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Colorado is a rectangle? Think again.
The Centennial State has 697 sides‚ not four.
- Colorado looks like a rectangle. It isn't.
- The Centennial State has not four, but 697 sides. That makes it a hexahectaenneacontakaiheptagon.
- Does that make Wyoming the only real rectangular state? Well, about that…
America loves its straight-line borders. The only U.S. state without one is Hawaii – for obvious reasons (1).
West of the Mississippi, states are bigger, emptier and boxier than back East. From a distance, all seem to be made up of straight lines.
Only when you zoom in do you see their squiggly bits: the northeast corner of Kansas, for instance. Or Montana's western border with Idaho that looks like a human face. Or Oklahoma's southern border with Texas, meandering as it follows the Red River.
New Mexico comes tantalisingly close to having only straight-line borders. There's that short stretch north of El Paso that would have been just 15 miles (24 km) long if it was straight instead of wavy.
No, there are only three states whose borders are entirely made up of straight lines: Utah, which would have been a rectangle if Wyoming hadn't bitten a chunk out of its northeastern corner; Wyoming itself; plus Colorado.
Red: states with only straight-line borders. Yellow: states with some straight-line borders. Green: states without straight-line borders.Image: mapchart.net
Except that they aren't. For two distinct reasons: because the earth is round, and because those 19th-century surveyors laying out state borders made mistakes.
Congress defined the borders of Colorado as a geospherical rectangle, stretching from 37°N to 41°N latitude, and from 25°W to 32°W longitude (2). While lines of latitude run in parallel circles that don't meet, lines of longitude converge at the poles.
Which means that Colorado's longitudinal borders are slightly further apart in the south. So if you'd look closely enough, the state resembles an isosceles trapezoid (3) rather than a rectangle. Consequently, the state's northern borderline is about 22 miles (35 km) shorter than its southern one. The same goes, mutatis mutandis, for Wyoming.
That's not where the story ends. There's boundary delimitation: the theoretical description of a border, as described above. But what's more relevant is boundary demarcation: surveying and marking out the border on the ground. Colorado entered the Union in 1876.
Only in 1879 did the first boundary survey team get around to translating Congress's abstract into actual boundary markers. The official border would not be the delimited one, but the demarcated one. Unfortunately, 19th-century surveyors lacked satellites and other high-precision measurement tools.
Let's not be too harsh: considering the size of the task and the limitation of their tools — magnetic compasses and metal chains — they did an incredible job. They had to stake straight lines irrespective of terrain, often through inhospitable land.
But yes, errors were made — and were in fact quite habitual. Take for example the 49th parallel, which for more than 1,200 miles forms the international border between the U.S. and Canada. Rather than being a straight line, it zigzags between the 912 boundary monuments established by successive teams of surveyors (the last ones in 1872–4). The markers deviate by as much as 575 feet north and 784 feet south of the actual parallel line.
Colorado, not as rectangular as you think. Image: FascinatingMaps.com
The same kind of thing happened when the first surveying teams went out to demarcate the Colorado border. This map magnifies four of the most egregious surveying inaccuracies, where the difference between the boundaries delineated by Congress and the border demarcated by the surveyors is greatest.
Four Corners (and four more)
Four Corners. Clockwise from top left: Utah, Colorado, New Mexico, Arizona. Image source: Getty Creative
Located in a dusty, desolate corner of the desert, the Four Corners monument seems very far from the middle of anything. Yet this is the meeting point of four states: Utah, Colorado, New Mexico and Arizona. It is the only quadripoint in the United States (4). The monument's exact location is at 36°59'56″N, 109°02'43″W.
However, it's not where Congress had decreed the four states to meet. That point is about 560 feet (170 m) northwest of the quadripoint's current location, at 37°N, 109°02'48″W. Did you drive all the way through the desert to miss the actual point by a few hundred feet?
No, you didn't: in 1925, the Supreme Court ruled that the borders as surveyed were the correct ones. But perhaps the original quadripoint deserves a small marker of its own, if only to provide the site with an extra attraction. Or why not go for three? Some sources say the original point deviates by 1,807 feet (551 m).
The La Sal/Paradox deviation
Paradox Valley in Colorado, near the (crooked) border with Utah. Image source: Wikimedia Commons/Tony Webster, CC BY 2.0
In 1879, a survey party marched north from Four Corners, placing markers at every mile. The surveyors eventually reached the Wyoming border, but not where they thought they'd end up. Later surveys, in 1885 and 1893, found out where the original surveyors had gone wrong, but by that time the border as surveyed had become the official one. Changing it would have required both Colorado and Utah to agree on a solution, and Congress to approve it.
The biggest error occurs just south of the road connecting La Sal, Utah to Paradox, Colorado. Across an eight-mile stretch, the surveyors strayed westward before regaining true north. The resulting deviation is 3860 feet (1.18 km).
