From coconuts to GPS: A brief history of navigation

It's good, but it's no coconut. Image: Getty.

If I ask Google:

It helpfully displays a map of where I used to live:

Google is very good at knowing where I used to be. My phone is constantly keeping track of my location and uploading it to their servers. It has stored my location 579,088 times since September 2013.

Each location stored looks like this:

{
 “timestampMs” : “1431497952458”,
 “latitudeE7” : 513453840,
 “longitudeE7” : -1015043,
 “accuracy” : 27,
}

This isn’t that easy to read. The E7 is an instruction to divide by 10,000,000, to reach a traditional set of latitude and longitude coordinates. “timestampMs” tells us that wherever 51.345384° N -0.1015043° E is, I was there at 1,4314,9795,2458 milliseconds after midnight on the 1st January 1970.

Even knowing what each of those numbers represent, we need to do some work to get these back into a human context. By putting the numbers through mapping software I can find out that “51.345384°, -0.1015043°” is Purley Oaks station in South Croydon. By running the timestamp through a conversion system, I can see I was apparently there at 7:19:12 AM on the 13 May 2015. This makes perfect sense, it was part of my daily commute at the time — I’d have been there most days at that time.

Most of the data stored about my location places me somewhere I lived or somewhere I worked. Just occasionally, I do something interesting and the database gets to store whole new sets of coordinates. If I take several years of this data I can produce maps of the sums of my positions over time:

This is my life as latitude and longitude, expressed in a way that can be easily understood by a human. Where I’ve spent any amount of time the map is redder; journeys appear as snail trails across the country.

Google’s algorithms don’t require any of this “coloured in map” nonsense. After a few weeks, your Android phone can make a reasonable guess at where your work and home are, based on where you spend most of your days and where you spend most of your nights. It doesn’t need to ask — that would be intrusive.

To determine a position on a globe while inconveniently being stuck on that globe you need fixed external references. Fortunately the universe is full of these.

One of simpler means sailors used to work out their relative position from destination was a kamal – a board with a hole in the middle. By putting a string through the hole and holding one end of the string in your teeth, you position the lower edge of the board on the horizon and move it further away until the board obscures your target star (typically Polaris — if visible).

An enthusiastic Wikipedia editor showing how the kamal works. Image: Markus Nielbock/Wikimedia Commons.

The length of the string between your teeth and the board tells you your latitude. By knowing the length of string required for certain ports, you could adjust course to navigate to a place. Using nothing more than your teeth, a string, a plank of wood, a star – and the horizon.

In Polynesia (lacking in a helpful pole star) titiro ‘ētū – “star peekers” – made of nothing but coconuts and seawater were used to navigate to specific islands. To use these, you cut off the top of the coconut and make a ring of holes around the base. You then make a hole near the top for the target star and fill it with water up to the holes (with coconut oil to maintain surface tension). You look through the device at the star at its highest point; if the water inside the device is flat, you are on the same latitude as your destination. The stars will guide you with the simplest of tools, if you know how to use them.


Progression east-west (longitude) can be understood if you know the difference between high-noon on a clock set at a fixed location (Greenwich) and a clock set at the current location. Each hour difference represents 15° of travel longitudinally (1/24 of 360°). Simple enough, if you have a clock that can keep time on the ocean – but that was a complicated problem to solve. Before that, all sailors could really do is line up on the right latitude and go for it.

To make use of more markers than the sun and North Star, you could use nautical almanacs and sextants. These almanacs were essentially large lists of what celestial objects should appear at certain points of the sky, and at what time they can be expected to do so. By using the sextant to compare predicted appearances to actual locations, you can determine the distance to fixed positions.

The Global Positioning System (GPS) has mostly replaced the need for these tables. Reliable but not available on-demand stars have been replaced by artificial celestial bodies that spend their whole lives yelling about where they are and what time they think it is. By comparing signals from several different satellites to the time your GPS device thinks it is, you can triangulate your position on the earth within a few meters.

Few mobile phones contain true GPS: mostly they use aGPS or WPS. aGPS uses the resources of the mobile network to speed up reconciliation based on fragmented signals, but WPS (Wireless Positioning System) is something different altogether. It takes advantage of the fact that we littered our world (especially urban areas, where GPS struggles) with millions of radio location beacons, in the form of Wi-Fi access points.

While the vans with the weird cameras were taking pictures of every road in the world, they were also mapping the radio landscape we have made: each house with a Wi-Fi access point, broadcasting a unique identifier. By mapping these to a true GPS reading, location services can provide a guide to any device with a wifi chip. If you read Device #1053443 with 50 per cent strength and Device #10232321 with 74 per cent strength and Device #24324239 with 60 per cent strength, the chances are you are “here” — the most likely place where those signals converge at that strength.

