The Birth of Coordinates

As I considered the list of Map Happenings that Rocked Our World, it seemed obvious that the next most significant event after the invention of the first map was the invention of coordinates.

However, after I did some digging, I was a little surprised. The geographic coordinate system of latitude and longitude was invented way, way before the simple x, y, z coordinate system (also known as the Cartesian coordinate system).

Personally I would have thought some bright gal or bloke might have invented a local coordinate system using x and y for their village or town way before some other bright person invented a system for plotting your location on the entire world. But no, apparently that was not the case. 

The concept of latitude and longitude was essentially invented by a Greek chap called Eratosthenes (c. 285-205BC). He wrote on a wide range of subjects — including mathematics, geography, astronomy, poetry and music theory. In about 245BC the King of Egypt, Ptolemy III, appointed him to be the chief librarian at the Library of Alexandria. Eratosthenes’ work included inventing the first global projection of the world and inventing the concept of parallels and meridians — thus lines of latitude and longitude.

One very interesting fact about Eratosthenes is that he is usually credited for inventing the term ‘geography’ and founding the science of geography. How about something like that on your résumé, eh?  

But wait there’s more! 

Eratosthenes’ other achievements include being the first to accurately calculate the circumference of the earth and the earth’s axial tilt, inventing the armillary sphere and for developing a simple algorithm for finding prime numbers. His masterpiece was a (now mostly lost) three volume work called “Geography” and an accompanying world map.

Phew.

So what happened next?

Well let’s fast forward to the first century AD and the Roman province of Syria. It was there that the geographer and mathematician Marinus of Tyre was born.  Like Eratosthenes, Marinus wrote a treatise on geography. Alas his work is lost and is only known due to being referenced by other scholars. But Marinus did some awesome work to advance coordinate systems:

His main legacy was assigning latitude and longitude coordinates to thousands of places — essentially he built the world’s first gazetteer. But this was well before the time when Greenwich, England was the prime meridian¹. Marinus compiled a map of cylindrical projection, thereby also inventing the equirectangular projection. For longitude he designated the zero point to be the Fortunate Isles which passes through the Canary Islands (now ~ 14°1’W). At that time the world was thought to stretch from the Fortunate Isles in the west to China in the east. He designated the island of Rhodes in Greece as his zero reference point for Latitude. This is perhaps not surprising as Marinus lived in Rhodes.

Oh, one other thing — Marinus also coined the term Antarctic — that being opposite to the Arctic. 

Yup, clearly another outstanding résumé. 

Next up: another superstar geographer — Claudius Ptolemy² (c. 100-170AD). Like Eratosthenes,  Ptolemy lived in Alexandria and like Eratosthenes was also multi-talented: a mathematician, astronomer, astrologer, geographer and a music theorist. During his life he devoted most of his energy to astronomy, but geography was far from ignored. His seminal work in this area  was “The Geography”, an eight volume masterpiece. Building on Marinus’ work he extended the gazetteer to over 8,000 places. 

But it was Ptolemy who suggested that the lines of latitude be divided into degrees and minutes. The equator would be defined at 0 degrees and 90 degrees north at the North Pole. Lines of longitude were divided into 180 degrees east and west of a prime meridian, which, like Marinus, he kept at the Canary Islands. Ptolemy thus laid the foundation for all modern maps we use today. His work was so highly regarded it was copied and referenced for many hundreds of years and it was still influential in the Renaissance. Alas no manuscript of the Geography survives from earlier than the 13th century. 

In the 18th century most countries in Europe adopted their own prime meridian, usually through their capital. Hence in France the Paris meridian was prime, in Germany it was the Berlin meridian, in Denmark the Copenhagen meridian, and in the United Kingdom the Greenwich meridian. It was the work of Nevil Maskelyne (1732-1811) that eventually tipped the balance towards Greenwich. Maskelyne was the fifth British Astronomer Royal. Between 1765 and 1811 Maskelyne published 49 issues of the Nautical Almanac based on the meridian of the Royal Observatory in Greenwich. This almanac was the first to contain data dedicated to the convenient determination of longitude at sea. Even the French translations of this almanac continued to reference Greenwich as the prime meridian.

In October 1884 the Greenwich Meridian was selected by the delegates to the International Meridian Conference held Washington, DC to be the common zero of longitude throughout the world. The French argued for a neutral line, but eventually even these cheese-eating surrender monkeys abstained.

Thus history was made.  

But what of today?

Well a number of organizations have developed their own coordinate systems, with varying success. Countries did it to help them increase the accuracy of land surveys³. For example, the British have the Ordnance Survey National Grid and in the USA there is the State Plane Coordinate System. 

