In Defense of “A Defense”

Last month, in Mitch Cieminski’s article, “The Mercator Needs no Defense”, he made several compelling arguments advocating for the globe in favor of maps, and the Mercator Projection in particular. While the globe has its distinct advantages, so too do maps. We could argue for days about when maps are better than globes and which projection is best (the answer is Lee), but I fear Mr. Cieminski as well as many other readers may have taken my argument too far. To be clear, my article was merely a thought experiment, not to be taken seriously. After all, the entire notion of a map projection is nonsensical. To “project” the Earth onto a plane implies the Earth is not a plane to begin with. Round Earth Theory is an unfortunately widespread misconception that seems to have, in spite of obvious evidence all around us and empirical measurements of the Earth’s lack of curvature, made its way into Olin. I assumed while writing my little thought experiment that all readers would be aware of the true nature of the Earth, but I see now that I will need to educate the Olin community.
When first confronted with the planar Earth model, it is easy for one to brush it off as conspiracy theory nonsense. This is an acceptable response. In your defense, the government has been feeding you lies all your life in an attempt to make you easier to control. Therefore, I ask that you open your mind and temporarily cast aside all of the “facts” that you think you know, and instead of blindly relying on science for all the answers, actually think critically about the world and compose your model of the universe out of empirical evidence. Chances are, your teachers in elementary school were all under the same illusion as you are, so nothing they told you can be taken for granted. Photographs are easily falsified, so pictures of spherical earths and ship masts are not acceptable evidence, either. The only way to truly learn about the world is to trust your own twenty-one senses.
Now that that is out of the way, let me tell you what the Earth really looks like. The world is a large disc about 40,000 kilometers across with the North Pole in the center and the ice wall known as Antarctica surrounding it on all sides. The true map corresponds to what round-earthers call the “Polar projection” and can be found on the flag of the UN. What lies beyond the coast of Antarctica is a matter of great interest to those who know the truth. The sun and moon are both 50 km across and 5,000 km above the Earth’s surface. The sun circles the North Pole, sweeping its spotlight-like light across the time-zones. The moon follows a similar path, though at a slightly lower altitude, allowing for solar eclipses. A similarly sized third celestial body known as “the dark object” also orbits at a lower altitude, but is only visible when it moves in front of the moon during lunar eclipses (if that sounds ridiculous to you, remember that according to NASA, most of the mass in the galaxy is invisible). The entire system accelerates upward at 9.8 meters per second squared, creating the phenomenon most people know as “gravity”.
A common misconception regarding the spotlight sun model is that in order for the sun to set, it must sink beneath the Earth, which would plunge the entire world into darkness simultaneously. This is obviously not the case, as can be proven by anyone who has ever Skyped with someone in a different time zone. In actuality, the sunset is an illusion. As the sun moves horizontally farther away from an observer, it appears to move closer to the horizon because of perspective. It also appears to stay the same size, though, because of the way bright lights refract through large quantities of air. This phenomenon is why you can see the streetlights on the other side of a city even though when turned off they are far too distant to see. When the edge of the sun’s spotlight approaches the observer, the sun is so far away that it appears to be touching the horizon. At this point, high amounts of glare and refraction cause the sun to look far larger and less circular than it should, a fact that even round-earthers will admit (this is related to why one can look directly at a sunset without damaging one’s eyes). Thus, when the sun turns away and finally disappears, it looks as though it has descended beneath the horizon.
At this point, I can practically feel your skepticism. “The Earth can’t be flat,” you think. “For one thing, if the Earth were flat, we wouldn’t have a horizon!” This notion is complete trash. The existence of a horizon does not depend on a round Earth, as anyone who has played a superflat map in Minecraft can tell you. “If the Earth were planar, though,” people say, “you would be able to see from Boston to London. Instead, London is hidden from us by the Earth’s curvature.” This is also completely false. If you have ever stood on the southeastern tip of O’ahu and gazed over the Ka’iwi channel, chances are you will have seen naught but water. If it is a particularly clear day, you may have seen Haleakala on Maui. If it is exceptionally clear and the air highly transparent, you may have even glimpsed the silhouette of Mauna Kea. How far down the archipelago you can see is purely a function of clarity. Distant objects are hidden from us only by the omnipresent haze of slightly opaque air, which is why the clearer the day, the farther you can see. If the Earth truly curved, you would not be able to see Mauna Kea at all, it being a measly 4.2 kilometers above sea level and a whopping 280 kilometers away.
