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 firstname.lastname@example.org.
(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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Join Radiolab's Latif Nasser at 1pm ET on Monday as he chats with Malcolm Gladwell live on Big Think.
University of Utah research finds that men are especially well suited for fisticuffs.
- With males having more upper-body mass than women, a study looks to find the reason.
- The study is based on the assumption that men have been fighters for so long that evolution has selected those best-equipped for the task.
- If men fought other men, winners would have survived and reproduced, losers not so much.
Built for mayhem<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yMjY2NDIyMy9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYxMzk4NTQ2OX0.my6nML12F3fEQu3H4G0BScdqgaMZkRQHxgyj-Cmjmzk/img.jpg?width=980" id="906fc" class="rm-shortcode" data-rm-shortcode-id="dd77af7a881631355ed8972437846394" data-rm-shortcode-name="rebelmouse-image" />
Image source: Ollyy/Shutterstock<p>The researchers are, of course, talking averages here, not stating a rule: There are plenty of accomplished female pugilists, as well as lots of males who have no idea how to throw a punch.</p><p>Even so, says co-author <a href="https://www.wofford.edu/academics/majors-and-programs/biology/faculty-and-staff" target="_blank">Jeremy Morris</a> says, "The general approach to understanding why sexual dimorphism evolves is to measure the actual differences in the muscles or the skeletons of males and females of a given species, and then look at the behaviors that might be driving those differences."</p><p>Carrier has been interested in the idea that millennia of male fighting has shaped certain structures in male bodies. Previous research has reinforced his hunch:</p> <ul> <li><a href="https://jeb.biologists.org/content/216/2/236" target="_blank">When a hand is formed into a fist, its structure is self-protective</a>.</li> <li><a href="https://unews.utah.edu/flat-footed-fighters/" target="_blank">Heels planted firmly on the ground augment upper-body power</a>.</li> <li><a href="https://www.ncbi.nlm.nih.gov/pubmed/24909544" target="_blank">A study examined facial bone structure as being especially well-suited for taking a punch</a>.</li> </ul> <p>(That last one is our favorite. Do you know the German word "<a href="https://www.urbandictionary.com/define.php?term=Backpfeifengesicht" target="_blank">backpfeifengesicht</a>?" It's an adjective describing "a face that badly needs a punching.")</p><p>"One of the predictions that comes out of those," asserts Carrier, "is if we are specialized for punching, you might expect males to be particularly strong in the muscles that are associated with throwing a punch."</p>
Testing the theory<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yMjY2NDIzMy9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYwNzMxMTE2MH0.UXJICMy57UPYUWskhK98alctOrPidJL9yxMkz3HDQrM/img.jpg?width=980" id="98718" class="rm-shortcode" data-rm-shortcode-id="b12287684ac3e740b70392e6433a6b8f" data-rm-shortcode-name="rebelmouse-image" />
Image source: Ollyy/Shutterstock<p>The researchers measured the punching — and spear-throwing — force of 20 men and 19 women. The assumption was that early humans were punchers <em>and</em> spear-throwers.</p><p>Prior to testing, each participant had filled out an activity questionnaire so that "we weren't getting couch potatoes, we were getting people that were very fit and active," says Morris.</p><p>For punching, participants operated a hand crank that required movement similar to throwing a haymaker. The purpose of the hand crank was to spare participants any damage that might be inflicted on their fists by throwing actual punches. Subjects were also measured pulling a line forward over their heads to assess their strength at throwing a spear.</p><p>Even though all of the participants, male and female, were routinely fit, the average power of males was assessed as being 162% greater than females. There were no gender differences in throwing strength recorded. Other untested, though presumably likely, hand-to-hand combat activities come to mind including tackling, clubbing, running, kicking, scratching, and biting.</p><p>Carrier's takeaway: "This is a dramatic example of sexual dimorphism that's consistent with males becoming more specialized for fighting, and males fighting in a particular way, which is throwing punches."</p>
Boys will be boys<p>It, er, strikes us as odd that, even in science fiction — hi-tech weaponry notwithstanding — the hero <em>is</em> going to wind up duking it out with some bad guy, or alien, in the climactic battle. What is it about men punching, anyway? Are they more sexually attractive? The study suggests so:</p><p style="margin-left: 20px;"><em>The results of this study add to a set of recently identified characters indicating that sexual selection on male aggressive performance has played a role in the evolution of the human musculoskeletal system and the evolution of sexual dimorphism in hominins.</em></p><p>It's tough to contribute to the gene pool after being killed in battle.</p><p>Also, while the authors aren't <em>quite</em> saying that males' historical fighting role is mandated by biology and not by social expectations, neither are they quite <em>not</em> saying it.</p><p>As Carrier explain to <a href="https://attheu.utah.edu/facultystaff/carrier-punch/" target="_blank">theU</a>: "Human nature is also characterized by avoiding violence and finding ways to be cooperative and work together, to have empathy, to care for each other, right? There are two sides to who we are as a species. If our goal is to minimize all forms of violence in the future, then understanding our tendencies and what our nature really is, is going to help."</p>
The Labour Economics study suggests two potential reasons for the increase: corruption and increased capacity.