Things go south after Edith
Border deviation near Edith, CO. Image source: Google Maps/Ruland Kolen
West to east, Colorado's border with New Mexico starts out fairly straight. However, just east of Edith, the border swerves southeast for about 3,400 feet (1 km) before resuming its course due east, now 2,820 feet (860 m) further south than before.
Why? It seems that for once, the surveyors have given in to the dictates of topography: the deviation follows a small valley oriented northwest-southeast.
Panhandling into Oklahoma
The Colorado border swerves south, eating into the Oklahoma Panhandle. Image source: FascinatingMaps.com
Almost at the end of their surveying mission, it seems the party lost the plot again. In the last 53 miles (85 km) before the border turns north, the stretch where Colorado rubs against Oklahoma, the line again swerves to the south, by as much as 1,770 feet (540 m).
Don't blame the terrain: appropriately for a place so close to the Oklahoma Panhandle, it's as flat as a pancake. Perhaps the surveyors were confused by the very featurelessness of the place.
Colorado is a 697-sider
Each dot is a twist in Colorado's supposedly straight borders. Image source: FascinatingMaps.com
These are just four of the biggest, most easily spotted surveying errors. In total, Colorado's borders have hundreds twists and turns — most much smaller than the Big Four. Here they are: every dot on is a border deviation, as indicated on the OpenStreetMap of Colorado.
Accordingly, the state has not just four sides, but a total of 697 sides. So if Colorado is not a rectangle, what is it? Well, not a pentagon, (Greek for 5-sider), hexagon (6-sider) or a heptagon (7-sider), but a — hold on to something — hexahectaenneacontakaiheptagon (697-sider).
Don't get your hopes up, Wyoming
Wyoming: just as fallible as Colorado — but more willing to admit its mistakes. Image source: FascinatingMaps.com
With Colorado thoroughly disqualified to as one of America's two truly rectangular states, does that leave Wyoming holding the crown all on its own? Nope. Turns out the surveyors who plotted the Equality State's outline were just as fallible as the Colorado set.
This map shows a few larger ones of the many deviations in on all four sides of Wyoming. Interestingly, the deviations shown come in pairs, whereby the second ones seem to correct the deviation of the first ones.
So, while Wyoming is just as imperfect as Colorado, it does seem that at least it is better at admitting (and correcting) its mistakes than its southern neighbor.
Strange Maps #945
Got a strange map? Let me know at email@example.com.
(1) If you're not into the whole obviousness thing: Hawaii is a bunch of islands, which therefore don't have a land border — neither with other U.S. states or third countries.(2) That's west of the Washington Meridian — the third one, to be exact. Over time, four Washington meridians were defined as prime meridians for the U.S. They passed through the Capitol, the White House, the Old Naval Observatory and the New Naval Observatory. Defined by Congress in 1850 at 77°2'48.0"W of Greenwich, the third Washington meridian was used as the base line for a number of western state borders, including:
- at 17°W, a stretch of border with Texas in the west, and Arkansas and Louisiana in the east. This line passes through the two-state conurbation of Texarkana;
- at 25°W, the Colorado-Kansas border (and part of the Nebraska-Colorado border);
- at 26°W, a stretch of the border between Texas and New Mexico (the Oklahoma-New Mexico border, just to the north, is set back two miles to the east);
- at 27°W, the 555-mile stretch from Colorado north to the Canadian border, separating Montana and Wyoming in the west from the Dakotas and Nebraska in the east;
- at 32°W, the straight line from Wyoming to Mexico, separating Utah and Arizona in the west from Colorado and New Mexico in the east (also running through Four Corners, where these four states meet).
(3) An isosceles trapezoid is a four-sided shape with two parallel sides and two non-parallel but equal sides.
(4) The only state-level quadripoint. There are, in fact, dozens of quadripoints between U.S. counties, hundreds between U.S. municipalities, and indeed thousands (of usually bilateral ones) on the edges of checkerboard-patterned Indian reservations and other federally reserved territories.
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Northwell Health is using insights from website traffic to forecast COVID-19 hospitalizations two weeks in the future.
- The machine-learning algorithm works by analyzing the online behavior of visitors to the Northwell Health website and comparing that data to future COVID-19 hospitalizations.
- The tool, which uses anonymized data, has so far predicted hospitalizations with an accuracy rate of 80 percent.
- Machine-learning tools are helping health-care professionals worldwide better constrain and treat COVID-19.
The value of forecasting<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNTA0Njk2OC9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYyMzM2NDQzOH0.rid9regiDaKczCCKBsu7wrHkNQ64Vz_XcOEZIzAhzgM/img.jpg?width=980" id="2bb93" class="rm-shortcode" data-rm-shortcode-id="31345afbdf2bd408fd3e9f31520c445a" data-rm-shortcode-name="rebelmouse-image" data-width="1546" data-height="1056" />
Northwell emergency departments use the dashboard to monitor in real time.
