I have run into this phenomenon myself. Some people who recognize that common maps wrap around left-to-right falsely extend that recognition to wrapping around top-to-bottom.
http://phys.org/news/2015-05-difficulty-world-edge.html
— daan
Map cognition: The wrap-around
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Atarimaster
- Posts: 446
- Joined: Fri Nov 07, 2014 2:43 am
Re: Map cognition: The wrap-around
Very interesting, thanks for providing the link!
Yesterday, I asked my wife and my nephew to show me where the plane will reappear when it leaves the map "here" (while pointing to the south pole), and both of them indeed pointed to the north pole.
However, when I subsequently asked: "So, the plane arrives at the north pole when it passed over the south pole?", both said something like: "Uuuh, wait, that's gotta be wrong..."; and then on the next attempt they were right. I wonder how many of the research participants would have realized their mistake, too, when they'd been asked the same question.
However, this study supports my suspicions about heavily interrupted maps (e.g. the Dymaxion map projection):
While having very low distortions, they probably are very bad at illustrating how the world is "layed out". I guess most people would fail to indicate where an aircraft will come back when it passed any of the edges of an Dymaxion map.
When Dr. Böhm introduced his second variation of Wagner VIII (see below) he assumed that the half-ellipsoidal pole line might help people (who are inexperienced with maps) to understand the earth's spherical shape. I think it'd really be interesting to know if people would have less difficulties to indicate where the aircraft comes back when a map projection like this is used...
Yesterday, I asked my wife and my nephew to show me where the plane will reappear when it leaves the map "here" (while pointing to the south pole), and both of them indeed pointed to the north pole.
However, when I subsequently asked: "So, the plane arrives at the north pole when it passed over the south pole?", both said something like: "Uuuh, wait, that's gotta be wrong..."; and then on the next attempt they were right. I wonder how many of the research participants would have realized their mistake, too, when they'd been asked the same question.
However, this study supports my suspicions about heavily interrupted maps (e.g. the Dymaxion map projection):
While having very low distortions, they probably are very bad at illustrating how the world is "layed out". I guess most people would fail to indicate where an aircraft will come back when it passed any of the edges of an Dymaxion map.
When Dr. Böhm introduced his second variation of Wagner VIII (see below) he assumed that the half-ellipsoidal pole line might help people (who are inexperienced with maps) to understand the earth's spherical shape. I think it'd really be interesting to know if people would have less difficulties to indicate where the aircraft comes back when a map projection like this is used...
Re: Map cognition: The wrap-around
Hello Tobias.
I think you’ve made a key observation. After reading the lay account of Hennerdal’s research (the link I posted), I tracked down and read the original paper. I think his thesis is too ambitious. There’s a distinct difference between jumping to a conclusion, and the interesting cognitive process that most of his paper is actually about. A lot of people who don’t deal with maps much will immediately answer as your wife and nephew did. There’s a left-right wrap-around; why wouldn’t there be a top-bottom wrap-around? When challenged, of course they re-think the situation. That sounds distinctly different to me than estimating track continuations across complicated interruptions. In this latter situation, a person must make an effort to figure out the topology of the map. There’s no jumping to conclusions.
Hennerdal found that children are much worse at this than adults, and he speculates this result ties into Piaget’s stages of cognition. It may well. But there are significant weaknesses in his study, and in particular, the naïve, immediate answer of top-to-bottom wrap-around probably predicts nothing about success in a Berghaus Star (or Fuller dymaxion) test. So… I very much agree with you. I can’t really predict how people’s responses would change on Böhm’s second variation on Wagner VIII, but I think your notion is reasonable.
Best regards,
— daan
I think you’ve made a key observation. After reading the lay account of Hennerdal’s research (the link I posted), I tracked down and read the original paper. I think his thesis is too ambitious. There’s a distinct difference between jumping to a conclusion, and the interesting cognitive process that most of his paper is actually about. A lot of people who don’t deal with maps much will immediately answer as your wife and nephew did. There’s a left-right wrap-around; why wouldn’t there be a top-bottom wrap-around? When challenged, of course they re-think the situation. That sounds distinctly different to me than estimating track continuations across complicated interruptions. In this latter situation, a person must make an effort to figure out the topology of the map. There’s no jumping to conclusions.
