{"id":266,"date":"2021-10-26T01:32:12","date_gmt":"2021-10-26T01:32:12","guid":{"rendered":"http:\/\/princetonillinois.com\/?p=266"},"modified":"2021-10-26T01:32:12","modified_gmt":"2021-10-26T01:32:12","slug":"princeton-astrophysicists-re-imagine-world-map-designing-a-less-distorted-radically-different-way-to-see-the-world-princeton-university","status":"publish","type":"post","link":"https:\/\/princetonillinois.com\/?p=266","title":{"rendered":"Princeton astrophysicists re-imagine world map, designing a less distorted, 'radically different' way to see the world – Princeton University"},"content":{"rendered":"

Princeton professors J. Richard Gott and Robert Vanderbei worked with Drexel professor David Goldberg to create a revolutionary new map: a two-sided disk that can slip inside a textbook or be stacked neatly for storage. It provides more accurate distances than any existing flat map, while keeping visual distortions at a minimum.
For centuries, mapmakers have agonized over how to accurately display our round planet on anything other than a globe. <\/span><\/span><\/span><\/span>
Now, a fundamental re-imagining of how maps can work has resulted in the most accurate flat map ever made, from a trio of map experts: <\/span>J. Richard Gott<\/span><\/a>, an emeritus professor of <\/span>astrophysics<\/span><\/a> at Princeton and creator of a <\/span>logarithmic map of the universe<\/span><\/a> once described as \u201carguably the most mind-bending map to date\u201d; <\/span>Robert Vanderbei<\/span><\/a>, a professor of <\/span>operations research and financial engineering<\/span><\/a> who created the \u201c<\/span>Purple America<\/span><\/a>\u201d map of election results; and David Goldberg, a professor of physics at Drexel University.<\/span><\/span><\/span><\/span>
Their new map is two-sided and round, like a\u00a0phonograph record or vinyl LP. Like many radical developments, it seems obvious in hindsight. Why not<\/em> have a two-sided map that shows both sides of the globe? It breaks away from the limits of two dimensions without losing any of the logistical convenience \u2014 storage and manufacture \u2014 of a flat map.<\/span><\/span><\/span><\/span>
\u201cThis is a map you can hold in your hand,\u201d Gott said.<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
In 2007, Goldberg and Gott invented <\/span>a system to score existing maps<\/span><\/a>, quantifying the six types of distortions that flat maps can introduce: local shapes, areas, distances, flexion (bending), skewness (lopsidedness)\u00a0and boundary cuts (continuity gaps). The lower the score, the better: a globe would have a score of 0.0. <\/span><\/span><\/span><\/span>
\u201cOne can\u2019t make everything perfect,\u201d said Gott, who is also a 1973 graduate alumnus of Princeton. \u201cA map that is good at one thing may not be good at depicting other things.\u201d The Mercator projection, popular on classroom walls and used as the basis for Google maps, is excellent at depicting local shapes, but it distorts surface areas so badly near the North and South Poles that polar regions are usually simply chopped off. <\/span><\/span><\/span><\/span>
In the Mercator projection, the polar regions are completely distorted \u2014 Antarctica looks bigger than all other continents combined \u2014 and distances are misleading: Japan and Hawaii look very far apart. Under\u00a0the system designed by\u00a0Goldberg and Gott to quantify map errors, where lower numbers represent less distortion, the Mercator projection receives a score of 8.296.
Using their metrics, the best previously known flat map projection was the Winkel Tripel,<\/span> with a Goldberg-Gott score of 4.563. But that still had the \u201cboundary cut\u201d problem of splitting the Pacific Ocean and creating the illusion of great distance between Asia and Hawaii.<\/span><\/span><\/span><\/span>
The Winkel Tripel projection, chosen by the National Geographic for its world maps, represents the poles more accurately than the Mercator, but it still distorts Antarctica badly and creates the illusion that Japan is hugely to the east of California, instead of its nearest neighbor to the west. Goldberg-Gott score: 4.563
Clearly, a completely new approach was needed. Gott drew a comparison to Olympic high jumpers: In 1968, Dick Fosbury shocked sports fans by arching his back and jumping over the bar backwards. He set a new record and won a gold medal, and high jumpers have jumped backwards ever since.<\/span><\/span><\/span><\/span>
\u201cWe\u2019re like Mr. Fosbury,\u201d Gott said. \u201cWe\u2019re doing this to break a record, to make the flat map with the least error possible. So, like him, we\u2019re surprising folks. We\u2019re proposing a radically different kind of map, and we beat Winkel Tripel on each and every one of the six errors.\u201d<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
The inspiration came from Gott\u2019s work on polyhedra \u2014<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0solid\u00a0figures with\u00a0many faces.
