0977: "Map Projections"

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Re: 0977: "Map Projections"

Postby steve waterman » Wed Nov 16, 2011 12:38 am UTC

responding to the recent post by map

i will try and respond to your various complaints, and perhaps it is best to post the various responses one at a time so that this does not go one for pages.

Unfortunately, to defend my map and myself, I will need to compare various projections...which you feel is just more spam and promotion. While there is always going to be..."the world's best burger", it is more than thae...there is some quantifiable math behind comparing maps to one another...

adddressing Your gripe #1

To start, as the cartoon deliberately points out, the geometry is Cahill’s and is over a century old.


incorrect. First the cartoon makes absolutely no mention of Cahill nor shows his projection.
( My mistake...I only meant to say...that the Cahill 1909 map not shown. )

The Waterman projection is certainly not Cahill's geometry...as you seem to be implying.

Someone else asked how your projection differs from Cahill’s.


This you have stated correctly.

We’re all waiting for an answer.


So, I will address this question...though I suspect few are that interested.

Cahill's century old map did not deem to have an Antarctica...just open ocean to the south pole.
Cahill's map was only in black and white.
Cahill's map was projected upon a regular octahedron.
Cahill's map used a different offset...22.5 degrees.
Cahill'x map used 7.5 intervals for latitudes and longitudes.
Cahill's had only the one modular appearance.

my map...
Has an Antarctica...without any need for a special dedicated inset ( and thus ignoring the rest of the world for that inset. )
Has color and a distance scale.
Was projected upon a truncated octahedron whose edge ratio is 2 to 1.
Is off set...20 degrees
Used 5.0 intervals for latitudes and longitudes.
Amongst many other possible modular forms, has both an Atlantic and Pacific centered versions.
Has supporting data...like a Tissot Indicatrix and even distancing maps, and angular deformation maps.
Uses the mathematics of close pack spherea to generate its base polyhedral object.
Has been projected with a gnomonic method ( 2011 ) and an equal line delineation method ( 1996 ).

I will post separate rebuttal/response/defence/logic/justification for these/your other gripes...
gripe #2 equal area projections...Werner, Gall-Peters, Lambert cylindical, Eckbert Iv and "the 100's of other equal area projections"
gripe #3 myrihedral projections
gripe #4 Antarctica ( or say, any country/city ) can be an inset[
gripe #5 you incorrectly imply that I stated..."only true projection is a waterman", whichI never have said either here or elsewhere.

I also would like to address the Fuller dymaxion as another has stated that this was/is their favorite here just recently.

Should I continue with your personal gripes 2 through 5 ...or is this all going to be just more self-promotion and spam to you and/or others here ?

Lastly, for this posting...i contend that EVERY projection IS interrupted...anyone have an opinion on this ?
Last edited by steve waterman on Mon Nov 21, 2011 9:49 pm UTC, edited 1 time in total.
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Re: 0977: "Map Projections"

Postby whateveries » Wed Nov 16, 2011 1:23 am UTC

steve waterman wrote:...Should I continue with your personal gripes 2 through 5 ...



um, no, but what your stance on ponies is, would be interesting. :P

it's fine.

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Re: 0977: "Map Projections"

Postby steve waterman » Wed Nov 16, 2011 1:35 am UTC

gripe #3 myriahedral projections

Jarke J. (Jack) van Wijk is a Dutch computer scientist, a professor in the Department of Mathematics and Computer Science at the Eindhoven University of Technology, and an expert in information visualization...he is the author of myrihedral projections.

He won the 2009 Henry Johns Award of the British Cartographic Society for best cartographic journal article.

A video can be clicked on from this page
http://www.newscientist.com/article/dn1 ... th.html%22

and quite specifically...
If you go to google and type - myriahedral projections waterman...this should pop up on the first page...a pdf
The Cartographic Journal vol 45 no 1 pp 32-42 feb 2008...where on page 33 he has a paragraph that mentions, in order with comments,
Goode, Da Vinci, Durer, Cahill, Fuller and ends the paragraph with "Steve Waterman has developed an appealing polyhedral map, based upon sphere packing." Jarke J. (Jack) van Wijk Certainly, he has other interesting/important things to say in that paragraph regarding "cuts"...and worth the download.
Last edited by steve waterman on Mon Nov 21, 2011 9:52 pm UTC, edited 1 time in total.
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Re: 0977: "Map Projections"

Postby steve waterman » Wed Nov 16, 2011 2:37 am UTC

um, no, but what your stance on ponies is, would be interesting.

um, I never stand on a pony, never have...one of us might get hurt, should either of us make a sufficient mistake in our own tactics.

too late dude, i already posted gripe #3...before you message was read....about myriahedral projections.

so...anyone else care to shut me down...? or anyone else care about this in a positive light ?

I will say...this is the ONLY thread here for me...and i thought a forum was for an educated discussion.
it seems to me if I weren't the author , that I WOULD be allowed to compare map properties, of these 1/2 dozen posts.
Have you see an ad or phone number etc, or me asking for people to purchase maps ?