Credit: Northwell Health<p>One unique benefit of forecasting COVID-19 hospitalizations is that it allows health systems to better prepare, manage and allocate resources. For example, if the tool forecasted a surge in COVID-19 hospitalizations in two weeks, Northwell Health could begin:</p><ul><li>Making space for an influx of patients</li><li>Moving personal protective equipment to where it's most needed</li><li>Strategically allocating staff during the predicted surge</li><li>Increasing the number of tests offered to asymptomatic patients</li></ul><p>The health-care field is increasingly using machine learning. It's already helping doctors develop <a href="https://care.diabetesjournals.org/content/early/2020/06/09/dc19-1870" target="_blank">personalized care plans for diabetes patients</a>, improving cancer screening techniques, and enabling mental health professionals to better predict which patients are at <a href="https://healthitanalytics.com/news/ehr-data-fuels-accurate-predictive-analytics-for-suicide-risk" target="_blank" rel="noopener noreferrer">elevated risk of suicide</a>, to name a few applications.</p><p>Health systems around the world have already begun exploring how <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7315944/" target="_blank" rel="noopener noreferrer">machine learning can help battle the pandemic</a>, including better COVID-19 screening, diagnosis, contact tracing, and drug and vaccine development.</p><p>Cruzen said these kinds of tools represent a shift in how health systems can tackle a wide variety of problems.</p><p>"Health care has always used the past to predict the future, but not in this mathematical way," Cruzen said. "I think [Northwell Health's new predictive tool] really is a great first example of how we should be attacking a lot of things as we go forward."</p>
Making machine-learning tools openly accessible<p>Northwell Health has made its predictive tool <a href="https://github.com/northwell-health/covid-web-data-predictor" target="_blank">available for free</a> to any health system that wishes to utilize it.</p><p>"COVID is everybody's problem, and I think developing tools that can be used to help others is sort of why people go into health care," Dr. Cruzen said. "It was really consistent with our mission."</p><p>Open collaboration is something the world's governments and health systems should be striving for during the pandemic, said Michael Dowling, Northwell Health's president and CEO.</p><p>"Whenever you develop anything and somebody else gets it, they improve it and they continue to make it better," Dowling said. "As a country, we lack data. I believe very, very strongly that we should have been and should be now working with other countries, including China, including the European Union, including England and others to figure out how to develop a health surveillance system so you can anticipate way in advance when these things are going to occur."</p><p>In all, Northwell Health has treated more than 112,000 COVID patients. During the pandemic, Dowling said he's seen an outpouring of goodwill, collaboration, and sacrifice from the community and the tens of thousands of staff who work across Northwell.</p><p>"COVID has changed our perspective on everything—and not just those of us in health care, because it has disrupted everybody's life," Dowling said. "It has demonstrated the value of community, how we help one another."</p>
A leading British space scientist thinks there is life under the ice sheets of Europa.
- A British scientist named Professor Monica Grady recently came out in support of extraterrestrial life on Europa.
- Europa, the sixth largest moon in the solar system, may have favorable conditions for life under its miles of ice.
- The moon is one of Jupiter's 79.
Neil deGrasse Tyson wants to go ice fishing on Europa<div class="rm-shortcode" data-media_id="GLGsRX7e" data-player_id="FvQKszTI" data-rm-shortcode-id="f4790eb8f0515e036b24c4195299df28"> <div id="botr_GLGsRX7e_FvQKszTI_div" class="jwplayer-media" data-jwplayer-video-src="https://content.jwplatform.com/players/GLGsRX7e-FvQKszTI.js"> <img src="https://cdn.jwplayer.com/thumbs/GLGsRX7e-1920.jpg" class="jwplayer-media-preview" /> </div> <script src="https://content.jwplatform.com/players/GLGsRX7e-FvQKszTI.js"></script> </div>
Water Vapor Above Europa’s Surface Deteced for First Time<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="9c4abc8473e1b89170cc8941beeb1f2d"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/WQ-E1lnSOzc?rel=0" width="100%" height="auto" frameborder="0" scrolling="no" style="position:absolute;top:0;left:0;width:100%;height:100%;"></iframe></span>
Can computers do calculations in multiple universes? Scientists are working on it. Step into the world of quantum computing.
- While today's computers—referred to as classical computers—continue to become more and more powerful, there is a ceiling to their advancement due to the physical limits of the materials used to make them. Quantum computing allows physicists and researchers to exponentially increase computation power, harnessing potential parallel realities to do so.
- Quantum computer chips are astoundingly small, about the size of a fingernail. Scientists have to not only build the computer itself but also the ultra-protected environment in which they operate. Total isolation is required to eliminate vibrations and other external influences on synchronized atoms; if the atoms become 'decoherent' the quantum computer cannot function.
- "You need to create a very quiet, clean, cold environment for these chips to work in," says quantum computing expert Vern Brownell. The coldest temperature possible in physics is -273.15 degrees C. The rooms required for quantum computing are -273.14 degrees C, which is 150 times colder than outer space. It is complex and mind-boggling work, but the potential for computation that harnesses the power of parallel universes is worth the chase.
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