Polyhedral maps are nothing new \u2014 in 1943, <\/span><\/span>Buckminster Fuller broke the world into regular shapes, and provided instructions for how to fold it up and assemble it as a polyhedral globe \u2014 but while he could protect the shapes of continents, Fuller shredded the oceans and increased many distances, such as between Australia and Antarctica.<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
Buckminster Fuller popularized the \u201cDymaxion\u201d polyhedral projection, based on an unfolded icosahedron. Antarctica is \u201cround, as it properly should be,\u201d said Gott, but this projection \u201cshatters\u201d the oceans. Goldberg-Gott score: greater than 15
In a <\/span><\/span>recent paper<\/span><\/span><\/a>, Gott began considering \u201cenvelope polyhedra,\u201d with regular shapes glued together back-to-back, which led to the breakthrough idea for the double-sided map.<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
It can be displayed with the Eastern and Western Hemispheres on the two sides, or in Gott\u2019s preferred orientation, the Northern and Southern Hemispheres, which conveniently allows the equator to run around the edge. Either way, this is a map with no boundary cuts. To measure distances from one side to the other, you can use string or measuring tape reaching from one side of the disk to the other, he suggested.<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\u201cIf you\u2019re an ant, you can crawl from one side of this \u2018phonograph record\u2019 to the other,\u201d Gott said. \u201cWe have continuity over the equator. Africa\u00a0and South America are draped over the edge, like a sheet over a clothesline, but they\u2019re continuous.\u201d<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
This double-sided map has smaller distance errors than any single-sided flat map \u2014 the previous record-holder being a 2007 map by <\/span><\/span>Gott with Charles Mugnolo<\/span><\/span><\/a>, a 2005 Princeton alumnus. In fact, this map is remarkable in having an upper boundary on distance errors: It is impossible for distances to be off by more than \u00b1 <\/span><\/span>22.2%. By comparison, in the Mercator and Winkel Tripel projections, as well as others, distance errors become enormous approaching the poles and essentially infinite from the left to the right margins (which are far apart on the map but directly adjacent on the globe). In addition, a<\/span><\/span><\/span><\/span><\/span><\/span><\/span>reas at the edge are only 1.57 times larger than at the center.
Gott, Goldberg and Vanderbei’s revolutionary, double-sided disk map minimizes all six types of map distortions. They\u00a0used an equidistant azimuthal projection: a compromise projection, like the Winkel Tripel, with small errors in both local shapes and areas, instead of optimizing one at the expense of the other. Antarctica and Australia are more accurately represented than in most other maps, and distances across oceans or across poles are both accurate and easy to measure, unlike one-sided flat maps. Goldberg-Gott error score: 0.881
The map can be printed front-and-back on a single magazine page, ready for the reader to cut out. The three cartographers imagine printing their maps on cardboard or plastic and then stacking them like records, to be stored together in a box or slipped inside the covers of textbooks. <\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\u201cA thin box could hold flat, double-sided maps of all the major planets and moons in the solar system,\u201d Gott said, \u201cor a stack of Earth maps giving physical data, political boundaries, population density, climate, languages, explorers\u2019 voyages, empires at different historical periods or continents at different geological epochs.\u201d <\/span><\/span><\/span><\/span><\/span><\/span><\/span>
To the best of their knowledge, no one has ever made double-sided maps for accuracy like this before. A <\/span><\/span>1993 compendium<\/span><\/span><\/a> of nearly 200 map projections dating back 2,000 years did not include any, nor did they find any similar patents.<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\u201cOur map is actually more like the globe than other flat maps,\u201d Gott said. \u201cTo see all of the globe, you have to rotate it; to see all of our new map, you simply have to flip it over.\u201d<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
“Flat maps that improve on the Winkel Tripel<\/a>,” by J. Richard Gott III, David M. Goldberg and\u00a0Robert J. Vanderbei, was published on Arxiv on Feb. 15. You can see\u00a0and interact with their double-disk maps of Earth, Mars, Jupiter, the sun, and other heavenly bodies at this interactive tool<\/a> on Vanderbei’s website.<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/em><\/p>\n

source<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Princeton professors J. Richard Gott and Robert Vanderbei worked with Drexel professor David Goldberg to create a revolutionary new map: a two-sided disk that can slip inside a textbook or be stacked neatly for storage. It provides more accurate distances than any existing flat map, while keeping visual distortions at a minimum.For centuries, mapmakers have agonized over how to accurately<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-266","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t