I have presented facts and graphs and for example...Tissot's...factual, mathematical. I am just pointing out stats and some shape comparisons with other projections. Yes, I am giving MY criteria...but one may "weigh" in as one desires..as would be ...how important is shape and area..or which is more important, shape or area...and exactly by how much/to what degree. Consider the many many properties that projections have. There is no book/way/procedure to quantify a "best burger in town"/best world projection...it depends upon ones personal tastes and condiment choices, not to mention - possible usages.

So, I guess that I will end with...a good map projection should represent the globes properties properly...but it never can. Some apparently seem better than others in compromising the various features to minimize the distortions to all collective properties concerned...and always to varying degrees. Oddly, this answers the other gripes as well. So, I feel that I would like to post a comment about the fuller map and that would bring me up to date. So, I will confine myself here in the future to not discuss my map at all...unless directly asked about some aspect...whereupon I should be allowed to respond with factual data, if I indeed, do happen to have any and also desire to share it/give it away publically.
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Re: 0977: "Map Projections"

Postby Frankie » Wed Nov 16, 2011 3:24 am UTC

steve waterman wrote:Unfortunately, to defend my map and myself, I will need to compare various projections...which you feel is just more spam and promotion.

If you are the real Steve Waterman, you are an absolutely terrible spokesman for your own cause.
If you are pretending to be Steve Waterman, you are an absolutely terrible comedian and a disappointingly boring troll.

steve waterman wrote:
Mapprehension wrote:To start, as the cartoon deliberately points out, the geometry is Cahill’s and is over a century old.

incorrect. First the cartoon makes absolutely no mention of Cahill nor shows his projection.
The waterman projection is certainly not cahill's geometry...as you seem to be implying

1: Re-read the comic, it very clearly mentions Cahill in relation to Waterman.
2: Waterman projection is very obviously a Cahill variant, with the equilateral triangles adjusted to pseudo-Reuleaux shapes, and the pieces of Antarctica moved to a separate map section. It's a reasonable improvement, but that's all.

Hmm... let's consider Alan Morgan's law. Insufficiently advanced, therefore probably a troll, but "Arno Peters wannabe" is not out of the question. Either way, I won't trade any further messages with you.

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Re: 0977: "Map Projections"

Postby steve waterman » Wed Nov 16, 2011 6:39 am UTC

Just because Randall showed/implied ? the waterman as a possible Cahill rip-off does not make that true...

Cahill polyhedra base is identical to the root 2 depictions.
Waterman sphere packed base is identical to the root 5 depictions.
just please have a look at this one page....do you see that these are not the same...the root 2 and root 5 ?
http://paulbourke.net/geometry/waterman/index.html

So..it seems that I need to defend, what I now perceive, is an attack on my character , as in, ripping off the Cahill 1909 map with a simple plopping of Antarctica together...well since you raise the issue...

i worked in decoding the metrics of pack spheres for many years, starting around 1988 and then realized that they extrapolated into symmetrical polyhedra,
I then had all those shown on Paul's Bourke page to select from to project upon. One handled land sinus best, when it was rotated around the z axis by 20 degrees...so, i used that waterman root 5 to manifest, first...an equal line delineation projection ( as per my 1996 poster ) and a gnomonic projection ( as per 2011 ) so that i could tie into satellite imagines...which just recently has been accomplished. Only after that 1996 version was being sold, did I even ever hear of Cahill, as it so happens, and not that that actually matters. Later I had like 100 unlimited series of watermans to chose from...and still the w5 fcc swept from 0,0,0 remained/remains best!

My basis is understanding the math behind pack spheres and hence polyhedra generated from various clusters. Here are other maps/choices done on waterman polyhedra by Izidor Hafner. indeed I have a couple hundred different maps like those below.
http://www.watermanpolyhedron.com/CART2dmaps.html

and i have new gored globes as rotatable 3d waterman polyhedra complete with countries with color.
http://watermanpolyhedron.com/2011IH1.html
hardly a rip off or copy or a parody or the other "internet" slur you throw at me. i really find your little comment as ugly.
But hey, you will just dismiss me likely...without checking any of these links.

I do understand the oddity...no one has ever started from sphere packing...most pick known polyhedra...as Cahill did (Platinic solid, the octahedron )...
and as Fuller did twice...
( first with the cuboctahedron....my root 1 of that same page above, and then with the Platonc solid, the 5-fold, icosahedron )
However, it order to minimize the land breaks in large masses, he needed to offset his poles...neither to a face center nor a vertex. In consequence,
the shape of important referqnce lines is effected.
Image



Izidor Hafner has done all the standard polyhedra...
http://matematika.fe.uni-lj.si/people/i ... rious.html

land sinues, land sinues, land sinues...none of those work as well as the w5, either.