These vans are no longer necessary: while walking around your phone will pick up on any new or unknown access points. With sufficient logs of these devices, their location can be deduced by comparison to known devices and used for future navigation. As well as recording our every step, our phones are automated radio cartographers. This is still ultimately working on similar principles to the nautical almanac and sextant, it just has a much larger look-up table and uses thousands of man-made stars to light the way.

As navigation has become much easier there is also the risk of becoming too dependent on what might turn out to be fragile technology. The US Navy is currently re-introducing celestial navigation training. so that its sailors can figure out where they are in the event of an attack on the GPS system. After the apocalypse, we might find ourselves getting around by holding a bricked phone up to the horizon and measuring the length of the headphone cord to our teeth. 

 
 
 
 

Transport for London’s fare zones secretly go up to 15

Some of these stations are in zones 10 to 12. Ooooh. Image: TfL.

The British capital, as every true-blooded Londoner knows, is divided into six concentric zones, from zone 1 in the centre to zone 6 in the green belt-hugging outer suburbs.

These are officially fare zones, which Transport for London (TfL) uses to determine the cost of your tube or rail journey. Unofficially, though, they’ve sort of become more than that, and like postcodes double as a sort of status symbol, a marker of how London-y a district actually is.

If you’re the sort of Londoner who’s also interested in transport nerdery, or who has spent any time studying the tube map, you’ll probably know that there are three more zones on the fringes of the capital. These, numbered 7 to 9, are used to set and collect fares at non-London stations where the Oyster card still works. But they differ from the first six, in that they aren’t concentric rings, but random patches, reflecting not distance from London but pre-existing and faintly arbitrary fares. Thus it is that at some points (on the Overground to Cheshunt, say) trains leaving zone 6 will visit zone 7. But at others they jump to 8 (on the train to Dartford) or 9 (on TfL rail to Brentwood), or skip them altogether.

Anyway: it turns out that, although they’re keeping it fairly quiet, the zones don’t stop at 9 either. They go all the way up to 15.

So I learned this week from the hero who runs the South East Rail Group Twitter feed, when they (well, let’s be honest: he) tweeted me this:

The choice of numbers is quite odd in its way. Purfleet, a small Thames-side village in Essex, is not only barely a mile from the London border, it’s actually inside the M25. Yet it’s all the way out in the notional zone 10. What gives?

TfL’s Ticketing + Revenue Update is a surprisingly jazzy internal newsletter about, well, you can probably guess. The September/October 2018 edition, published on WhatDoTheyKnow.com following a freedom of information request, contains a helpful explanation of what’s going on. The expansion of the Oyster card system

“has seen [Pay As You Go fare] acceptance extended to Grays, Hertford East, Shenfield, Dartford and Swanley. These expansions have been identified by additional zones mainly for PAYG caping and charging purposes.

“Although these additional zones appear on our staff PAYG map, they are no generally advertised to customers, as there is the risk of potentially confusing users or leading them to think that these ones function in exactly the same way as Zones 1-6.”


Fair enough: maps should make life less, not more, confusing, so labelling Shenfield et al. as “special fares apply” rather than zone whatever makes some sense. But why don’t these outer zone fares work the same way as the proper London ones?

“One of the reasons that the fare structure becomes much more complicated when you travel to stations beyond the Zone 6 boundary is that the various Train Operating Companies (TOCs) are responsible for setting the fares to and from their stations outside London. This means that they do not have to follow the standard TfL zonal fares and can mean that stations that are notionally indicated as being in the same fare zone for capping purposes may actually have very different charges for journeys to/from London."

In other words, these fares have been designed to fit in with pre-existing TOC charges. Greater Anglia would get a bit miffed if TfL unilaterally decided that Shenfield was zone 8, thus costing the TOC a whole pile of revenue. So it gets a higher, largely notional fare zone to reflect fares. It’s a mess. No wonder TfL doesn't tell us about them.

These “ghost zones”, as the South East Rail Group terms them, will actually be extending yet further. Zone 15 is reserved for some of the western-most Elizabeth line stations out to Reading, when that finally joins the system. Although whether the residents of zone 12 will one day follow in the venerable London tradition of looking down on the residents of zones 13-15 remains to be seen.

Jonn Elledge was the founding editor of CityMetric. He is on Twitter as @jonnelledge and on Facebook as JonnElledgeWrites.