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Thanks to the orientation and position of the planet, PommeDeTerra has a habitable island with a temperate climate at it's south pole that looks a little like this:

My "unique" island.

This island is very similar to Europe with the same soil types, geographical formations, flora, and wildlife. The planet has no tilt on its rotation axis, so the sun never sets and seems to fly in circles along the horizon. (I'm not interested in the effects of this in this question.)

My humans have existed perfectly fine so far, and have reached a point where they now have seafaring ships and the invention of the compass. In Europe, this led to the cartography of most of Europe and the beginning of long-distance trade.

How would living at a pole affect mapping and navigation?

Navigation on land would be pretty much the same, since sign posts and roads would still work. Maps would look different, though.

Of course, North is now "out to sea" and South is now "To the centre" (making it very easy to find the capital city). Navigation based on the sun or stars will be useless, unless someone finds a clever way to combine a measurement of the time with the position of the sun.

International trading would involve heading away from the pole to areas where the sun rises and sets, making navigation based on the sun impossible at night. I suppose at this point people could switch to using a compass since they are away from the confusing polar regions, but I'm not sure how it would work.

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    $\begingroup$ Well for one thing, starting out would be dead easy, as there is only one direction you can go. $\endgroup$ – A. I. Breveleri Aug 16 '17 at 16:17
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    $\begingroup$ I imagine without the proper vocabulary or knowledge, but knowing that there is some significance to the center point on their compasses, and knowing the paths of the heavenly bodies, the citizens might use Discworld-like terms for navigating. Hubwards, rimwards (do they know it's a globe?), turnwise, widdershins. Just saw an answer directly mention this, woops! $\endgroup$ – Ross Aug 16 '17 at 16:41
  • $\begingroup$ The planet has no tilt on it's rotation axis? So you have no life... because you have no seasons, which means no crops. You can always handwave it, but playing out the evolution of such a planet is bad news: worldbuilding.stackexchange.com/a/14296/294 $\endgroup$ – corsiKa Aug 16 '17 at 21:24
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    $\begingroup$ Bear in mind that the magnetic pole isn't necessarily the geographic pole. See en.wikipedia.org/wiki/North_Magnetic_Pole $\endgroup$ – Andon Aug 16 '17 at 22:40
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    $\begingroup$ @corsiKa that's why I said "I'm not interested in the effects of this in this question" immediately afterwards. $\endgroup$ – Aric Aug 17 '17 at 7:42
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If you would rely on the sun for your direction, you will have to be able to track time accurately. If your time tracking is 10% off, you'll walk in a 10 day (poorly drawn) circle.

A compass would be quite useless around the poles, so they would likely not be invented: the inventor won't recognise their use.

So navigation would probably rely heavily on landmarks like mountain peaks or towers.
You can do the math to figure out your position relative to landmarks. Land surveys would play a very important role in mapping. Angles and distances between different landmarks would be noted on the maps to assist with triangulation of your position.

Another important aid in navigation would be accurate time-keeping. Given the time and the position of the sun, you can figure out in which direction you're headed. To this end, portable clock technology would be much more advanced, and maps would denote absolute directions at specific points so you can calibrate your clock.

If you go out to sea, the only way to determine direction would be with clocks. It will probably take quite a while for people to figure out that other means of determining position and direction become available as they travel further from the pole. They will likely pick these up quite fast as they're already quite proficient taking accurate measurements of angles.

Another fun consequence: time and angle measurement would probably be equal: 3 hours would be expressed in the angle the sun travels along the horizon in 3 hours. A sensible design for a clock would be a single hand pointing towards the sun relative to an absolute direction. The markings around the edge denote both time and an absolute direction.

As they travel far enough and experience nights, navigating by stars would be identical to navigating by the sun. It would probably take them some time to figure out that the stars and sun move relative to eachother throughout the year.

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  • $\begingroup$ With international trading, they would have to enter areas where the sun rises and sets. This would make things a little difficult, I think. $\endgroup$ – Aric Aug 16 '17 at 13:17
  • $\begingroup$ I suppose the clock would have a single hand that points to the sun's position relative to an arbitrary "up" angle, too. $\endgroup$ – Aric Aug 16 '17 at 13:20
  • $\begingroup$ @AricFowler I've updated my answer to include those two points $\endgroup$ – Swier Aug 16 '17 at 13:28
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    $\begingroup$ A compass is only useless around the magnetic poles, which aren't necessarily in the same place as the axial poles. $\endgroup$ – Matt Bowyer Aug 17 '17 at 12:58
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    $\begingroup$ @MattBowyer good point, though after looking into it a bit, most other planets' magnetic and axial poles are roughly in the same place. $\endgroup$ – Swier Aug 18 '17 at 7:39
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I can - and certainly am not alone - think of at least one fictious world with a similar setting :

enter image description here

Discworld is a collection of books written by Terry Pratchett telling the adventures and daily lives of characters who live - for the most part - on Discworld. Contrarily to your world, theirs is a disc, but there are some similarities that you can build upon.