Note...i have some 20 years of hand-made artifacts depicting that journey...sphere packs polyhedra other globes, like a w42, and well more stuff and paper and graphs than seems possible. However, you are at liberty to believe what you want. My life has been about the work, not it's promotion...that only gets me side-tracked to the work. My real work, i believe is in physics. Even saying that word..makes all my math and sphere pack work hugely suspect. I only got into physics following the path of sphere packing math. This is what i do, and who I am. i gave up on maps for many years, because i felt that i had more work to do outside of cartography using waterman polyhedra. i am 10 times more dedicated in physics than cartography...and about 1/10 the feedback as i ever had in cartography. No, make that 1/100th. This too does not invalidate my physics theories. I looked through some physics stuff here and doubt i will start discussion on any of it. Much of my physics work is sphere pack based and most importantly...mathematical...and presented on my site.

like it or not, having an understanding of math of sphere packing is like newton having his calculas...one can look at things very differently, and can answer some questions differently mathematically...i can construct whacks of new symmetrical polyhedra with it..i can investigate a nucleus with it...perhaps paramount to all that..I can ask some really good Physics questions. So now you have double cause to dismiss me, cartography and physics...they are like totally subjective. However, my math can not be defeated by subjectivity in either of those arenas, and being math..can either be proven or not. Math is my tool/genius, not in stealing Cahill's simple design nor simple math. Tomorrow is another comic, and this thread seems to been ending most rapidly and quite poorly...and surely talking ABOUT Physics should seal its fate. Remember this was not about my work, it is about defending your accusation that my map was basically derived from Cahill's. My numerous derivative artifacts can speak for themselves...including MY w5 maps. and hundreds of other unique maps and globes. i am now quite used to people pulling this crap on me. Ignoring the math, and go after me personally...i have heard it all dude, though this accusation of using cahill map is a new tactic...usually i am told that i am confused and do not understand...while they refuse to talk math. i recognize this current tempo and know this thread will only deteriorate further. So I offer no more cartographic input and will sadly only respond if further personally attacked on this public forum. All in all, i only have thanks to Randall for bringing up the issue...is the waterman projection really just the cahill projection ?

I am curious if Randall will rectify his implication with a another comic ( someday ). Does he indeed, now feel the implied was/is unmerited.

I do not request a retraction, but would surely appreciate some rectification, if deemed appropriate.

So I am officially done with this thread.
Last edited by steve waterman on Sat Nov 19, 2011 2:21 am UTC, edited 1 time in total.
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Re: 0977: "Map Projections"

Postby Maybe Not » Wed Nov 16, 2011 6:52 am UTC

OK, one more cartogram thing. Here's a nice SVG woojit of a map resized to give linear population density http://www.worldmapper.org/svg/map2/index.html

I'd argue the most relevant aspect of world maps in developing geographical knowledge is the topology of states and regions. The shapes are just mnemonics. I guess you could call the above an anthropocentric projection.

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Re: 0977: "Map Projections"

Postby k1w1 » Wed Nov 16, 2011 7:15 am UTC

Capt. Jon wrote:Has anyone posted a Sinu-Mollweide yet? I've currently got this above my desk:

Image

If anyone wants a bit of map based fun, sit down with a blank sheet of paper away from any maps and try and draw the world.

Cool, you have that bit and leave us with Australia, NZ, and Antartica.

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Re: 0977: "Map Projections"

Postby k1w1 » Wed Nov 16, 2011 7:25 am UTC

minetruly wrote:I can't believe he left out the map that shows all the countries upside-down.

Image

Right way up but 180 off centre and chopping Polynesia in two. Respect to the polyneian navigators that settled this half of the world without maps. Fiji, Samoa, Tonga, Tahiti, Hawaii ?? Kiribati, Guam, Midway ?? Easter Island, Galapagos ?? Oh forget it, Capt Cook wasted his time...

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Re: 0977: "Map Projections"

Postby k1w1 » Wed Nov 16, 2011 7:55 am UTC

Wnderer wrote:
5th Earth wrote:I have always favored the dymaxion projection--though, as a Bucky-phile, I feel obligated to point out that the better projection uses a cuboctohedron rather than an icosohedron, as it has less total distortion.
Map-of-human-migrations.jpg


Dymaxion projections are very useful if you are planning long distance hiking and kayaking trips.

Yep, Thor Heyerdahl's trip looks longer on that. If you do canoe from Chile to New Zealand it isn't as far as it seems on this projection & you won't be the first. Bring some more kumera.

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Re: 0977: "Map Projections"

Postby Eebster the Great » Wed Nov 16, 2011 9:43 am UTC

Steve, your obsession with sphere packing has reached unhealthy levels. There is no reason, for instance, to define all physical phenomena in terms of close sphere packing.

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Re: 0977: "Map Projections"

Postby mcv » Wed Nov 16, 2011 9:47 am UTC

infinitera wrote:For all you Mercator fans - why not the August or Eisenlohr projections? Conformal map, but displays the whole world without infinite poles.

http://www.quadibloc.com/maps/mcf0702.htm

North is not up. Also lots of shape deformation on the sides.

Each projection has its strong points and its weak points, and there's no single projection which does everything.

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Re: 0977: "Map Projections"

Postby mcv » Wed Nov 16, 2011 10:06 am UTC

steve waterman wrote:so issue 1...the shape of antarctica
issue 2...the relative areas of land masses to one another
and an issue 3...is the entire earth completely projected up through 90 degrees ?
or issue 4...without projecting some portions twice ?

These 4 issues all seem like individual deal breakers to me, for an acceptable projection.

Why only these 4? Why does only the shape of Antarctica matter, and not the shape of other continents? Why relative areas, and not relative distances? Why is having some portions twice worse than having locations that are geographically close on complete opposite sides of the map, or maybe separated by huge tears?