Hennerdal found that children are much worse at this than adults, and he speculates this result ties into Piaget’s stages of cognition. It may well. But there are significant weaknesses in his study, and in particular, the naïve, immediate answer of top-to-bottom wrap-around probably predicts nothing about success in a Berghaus Star (or Fuller dymaxion) test. So… I very much agree with you. I can’t really predict how people’s responses would change on Böhm’s second variation on Wagner VIII, but I think your notion is reasonable.
Best regards,
— daan
Re: Map cognition: The wrap-around
Hi,
Glad to see that you are interested in my research. Just want to say that I do not argue that the difference between children and adults is due to Piaget’s stages of cognition. I state that the naïve understanding (expressed as linear peripheral continuity) can be explained by Euclidean understanding (the last of stages proposed by Piaget and Inhelder). The fact that some children and even more adults do not answer according to this naïve understanding, is probably because something help them to realise that Euclidian understanding is not suitable for understanding this map (in the way it is suitable for understanding a map of a smaller part of the earth). The help could be that someone say “So, the plane arrives at the north pole when it passed over the south pole?”, or like in my study that Australia is split into two (as one of the cases of the test for the star projection) or that the South Pole could be easily identified due to the grid (as in one cases of the test for Fullers projection). But the mentioned variation of Wagner VIII can probably also help some map readers to realise this. The best way of realising that you cannot use Euclidean understanding for finding the peripheral continuation is of course to understand the spherical geometry and how the projection represent the round earth, something I guess adults may be better than children at.
My article can be found here: http://www.tandfonline.com/eprint/5IMZG ... vxtmX/full
Regards
Pontus Hennerdal
Glad to see that you are interested in my research. Just want to say that I do not argue that the difference between children and adults is due to Piaget’s stages of cognition. I state that the naïve understanding (expressed as linear peripheral continuity) can be explained by Euclidean understanding (the last of stages proposed by Piaget and Inhelder). The fact that some children and even more adults do not answer according to this naïve understanding, is probably because something help them to realise that Euclidian understanding is not suitable for understanding this map (in the way it is suitable for understanding a map of a smaller part of the earth). The help could be that someone say “So, the plane arrives at the north pole when it passed over the south pole?”, or like in my study that Australia is split into two (as one of the cases of the test for the star projection) or that the South Pole could be easily identified due to the grid (as in one cases of the test for Fullers projection). But the mentioned variation of Wagner VIII can probably also help some map readers to realise this. The best way of realising that you cannot use Euclidean understanding for finding the peripheral continuation is of course to understand the spherical geometry and how the projection represent the round earth, something I guess adults may be better than children at.
My article can be found here: http://www.tandfonline.com/eprint/5IMZG ... vxtmX/full
Regards
Pontus Hennerdal
Re: Map cognition: The wrap-around
I apologize to Hennerdal. He posted his response back in June as a new member, but I missed the moderation request until last week. His response languished that whole time.
Hennerdal: Thanks for correcting my misrepresentation of your speculation concerning Piaget’s stages of cognition. That was careless of me. I don’t think even my misinterpretation would have been an important flaw in your study. It’s fine to speculate, and I think the better results evidenced by adults surely relates to greater cognitive maturity (whether covered by Piaget’s model or not).
My bigger concern is the distinction between a subject’s jumping to a conclusion versus having presence of mind to realize the situation needs to be thought through.
Tobias (=Atarimaster), here’s your chance to engage with the author directly.
— daan
Hennerdal: Thanks for correcting my misrepresentation of your speculation concerning Piaget’s stages of cognition. That was careless of me. I don’t think even my misinterpretation would have been an important flaw in your study. It’s fine to speculate, and I think the better results evidenced by adults surely relates to greater cognitive maturity (whether covered by Piaget’s model or not).
My bigger concern is the distinction between a subject’s jumping to a conclusion versus having presence of mind to realize the situation needs to be thought through.
Tobias (=Atarimaster), here’s your chance to engage with the author directly.
— daan
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Atarimaster
- Posts: 446
- Joined: Fri Nov 07, 2014 2:43 am
Re: Map cognition: The wrap-around
Oh, nice!
A belated "Thank you" to Hennerdal for your statement and the link to your article.
I think I’m going to read it in my upcoming vacation, along with some of Bernhard Jenny’s stuff I’ve downloaded from cartography.oregonstate.edu.
A belated "Thank you" to Hennerdal for your statement and the link to your article.
I think I’m going to read it in my upcoming vacation, along with some of Bernhard Jenny’s stuff I’ve downloaded from cartography.oregonstate.edu.