Since their world is a rotating disc, their 2 cardinal directions aren't carthesian axis like our North-South/East-West (even though due to its spherical shape, our axis aren't perfectly carthesian...) but polar directions : closer-further to/the axis and clockwise or counterclockwise rotation around the axis.

Although your people live on a spherical planet, developing their civilization around the pole on such a wide landmass is likely to lead them to that kind of standard. Indeed, the ancients used astronomy heavily regarding all sorts of things, especially when it came to maps, periodic events and navigation/travel. They would get that the sky rotates around an axis that goes through a fixed point of their land pretty quickly, certainly way before the invention of writing. That point would be of very significant importance, maybe the center ( ;) ) of some major cult, as well as their maps.

If the pole is their point of reference, then all directions are related to it in some way and you end up with a discworld-like system. In fact, our pseudo carthesian system surely happens only because it was used mostly to travel along the Est-West axis and/or in places where the paralels are.. well... fairly paralel. That system being more and more distorted as you get closer to the poles until the point where your paralels all cross themselves, it would be unlikely that people who originate from that very same pole would develop it in the first place.

In my opionion, a map centered on the pole would make a lot of sense even today, so I guess it would be even more obvious to a civilization that considers it the default setting.

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    $\begingroup$ Loving this map, where the illustration of a winged demigod creating the turnwise winds is not merely a fanciful metaphor. $\endgroup$ – A. I. Breveleri Aug 16 '17 at 16:14
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    $\begingroup$ I think this is the key. Use polar coordinates for a polar civilization. Coordinates would consist of an angle and a distance (from the pole). Travel would be in directions of "inward", "outward", "with the spin", and "against the spin". (with more convenient terms in practical use) $\endgroup$ – Nate White Aug 16 '17 at 17:01
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    $\begingroup$ @A.I.Breveleri Well, being real wouldn't prevent him from being also a metaphore :D $\endgroup$ – ksjohn Aug 16 '17 at 17:23
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I would suggest redefining the cardinal directions that your civilization uses. As with Earth, defining lines of longitude will have to be done somewhat arbitrarily, so choose one direction and call that "North", or some other name to avoid confusion. The opposite direction becomes "South", and the perpendicular directions are "East" and "West".

Your true North and South would also provide valuable information, that is, distance from home. I would imagine people might use some simple notion like "Outward" and "Inward" to describe what we would refer to as latitude (e.g. "We have sailed 50 km outward from the Northeast coast.") Additionally, navigation by compass is very intuitive for inward/outward travel (If using the standard colors of a modern compass, your people would likely devise a saying like "Follow white, home in sight; follow red, new waters ahead"), but will be fairly useless for longitudinal travel.

Maps would most likely be roughly circular and pseudoantarctic-centric, as until the far side of the planet has been explored, the main continent serves as the center of this population's world. It may look approximately like the following map until your humans better understand the roundness of your planet and scale the continents more appropriately:

Map

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    $\begingroup$ How do you tell what direction true north is if the compass only points toward the middle? $\endgroup$ – corsiKa Aug 16 '17 at 21:25
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    $\begingroup$ @corsiKa: This is equivalent to asking "how do I know I'm still in Washington, and haven't moved east into Idaho yet?" in the real world. The compass can only tell you which way the magnetic north and south poles are, not your distance to the poles nor the angle from them. If you start at the pole, you'd go "north" to some landmark on the coast, then continue along a magnetic north direction as you sailed outwards. Provided the currents don't push you too far, you'll end up where you want, which you can confirm (or disprove) by using additional landmarks. $\endgroup$ – MichaelS Aug 16 '17 at 22:14
  • $\begingroup$ Using a compass and the stars in the sky, you can tell if you're in Washington or Idaho with some degree of accuracy. The better your time keeping, the higher the accuracy. At the pole you have only the position of the sun in the sky which, without a celestial marker to compare to, is useless. You would need perfect mobile timekeeping to say where you are without using landmarks. But if you're using landmarks anyway, a compass is kind of useless. $\endgroup$ – corsiKa Aug 16 '17 at 23:50
  • $\begingroup$ @corsiKa: The point of a compass on land is so you can find a landmark that's beyond the horizon with any kind of accuracy. Additionally, using a compass and multiple landmarks, you can use triangularization to find a pretty specific point in a valley or forest without having any obvious local landmarks. Note also that you can easily find your latitude near the pole with a simple sextant. It's only longitude that's difficult, and is just as hard near the poles as not. If anything, accuracy is better near the poles, since a degree of error is fewer miles there. $\endgroup$ – MichaelS Aug 17 '17 at 0:00
  • $\begingroup$ The hard part is not "being near the poles" it's there's no axial tilt. First, sun all day means no stars to use the sextant on. Second, without a sunrise or sunset to approximate your longitude you need a perfect mobile time keeping device for similar reasons as did navigators. $\endgroup$ – corsiKa Aug 17 '17 at 0:08
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If the planet has magnetic poles and one of them is on the continent, the magnetic inclinometer would probably be invented simultaneously with the compass. The inclination of the magnetic field, as measured by the inclinometer, would give a useful indication of the distance from the pole.

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Other answers have talked about concepts of north, south, east, west, outward, inward, etc. But there's the additional problem of finding your current longitude and latitude, which is something a compass cannot provide.

Your first method of figuring these out would be simple landmark navigation. Go north from Jumpoff Point to the Isle of Reckoning. From there, head north-northwest until you sea the Misty Lagoon over the horizon. Etc.

But we can use the sun and the stars to get much better positional data. At first, your people might have no concept of stars or star-mapping, because the ever present Sun in their sky might hide all the stars, depending on the atmospheric conditions present. However, if it's like Earth, we can still see a few stars on the horizon opposite the Sun at dusk and dawn. Likewise, your people would see the stars, and recognize that certain stars are visible at certain times of day.

Summary.
A simple sextant will give your mariners their current latitude by measuring the vertical angle of the Sun at noon (or some other object at its apex in the sky). Using accurate clocks can allow calculations at times other than noon.

Longitude is much more difficult, requiring precise time-keeping to measure. While the math itself is easy, we didn't develop properly precise clocks until the late 1700s.1

As such, landmark navigation will remain common for quite some time, particularly for longitude.

Time of Day defined.
For the sake of clarity, let's assume your people define the time of day according to which part of the horizon the Sun is at. So if the Sun is currently at 0°, it's 0:00, if the Sun is at 90°, it's 6:00, etc.

0° will likely be defined by some landmark. For example, the angle from the south pole to The Great Oak Forest might be 0°.

Time of Year defined.
Now, your people are going to realize that the stars visible at 0:00 will change over time. This will lead to the concept of a "star day", which is identical to our real-world notion of a year, without the seasonal variations. So maybe they define "January" as the month when the Gemini constellation is visible at 0:00, and "July" as the month when the Sagittarius constellation is visible at 0:00.

Originally, I thought there was a way to determine longitude from time of year, but I don't think that's accurate. Still, knowing which constellations are "equatorial constellations" allows your sailors to find the time of day even at night. Additionally, knowing the time of year can help keep local clocks accurate over long voyages.

Long-distance Time-keeping.
In order to find longitude, your sailors will need to know the current time relative to some known longitude. Generally, they'll probably compare local time to the time at the south pole, which we'll call "proper time".

With advanced satellites, they can use some kind of GPS, which would obviously also give them exact coordinates directly.

With basic radio technology, they can use radio stations to broadcast the current time. As the people expand their reach, then can have repeater stations set up so station A broadcasts every so often (say, every five minutes). Near the edge of A's broadcast radius, you have stations B, C, D, etc. around the ring. Each of them keeps a clock in sync with station A's broadcast, then broadcasts on a second frequency. Another ring of stations listens to the second frequency to sync their clocks and broadcasts on a third frequency. Etc.

With less advanced technology, your sailors will have to rely on simpler methods of time-keeping. Water-clocks, wound-spring clocks, etc. will all work to varying degrees of precision. Each port will be able to maintain an accurate clock, and the ships will re-sync their clocks accordingly.