What makes a projection acceptable depends entirely on what you're going to use it for. For navigation (possibly the single most important use of maps throughout the ages), having north up and west left, 45 degrees north-west exactly in between is really, really convenient, and Mercator is the only one that offers that. That advantage comes at a steep price in other aspects, so it depends entirely on what you need the map for. For different uses, different aspects of the projection are most important.

Concluding, [ rhetorically speaking } who has an equivalent or better map projection than a waterman does, taking these important issues into account ???
( or even also considering angular deformation, point to point distancing, or an obvious equator if you like as well )

If you dislike any kind of deformation, but don't mind not having north up or having huge tears, then Waterman and Dymaxion are obviously superior. But in order to grasp the relative positions between continents, north up and less tears might be preferable, and you may have to accept some deformation.

What projection should be used in our classrooms to educate our young ???

Definitely not one single projection. Expose them to different map types. It would be awesome to have a Waterman in the classroom. For a general (though somewhat deformed) view of the whole world, Goode Homolosine, Robinson or Winkel-Tripel are probably the best compromises. You really need a globe too. But most important is to expose them to several different projections so they learn not to see any single projection as the "real" map of the world. None of them are perfect.

Edit: I only now realize that I'm responding to the creator of the Waterman Butterfly. Awesome! It is by far the most poetic map, and I would love to have one on my wall at home.

Some advice though: don't take internet discussions too seriously. Accept the praise, consider the constructive criticism, ignore the unconstructive criticism.
That said, while Cahill obviously lacks the polyhedric accuracy of your map, the overall butterfly division of continents is unmistakably similar. That doesn't mean it's a rip-off; all maps are in one way or another based on or inspired by previous maps. That's how progress works. In terms of accuracy and approach, Dymaxion is much closer related to your map, but it lacks the aesthetic, and with only 20 sides it's still more deformed. But there's nothing wrong with pointing out what you're improving upon.

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Re: 0977: "Map Projections"

Postby chrth » Wed Nov 16, 2011 12:57 pm UTC

Just wanted to point out that when I was checking out a school last night for my son, I couldn't help but notice the Mercator map in every classroom because of this comic.

That said, they're building a new, more modern school next year, so I'll need to check that out to see what they've done about the maps.

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Re: 0977: "Map Projections"

Postby keithl » Wed Nov 16, 2011 3:32 pm UTC

So, what projection do they use for world maps at Admundsen-Scott south pole station? With Mercator, the bathroom down the hall is about 100 kilometers away ...

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Re: 0977: "Map Projections"

Postby Frankie » Wed Nov 16, 2011 4:23 pm UTC

chrth wrote:That said, they're building a new, more modern school next year, so I'll need to check that out to see what they've done about the maps.

No. You absolutely should not "check that out to see what they've done". Good schools come from involved parents. If your child will go there, you talk to the instructional leadership right away, explain why Mercator is a poor choice (accurate size is more important than shape for both social studies and earth sciences, rounded maps are better teaching tools than rectangular ones, etc) and ask them to pick new maps appropriately. Maybe they're going to transplant the existing ones for budget reasons, but any replacement maps should not be Mercator.

mcv wrote: while Cahill obviously lacks the polyhedric accuracy of your map, the overall butterfly division of continents is unmistakably similar. That doesn't mean it's a rip-off; all maps are in one way or another based on or inspired by previous maps. That's how progress works.

Hear, hear. Inventors and scientists should follow Isaac Newton's adage and gratefully acknowledge their predecessors. Sadly, the alleged Mr Waterman seems to follow Arno Peter's example of self-aggrandizing egotism.

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Re: 0977: "Map Projections"

Postby chrth » Wed Nov 16, 2011 4:48 pm UTC

Frankie wrote:No. You absolutely should not "check that out to see what they've done"


I felt that my child would not be going there was implicit in my comment. Besides, what do I care if the school is teaching all the other kids wrong? My child will learn to critically think about what he learns in school because I am going to be there to ensure he does.

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Re: 0977: "Map Projections"

Postby steve waterman » Wed Nov 16, 2011 4:51 pm UTC

keithl wrote:So, what projection do they use for world maps at Admundsen-Scott south pole station? With Mercator, the bathroom down the hall is about 100 kilometers away ...


The Mercator maps usually stops at 85 degrees...they have no north or south pole that they dare to show/label/acknowledge.
So, the Polarites/Polarians can just fudge it... take a piece of the globe ( ignore all the rest ) and make a lovely inset....
or blow it up big and make IT the poster.
It will will very accurate...the smaller the earth's surface piece you take...the more accurate it becomes.

Some projections either have no polar point or like the Mercator would have a singular earth point given as the same length as the equator...or some lesser percentage of the equator...Robinson, Winkel-tripel for example,
however, Mercators are deceptively clever...and do not plot the whole planet ( usually ) and their tissot's seems contrived in the poles as well..only up to 75 degrees. ...and so, vacant actually...where they are worst. Try to draw a square of 1000 mile edge on your favorite projection...but you need to use the proper coordinates of those 4 points to manifest its "square"...good luck with your non-polyhedral map.

