Projecting Much?

A whole lot of projecting.

The oldest surviving world map is a clay tablet from Babylon, drawn around the 7th century BCE. It shows the world as a flat disk ringed by a "bitter river" - with Babylon sitting at the center, roughly the size of a continent. Early Greek cosmology drew a similar disk; classical Chinese astronomy held a "round sky over a square earth" (the Gaitian model of the Zhoubi Suanjing) for centuries, even as the rival Huntian school argued for a celestial sphere. Nobody was being stupid. A disk is what the horizon looks like. The center is where you are standing.

The Greeks talked themselves out of it. Pythagoras and Parmenides proposed a sphere on philosophical grounds - circles being perfect and all - but Aristotle assembled the physical case: the Earth's shadow on the moon during an eclipse is always round, ships disappear hull-first over the horizon, and the stars shift as you travel north or south. Around 240 BCE, Eratosthenes turned the sphere into a number. Told that the summer-solstice sun shone straight down a well in Syene while casting a 7.2-degree shadow in Alexandria, he multiplied the angle out across the known distance between the two cities and landed within a few percent of the Earth's true circumference. Two shadows and some geometry, measuring a planet.

Eight centuries of refinement later, the scholar al-Biruni claimed a subtler trick: climb one mountain of known height, measure the dip of the horizon, and solve for the radius of the Earth from a single vantage point. His reported precision is remarkable - widely cited, though modern historians debate whether his instruments could truly deliver it. The method is sound either way, and it marks something important: by the Islamic Golden Age, the shape of the Earth was an engineering problem, not a cosmological one.

Newton predicted that a spinning Earth should bulge at the equator and flatten at the poles. The Cassini family - France's dynasty of royal astronomers - measured the opposite: an Earth stretched long like an egg. The argument mattered for every chart in every navy, so in the 1730s France did the expensive thing and sent two expeditions to measure a degree of latitude at the extremes: Maupertuis to Lapland, La Condamine to Peru. A polar degree came back longer than an equatorial one. Newton was right; the Earth is an oblate spheroid, about 21 kilometers wider than it is tall.

The satellite era broke the shape again. Gravity-mapping missions - GRACE and its successor GRACE-FO, Europe's GOCE - revealed that the surface that actually defines "sea level" is neither sphere nor spheroid but the geoid: the lumpy, potato-shaped surface where Earth's gravity potential is equal everywhere. It dips about a hundred meters below the reference ellipsoid south of India and swells above it over the North Atlantic. There is no formula for it. It has to be measured, point by point, and re-measured as ice sheets melt and aquifers drain, because the geoid moves.

This is not trivia. Your GPS receiver computes position against WGS84 - the smooth mathematical ellipsoid - because satellites orbit math, not potatoes. True elevation is measured against the geoid, because water flows downhill along gravity, not geometry. The gap between the two is the geoid separation, and if your phone or hiking app skips the correction (EGM96 or EGM2008, in practice), your "elevation" can be off by tens of meters. A geocacher squinting at a raw GPS altitude readout is hitting a low-stakes version of the exact problem Eratosthenes was solving: the instrument reports against a model of the Earth, and the model is a choice.

Which raises a question with a satisfyingly physical answer: if the geoid has to be measured point by point - who measured it, and where are the points?

For more than a century, the National Geodetic Survey and its predecessors have been bolting small bronze disks into bedrock, bridge abutments, courthouse steps, and mountain summits. Each one is a point whose position - and, for the vertical network, whose precisely leveled elevation - is known and published. These marks are the datum: the physical anchors against which American elevation is defined, the place where the abstract geoid math touches an actual sidewalk. Many of them double as benchmark-hunting targets for geocachers, which means the 19th-century survey network has a 21st-century fan club.

Hover any resolved disk and the tooltip reports the mark's geoid separation - the very number your GPS needs to turn ellipsoid height into real elevation. The potato, one bronze disk at a time.

Knowing the Earth's shape and drawing it flat are different problems - flattening a sphere always costs something, and the choice of what to sacrifice is the projection. Mercator's 1569 chart made a specific, brilliant trade: it distorts area so that rhumb lines - courses of constant compass bearing - draw as straight lines. For a sailor that is everything. The price grows toward the poles: on a Mercator, Greenland reads about the size of Africa. Africa is roughly fourteen times larger. Europe's naval powers adopted the chart, empires shipped it everywhere, and four centuries of repetition installed a navigation tool as the world's mental image of itself.

The center got voted on, too. In 1884, delegates from 25 nations met in Washington to pick a prime meridian, and Greenwich won 22 to 1 - San Domingo voting against, France and Brazil abstaining. The tell is in the run-up: an 1879 survey found 72% of the world's shipping tonnage already navigated on Greenwich-based charts, a legacy of British naval dominance. The vote ratified the market. France, unpersuaded, avoided the word "Greenwich" in official documents for decades, preferring "Paris mean time, retarded by 9 minutes 21 seconds."

A century later the map's politics went mainstream. Arno Peters unveiled an equal-area world map in 1973 as a corrective to Mercator's inflated North - without much crediting James Gall, who published the same projection in 1855. Aid organizations and UNESCO-adjacent groups adopted it; it eventually got a whole scene on The West Wing. Cartographers pushed back hard - Peters' map badly stretches the tropics it claims to champion, and his rhetoric oversold its neutrality. By 1989 seven North American cartographic societies had passed a joint resolution urging that no rectangular projection be used for general world maps. The profession's own conclusion, after 400 years: there is no neutral rectangle.

Every map is a choice. Here is yours - the same Mercator, with the center handed to you.

Each projection preserves something and pays for it with something else: bearings (Mercator, Craig), area (Gall–Peters, Mollweide), continuity of the oceans (Spilhaus's heirs), the dignity of whoever gets the middle. The interesting part is rarely the formula - it is who needed the property and what they were willing to trade.

The canon

The deep cuts

Everything on this page is computed, not embedded. The recentering tool and benchmark globe share one canvas component: the benchmark map runs it as a d3-geo orthographic globe, and the recentering tool runs the very projection under discussion - an oblique Mercator whose rotation triple the click re-aims. The idle drift, the grab, and the click-to-fly are all manipulations of that rotation, interpolated frame by frame. The gallery renders each projection live from d3-geo, d3-geo-projection, and d3-geo-polygon; Cassini has no library implementation, so it is built from Snyder's published spherical formulas via d3.geoProjection, and AuthaGraph - whose exact construction was never published - appears through Imago, its open-source reconstruction, with the substitution stated on the card. The benchmark data is a quadtree crawl of NOAA's public NGS Data Explorer web services (the API caps at 500 marks per query, so dense tiles subdivide recursively), reduced to a half-degree density surface plus regional point shards that lazy-load as you zoom - no backend anywhere, just static files and range math. Archival images come from Wikimedia Commons under public domain or CC0. The limitation worth naming: the benchmark network shown is US-only, one country's answer to a planetary question - the data layer is structured so other national networks can be added, but today it is an honest sample, not a census.