Cool hand rebuke<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDQyMTIyNy9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTY0NjY1NTYyOH0.0MCPKN3If94mYCNf3mMNrnTvJXjXN_bKLhgk9203EXk/img.jpg?width=917&coordinates=0%2C0%2C0%2C0&height=453" id="1627b" class="rm-shortcode" data-rm-shortcode-id="6d76421ba1ea0de4b09956b97e80c384" data-rm-shortcode-name="rebelmouse-image" />
A chart showing prison population rates (per 100,000 people) in 2018. The United States has the highest rate of incarceration in the world.
Who profits with for-profit prisons?<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="97ac37e6c7f6f22ec130ea2d56871701"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/dB78NV2WpWc?rel=0" width="100%" height="auto" frameborder="0" scrolling="no" style="position:absolute;top:0;left:0;width:100%;height:100%;"></iframe></span><p>The Labour Economics study suggests that privately-run prisons do convicts a few favors at the moment of sentencing. However, proponents of private prisons often point to other benefits when making their case. Specifically, they argue that private prisons reduce operating costs, stimulate innovation in the correctional system, and reduce recidivism—the rate at which released prisoners are rearrested and return to prison.</p><p>In regard to recidivism, the research is mixed. <a href="https://journals.sagepub.com/doi/abs/10.1177/0011128799045001002" target="_blank">One study</a> compared roughly 400 former prisoners from Florida, 200 released from private prisons and 200 from state-run facilities. It found the private-prison cohort maintained lower rates of recidivism. However, <a href="https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1745-9133.2005.00006.x" target="_blank" rel="noopener noreferrer">another Florida study</a> found no significant rate differences. And two other studies—one from <a href="https://journals.sagepub.com/doi/abs/10.1177/0011128799045001002" target="_blank" rel="noopener noreferrer">Oklahoma</a> and another out of <a href="https://journals.sagepub.com/doi/abs/10.1177/0734016813478823" target="_blank" rel="noopener noreferrer">Minnesota</a>, both comparing much larger cohorts than the first Florida study— found that prisoners leaving private prisons had a greater risk of recidivism.</p><p>The research is also inconclusive regarding cost savings. <a href="https://www.hamiltonproject.org/assets/files/economics_of_private_prisons.pdf" target="_blank" rel="noopener noreferrer">A Hamilton Project analysis</a> noted that such comparisons are difficult because private prisons, like all private companies, are not required to release operational details. In comparing what studies were available, the authors estimate the costs to be comparable and that "in practice the primary mechanism for cost saving in private prisons is lower salaries for correctional officers"—about $7,000 less than their public peers. They add that competition-driven innovation is lacking as the three largest firms control nearly the entire market.</p><p>"We aren't saying private prisons are bad," Galinato said. "But states need to be careful with them. If your state has previous and regular issues with corruption, I wouldn't be surprised to see laws being more skewed to give longer sentences, for example. If the goal is to reduce the number of incarcerated individuals, increasing the number of private prisons may not be the way to go."</p>
What exactly does "questions are the new answers" mean?
- Traditionally, intelligence has been viewed as having all the answers. When it comes to being innovative and forward-thinking, it turns out that being able to ask the right questions is an equally valuable skill.
- The difference between the right and wrong questions is not simply in the level of difficulty. In this video, geobiologist Hope Jahren, journalist Warren Berger, experimental philosopher Jonathon Keats, and investor Tim Ferriss discuss the power of creativity and the merit in asking naive and even "dumb" questions.
- "Very often the dumb question that is sitting right there that no one seems to be asking is the smartest question you can ask," Ferriss says, adding that "not only is it the smartest, most incisive, but if you want to ask it and you're reasonably smart, I guarantee you there are other people who want to ask it but are just embarrassed to do so."