Polyhedral maps never share this polar deception and always have a singular point for their poles...and always maintain a compromise of relative shape,
( not just of Antarctica )...but all land masses, area and distances. All non-polyhedral projections..{ not insets of a small earth portion ) distort the shape of Antarctica...unless they project outwards from the south pole and well, then simply ignore the resultant massive distortions elsewhere.

Seen a map by Mercator where they do plot to the pole ?....rarely seen but available and the size for Antarctica borders upon humorous/cartoon-ish/comic.
That tissot is also humorous.

here is a mercator up to 85 degrees
http://www.progonos.com/furuti/MapProj/ ... ojNav.html
and the tissot for that...seen here
http://www.progonos.com/furuti/MapProj/ ... stort.html

Any projection not having a singular polar point, but rather is represented as a line, say the WinKel-tripel as an example, would have a tissot ellipse of infinite size at its' 90 degree "location(s)"...and hence, a better "marketing strategy" ( for those types of projections ), to merely keep that fact
disclosed/un-shown/ignored/lost/unimportant/a company secret/over-looked/devalued/cloaked/invisible/away from mathematical scrutiny.

Nobody wanted to banter this first statement below, now I have additional speculation/postulation/truth/muse/math/no counter-examples...
1 All world map projections are interuptted
2 All polyhedral maps can and MUST attach/close all of their interruptions simultaneously in 3d, well,.... back into that origin polyhedron.
3 No non-polyhedral world map projection can ever attach all its interruptions, physically, simultaneously....back into a 3d sphere-like shape, that looks anything like a sphere...likely just a fold in half...and really, still 2d.

I can think of no counter-examples...got a candidate any of these, anybody ?
Last edited by steve waterman on Wed Nov 16, 2011 8:31 pm UTC, edited 3 times in total.
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Re: 0977: "Map Projections"

Postby PM 2Ring » Wed Nov 16, 2011 7:07 pm UTC

dumbzebra wrote:I played around with the moveable globe-grid thingy on the website linked above the comic:

Turns out, if you dig a whole through the center of the earth you almost never encounter anything else than water on the other side.
It's even less likely to "dig a hole to china".

You may be interested to check out some antipodes maps.
From http://bigthink.com/ideas/21154
Spoiler:
Image

Also see http://www.antipodemap.com/ for a dual Google Maps set-up.


steve waterman wrote:Seen a map by Mercator where they do plot to the pole ?

Huh? That's simply not possible on a normal Mercator projection: the poles are infinitely far away from the equator. OTOH, if you don't mind having a ridiculously tall map, with the severely distorted areas in the polar regions that that entails, you can get very close to the poles with a Mercator chart.


It might seem like I've been championing the Mercator in this thread. I'm not. I've merely pointed out that it's excellent for its intended purpose of plotting rhumb lines. It's certainly a poor choice of map as the primary projection that school kids are exposed to; IMHO an area-preserving projection (or two) would be a much better choice for a classroom map.

In this electronic age, I don't think it makes a whole lot of sense to argue about which projection is the best choice for a classroom. School kids throughout much of the world can access all sorts of projections via computer. If you want a large map in the classroom, make it electronic so it can display any projection you want it to. I suspect that it won't be too far in the future that the old-fashioned classroom map will be seen as ancient technology, like the slide-rule or abacus.
Last edited by PM 2Ring on Wed Nov 16, 2011 8:00 pm UTC, edited 1 time in total.

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Re: 0977: "Map Projections"

Postby Netreker0 » Wed Nov 16, 2011 7:53 pm UTC

I think I get what jpk is saying a little better now. He's got nothing against map lovers or pretentious snobs, but finds the (probable) fact that Randall is pretending to be a pretentious snob for the sake of a joke to be offensive, much like how, when I was in school, the real skaters hated the guys who dressed liked them just to be "non-mainstream." So the fact that his first post was entirely pretentious and unpleasant actually wasn't hypocritical at all.

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Re: 0977: "Map Projections"

Postby mcv » Wed Nov 16, 2011 8:48 pm UTC

PM 2Ring wrote:In this electronic age, I don't think it makes a whole lot of sense to argue about which projection is the best choice for a classroom. School kids throughout much of the world can access all sorts of projections via computer. If you want a large map in the classroom, make it electronic so it can display any projection you want it to. I suspect that it won't be too far in the future that the old-fashioned classroom map will be seen as ancient technology, like the slide-rule or abacus.

Good point. I'm getting the impression that all Dutch schools have an electronic (formerly black-)board these days. Showing a variety of maps there should be trivial. Somebody just needs to inform the teachers and give them access to the right maps.

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Re: 0977: "Map Projections"

Postby steve waterman » Wed Nov 16, 2011 9:26 pm UTC

mcv wrote:
PM 2Ring wrote:In this electronic age, I don't think it makes a whole lot of sense to argue about which projection is the best choice for a classroom. School kids throughout much of the world can access all sorts of projections via computer. If you want a large map in the classroom, make it electronic so it can display any projection you want it to. I suspect that it won't be too far in the future that the old-fashioned classroom map will be seen as ancient technology, like the slide-rule or abacus.

Good point. I'm getting the impression that all Dutch schools have an electronic (formerly black-)board these days. Showing a variety of maps there should be trivial. Somebody just needs to inform the teachers and give them access to the right maps.