“But why, then, does increasing one’s altitude make more things visible?” you ask. This is common sense. Spherical or planar, the Earth’s surface is not perfectly smooth. In any direction from where you read this, you almost certainly see buildings, hills, mountains, and – if you are somewhere besides Olin – trees. Moving higher up enables an observer to see over these things. On a round Earth, in order to observe the horizon actually moving away, one would have to stand in a high place surrounded by bare flatland with some kind of metric to gauge the “distance” of the horizon (the ocean won’t work because there is no good way to tell how much of it one can see). If such a place existed and were easily accessible, you could test it for yourself and see that as you go higher, you don’t actually see more, but less.
There exist many other common “proofs” that the Earth is round. All are easily explained away by the actual model of the Earth. The fact that vertical sticks cast different shadows on different parts of the Earth is just as justifiable for a globe Earth and a distant sun as it is for a plane Earth and a nearby sun. The fact that other planets are round means little given that the Earth is the center of the Universe and is thus inherently special. The perceived curvature of the Earth one sees when in a plane is an illusion caused by the thick, pressurized airplane window. If that weren’t the case and the Earth’s radius were what the Government tells us it is, planes wouldn’t even fly high enough to see the curvature of the Earth. Similarly, the visual phenomenon of ships appearing mast-first over the horizon is an illusion; any ship at that distance appears small enough that it is easy to trick oneself into seeing what one expects to see. Besides, when was the last time any of you saw a ship with a mast (indefinitely docked historical ships don’t count)?
With all this in mind, the notion that the Earth is not round should be just as plausible as what you were led to believe. Given that, on top of all of this, the Earth _looks_ flat, the burden of proof should really rest on the round-earthers, not us. However, since I know you are all still skeptical, here is some evidence: the Bedford Level Experiment. In 1838, Samuel Birley Rowbotham observed a boat row 10 kilometers down a straight stretch of the Old Bedford River. If the Earth were round, by the time it got 10 kilometers away, the 1-meter mast should have been a full 3 meters below his line of sight. Instead, to his surprise, its height did not appear to change at all as it moved away from him, remaining perfectly visible above the water for the entire 10-kilometer stretch, proving that the Earth is not, in fact, curved, but flat. The masses, of course, paid little heed to the discovery, as confirmation bias will tend to make one do, particularly when the evidence so thoroughly disproves the public’s most basic of understanding of the world. I assume that if you have read this far that you are critical enough to honestly process this information and come to the correct conclusion.
But why would someone do such a thing? If all this is true, then many people must be in on it and have good reason to keep it a secret. To start, whether the space industry is in on it is unknown at this point. In all likelihood, space travel is impossible, so when NASA created the pictures of the Earth for the Apollo program, they depicted it as they expected it to be – round. The fake pictures of a round Earth may simply be the result of the government lying to NASA along with the rest of the citizenry. Why would the Government lie to the citizenry, though? No one is sure, but the best explanation I have found is this: when one thinks they live on a tiny orb orbiting the sun along with seven other planets, hurtling through an unthinkably large galaxy in an unthinkably large universe, it makes one feel insignificant.
And people who feel insignificant are easier to control. Take a look around. The first mentions of a spherical Earth are from the third century. One of the galaxies allegedly in the local group is called “Triangulum”. The first digit of pi is 3. We have three branches of government! Wake up, sheeple. The Illuminati have been lying to you all your life about the nature of the Earth in an attempt to manipulate you. First they tell us the Earth is round. What’s next? Area 51 is a hoax? Lizard people are fake? Olin, it’s time to stand up, look around, and rise against our masters. Judgement day is near. Until then, remember to wear plenty of iron, and never use the same parking stall twice. Stay flat, comrades.

