By AVERY ELIZABETH HURT from Science News for Students
Release date: April 16, 2021
When cartographers — people who make maps — set out to portray the Earth, they have to turn a 3-D sphere into a 2-D map. And that’s a lot harder than it sounds. Smooshing the globe into a flat image usually distorts lots of surface features. Some expand. Others shrink, sometimes by a lot. Now three scientists have come up with a clever way to limit those distortions.
Their big trick? Divide the map onto two pages.
“Wow!” said Elizabeth Thomas on learning of the new map. Thomas is a climate scientist at the University at Buffalo in New York. She says maps made the new way could be very useful. For instance, it better conveys to scientists, like her, who study the Arctic, how far this area is from other places on the planet. It shows how really vast the Arctic is, too.
“Anything that involves visualizing data on maps will be easier with this new type of projection,” she says. “This includes things like changes in ocean currents. It could also help see the average position of atmospheric fronts, like the polar vortex.”
Displaying size differences
A drawing of a curved object (such as Earth’s surface) onto a flat piece of paper is called a projection. Over the centuries, mapmakers have come up with many different types. All distort the relative size of Earth’s features.
The most common map used these days is the Mercator projection. It’s may even be on your classroom wall. Though good, it has problems. Parts farthest from the equator look much bigger than they really are. Greenland looks bigger than Africa, for instance, yet is just seven percent its size. Alaska looks about the same size as Australia despite being less than one-fourth as big.
Some projections also distort the distances between places. To make a flat map from a round globe, you have to cut the image somewhere. This means the map stops at the edge of the paper, then takes up again on the far edge of the paper. Known as a boundary problem, it creates the impression of big spaces between places that are actually closer together. For example, Hawaii is much closer to Asia than it looks on a Mercator projection.
No one projection is necessarily the best. The Mercator projection is very good for navigation and for making local maps. Google uses a form of it for city maps. Other projections might do a better job with distance or with the size of continents. The National Geographic Society uses the Winkel tripel projection for its world maps. But no map perfectly portrays the whole planet.
Still, many people would prefer a map with the fewest distortions. And that’s what three scientists appear to now offer. They posted a paper describing their new mapmaking technique February 15 on ArXiv. It’s an online database of scholarly articles.
Why just one page?
J. Richard Gott and David Goldberg are astrophysicists. Gott works at Princeton University in New Jersey. Goldberg studies galaxies at Drexel University in Philadelphia, Penn. When Goldberg was in graduate school, Gott was one of his teachers. About a decade ago, the two developed a system for scoring the accuracy of maps. They based scores on six types of distortion. A score of zero would be a perfect map. The Winkel tripel projection scored the best. It earned an error score of just 4.497.
A few years back, Gott phoned Goldberg with an idea: Why does a world map have to be only on one page? Why not split the globe, projecting each half on a separate page? Robert Vanderbei, a mathematician at Princeton, joined the pair on this. Together, they created a radically different map. It has an error score of only 0.881. “Compared to the Winkel tripel, our map improves on every category,” says Goldberg.
Their projection sticks two circular sheets, each a flat disc, back to back. It shows the Northern Hemisphere on one side, the Southern Hemisphere on the other side. One of the poles is at the center of each. The equator is the line that forms the edge of these circles. In a February 17 article in Scientific American, Gott describes it as if you’d taken the Earth and squashed it flat.
“Distances between cities are measured by simply stretching a string between them,” Gott explains. To make measurements that cross a hemisphere, pull the string across the equator at the edge of the map. This new projection, Gott says, would let an ant walk from one side to the other without ever touching a spot that didn’t represent a real spot on Earth. So it totally gets rid of the boundary problem.
And this projection isn’t just for maps of Earth. “It can be any roughly spherical object,” Goldberg points out. Vanderbei has already made maps of Mars, Jupiter and Saturn this way.
Something for everybody
The ArXiv post on the new approach to mapping spheres was not peer reviewed. This means other scientists have yet to judge it. But Thomas is not the only scientist excited about its prospects.
“I think it would be really neat to make a version of the map that shows the arrangements of the continents in periods such as the Triassic and the Jurassic,” says Nizar Ibrahim. He’s a paleontologist in Michigan who works at the University of Detroit. This new projection, he says, “could help students better understand how landmasses and our planet changed over time.”
Licia Verde works at the Institute of Cosmos Sciences at the University of Barcelona in Spain. She says the new map would help better visualize “the surface of other planets — or even our own night sky.”
The only drawback to the new projection: You can’t see all of Earth at once. Then again, you can’t see all of our actual planet at one time either.