All projections are right,mathematically, as I view them... Duplicative replication is not the issue for that criteria.
No projection of a sphere is right, physically. Distortion is inherent to the mathematical process.
No two projection types have identical aspects.
Most aspects, taken individually, can be mathematically quantified, and slotted against all the other projections...and deemed as better or worse than some other projection...in that one particular aspect.
That has really never been done, perhaps to a few ...however, shape certainly has subjective undertones and would be a subjective algorithm to obtain that mathematical data, whereas, area and distances ...should be shown already in a library book somewhere... or on the internet. It is 2011, where do I go to look up those figures for each projection..or a simple top to bottom list per aspect. [ rhetorical ]
Last edited by steve waterman on Mon Nov 21, 2011 9:54 pm UTC, edited 2 times in total.
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Re: 0977: "Map Projections"

Postby solarion » Wed Nov 16, 2011 10:45 pm UTC

Needs more Mcarthur's Corrective.

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Re: 0977: "Map Projections"

Postby neoliminal » Thu Nov 17, 2011 3:18 am UTC

Silly me. All this time I've been using this 1 to 1 scale map of the earth. I call it earth.
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Re: 0977: "Map Projections"

Postby Idhan » Thu Nov 17, 2011 6:30 am UTC

I've been thinking about the "North is up, South is down, Prime Meridian goes through Greenwich" convention, and while I suppose it was decided by politics, power, and historical accident, I'm thinking that it that it actually turns out to be coincidentally pretty close to being the optimal convention for certain fairly plausible (IMHO) parameters.

To be more specific, if you cut the world into the most land-bearing hemisphere and the most oceanic hemisphere (land hemisphere and water hemisphere), the center the the land hemisphere is around 47.41 degrees north, 2.62 degrees west.

Suppose we assume that 1) most people read from top to bottom; this may not universally be the case, but it is true for some very populous groups, such as users of the Latin alphabet and Chinese logographic script; as such, if "more important" things can go at the top or bottom of a page, they should go to the top 2) for most projections (non-cylindrical, at least), areas closer to the prime meridian will be less distorted, and 3) between distorting oceans and distorting land, we should sacrifice accuracy in the oceans to make the land less distorted.

With these three assumptions, we might make the prime meridian around 2.62 degrees west of the current one (to center the prime meridian on the Land Hemisphere more), and keep the North-on-top convention. That's a pretty small change -- or, to put it another way, our current convention regarding prime meridian is fairly close to optimal.

(None of this, by the way, should be taken as a denigration of alternative maps, which put the prime meridian in the pacific or have the southern hemisphere pointing up. Just as there is no one perfect map projection, there is also no one perfect selection of prime meridian or orientation. I'm just saying that, if you go with some fairly plausible parameters (basically, a prioritization of land over ocean in terms of minimal distortion and emphasis) the current conventions are pretty close to optimal.)

P.S.: I'd take the Lambert/Lagrange conformal circular world map adapted from stereographic over the Van der Grinten.
Last edited by Idhan on Thu Nov 17, 2011 5:25 pm UTC, edited 1 time in total.

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Re: OOOhhhh, Doughnuts!

Postby MadTigger » Thu Nov 17, 2011 8:45 am UTC

Mercator is the coolest, because it is trivial to map onto a doubly curved negative space. Any map that is a toroidal world is awesome!

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Re: 0977: "Map Projections"

Postby marcel » Thu Nov 17, 2011 10:50 am UTC

The mercator is the best, for the simple reasons stated above, that it has the most practical purposes.

I can tell you that the first picture in this comic is incorrect. I am very much into maps, and therefore my favourite map projection is the mercator.

Anybody who is into maps for the reason of actually wanting to use them to travel, and specifically for sailing, is likely into the mercator projection.


I also believe that people here have missed the main point about this comic, and that is that it is not about maps at all. It is just about showing the prejudices people get about others based on their preferences.
It would have been the exact same comic if it had involved OS's, cars, music, or whatever. The only reason it is about maps, is that it is much more obscure. If it had been about OS's, considering the geekiness of the average XKCDer the flame war in this forum would have been of epic proportions.

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Re: 0977: "Map Projections"

Postby eran_rathan » Thu Nov 17, 2011 12:41 pm UTC

steve waterman wrote:
mcv wrote:
PM 2Ring wrote:In this electronic age, I don't think it makes a whole lot of sense to argue about which projection is the best choice for a classroom. School kids throughout much of the world can access all sorts of projections via computer. If you want a large map in the classroom, make it electronic so it can display any projection you want it to. I suspect that it won't be too far in the future that the old-fashioned classroom map will be seen as ancient technology, like the slide-rule or abacus.

Good point. I'm getting the impression that all Dutch schools have an electronic (formerly black-)board these days. Showing a variety of maps there should be trivial. Somebody just needs to inform the teachers and give them access to the right maps.