SERV Activity Update

SERV Auction: Justin Kunimune
The SERV Auction has kicked off with the Silent Auction opening this week. Be sure to look through the bids for things that interest you; all money raised will go to the charity chosen by the community. Also be sure to come to the Live Auction on Friday in the Dining Hall during lunch! Proceeds go to Unidos por Puerto Rico.

Big Brothers Big Sisters: Justin Kunimune
The program has started up for the semester, with a total of thirty matches. There have been three outings at Babson thus far, with plenty more scheduled for the rest of the semester.

Charles River Center: Emma Price
The Charles River Center is a non-profit organization based in Needham that works to improve the lives of people with developmental disabilities and help support their families. They have a variety of different programs for people of all ages, all with really fun activities like Zumba and yoga!

MSPCA (Massachusetts Society for the Prevention of Cruelty to Animals): Emma Price
MSCPA is a great organization that takes in animals all over the state, makes sure they’re healthy, and finds good homes for them. They take all variety of animals and have volunteer positions like cat adoption room monitor (that’s what I do), dog walker, small animal monitor, and a ton more!

Bikes Not Bombs: Maggie Jakus
Bikes Not Bombs is an organization that recycles old bicycles and sends bikes to economic development programs around the world as well as youth education programs in the nearby area. They have volunteer nights on Thursdays when volunteers prepare bikes for shipment. You also get to learn a lot about bikes!

SERV Activity Updates

Jimmy Fund Walk: Justin Kunimune
The Jimmy Fund Walk happened this month. Two students, one faculty, and two staff members turned out for the quarter-marathon walk, raising over $3,000 for cancer research from the Olin community and beyond.

Charles River Center: Emma Price
The Charles River Center is a non-profit organization based in Needham that works to improve the lives of people with developmental disabilities and help support their families. They have a variety of different programs for people of all ages, all with really fun activities, like zumba and yoga!

MSPCA (Massachusetts Society for the Prevention of Cruelty to Animals): Emma Price
MSCPA is a great organization that takes in animals all over the state, makes sure they’re healthy, and finds good homes for them. They take all variety of animals and have volunteer positions like cat adoption room monitor (that’s what I do), dog walker, small animal monitor, and a ton more!

Bikes Not Bombs: Maggie Jakus
Bikes Not Bombs is an organization that recycles old bicycles and sends bikes to economic development programs around the world as well as youth education programs in the nearby area. They have volunteer nights on Thursdays when volunteers prepare bikes for shipment. You also get to learn a lot about bikes!

A Defense of the Mercator Projection

If you’ve ever dabbled in cartography, geography, cultural imperialism, or that one scene from The West Wing, you’ve probably heard of the Mercator projection. If not, you’ve certainly seen it. The Mercator projection is the most common map projection for general-purpose world maps.

What is a map projection?

Map projection” describes any method of rendering the surface of the Earth onto a plane for easy viewing and storage. Because the sphere has curvature and the plane does not, any projection must have distortion in it, and because of the Hairy Ball Theorem, that distortion must always be extreme somewhere. Since it is mathematically impossible to create a perfect map of the Earth, there is much ongoing debate about which projections are best in which contexts. In such debates, to the Mercator projection is typically pointed as an overused, obsolete projection. It is, in a manner of speaking, the Comic Sans of map projections. Today, however, I seek to change the negative perception of Mercator by demonstrating that not only is it better than many of its commonly cited alternatives, but is actually the best map projection for many modern uses.

The Mercator Projection

The Mercator Projection

Firstly, why do people dislike Mercator? As previously stated, every projection must distort something. In Mercator, this is size. Landmasses near the poles appear much larger than those near the equator. The most commonly cited falsehood present in a Mercator map is the size of Greenland relative to that of Africa – Mercator shows them as roughly the same size, whereas Greenland is, in fact, 14 times smaller. This distortion is necessary to preserve what Mercator is designed to preserve: loxodromes.

A loxodrome, or rhumb line, is a line of constant bearing. While it is not the shortest path between two points on the Earth’s surface, it is the simplest one for sailors navigating with charts and compasses. In 1569, therefore, with this user group in mind, the Belgian Gerardus Mercator designed his projection such that loxodromes rendered as straight lines. Furthermore, the angles of loxodromes on the map matched their bearings on the Earth, such that sailors could calculate the bearing in which to sail with a Mercator projection and a protractor.

Over time, as European explorers, Mercator projections in hand, took over the world, Mercator became the de facto standard projection for all world maps, be they for decoration or education. As a result, many laymen began taking its distortion for truth, believing that regions near the equator were in fact as small as they appeared on the map. Because regions near the equator tended to be poorer than regions near the North Pole, this faulty mindset came to be criticized as cultural imperialism.

To be clear, the fact that Mercator’s Europe appears so large compared to Africa is a coincidence, not an intentional slight to non-Europeans. Cartographers across the world acknowledged the overuse of Mercator and, over the centuries, proposed many alternatives in an attempt to disperse the misconceptions caused by it. None were successful in overcoming Mercator’s tight grip on society.