On the commercial side various organizations are valiantly trying to wrench people away from latitude and longitude. Why? Because it’s really difficult to designate a precise, easily-to-remember designation for a location when that location has no address. And it’s certainly very difficult to remember long strings of numbers.

There are two companies active in this space that I’ll highlight: one is Google and the other is an organization called What3Words.

• Google’s approach to solving this problem is to assign six character alphanumeric codes to every place on the earth called Plus Codes. For example the Great Pyramid at Giza is located at X4GJ+98. Each individual code represents about a 14 meter by 14 meter square, which is about half a basketball court.
• What3Words’ approach is a little more ‘cute’, assigning, you’ve guessed it, three words to each location. So in their system the Great Pyramid of Giza is located at ‘rooms.collect.denim’. It’s also available in 50 languages, so the same location in Greek is “κανονικά.καλώδιο.φώτα”. What3Words is a little more precise than Plus Codes and has a resolution of about 3 meters. 

While Google has open sourced Plus Codes they’re frankly still struggling to get traction. Personally I don’t know anyone in casual conversations that has given me, asked me for or even talked about Plus Codes. Unfortunately I think the general public has little or any awareness of their existence. But they exist in plain site. Go check Google Maps. 

What3Words has been more successful — a number of well known organizations have adopted it. Even the whole country of Mongolia has adopted it. But What3Words has another problem. Google doesn’t need to make money from Plus Codes because it’s not central to their business. But coordinates are What3Words’ only business — so they have to make money. Unless some big rich company decides to buy What3Words out of the goodness of their heart (unlikely) — it’s going to remain a closed, proprietary system. As a result many organizations, particularly tax funded organizations, will continue to be trepidatious. 

Both Google and What3Words tout their systems as being valuable for first responders and emergency services, and while it can help, it’s not always a rosy picture. I must credit Nick Heer at Pxlnv.com for pointing out the limitations. Nick stumbled across a catalogue of how What3Words is insufficient for emergency use: see What 3 Words is a Mess. Not a pretty picture. However, I’m also guessing there are probably as many good stories as there are bad and nobody’s put a similar catalogue together either. 

But will these systems ever get adoption? I can’t see Google Maps using What3Words as it competes with Plus Codes. And I’d be very surprised to see Apple Maps adopting either system. I’m guessing the producers of other popular mapping apps in use around the world feel the same way. Time will tell. 

Well that’s about it for this week — but there is one more thing…

Remember my earlier reference to the simple x, y, z coordinate system, also known as the ‘Cartesian’ coordinate system?

Well it was actually invented by none other than the famous French philosopher and mathematician, René Descartes in the 17th century. Let me credit Wild.Maths.Org for telling the story:

The coordinate system we commonly use is called the Cartesian system, after the French mathematician René Descartes (1596-1650), who developed it in the 17th century. Legend has it that Descartes, who liked to stay in bed until late, was watching a fly on the ceiling from his bed. He wondered how to best describe the fly’s location and decided that one of the corners of the ceiling could be used as a reference point.

Imagine the ceiling as a rectangle drawn on a piece of paper: taking the left bottom corner as the reference point, you can specify the location of the fly by measuring how far you need to go in the horizontal direction and how far you need to go in the vertical direction to get to it. These two number are the fly’s coordinates. Every pair of coordinates specifies a unique point on the ceiling and every point on the ceiling comes with a unique pair of coordinates. It’s possible to extend this idea, allowing the axes (the two sides of the room) to become infinitely long in both directions, and using negative numbers to label the bottom part of the vertical axis and the left part of the horizontal axis. That way you can specify all points on an infinite plane.

One last tidbit before we part ways: the word ‘Cartesian’ is an adjective meaning “relating to Descartes and his ideas”. 

There you go. 

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Footnotes:

¹ The prime meridian, also known as the zero meridian is the origin or zero point of longitude. 

² Not to be confused with King Ptolemy III

³ The earth is not a perfect sphere. As a result compromises have to me made in global coordinate systems that reduce accuracy. A dedicated local coordinate system can compensate for this imperfection and increase the overall accuracy of a land survey.

Credits and Acknowledgments:

• Cameron McPhail for his 2011 thesis “Reconstructing Eratosthenes’ Map of the World: A Study in Source Analysis”
• Chris Maeder at CivilGeo.com for his article Tales in Geography: Early Cartographers Shape Modern Mapping
• Nick Heer at Pxlnv.com 
• Telemachus Odysseides for his wonderful site, Greatest Greeks, in particular his piece on Marinus of Tyre 
• Wild.Maths.Org at the University of Cambridge, England 
• Wikimedia and all those who contributed to Wikipedia.