All projections are right, mathematically, as I view them... Duplicative replication is not the issue for that criteria.
No projection of a sphere is right, physically. Distortion is inherent to the mathematical process.
No two projection types have identical aspects.
Most aspects, taken individually, can be mathematically quantified, and slotted against all the other projections...and deemed as better or worse than some other projection...in that one particular aspect.
That has really never been done, perhaps to a few ...however, shape certainly has subjective undertones and would be a subjective algorithm to obtain that mathematical data, whereas, area and distances ...should be shown already in a library book somewhere... or on the internet. It is 2011, where do I go to look up those figures for each projection..or a simple top to bottom list per aspect. [ rhetorical ]



The earth isn't a sphere, its more properly modeled with an ellipsoid (if you want a regular geometric shape to make your math easier - otherwise, you need to be using the geoid - current one is Geoid-09, based on the WGS84(2004 revision), until they come up with the new one that was started last year.)
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Re: 0977: "Map Projections"

Postby chrth » Thu Nov 17, 2011 2:04 pm UTC

While I understand the desire for "accuracy", let's all take a moment to recognize a very important fact:

No one ever got killed because they thought Antarctica or Greenland were much larger than they actually are due to the Mercator projection.

Looking through the range of popular misconceptions, it probably ranks down towards the bottom in terms of likelihood of negative impact on your life.

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Re: 0977: "Map Projections"

Postby OP Tipping » Thu Nov 17, 2011 2:20 pm UTC

Globe is best. I have a soft-spot for the dymaxion.

But basically I am content with anything that is fairly close to conformal and fairly close to equal area. I'm sure there are millions of people in the world who think Greenland is the size of South America ...

The points made above in defence of the Mercator, that it was handy for navigation, are reasonable except that we now have computers and satellites... Rhumb lines are for losers.





EDIT: "No one ever got killed because they thought Antarctica or Greenland were much larger than they actually are due to the Mercator projection." Can you prove that??? :-)
But seriously, I think it is usual to have half a fkn clue about geography.

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Re: 0977: "Map Projections"

Postby jpk » Thu Nov 17, 2011 2:54 pm UTC

OP Tipping wrote:
EDIT: "No one ever got killed because they thought Antarctica or Greenland were much larger than they actually are due to the Mercator projection." Can you prove that??? :-)


Hang on, I'll go make an edit on some wiki pages. You'll have your proof presently.

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Re: 0977: "Map Projections"

Postby The Moomin » Thu Nov 17, 2011 2:58 pm UTC

chrth wrote:While I understand the desire for "accuracy", let's all take a moment to recognize a very important fact:

No one ever got killed because they thought Antarctica or Greenland were much larger than they actually are due to the Mercator projection.

Looking through the range of popular misconceptions, it probably ranks down towards the bottom in terms of likelihood of negative impact on your life.


However, France has lost more land to the increase in accuracy of surveying than they did through any wars. (This was admittedly when France still had kings I believe) I watched a fascinating documentary on the history of mapmaking and that's one of the things I learnt from it. I can imagine rulers wanting to conquer foreign lands upon learning that their realm isn't quite as expansive as first thought. Which would inevitably lead to mass horrific death as these things do.

On a related note, has anyone read the book about the first ordnance survey undertaken on the UK? It looks to be an intriguin read and I wondered if anyone could recommend it?
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Re: 0977: "Map Projections"

Postby chrth » Thu Nov 17, 2011 2:58 pm UTC

OP Tipping wrote:EDIT: "No one ever got killed because they thought Antarctica or Greenland were much larger than they actually are due to the Mercator projection." Can you prove that??? :-)
But seriously, I think it is usual to have half a fkn clue about geography.


I do as well, but for me, geography is about knowing where things are, not how big they are. Very few people care what the land area of Paris is, they just care it's in France, and it's probably more important that you know it's in the north of France rather than in the south.

Going back to the school open house I went to earlier this week, one of the teachers mentioned that her specific class was learning "all the states and their capitals". I resisted rolling my eyes, but seriously outside of Washington who gives a crap that Olympia is the capital? Seattle is where it's at!

(Note: I actually do support the memorization of dates, though. Maybe not months and days, but definitely years. My reasoning is due to how history is taught in silos. For example, in 1776 there were three very important documents published: The Declaration of Independence, the Decline and Fall of the Roman Empire, and the Wealth of Nations. Since it is unlikely that all three would be discussed concurrently as their subject matter varies so widely, knowing when each occured helps build a more complete picture on your mind. I still remember hearing the comment that "Catherine the Great was a contemporary of George Washington" and my gast being flabbered)


EDIT: Let us also consider the lands that are being "embiggened" by the Mercator projection. Antarctica. Greenland. Russia. The Canadian tundra. Maybe Australia a little bit, and Tierra del Fuego. With the exception of Russia (which is pretty damn big even without a projection), we're not causing a true geo-political impact simply by size misrepresentation, no matter the charges of cultural imperialism levied against it.
Last edited by chrth on Thu Nov 17, 2011 3:03 pm UTC, edited 1 time in total.

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Re: 0977: "Map Projections"

Postby chrth » Thu Nov 17, 2011 3:00 pm UTC

The Moomin wrote:However, France has lost more land to the increase in accuracy of surveying than they did through any wars. (This was admittedly when France still had kings I believe) I watched a fascinating documentary on the history of mapmaking and that's one of the things I learnt from it. I can imagine rulers wanting to conquer foreign lands upon learning that their realm isn't quite as expansive as first thought. Which would inevitably lead to mass horrific death as these things do.


But that is a flaw of surveying and mapmaking in general, not projections.

