And I thought tectonics were confusing (please critique my currents)

[waldronate]

An image of the polar region mapped onto a sphere might help (globe in lower left and zoomed-in on main part):

I added an extra magenta grid to make it clear where the pole converges.

[Naima]

First we assume that the planet is a perfect sphere. It's not perfect but the different is very small and it's simpler to work with a perfect sphere.
On a sphere, the pole is simply a dot.
The funny thing is that a dot is a 1 dimension thing, so the area covered by the dot is actually 0.
Therefore to be honest, it's not possible to map the pole.
I guess we have to stop at the latitude 89,99999999...
But this extreme latitude is so close to the pole that it is extremely small. It's size approaching nothing as you move closer to the pole. The infinitely small.
For sanity, we'll assume that it ends when there is only a single atom left. And that is the top and bottom of your map, your poles.
So if the whole latitude is made of only one atom, can it be made of 2 different elements at the same time? Not with current physics, as far as I am aware.
So that's the thing, the pole approaches the infinitely small.

Sorry I still do not get it, are you saying that on a planet there is no possibility to have poles without Land?

[Azélor]

No, what I'm saying is that it is impossible to have a specific point in space that is made of 2 different things. It can be land or water but not both.

On the map here, the contibental shelf suggest that the ocean extends beyond the north pole. But it is impossible.

[waldronate]

He's saying that an Equirectangular projection of a sphere transforms the singular points at the poles into lines on the Equirectangular projection that go all of the way across the top or bottom of the image. Because it's a single physical point on the world being logically transformed into a line on the map, the value of that point should be shown all of the way across that line. That is, the line across the top of the Equirectangular map should have the same value. In this case, the topmost line has two different values, with those areas showing up as a spiky squeezed area on the reprojected map that I attached in my previous post.

For practical maps (that is, finite resolution raster maps), it's possible to have both land and water across a single scan line at the top and bottom, but they have to be very carefully drawn to avoid polar pinching. The attached map shows an Equirectangular map of the world with some polar islands where the coast is right at the poles and what those poles would look like on a sphere (Orthographic projection).

[Naima]

Ah ok I thought that he meant that phisically a continent is required on poles.

[rvgriffiths]

Fluid dynamic is complicated, you don't have to dig too deep to get a plausible world.

Phew, that is very good to know. My brain likes to get wound up about plausibility :p.

Other things:
I think Jean-Abel meant that the north pole is missing a bit of land. You need to have a small strip of land at the edge, or it could be water.
But right now the north pole is made of water and land at the same time. That is not possible.

That explains the problem I was having with orthographic projections! I fiddled a bit but didn't realize what the issue was. Adjusted to make it land.

Yes, Azélor is right about the north poles, there's definitely an issue about it. His current map is great too but they tend to follow the coastlines too strictly, I would suggest a mix between his and Jerron's.

Okay, attempt 2, trying to mesh both maps and pull away from the currents a little. Not onfident about the equatorial island chain, I feel like everything gets muddled in there.

[Azélor]

There are still currents under the icecap, unless there is a landmass as well.

[rvgriffiths]

Okay, another take. Added land at the top, fixed the currents to go back under the ice, and adjusted the center land after deciding on it for my story's setting. There are some gaps where I wasn't sure of myself, and I still think those islands are messy, but is this plausible enough to start figuring out climates? Or have I committed more current crimes?

[waldronate]

I recommend a quick bit of research on "thermohaline circulation" and the Gulf Stream. The warmer equatorial waters on the left-hand side of the ocean might well drive straight up into the ice cap, pushing back the ice and making the pole a bit warmer than expected. As an example of the moderating effects of the ocean in general and a warm current in particular, Edinburgh is slightly north of Moscow, but it's a bit less icy in winter.