In 1973, however, one Arno Peters claimed to have the solution, a revolutionary new projection that perfectly preserved the sizes of countries.  This map, according to Peters, was the only “area-correct” map, with “absolute angle conformality,” “no extreme distortions of form”, and “total… distance-factual[ity]”.*

The Gall-Peter's Projection

The Gall-Peter’s Projection

Cartographers were unimpressed. Some might even say they were Galled. Peter’s projection, a simple cylindrical equal-area projection, was by no means original. The exact projection had already been described in 1855 by James Gall, and it differed only in aspect ratio from the also preexisting Tobler World in a Square (1986), Balthasart (1935), Trystan Edwards (1953), Smyth-Craster (1870), Behrmann (1910), and Lambert cylindrical (1772) projections (all pictured at the end of the article).

Whether Peters knew about the existence of any of these maps is a matter of debate, but there is no uncertainty that most of the things he claimed about his “invention” were completely false.

The only area-correct map? There are dozens of named equal-area projections, most of which, such as Tobler’s elliptical projection (pictured at the end of the article), are more accurate than Gall-Peters. Absolute angle conformality? Gall-Peters is by no means conformal; that is a specific term reserved for the elite likes of Mercator, Stereographic, Pierce Quincuncial, and a few others. No extreme distortions of form? Landmasses near the poles are distorted beyond recognition, and landmasses on the equator are twice as tall as they should be, a factor that arguably borders on “extreme”. Total distance factuality? The only correct distances are East-West distances along the standard parallel, which Peters chose as 45 degrees. While the Eurocentricism present in Mercator is a coincidence, it is harder to argue the same for Peter’s arbitrary choice of the standard parallel that intersects most of the Western world. Other popular claims, that North-South lines run vertically and East-West lines run horizontally, are true of all cylindrical projections, including Mercator, and pose no real benefit by themselves.

Despite all this, his campaign worked. The “Peters World Map” spread like wildfire, fanned by Peter’s compelling case of falsehoods and the world’s burgeoning dislike for Eurocentricism and cultural imperialism. It even continues to be popular today. In 2001, it was featured prominently in an episode of The West Wing. The Oxford Cartographers officially sanction the Gall-Peters projection. Just this May, new legislature here in Boston required public schools to use the Gall-Peters projection to teach geography.

But enough about the Gall-Peters projection. The fact that its main competitor is awful doesn’t make Mercator any better. There are still hundreds of projections from which to choose, and compared to those, the Mercator is still outdated and biased, right?

I direct your attention to Google Maps, perhaps the most-viewed map in the world. While Google’s choice of the Mercator projection may seem a simple case of ignorance, Mercator is objectively the best projection for online map applications for the same reason it was objectively the best for naval explorers pre-GPS: loxodromes. If lines of constant bearing are straight lines, then the angles at which they intersect are also constant, both on the sphere and on the plane. This means that perpendicular intersections on Earth look perpendicular on the map.

Furthermore, because Mercator is cylindrical, North is always up, East always right, etc. This is not prejudice; this is convention. Navigation is significantly easier, especially for those not well versed in maps, when all maps of the same area face the same direction.

Together, these properties mean that a Google Maps user can zoom into the image and see their location mapped out with no distortion of shape or direction, and have that image match exactly any other local maps they might own. Who cares about size distortion when users will rarely look at an area bigger than 100 kilometers? Any other map projection would be incompatible with Google Maps, as either North would change direction unpredictably based on the user’s location, or streets would skew, making it difficult to compare the map to the user’s surroundings. For this reason, Mercator holds and deserves a special place in our internet culture.

Perhaps the most useful quality of Mercator, though, is its status as an anathema. People like few things more than something about which to complain. Mercator has long been the first thing novice cartographers learn to dislike. I realise that, if my case was successful, I may have damaged this property for you. Worry not. If you need a map projection to truly hate, and the Gall-Peters projection is not ugly enough (controversy aside, it’s not _that_ bad of a projection), then look no further than the space between the pool room and the mail room, where a Van der Grinten projection hangs for the college to see.

The Van der Grinten  Projection

The Van der Grinten Projection

The Van der Grinten projection, National Geographic’s projection of choice from 1922 to 1988, is often confused with Mercator. Make no mistake, though. Loxodromes are not straight lines on Van der Grinten, nor is North always up. Invented in 1898 by Alphons J. Van der Grinten with the intention of reducing the distortion of Mercator, this projection fails on practically every count.

While the distortion present in Van der Grinten is technically less than that in Mercator, Greenland still looks almost as big as Africa, and by changing the shape of the map from an infinitely tall cylinder to a circle, Van der Grinten destroyed all of the useful properties that made Mercator popular. Alaska, displayed on Mercator with a disproportionate size but reasonable shape, appears on Van der Grinten even more disproportionately large and stretched disproportionately tall. On the bright side, Van der Grinten’s Europe appears with less distortion than it does in Mercator.