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Re: 0977: "Map Projections"

Postby The Moomin » Thu Nov 17, 2011 3:13 pm UTC

chrth wrote:
The Moomin wrote:However, France has lost more land to the increase in accuracy of surveying than they did through any wars. (This was admittedly when France still had kings I believe) I watched a fascinating documentary on the history of mapmaking and that's one of the things I learnt from it. I can imagine rulers wanting to conquer foreign lands upon learning that their realm isn't quite as expansive as first thought. Which would inevitably lead to mass horrific death as these things do.


But that is a flaw of surveying and mapmaking in general, not projections.


True. But the point is if you are led to believe your realm is of a certain size relative to others by Mercator, only to find it is not in actuality of comparable size. . .Doom. People to tend to get upset and angered when they find the real world does not correlate with their perception of it. I know this well from random reprimands for pointing out reality to the boss at work.
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Re: 0977: "Map Projections"

Postby tomandlu » Thu Nov 17, 2011 3:19 pm UTC

The Moomin wrote:On a related note, has anyone read the book about the first ordnance survey undertaken on the UK? It looks to be an intriguin read and I wondered if anyone could recommend it?


Nope, but can I recommend "This Thing of Darkness"? - it's a fictionalised account of the voyages of the beagle, with some fascinating stuff about mapping South America, Captain Fitzroy and Darwin. Fitzroy's maps were still the best available long into the 20th century and were only retired when satellite images became available... Fitzroy tends to get a bad press and written off as a religious nay-sayer to evolution, but he was a fascinating and tragic figure with some awesome accomplishments to his name...

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Re: 0977: "Map Projections"

Postby eran_rathan » Thu Nov 17, 2011 5:14 pm UTC

chrth wrote:
The Moomin wrote:However, France has lost more land to the increase in accuracy of surveying than they did through any wars. (This was admittedly when France still had kings I believe) I watched a fascinating documentary on the history of mapmaking and that's one of the things I learnt from it. I can imagine rulers wanting to conquer foreign lands upon learning that their realm isn't quite as expansive as first thought. Which would inevitably lead to mass horrific death as these things do.


But that is a flaw of surveying and mapmaking people's perceptions of area in general, not projections.



FTFY.
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Re: 0977: "Map Projections"

Postby The Moomin » Thu Nov 17, 2011 5:40 pm UTC

tomandlu wrote:
The Moomin wrote:On a related note, has anyone read the book about the first ordnance survey undertaken on the UK? It looks to be an intriguin read and I wondered if anyone could recommend it?


Nope, but can I recommend "This Thing of Darkness"? - it's a fictionalised account of the voyages of the beagle, with some fascinating stuff about mapping South America, Captain Fitzroy and Darwin. Fitzroy's maps were still the best available long into the 20th century and were only retired when satellite images became available... Fitzroy tends to get a bad press and written off as a religious nay-sayer to evolution, but he was a fascinating and tragic figure with some awesome accomplishments to his name...

p.s. Hey! Another Moomin!


Thankyou for the recommendation :D I had a looksee and it looks like I'll have to get myself a copy.

Hey there! It's always a pleasure to meet another Moomin fan.

chrth wrote:
The Moomin wrote:However, France has lost more land to the increase in accuracy of surveying than they did through any wars. (This was admittedly when France still had kings I believe) I watched a fascinating documentary on the history of mapmaking and that's one of the things I learnt from it. I can imagine rulers wanting to conquer foreign lands upon learning that their realm isn't quite as expansive as first thought. Which would inevitably lead to mass horrific death as these things do.


But that is a flaw of surveying and mapmaking in general, not projections.


An afterthought: Are you suggesting that a flaw in surveying and mapmaking is that the methods of measurements are becoming more accurate?
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Re: 0977: "Map Projections"

Postby chrth » Thu Nov 17, 2011 6:25 pm UTC

eran_rathan wrote:But that is a flaw of surveying and mapmaking people's perceptions of area in general, not projections.
FTFY.


Not what we're talking about; see below.

An afterthought: Are you suggesting that a flaw in surveying and mapmaking is that the methods of measurements are becoming more accurate?


The original example that's being discussed isn't a modern one; we're talking about surveys back in the day where the actual distance of a "foot" varied from village to village; or when a border river was mischarted because it was confused with an overflowing creek. The original France example wasn't the result of a misinterpretation of a projection, it was the result of inaccurate measurements to begin with.

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Re: 0977: "Map Projections"

Postby Pfhorrest » Thu Nov 17, 2011 8:38 pm UTC

eran_rathan wrote:The earth isn't a sphere, its more properly modeled with an ellipsoid (if you want a regular geometric shape to make your math easier - otherwise, you need to be using the geoid - current one is Geoid-09, based on the WGS84(2004 revision), until they come up with the new one that was started last year.)

You know, a map that would be really interesting would be some kind of rectangular projection of the geoid, with the latitude and longitude lines drawn on it. Since lat and long are lines on a sphere approximating the geoid, if we project the actual geoid onto a rectangle rather than that sphere, the lat and long lines should appear distorted in proportion to how the geoid varies from that sphere, giving us a visualization of exactly how nonsphereical the geoid is in what geographic areas. I suppose it would end up like a sort of topographic map in the end.
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