I'm not sure what kind of accuracy they have, but numerous methods of determining time using other astronomical objects have been devised throughout the ages. Essentially, by accurately measuring various astronomical periods, such as the Moon's orbit around Earth, sailors can determine the current time by measuring relative motion of astronomical objects, such as comparing the Moon's position to the background constellations.2

Putting this together.
From here, they can combine three pieces of angular information to know where they are on the globe.3 4

First, they track the height of the Sun at noon. On the poles, the Sun will always be on the horizon. At the equator, the Sun will pass directly overhead (called the "zenith"). At any latitude in between, the Sun's height at noon will directly correspond with that latitude. From here, they can directly calculate their current latitude.

Second, they track the direction of the Sun's apparent motion. In the north hemisphere, the Sun appears to travel left-to-right. In the south hemisphere, it travels right-to-left. Combined with the above, this gives your people their exact latitude above or below the equator.

Third, they track the angular difference of an accurate clock between "proper" noon and local noon. This will be easier as they develop radio then satellite technologies, but can still be done with any kind of local clock. This angular difference gives the longitudinal difference between where they're at and some prime meridian.

Fourth, they can track various angles to or between astronomical objects, which may be helpful in more accurate time-keeping, but isn't directly helpful in determining position.

A note about the Sun's angle near the pole.
If you're extremely near the pole, and on or surrounded by land, it's possible the Sun will always be below the horizon, making it impossible to measure the Sun's angle at local noon. This would, in turn, make it impossible to know your precise latitude (and further, hard or impossible to know your precise longitude since you couldn't determine the exact proper time of local noon).

Note, however, that this is not likely to be a huge deal anyway. If you're on land, you can use landmarks to find your way pretty easily to begin with. It's really only when you're on the ocean that you'd have a really hard time finding your bearings. And on the ocean, the Sun will always be above the horizon at noon.

Regardless, I did some math. Let's say you're standing at sea level, and the horizon is covered by hills the height of Mt. Everest (about 5.5 miles in elevation). The angular height of the hills relative to the horizon is given by

$atan(\frac{5.498\text{ mi}}{X\text{ mi}})$

where X is the distance to the hills.

The latitude difference between you and the hills is given by

$\frac{X\text{ mi}}{24901\text{ mi (Earth circumference)}}\cdot 360°$.

Because the Sun's height at noon is equal to your latitude, we can set the above equations to equal each other and solve for X. This will give us the distance from the pole where Mt. Everest would prevent the Sun from rising.

I'm having trouble getting WolframAlpha to solve the equation directly, but my graphing calculator gives an answer of $X=\pm 147.578 mi$, which gives angles of 2.134° for both occluding height5 and latitude6.

Because the viewer is 147 miles from the pole, and the giant mountains are 147 miles from the viewer, this means anyone within 295 miles of the pole will never see the Sun.

Realistically though, you're not going to have a horizon full of Mt. Everest-sized hills while at sea level. Which means the occluding distance will be much smaller. Doing the same math for an elevation of 1320 ft gives a 63-mile occlusion radius, and an elevation of 500 ft gives a 39-mile radius.

In general, the more bumpy the terrain, the more likely it is that you've got a huge cliff between you and the horizon. But it also means you don't have to walk as far out of your way to get a better view.

So even at distances much closer than 300 miles from the pole, there's a good chance you could use the Sun's position at noon to get your current latitude (and, with good time-keeping, your current longitude, since you know the proper time of local noon). By deliberately using a route that keeps you at higher elevations, you could maintain an accurate log of your position throughout most of your trip.

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Compass-like-devices would be quite useful.

  1. As already mentioned in A. I. Breveleri's answer, by measuring magnetic inclination you get distance to magnetic pole even if sky is covered in clouds and you cannot see position of the stars and sun.

  2. And what is more important, if magnetic and true pole do not coincide, then by knowing magnetic declination and latitude(which is easy to measure) you get longitude(which is hard to get) without high(relatively) technologies required for lunar distance longitude measurement or chronometers.

In real history magnetic declination method didn't work well because most travels occur far from pole and distance between magnetic and true pole is low so angle is small and it should be measured with high precision. But if you travel close to pole then you can get good results with low precision(angle would be big).

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  • $\begingroup$ Do you have any sources for historical use of this method? Everything I'm finding is for going the other direction (i.e., given a location, finding your declination). $\endgroup$ – MichaelS Aug 17 '17 at 2:57
  • $\begingroup$ @MichaelS Try googling for "Halley magnetic deviations longitude" First link "His grand ambition was to solve the age old longitude problem through a better understanding of the Earth’s magnetic field. " $\endgroup$ – Vashu Aug 17 '17 at 3:33

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