2-D: Short for two-dimensional. This term is an adjective for something in a flat world, meaning it has features that can be described in only two dimensions — width and length.
3-D: Short for three-dimensional. This term is an adjective for something that has features that can be described in three dimensions — height, width and length.
Arctic: A region that falls within the Arctic Circle. The edge of that circle is defined as the northernmost point at which the sun is visible on the northern winter solstice and the southernmost point at which the midnight sun can be seen on the northern summer solstice. The high Arctic is that most northerly third of this region. It’s a region dominated by snow cover much of the year.
arXiv: A website that posts research papers — often before they are formally published — in the fields of physics, mathematics, computer science, quantitative biology, quantitative finance and statistics. Anyone can read a posted paper at no charge.
astrophysicist: A scientist who works in an area of astronomy that deals with understanding the physical nature of stars and other objects in space.
average: (in science) A term for the arithmetic mean, which is the sum of a group of numbers that is then divided by the size of the group.
climate: The weather conditions that typically exist in one area, in general, or over a long period.
continent: (in geology) The huge land masses that sit upon tectonic plates. In modern times, there are six established geologic continents: North America, South America, Eurasia, Africa, Australia and Antarctica. In 2017, scientists also made the case for yet another: Zealandia.
cosmos: (adj. cosmic) A term that refers to the universe and everything within it.
current: A fluid — such as of water or air — that moves in a recognizable direction.
data: Facts and/or statistics collected together for analysis but not necessarily organized in a way that gives them meaning. For digital information (the type stored by computers), those data typically are numbers stored in a binary code, portrayed as strings of zeros and ones.
database: An organized collection of related data.
distort: (n. distortion) To change the shape or image of something in a way that makes it hard to recognize, or to change the perception or characterization of something (as to mislead).
equator: An imaginary line around Earth that divides Earth into the Northern and Southern Hemispheres.
field: An area of study, as in: Her field of research was biology. Also a term to describe a real-world environment in which some research is conducted, such as at sea, in a forest, on a mountaintop or on a city street. It is the opposite of an artificial setting, such as a research laboratory. (in physics) A region in space where certain physical effects operate, such as magnetism (created by a magnetic field), gravity (by a gravitational field), mass (by a Higgs field) or electricity (by an electrical field).
fronts: (in Earth sciences) The boundaries that separate air masses — parcels of air having very different densities. Fronts extend both horizontally (up and down) and vertically (along a plane).
Greenland: The world’s largest island, Greenland sits between the Arctic Ocean and North Atlantic. Although it is technically part of North America (sitting just east of Northern Canada), Greenland has been linked more politically to Europe. Although this is the 12th biggest nation (based on surface area), Greenland averages the fewest people per square kilometer of its surface area.
Hawaii: This central Pacific island chain became the 50th U.S. state on Aug. 21, 1959. The entire crescent-shaped island chain spans some 2,400 kilometers (1,500 miles). Each of the state’s islands was created from one or more volcanoes that long ago sprang up from the ocean floor.
Jupiter: (in astronomy) The solar system’s largest planet, it has the shortest day length (10 hours). A gas giant, its low density indicates that this planet is composed of light elements, such as hydrogen and helium. This planet also releases more heat than it receives from the sun as gravity compresses its mass (and slowly shrinks the planet).
Mars: The fourth planet from the sun, just one planet out from Earth. Like Earth, it has seasons and moisture. But its diameter is only about half as big as Earth’s.
online: (n.) On the internet. (adj.) A term for what can be found or accessed on the internet.
paleontologist: A scientist who specializes in studying fossils, the remains of ancient organisms.
peer review: (in science) A process in which scientists in a field carefully read and critique the work of their peers before it is published in a scientific journal. Peer review helps to prevent sloppy science and bad mistakes from being published.
polar vortex: A semi-permanent weather system involving a large air mass in Earth’s upper atmosphere. It consists of an area of low atmospheric pressure. In the Northern Hemisphere, this tends to center near Canada's Baffin Island and over northeast Siberia. Winter strengthens the vortex, because that’s when the temperature difference between the poles and mid-latitudes is greatest.
projection: Some feature that extends out (or projects) from the body of a structure. (in cartography) The depiction of some three-dimensional area (on land or in space) as a two-dimensional map.
spherical: Adjective for something that is round (as a sphere).
Journal: J.R. Gott III, D.M. Goldberg and R.J. Vanderbei. Flat maps that improve on the Winkel Tripel, February 15, 2021. arXiv:2102.08176 [astro-ph.IM].
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