator projection has distorted people's ideas about how the world looks - so that a special globe, like the one in Gilbert's office, of which the Gilbert's two-world perspective projection is an image - is often, by the layperson at least, not noticed as having anything "wrong" with it.

So his negative opinion, instead of being "intolerant, a non sequitur", and dismissive of "the projection's better qualities", is merely due to his being uninformed about the purpose of the projection.

[Atarimaster]

So his negative opinion, instead of being "intolerant, a non sequitur", and dismissive of "the projection's better qualities", is merely due to his being uninformed about the purpose of the projection.

Yes, but if you can’t see the purpose of a map projection (or anything else, for that matter) I think you should ask for the purpose instead of claiming that it “doesn’t make sense”.

[Piotr]

While most map projections are created to optimize distortion characteristics, sometimes a map projection is instead meant to illustrate a point. And Gilbert's two-world perspective projection was intended to illustrate how pervasive use of the Mercator projection has distorted people's ideas about how the world looks - so that a special globe, like the one in Gilbert's office, of which the Gilbert's two-world perspective projection is an image - is often, by the layperson at least, not noticed as having anything "wrong" with it.

I get it but how does specifically the fixed perspective at an arbitrary point help in illustrating this?

[daan]

So his negative opinion, instead of being "intolerant, a non sequitur", and dismissive of "the projection's better qualities", is merely due to his being uninformed about the purpose of the projection.

Isn’t intolerance a narrow view of what is acceptable? Isn’t intolerance generally a consequence of being uninformed?

The conclusion Piotr drew, “Gilbert two-world perspective doesn't make sense”, does not follow from “It's literally Conformal Longitude Mix by a factor of 0.5, followed by a hard-coded perspective.” Is it not, then, a non sequitur?

Does Piotr acknowledge any of the projections better qualities, not only as expressed in Gilbert’s stated purpose, but also those beyond that as remarked on by DeLucia and Snyder?

My response was brusque but correct, as far as I can tell. I’m intolerant of ignorant truculence. I admit that. What you do not know is that Piotr flagged as off-topic my moving his topic to the right forum. I warned him about this behavior, and I have suspended in the past for this sort of time-wasting, attention seeking behavior. I’m fine engaging with him about map projections as long as he leaves his trolling behind.

But in this case, one can indeed confidently assert that the Gilbert two-world perspective projection is not suitable for an atlas map of any kind whatsoever. It really is of no use or value for general-purpose mapping.

We will have to disagree about this, both because suitability for atlas maps (or even “general-purpose mapping”) is a narrow criterion to judge a projection by—and certainly is no criterion for Geocart—and because DeLucia and Snyder justified the projection beyond what you have. Whether I agree with them or not isn’t material; opinions about what mostly amounts to æsthetics (but are so often argued as objective) isn’t anything I would put time into.

— daan

[quadibloc]

I’m intolerant of ignorant truculence. I admit that.

I apologize if it seems as if I'm being critical of you. If anything, you have the patience of a saint for even tolerating him at all for this long. But if you're not simply going to kick him off the forum, however much he may deserve worse than a brusque answer, it remains the case that it is unhelpful to answer someone like that in that way; it may feel good, but it won't help in either getting him to go away satisfied, or persuading him that a greater degree of civility would produce results.

If you're going to bother talking to him at all, you may as well go the whole nine yards.

because DeLucia and Snyder justified the projection beyond what you have.

Since the projection is conformal in the center, theoretically one could use it for general-purpose atlas maps, yes. I still don't think anyone would choose to use it for that purpose. And I agree the this is a narrow criterion by which to judge a projection, but a naive view of map projections leads people to think of that first.

[quadibloc]

Yes, but if you can’t see the purpose of a map projection (or anything else, for that matter) I think you should ask for the purpose instead of claiming that it “doesn’t make sense”.

Well, of course. But whatever my personal opinion of the quality of Piotr's posting behavior may be, I don't think it serves a useful purpose to be confrontational in return.

As another example of this phenomenon, think of the Gnomonic projection. Unlike the Stereographic projection, it is not conformal. But its deviations from conformality make its representation of areas even worse than that of the Stereographic. So it isn't equal-area, conformal, or anything in between. What kind of a stupid projection is that?

Well, of course the Gnomonic projection, while not usually suitable for general mapping (although due to simplicity of calculation, it is used that way for polyhedral maps), serves a special purpose. It lets you find what areas of the Earth you would have to pass over to travel on a great-circle course between any two places. This is obviously very useful for air travel. I mean, you could even use it to find out the fastest course that a ship could take from New York to Liverpool... but, of course, in that case, it's up to the map user to consider the hazards posed by icebergs.

[quadibloc]

I get it but how does specifically the fixed perspective at an arbitrary point help in illustrating this?

If it is a perspective projection, and not an orthographic projection as I mistakenly thought, the perspective point was just chosen as what a typical user might see looking at a world globe.
I think it isn't that a fixed perspective itself helps, but rather that being able to change the projection would not help. Which is why Gilbert chose to define it that way.
And then Daniel Strebe didn't choose to generalize that projection, apparently because of a generalized policy evinced in the thread about the Nicolosi Globular projection: since mathematics yields an infinite number of possible map projections, he is offering in Geocart only those projections to which someone chose to assign a name - and he is respecting the original definition of each projection, rather than adding extensions, even if, in some cases, they might seem obvious or natural.
This isn't necessarily the kind of rule I would have followed, but it serves no purpose to be confrontational over the issue.

[daan]

If anything, you have the patience of a saint for even tolerating him at all for this long. But if you're not simply going to kick him off the forum, however much he may deserve worse than a brusque answer, it remains the case that it is unhelpful to answer someone like that in that way; it may feel good, but it won't help in either getting him to go away satisfied, or persuading him that a greater degree of civility would produce results.

If you're going to bother talking to him at all, you may as well go the whole nine yards.

It doesn’t make me feel good to respond that way. Quite the opposite. Yet I don’t want him gone, either; I want him to behave better than a World of Warcraft-style socialization affords, and this is my way of explaining my problems with his behavior. We can all attend to the technical aspects of his statements and inquiries (and thank you kindly for yours) so it’s not urgent, and often unnecessary, for me to do so. As site moderator, on the other hand, I’m in the unfortunate position of herding the cats into acceptable channels, hopefully before they get out of hand. Ignoring his rude behavior hasn’t resulted in improvement, and I think there’s a wide space between perfect behavior and ejection, so, this is how it has played out.

I’m not wedded to any particular policies in this regard, and I welcome feedback.

Cheers,
— daan

[quadibloc]

I’m not wedded to any particular policies in this regard, and I welcome feedback.

I was simply trying to make clear that my concerns were solely of a practical nature, and were not intended in any way as a moral criticism of what you had been doing. I can't give you useful feedback unless I ensure that it is not likely to be misconstrued.

[Piotr]

Another problem with Gilbert two-world perspective is that due to the perspective, portions of the world appear twice, making Gilbert two-world perspective non-bijective. With enough operations this non-bijectivity would cause Geocart to heavily glitch.