While the Mercator Projection is far from the best projection and is certainly overused, several of the projections designed to fix its problems are just as, if not more, problematic. Furthermore, its current place as the butt end of most map projection discussions is undeserved. Mercator has no place in a geography classroom, but it is the only projection for online mapping services, and holds an important place in our history. With all of this in mind, I hope that the next time you hear someone complain about Mercator and extol Boston for switching to Gall-Peters, you rise to Mercator’s defense and remind them just how awful Van der Grinten is in comparison.

 

*Citation note: Wikipedia’s Gall-Peters page shows these phrases in quotes with citations, but I have been unable to find the publications that these citations reference, so take that as you will as far as the credibility of these quotes.

The Trystan Edwards Projection

The Trystan Edwards Projection

Tobler's World in a Square Projection

Tobler’s World in a Square Projection

Tobler's Hyperelliptical Projection

Tobler’s Hyperelliptical Projection

The Smyth-Craster Projection

The Smyth-Craster Projection

The Lambert Cylindrical Projection

The Lambert Cylindrical Projection

The Berhmann Projection

The Berhmann Projection

The Balthasart Projection

The Balthasart Projection

SERV Activity Updates

The Daily Table: Emily Yeh

Daily Table is a nonprofit organization that makes affordable and healthy food available to people with low incomes. A group from Olin volunteers at Daily Table every Saturday (time TBD). If you’re interested, keep an eye out for an email to Carpe with more information!

 

Big Brothers Big Sisters College Campus Program: Justin Kunimune

Big Brothers Big Sisters has continued with its biweekly outings. As we approach the end of the semester, we prepare to say goodbye for our Littles for the summer.

 

Charles River Center: Emma Price

The Charles River Center is a non-profit organization based in Needham that works to improve the lives of people with developmental disabilities and help support their families. They have a variety of different programs for people of all ages, all with really fun activities (like zumba and yoga)!!

 

E-Disco: Micaela Chiang, Daniel Daughterly, Lauren Pudvan, Nicole Schubert

We have continued our monthly lessons at Schofield Elementary school. We hosted the 6th graders from Dana Hall and had them design for mythical creatures. We will be having students in the area come to Olin on April 29th to build and launch Bottle Rockets.

 

IgniteCS: Casey Alvarado, Emily Lepert, Brenna Manning, Vicky McDermott, Sophia Nielsen, Andrew Pan

We are hosting computer science workshops on Saturdays at nearby middle schools. Last semester we hosted two workshops at Dedham Middle School and Monsignor Haddad Middle School. This semester we hosted one at Pollard Middle School in Needham and will be returning to the Dedham Middle School. We are always looking for volunteers to help out at our workshops and for new members to join our curriculum design team!

 

The Food Project: Aaron Greiner, Gaby Clarke

The Food Project engages youth and works on food justice issues through running 70 acres of farm in the Greater Boston area and the North Shore. They work on advocacy, youth development, and much more. Their farms, which are largely run by youth and volunteers, produce food that is sold at affordable prices at places like farmers markets. They have volunteer opportunities at all of their farms throughout the week.

 

Massachusetts Correctional Institution (MCI) Framingham: Ashley Funk

MCI Framingham is the Massachusetts Department of Correction’s institution for incarcerated women. They have a number of opportunities for volunteers, though getting approved as a volunteer takes persistence and patience (lots of background checks and paperwork). Currently, I am volunteering in the greenhouses and providing support for the gardening program where the women grow plants to sell to the prison staff.

SERV Activity Update

The Daily Table: Emily Yeh
Daily Table is a nonprofit organization that makes affordable and healthy food available to people with low incomes. A group from Olin volunteers at Daily Table every Saturday (time TBD). If you’re interested, keep an eye out for an email to Carpe with more information!

Big Brothers Big Sisters College Campus Program:
Big Brothers Big Sisters resumed its outings this week. Bigs will continue to meet with their Littles every 1 to 2 weeks throughout the month.

Charles River Center:
The Charles River Center is a non-profit organization based in Needham that works to improve the lives of people with developmental disabilities and help support their families. They have a variety of different programs for people of all ages

E-Disco: Micaela Chiang, Daniel Daughterly, Lauren Pudvan, Nicole Schubert
E-Disco has begun planning events for this semester. We started our monthly lessons at Schofield Elementary school. The theme for this past lesson was time travel! The students made sumerian cuneiform nametags, learned morse code, and made skyscrapers.